Radio'Frequency Energy Quantification in Magnetic Resonance Imaging

By Leeor Alon

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Basic Medical Science Program in Medical Imaging New York University May 2014

Daniel K. Sodickson

© Leeor Alon All Rights Reserved, 2014

DEDICATION I am very fortunate to be surrounded by an amazing family. I want to thank my father for instilling curiosity in me since the early days, for promoting creativity, for questioning the mores and for being an amazing role model with regard to work ethic. I want to thank my mother for being so caring, for being the best advice giver, for being the voice of reason and inspiring me throughout my path. I want to thank my brother, for setting a great example, for being a best friend and for inspiring me to work in research and ultimately help others. Last but not least, I want to thank my beloved wife Hilary, whom I am luckiest to have met, for her unequivocal support, for putting up with my long hours in the lab, for wanting to read everything I write, and for inspiring me to develop and improve.

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ACKNOWLEDGEMENTS First, I want to thank Dr. Dan Sodickson for his mentorship, his contagious passion for science, his dedication to teaching and outstanding leadership. The past 5+ years would not have been as productive or enjoyable had I not had such a caring advisor and role model to rely upon. I would also like to thank Dr. Yudong Zhu who helped me for the first half of my Ph.D. and help introduce me to this incredible field. Another thank you goes to Dr. Chris Collins for his wonderful mentorship and creative brainstorming sessions over the past 1.5+ years. I would also like to thank my other thesis committee members, Drs. Henry Rusinek, Dan Turnbull, Jens Jensen and Tommy Vaughan for being so helpful over the course of the Ph.D. and for their valuable suggestions for improving my work. To my “lab brothers” Dr. Cem Murat Deniz and Mr. Gene Cho, we worked many hours together, sitting shoulder'to' shoulder into the wee hours of the night. I will miss sharing these experiences together and I am grateful for the long lasting friendships that we developed. I thank Dr. Assaf Tal for our long passionate discussions about physics and MR/NMR' you are a great bouncing board. Dr. Noam Ben'Eliezer, thank you for our “MR debates,” and your friendship. I want to thank Dr. Graham Wiggins for his RF coil design input, Dr. Ryan Brown for his willingness to help us build RF coils and invaluable input on our manuscripts. I want to thank Dr. Riccardo Lattanzi for being a supportive graduate advisor and Dr. Ricardo Otazo for his input on the topic of compressed iv

sensing. To all of the “residents” of room 420, Li Feng, Alicia Yang, Vishal Patil, Manushka Vaidya, Gang Chen, Gillian Haemer, Elan Grossman, thank you for your friendship over the years.

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Table of Contents DEDICATION ................................................................................................................. iii ACKNOWLEDGEMENTS ............................................................................................. iv LIST OF FIGURES ......................................................................................................... xi LIST OF TABLES ......................................................................................................... xix LIST OF APPENDICES ............................................................................................... xxi 1.

BACKGROUND ..................................................................................................... 1 Summary of Contributions...........................................................................................1 MRI E Historical Perspective........................................................................................6 MRI Basics (21E23) .........................................................................................................9 Interaction with the B0 field.....................................................................................................11 Interaction with the RF field....................................................................................................12 The Bloch Equations and Relaxation ...................................................................................15 Signal Acquisition .........................................................................................................................15 The Three Basic Categories of RF Pulses............................................................................16 Spatial encoding ........................................................................................................... 19 High Field MRI (25) ..................................................................................................... 20 High Field Advantages and Challenges ...............................................................................20 RF Energy Absorption in the Body ......................................................................... 23 Why limits on RF energy absorption (36)? .......................................................................23 SAR limits in MRI ..........................................................................................................................27

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The frequency dependence of SAR .......................................................................................30 EM field Simulations!....................................................................................................................32 RF Dosimetry and MR Temperature Measurement ......................................................33

2.

EFFECTS OF GEOMETRIC INACCURACIES ON SIMULATED FIELDS, SAR, AND TEMPERATURE..............................................................................38 PROLOGUE...................................................................................................................... 38 AUTHOR CONTRIBUTIONS:....................................................................................... 38 INTRODUCTION ............................................................................................................ 38 METHODS........................................................................................................................ 43 RESULTS .......................................................................................................................... 47 DISCUSSION AND CONCLUSION ............................................................................... 53

3.

SYSTEM AND SAR CHARACTERIZATION IN PARALLEL RF TRANSMISSION .................................................................................................57 PROLOGUE...................................................................................................................... 57 AUTHOR CONTRIBUTIONS:....................................................................................... 58 INTRODUCTION ............................................................................................................ 58 THEORY AND METHOD .............................................................................................. 61 RF energy dissipation and tissue heating ..........................................................................61 A linear system perspective.....................................................................................................62 Local and global SAR models...................................................................................................65 Calibration method ......................................................................................................................68 Simulation studies........................................................................................................................75 Phantom and in vivo studies ....................................................................................................76

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Evaluations of support for planning and monitoring ...................................................79 RESULTS .......................................................................................................................... 80 DISCUSSION AND CONCLUSION ............................................................................... 89

4.

METHOD FOR IN SITU CHARACTERIZATION OF RADIOFREQUENCY HEATING IN PARALLEL TRANSMIT MRI ...................................................95 PROLOGUE...................................................................................................................... 95 AUTHOR CONTRIBUTIONS:....................................................................................... 95 INTRODUCTION ............................................................................................................ 96 THEORY AND METHODS ............................................................................................ 98 RF energy dissipation and tissue heating ..........................................................................98 SAR model and temperature change................................................................................. 100 Experiments................................................................................................................................. 101 Simulations................................................................................................................................... 104 RESULTS ........................................................................................................................109 Experiments................................................................................................................................. 109 Simulations................................................................................................................................... 111 DISCUSSION AND CONCLUSION .............................................................................113

5.

A METHOD FOR SAFETY TESTING OF WIRELESS DEVICES USING MAGNETIC RESONANCE IMAGING............................................................ 119 PROLOGUE....................................................................................................................119 AUTHOR CONTRIBUTIONS:.....................................................................................119 INTRODUCTION ..........................................................................................................120 Temperature Measurement using MRI ............................................................................ 124

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NUMERICAL TECHNIQUES AND EXPERIMENTAL SETUP...............................126 Simulation Technique.............................................................................................................. 126 Phantom ........................................................................................................................................ 127 MRI Compatible Dipole Antenna and Power Measurement System ................... 129 Dipole Antenna Experiments ............................................................................................... 130 Cell Phone Experiments.......................................................................................................... 132 MR Temperature Mapping Error Analysis ........................................................136 RESULTS ........................................................................................................................137 Dipole'antenna Simulation and Experimental Results ............................................. 137 Mobile Phone Experimental Results ................................................................................. 138 MR Temperature Mapping Error Analysis Results ..................................................... 139 DISCUSSION ..................................................................................................................139 CONCLUSION ................................................................................................................144 Acknowledgements ...................................................................................................144

6.

WIRELESS DEVICE 10g SAR CALCULATION FROM 3D MRI TEMPERATURE MEASUREMENTS............................................................ 145 PROLOGUE....................................................................................................................145 AUTHOR CONTRIBUTIONS:.....................................................................................145 INTRODUCTION ..........................................................................................................146 THEORY .........................................................................................................................147 METHODS......................................................................................................................149 RESULTS ........................................................................................................................151 CONCLUSION ................................................................................................................153

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7.

SUMMARY ........................................................................................................ 155 Chapter summaries ...................................................................................................155 An outlook for the future.........................................................................................157

8.

PUBLICATIONS RESULTING FROM THE DISSERTATION WORK .... 160 Accepted Peer reviewed papers ...........................................................................160 In review .......................................................................................................................160 Selected Conference Abstracts ..............................................................................161 2010................................................................................................................................................. 161 2011................................................................................................................................................. 162 2012................................................................................................................................................. 162 2013................................................................................................................................................. 163 2014................................................................................................................................................. 164 Pending Patents..........................................................................................................164

9.

APPENDICES.................................................................................................... 166

10. BIBLIOGRAPHY .............................................................................................. 177

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LIST OF FIGURES FIGURE 1.1. A NET MAGNETIZATION IS CREATED WHEN THE BODY IS POSITIONED INSIDE A UNIFORM MAGNETIC FIELD..................................................................................................................................... 10 FIGURE 1.2. IN THE MICROSCOPIC SCALE, AN INCREASED NUMBER OF SPINS POINTING UP ARE OBSERVED, WHEN THE SAMPLE IS EXPOSED TO A MAGNETIC FIELD (B0). IN THE MACROSCOPIC SCALE, A NET MAGNETIZATION VECTOR M IS SHOWN.............................................. 11 FIGURE 1.3. COMMON COILS USED FOR IMAGING THE BODY. A. BIRDCAGE COIL. B. SURFACE COIL. ................................................................................................................................................................................................ 13 FIGURE 1.4 A. AN OSCILLATING B1 + USED TO TIP THE MAGNETIZATION IN THE LABORATORY FRAME OF REFERENCE. ONCE THE RF FIELD IS TURNED ON, THE MAGNETIZATION M IS TIPPED TO THE TRANSVERSE (XY) PLANE. B. THE ANGLE BETWEEN THE Z AXIS AND XY PLANE REACHES 90 DEGREES WHEN THE RF IS TURNED ON.!................................................................ 14 FIGURE 1.5. INVERSION PULSE FLIPPING THE MAGNETIZATION FROM THE +Z DIRECTION TO 'Z. 17 FIGURE 1.6. A. A 90 DEGREE EXCITATION PULSE IS APPLIED, TIPPING THE MAGNETIZATION ON THE Y' AXIS. B. RIGHT AFTER THE EXCITATION PULSE IS APPLIED NO DEPHASING IS PRESENT. C. AFTER TIME T, DEPHASING OCCURS AS RESULT OF CHEMICAL SHIFT AND B0 FIELD INHOMOGENEITY. D. A REFOCUSING PULSE IS APPLIED ALONG THE Y’ AXIS, ROTATING THE MAGNETIZATION VECTORS 180 DEGREES AROUND THE Y’ AXIS. D. AFTER THE REFOCUSING PULSE IS APPLIED THE SPINS ARE REVERSED. THE SPINS THE, WHICH ORIGINALLY “ADVANCED” THE MOST ARE NOW “LAGGED” THE MOST. D. AFTER TIME T, THE SPINS ARE REFOCUSED AND A MAXIMUM ECHO IS FORMED. ................................................................. 19 FIGURE 1.7. CONDUCTIVITY (A) AND RELATIVE PERMITTIVITY (B) AS A FUNCTION OF FREQUENCY (59,60). ............................................................................................................................................................................... 31 FIGURE 2.1. A . A. SINGLE' AND TWO COILS POSITIONED NEXT TO THE ABDOMEN OF THE HUGO BODY MODEL. IMAGING SLICE IS SHOWN IN YELLOW'GREEN. B. AN AXIAL SLICE OF THE

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ELECTRIC CONDUCTIVITY (Σ) AND PERMITTIVITY (Ε) MAPS USED FOR THE ORIGINAL AND ALTERED HUGO SIMULATIONS. C. SINGLE' AND TWO 'COILS POSITIONED NEXT TO THE ABDOMEN OF THE DUKE AND ELLA BODY MODELS.................................................................................... 42 FIGURE 2.2. |B1+|, |B1'|, |BZ|, |E|, 10G'AVERAGED SAR AND ∆T MAP COMPARISON BETWEEN SINGLE COIL ORIGINAL AND ALTERED HUGO HUGO SIMULATIONS AT 3T(A) AND 7T(B) FIELD STRENGTHS. (C) COMPARISON BETWEEN THE ORIGINAL AND ALTERED 2'COIL HUGO SIMULATIONS AT 7T FIELD STRENGTHS. SIMULATIONS SHOWN AT ISOMETRIC RESOLUTIONS OF 5X5X5 MM3. ................................................................................................................................ 48 FIGURE 2.3. |B1+|, |B1'|, |BZ|, |E|, 10G'AVERAGED SAR AND ∆T MAP COMPARISON BETWEEN SINGLE'COIL ELLA (ORIGINAL) AND DUKE (ALTERED) SIMULATIONS AT 7T FIELD STRENGTHS FOR SINGLE'(A) AND TWO'(B) COIL SCENARIOS AT ISOMETRIC RESOLUTIONS OF 2X2X2 MM3................................................................................................................................................................ 50 FIGURE 3.1. A SYSTEM PERSPECTIVE TO PARALLEL RF TRANSMISSION: THE TRANSMIT CHANNELS, THE TRANSMIT COIL AND THE SUBJECT TOGETHER FORM A SYSTEM, WITH W(N), THE PARALLEL RF PULSE WAVEFORMS, AS INPUTS, AND B1+ FIELD AND RF ENERGY DEPOSITION AS OUTPUTS. PARALLEL RF TRANSMISSION SYSTEM HARDWARE IS NORMALLY SET UP IN SUCH A WAY THAT THE ELECTROMAGNETIC FIELD INDUCED IN THE SUBJECT RESPONDS LINEARLY TO THE INPUTS. .............................................................................................................. 68 FIGURE 3.2. (A) GLOBAL SAR CALIBRATION AND PREDICTION IN A SIMULATION STUDY INVOLVING A HETEROGENEOUS HUMAN MODEL AND AN RF COIL COMPOSED OF 4 LOOP ELEMENTS. (B) BASED ON THE NET POWER VALUES QUANTIFIED BY THE FDTD CALCULATIONS FOR THE 20 INPUT'CONFIGURATION CASES PRESCRIBED FOR CALIBRATION, Φ WAS DETERMINED. IN EACH OF THE ADDITIONAL 19 INPUT'CONFIGURATION CASES THE NET POWER PREDICTED WITH WH Φ W, THE CALIBRATED GLOBAL SAR PREDICTION MODEL, APPEARED TO BE IN EXCELLENT AGREEMENT WITH THE NET POWER QUANTIFIED DIRECTLY BY FDTD, DEMONSTRATING THE VALIDNESS OF THE MODEL.................................................................................... 81

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FIGURE 3.3. INVESTIGATION OF IMPACT OF COIL'SUBJECT SETUP ON THE GLOBAL SAR MODEL. TWO DIFFERENT SETUPS WERE SIMULATED EACH INVOLVING FOUR IDENTICAL LOOP ELEMENTS OF SIZE 7 X 7 CM2 PLACED ABOUT 1 CM ABOVE A UNIFORM WATER PHANTOM (A,D). WITH EITHER SETUP THE SET OF INPUT CONFIGURATIONS INCLUDED 16 PROGRAMMED ONES FOR MODEL CALIBRATION AND 8 RANDOMLY GENERATED ONES FOR MODEL VALIDATION. IN B, MAGNITUDE OF ESTIMATED Φ FOR SETUP 1 SHOWS SIGNIFICANT POWER CORRELATIONS BETWEEN 1 AND 3, AND 2 AND 4, CONSISTENT WITH THE INTERFERENCE PATTERNS EXPECTED OF THE GEOMETRICAL ARRANGEMENT OF THE ELEMENTS AND THE OBJECT. SIMILAR OBSERVATIONS COULD BE MADE OF E FOR SETUP 2. IN ADDITION, FOR EACH SETUP THE VARIATION OF Φ’S DIAGONAL ENTRIES CORRELATES WITH LOADING DIFFERENCE CAUSED BY THE ELEMENTS’ VARYING PROXIMITY TO THE LOSSY OBJECT. ................................................................................................................................................................ 82 FIGURE 3.4. GLOBAL SAR MODEL CALIBRATION AND VALIDATION ON A 7T WHOLE BODY MR SCANNER. (A) STUDY INVOLVING 4'CHANNEL PARALLEL TX MR OF A CYLINDRICAL PHANTOM WITH HALF OF THE RUNGS OF AN 8'RUNG TX'RX ARRAY. (B) STUDY INVOLVING A MORE GENERAL COIL'OBJECT SETUP THAT HAD FOUR LOOP ELEMENTS ARBITRARILY PLACED ON A HEAD SHAPED PHANTOM AND FORMED A TX ARRAY COIL.

(C) FOUR

PRE'DESIGNED 18 MSEC'LONG STAIRCASE'SHAPED PARALLEL RF PULSES WERE USED TO INTRODUCE 36 INPUT CONFIGURATIONS, INCLUDING 16 FOR MODEL CALIBRATION (DEFINITIONS SHOWN IN THE TABLE) AND ADDITIONAL 20 RANDOMLY GENERATED ONES FOR CHECKING THE ACCURACY OF THE MODEL'BASED GLOBAL SAR PREDICTIONS. (D) FOR THE 4'LOOP ARRAY COIL SETUP, A COMPARISON OF MODEL'BASED SAR PREDICTIONS WITH ACTUAL MEASUREMENTS......................................................................................................................................... 84 FIGURE 3.5. STREAMLINED SAR MODEL CONSTRUCTION FOR PARALLEL TX MR. AN AUTOMATION OF DATA COLLECTION SHORTENED THE ENTIRE CALIBRATION AND VALIDATION PROCESS TO LESS THAN 18 SECONDS. RESULTS FROM AN IN VIVO STUDY INDICATED THAT THE

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PREDICTIONS GIVEN BY THE CALIBRATED GLOBAL SAR MODEL WERE IN EXCELLENT AGREEMENT WITH DIRECT MEASUREMENTS (A), WITH A WORST CASE PREDICTION ERROR OF LESS THAN 10% (B). RESULTS FROM A FURTHER STUDY ON THE USE OF A CALIBRATED SAR PREDICTION MODEL IN RF PULSE OPTIMIZATION INDICATED THAT THE MODEL OFFERED RELIABLE GUIDANCE TO THE PULSE DESIGN ALGORITHM – THE PREDICTED NET RF POWER AS A FUNCTION OF TIME WAS IN EXCELLENT AGREEMENT WITH THAT ACTUALLY MEASURED DURING THE PLAYOUT OF THE DESIGNED PARALLEL EXCITATION (C). ................................................................................................................................................................................................ 85 FIGURE 3.6. THREE CHANNEL PARALLEL TX STUDY WITH A COIL'OBJECT SETUP THAT HAD THREE LOOP ELEMENTS ARBITRARILY PLACED ON A HEAD SHAPED PHANTOM AND FORMED A TX ARRAY COIL. GLOBAL SAR MODEL CALIBRATION AND VALIDATION WAS PERFORMED, WHICH LED TO MODEL PREDICTIONS THAT ACCURATELY MATCHED NET POWER MEASUREMENTS (BOTTOM PLOT). THE POWER MEASUREMENT DATA WERE FURTHER PROCESSED TO CALIBRATE PREDICTIVE MODELS OF INDIVIDUAL CHANNEL FORWARD AND REFLECTED POWER, WHICH GAVE WH ΦFWD(N)W AND WH ΦRFL(N)W , NTH CHANNEL FORWARD AND REFLECTED POWER PREDICTIONS RESPECTIVELY, FOR ANY INPUT CONFIGURATION W. FOR THE RANDOMLY PRESCRIBED INPUT CONFIGURATIONS (STEPS 10 THROUGH 18), PREDICTIONS FROM THESE MODELS WERE IN EXCELLENT AGREEMENT WITH ACTUAL MEASUREMENTS (PLOTS LABELED CH N FWD AND CH N RFL). ............................ 88 FIGURE 3.7. CALIBRATION AND VALIDATION UNDER A BASELINE SETUP IN A SYSTEM MONITORING STUDY.

(A) MAGNITUDE DISPLAYS OF ΦFWD(N), ΦRFL(N) AND Φ, WHICH

WERE CALIBRATED USING POWER MEASUREMENTS CORRESPONDING TO INPUT CONFIGURATIONS 1 THROUGH 9. (B) COMPARISON OF MODEL PREDICTIONS WITH POWER MEASUREMENTS FOR ANY OF THE RANDOMLY GENERATED ONES OF INPUT CONFIGURATIONS 10 THROUGH 18 INDICATED ACCURATE PREDICTION. THESE MODELS /

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DATA MAY SERVE AS A REFERENCE FOR DETECTING POSSIBLE SYSTEM CHANGES FROM BASELINE AT A LATER TIME.!................................................................................................................................... 90 FIGURE 3.8. CASES 1 AND 2 IN A SYSTEM MONITORING STUDY. THE BASELINE WAS ALTERED TO EMULATE TWO SYSTEM FAULT SCENARIOS. IN CASE 1 THE BASELINE SETUP UNDERWENT A SYSTEM CHANGE IN WHICH ELEMENT 3 WAS FORCED TO OPEN. RE'CHARACTERIZATION WAS PERFORMED. (A) SHOWS UPDATEDΦFWD(N), ΦRFL(N) AND Φ. (B) SHOWS PREDICTIONS, MEASUREMENTS, AS WELL AS PREDICTIONS FROM BASELINE MODELS (CIRCLES).

(C) SHOWS MAXIMUM EIGENVALUES OF CASE 1 ΦFWD(N) AND ΦRFL(N)

(SOLID BARS) VS. THAT OF BASELINE ΦFWD(N) AND ΦRFL(N) (NON'FILLED BARS). IN CASE 2 THE BASELINE SETUP UNDERWENT A SYSTEM CHANGE IN WHICH CHANNEL 2 HAD AN EXTRA PHASE OFFSET OF ABOUT 45 DEGREES. RESULTS ARE SIMILARLY DISPLAYED IN D'F. NOTE THE PATTERN CHANGE OF A POWER CORRELATION MATRIX’S EIGENVALUES: FOR THE BASELINE, CASE 1 AND CASE 2, THE SIGNIFICANT EIGENVALUES OF Φ WERE, RESPECTIVELY, [4, 43], [5, 29], AND [19, 41]. IN TERMS THE LARGEST EIGENVALUES, FURTHER NOTE THE SHARP CONTRAST BETWEEN CASE 1 ΦFWD(3) AND BASELINE ΦRFL(3), AND BETWEEN CASE 2 ΦFWD(2) AND BASELINE ΦFWD(2) (C AND F). ...................... 93 FIGURE 4.1 A. SCHEMATIC OF THE EXPERIMENTAL CALIBRATION AND VALIDATION PROCEDURE. B. PHOTOGRAPH OF THE TRANSMIT'RECEIVE COILS AND AGAR GEL PHANTOM USED IN THE EXPERIMENTS. TRANSMIT'RECEIVE ELEMENTS TC1'3 ARE SHOWN IN THE PHOTOGRAPH. THE RECEIVE'ONLY COIL (NOT SEEN) IS OPPOSITE TO TC2 ON THE OTHER SIDE OF THE PHANTOM. ......................................................................................................................................................................104 FIGURE 4.2. FDTD MODEL OF A HUMAN BODY MESH (HUGO) WITH FOUR TRANSMIT COILS (C1'4) SHOWN IN BLACK PLACED ON TOP OF THE BODY MESH. .......................................................................108 FIGURE 4.3. RESULTS OF THE EXPERIMENTAL CALIBRATION PROCEDURE. A. TEMPERATURE DIFFERENCE MAPS MEASURED FOR THREE SLICES IN EACH STEP OF THE CALIBRATION PROCESS. EACH STEP (EACH ROW OF TEMPERATURE CHANGE MAPS) CORRESPONDS TO A

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DIFFERENT SET OF RF AMPLITUDE AND PHASE WEIGHTINGS APPLIED TO EACH COIL, AS SPECIFIED IN TABLE 4.1. B. ABSOLUTE VALUE OF Λ MATRIX ELEMENTS FOR FOUR DIFFERENT VOXEL POSITIONS INDICATED BY THE ORIGIN OF EACH RED ARROW. .................109 FIGURE 4.4. A. RESULTS OF THE EXPERIMENTAL PREDICTION AND VALIDATION PROCEDURE, DEMONSTRATING THE PREDICTIVE CAPABILITY OF THE LOCAL SAR MODEL. FOR EACH SET OF THE RANDOMLY SELECTED COIL WEIGHTINGS INDICATED IN STEPS 10'12 OF TABLE 4.1, AND IN EACH OF THREE AXIAL SLICES, A TEMPERATURE CHANGE MAP MEASURED USING MR THERMOMETRY IS COMPARED WITH THE PREDICTED TEMPERATURE CHANGE MAP DERIVED BY USING THE KNOWN COIL WEIGHTS AS INPUTS FOR THE LOCAL HEATING PREDICTION MODEL. GOOD AGREEMENT BETWEEN MEASUREMENTS AND PREDICTIONS IS OBSERVED, AS INDICATED ALSO BY THE DIFFERENCE MAPS BENEATH EACH MEASURED/PREDICTED PAIR...............................................................................................................................110 FIGURE 4.5. RF HEATING IN AN EMULATED HUMAN BODY. A. RESULTS OF THE PREDICTION AND VALIDATION PROCEDURE. UNAVERAGED SAR MAPS AND DIRECTLY SIMULATED CORONAL TEMPERATURE CHANGE MAPS ARE JUXTAPOSED NEXT TO TEMPERATURE CHANGE MAPS PREDICTED USING THE CALIBRATED HEATING PREDICTION MODEL, FOR EACH OF THE VALIDATION EXPERIMENTS 17'24 FROM TABLE 4.1. RESULTS SHOWN ARE FOR THE 60 AND 300 SECOND HEATING CASES AT A CORONAL SLICE OF INTEREST. B. RESULTS OF THE CALIBRATION PROCEDURE, ILLUSTRATING THE SPATIAL DEPENDENCY OF THE POWER CORRELATION MATRIX Λ FOR A CORONAL SLICE OF INTEREST. 4 X 4 COLOR PLOTS REPRESENT THE ABSOLUTE VALUE OF Λ MATRIX ENTRIES, AND EACH PLOT SHOWS Λ AT A DIFFERENT VOXEL POSITION, INDICATED BY THE ORIGIN OF THE CORRESPONDING RED ARROWS. C. PREDICTED (TOP) AND DIRECTLY QUANTIFIED (BOTTOM) TEMPERATURE CHANGE MAP FOR AN AXIAL SLICE OF INTEREST, SHOWING THE PREDICTION CAPABILITY OF THE MODEL IN A DEEPER REGION INSIDE THE HUMAN BODY MODEL, WHILE ACCOUNTING FOR PERFUSION AND DIFFUSION EFFECTS......................................................................112

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FIGURE 5.1 EXPERIMENTAL SETUP AND CONFIGURATION OF MATCHING NUMERICAL SIMULATIONS. (A) DIPOLE ANTENNA WITH Λ/2 LENGTH, (B) FIT SIMULATION SETUP OF THE DIPOLE ANTENNA AND THE GELATIN PHANTOM, (C) GELATIN PHANTOM AND FLUOROPTIC TEMPERATURE PROBES, (D) EXPERIMENTAL SETUP INSIDE THE MR SCANNER ROOM: THE GELATIN PHANTOM IS POSITIONED INSIDE AN MR COIL DESIGNED FOR KNEE IMAGING, WITH A MOUNTED GSM MOBILE PHONE AND SURROUNDING OIL PHANTOMS FOR CALIBRATION. ...............................................................................................................................................................122 FIGURE 5.2. FLUOROPTIC TEMPERATURE PROBE LOCATIONS AND TEMPERATURE MEASUREMENTS. (A) LOCATIONS OF THE FLUOROPTIC PROBES WITHIN THE PHANTOM, (B) SETUP OF DIPOLE ANTENNA CIRCUIT, (C) FLUOROPTIC PROBE TEMPERATURE MEASUREMENTS OF DIPOLE ANTENNA HEATING. HEATING OCCURRED FROM 2 MINUTES 30 SECONDS TO 9 MINUTES (HIGHLIGHTED IN YELLOW).............................................................................125 FIGURE 5.3. TEMPERATURE AND SAR MAPS OF THE DIPOLE ANTENNA'PHANTOM SETUP FROM MR EXPERIMENTS AND FIT SIMULATIONS. NET INPUT RF POWER TO THE DIPOLE ANTENNA WAS SCALED TO THE MEASURED VALUE IN FIT SIMULATIONS. (A) MR THERMOMETRY MEASUREMENT OF THE PHANTOM. (B) TEMPERATURE CHANGE MAPS FROM FIT SIMULATIONS (C) EXPERIMENTAL SAR MAPS OBTAINED FROM EQ. 5.3 USING PHANTOM PROPERTIES AND MR THERMOMETRY MAPS. (D) SAR MAP FROM FIT SIMULATION. BLUE CIRCLES REPRESENT THE PHANTOM BOUNDARY. (E) TEMPERATURE CHANGE FROM THE PHANTOM (LEFT'TO'RIGHT), RED INDICATES MR THERMOMETRY EXPERIMENTS AND BLUE INDICATES FIT SIMULATIONS...............................................................................................................................132 FIGURE 5.4. ERROR OF MR THERMOMETRY MEASUREMENTS COMPARED TO FLUOROPTIC TEMPERATURE PROBE MEASUREMENTS FROM PROBES A'C IN DIFFERENT EXPERIMENTS. ..............................................................................................................................................................................................134 FIGURE 5.5. MR'BASED TEMPERATURE MAPS ALONG WITH FLUOROPTIC PROBE TEMPERATURE MEASUREMENTS IN THE PHANTOM HEATED BY THE MOBILE PHONE. (A) LOCATIONS OF

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SLICES FOR THE TEMPERATURE MAPS. THE GREEN ARROWS INDICATE THE POSITION OF THE FLUOROPTIC PROBES. (B) FLUOROPTIC TEMPERATURE PROBE MEASUREMENTS. HEATING OCCURRED DURING MINUTES 24'39 (HIGHLIGHTED IN YELLOW)...............................135 FIGURE 5.6. SIMULATED TEMPERATURE MAPS OF POST'HEATING (A), AND AFTER WAITING 10 SECONDS POST'HEATING (B). TEMPERATURE ERROR ASSOCIATED WITH WAITING 10 SECONDS TILL THE MR IMAGING SEQUENCE STARTED (C). MAXIMUM ERROR WAS 0.074 °C AT THE SURFACE OF THE PHANTOM. EXPERIMENTAL TEMPERATURE ACQUISITION WAS PERFORMED WITH NO EXTERNAL SOURCE EMITTING RF, BUT THE IMAGING SEQUENCE ITSELF (D). THE MAXIMUM ERROR = 0.069 °C..............................................................................................137 FIGURE 6.1. A. PHANTOM'DIPOLE ANTENNA SETUP AND FLOW CHART OF THE PROCESS USED FOR THE SOLUTION OF THE INVERSE HEAT PROBLEM. THE PHANTOM DIMENSIONS WERE 10.2 CM IN DIAMETER AND 11 CM IN HEIGHT. B. GEL PHANTOM USED IN MR TEMPERATURE MAPPING EXPERIMENTS. THE PHANTOM PROPERTIES WERE AS FOLLOWS: Ρ = 1272(KG/M3), C=3543(J/KG·°C) AND K=0.457(W/M·°C). C. DIPOLE ANTENNA USED IN THE MR EXPERIMENTS. D. SCHEMATIC REPRESENTATION OF THE EXPERIMENT SETUP USED TO DRIVE THE DIPOLE ANTENNA WHILE MEASURING THE NET OUTPUT POWER. .........................150 FIGURE 6.2. A. SIMULATED ΔT AND 10G SAR MAPS (CORONAL SLICES) AT 5 SLICES INSIDE THE PHANTOM, COMPARING THE “TRUE” SIMULATED 10G SAR DISTRIBUTION AND THE RECONSTRUCTED 10G SAR DISTRIBUTION USING INVERSION OF THE HEAT EQUATION. B. EXPERIMENTALLY MEASURED ΔT MAPS AND RECONSTRUCTED 10G SAR MAPS AT 5 SLICES INSIDE THE PHANTOM. ............................................................................................................................................153 FIGURE 11.1. SCREEN CAPTURE OF GLACIUS – THE TEMPERATURE RECONSTRUCTION SOFTWARE ..............................................................................................................................................................................................172

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LIST OF TABLES TABLE 1.1. WHOLE BODY AND LOCAL SAR LIMITS PROVIDED BY THE IEC (58). LOCAL SAR IS AVERAGED OF 10 GRAMS OF TISSUE. .................................................................................................................. 29 TABLE 2.1. MAXIMUM LOCATION'SPECIFIC ABSOLUTE DIFFERENCE ||DIFF|| IN LOCAL RF MAGNETIC AND ELECTRIC FIELD COMPONENTS, 10G'AVERAGED SAR, AND ΔT BETWEEN THE ORIGINAL AND ALTERED TISSUE SIMULATIONS AT 3T FOR SINGLE'COIL AND AT 7T FOR SINGLE' AND TWO'COIL SIMULATIONS. ............................................................................................................ 51 TABLE 2.2. NRMSE VALUE (%) OF THE RF MAGNETIC AND ELECTRIC FIELD COMPONENTS, 10G' AVERAGED SAR, AND ΔT BETWEEN THE ORIGINAL AND ALTERED TISSUE SIMULATIONS IN THE DEFINED ROI. ........................................................................................................................................................ 52 TABLE 2.3. MAXIMUM 10G'AVERAGED SAR AND ΔT VALUES FOR THE VARIOUS SIMULATIONS IN THE DEFINED ROI. THE |DIFFERENCE| FOR 10G'AVERAGED SAR AND ΔT WAS COMPUTED BETWEEN THE MAXIMUM ORIGINAL AND ALTERED SIMULATIONS. ................................................. 53 TABLE 4.1. EXPERIMENTAL COIL WEIGHTINGS USED TO CHARACTERIZE Λ. STEPS 1'9 WERE USED TO CALIBRATE THE MODEL AND STEPS 10'12 WERE USED TO VALIDATE THE ACCURACY OF THE MODEL'BASED TEMPERATURE CHANGE PREDICTIONS................................................................105 TABLE 4.2. SIMULATED COIL WEIGHTINGS USED TO CHARACTERIZE Λ. STEPS 1'16 WERE USED TO CALIBRATE THE MODEL AND STEPS 17'24 WERE USED TO VALIDATE THE ACCURACY OF LOCAL HEATING PREDICTIONS BASED ON THE MODEL. .........................................................................107 TABLE 4.3. THE ROOT MEAN SQUARED ERROR BETWEEN THE MEASURED AND PREDICTED TEMPERATURE CHANGE MAPS FOR THE THREE SLICES OF INTEREST...........................................113 TABLE 4.4. MAXIMAL TEMPERATURE CHANGE AND THE ROOT MEAN SQUARED ERROR BETWEEN THE SIMULATED AND PREDICTED TEMPERATURE CHANGE MAPS FOR THE 60 AND 300 SECOND HEATING CASES.........................................................................................................................................113

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TABLE 5.1. PHYSICAL PROPERTIES OF THE GEL PHANTOM ..............................................................................128 TABLE 5.2. COMPONENTS OF THE GEL PHANTOM .................................................................................................129 TABLE 5.3. DIPOLE ANTENNA EXPERIMENT. PROBE TEMPERATURE MEASUREMENTS AND ERRORS IN MR THERMOMETRY...........................................................................................................................133 TABLE 5.4. MOBILE PHONE EXPERIMENT. PROBE TEMPERATURE MEASUREMENTS AND ERRORS IN MR THERMOMETRY. ............................................................................................................................................138 TABLE 5.5. MR TEMPERATURE MAPPING ' ERROR ANALYSIS..........................................................................140

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LIST OF APPENDICES APPENDIX A. MAXWELL’S EQUATIONS……………..…...…………..…………………………….166 APPENDIX B. MATLAB ALGORITHM FOR SYSTEM AND SAR CHARACTERIZATION FOR PARALLEL RF TRANSMISSION…………………………………………………………………..169 APPENDIX C. GLACIUS – TEMPERATURE RECONSTRUCTION SOFTWARE…………………………………….………………………………………....……..………….…..172

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1. BACKGROUND Summary of Contributions In the past 40 years, major advancements have occurred in the field of MRI and there has been exponential growth in the utilization of MRI for diagnostic purposes. Ultra high field MRI has made its way to the forefront of MR, providing faster acquisition speeds, higher signal to noise (SNR) and improved contrast. Alongside these technologic innovations, new challenges have arisen in the field, particularly in the area of MR safety, where the capability to monitor and predict RF energy deposition inside patients has been slow to advance and concerns regarding depositing too much RF energy into patients have limited the usage of high field clinical imaging. With these challenges in mind, I began my doctoral studies 5 years ago with the hope of improving RF safety evaluation at high field. During the first half of my Ph.D. studies, I focused on developing new tools for measuring and predicting global and local RF energy deposition in the MRI environment, particularly when using multiple transmitting coils to image the body. This work is detailed in Chapters 2 and 3 of this thesis. Midway along the course of my Ph.D. studies, I realized that MR temperature mapping techniques developed for measuring the energy deposited by MR coils are sufficiently sensitive for quantifying RF energy deposition from low'power RF/microwave transmitting devices and that these techniques could be used for 1

safety evaluation of both MR'compatible and non'MR compatible devices. The ability to use MR temperature mapping for safety evaluation of low'powered devices turned out to be particularly interesting, since the tools currently used to evaluate RF'emitting wireless devices are fraught with limitations (this will be discussed in chapter 5) and as of today, our understanding of the health effects associated with the repeated exposure to RF/microwave EM radiation is not fully conclusive. In fact, just a year ago, the United States Government Accountability Office (GAO) expressed concern that there is a need to update safety emission standards where these devices are concerned (1). With regard to these concerns, I believe that the experimental techniques described in Chapters 4 and 5 of this dissertation will be used for RF safety evaluation method of low power devices. These chapters lay out the experimental methodologies for the measurement of small temperature changes caused by exposure to low power RF/microwave emitting devices and the conversion of temperature change to 10g average SAR, respectively. Each of the chapters in this dissertation has been designed to be self' contained and accessible to an outside reader well versed in the field. This background chapter “fills in the blanks” with regard to the history of the field, why RF safety is important, the difficulties associated with estimation of the energy transmitted in tissue and more. Brief prologues at the beginning of each subsequent chapter place the content of that chapter in the broader context of the dissertation work. A Summary chapter reiterates key findings and outlines the current state of research in each of the areas explored. This is followed by a listing of publications 2

directly related to the thesis work, along with three Appendices covering additional material and describing software developed in the course of the work. The contributions made in each chapter of this thesis are summarized below: 1.

Simulation software is often used to assess the exposure of RF antennas, however, it is not clear how the results produced from simulations can be applied to subject'specific in'vivo scanning of patients. Chapter 2 investigates effects of geometric inaccuracies in finite difference time domain (FDTD) simulated magnetic fields and how they affect the accuracy of Specific Absorption Rate (SAR) and temperature change estimation. Numerical simulations were performed using the FDTD method for human body model with one or two surface coils positioned next to the abdomen. Variations were imposed on the subject anatomy simulating uncertainties associated with patient scanning. The errors between simulated B!! fields for different setups were smaller than errors in 10g average SAR and ΔT. Relative agreement between simulated B!! fields did not guarantee agreement in 10g'average SAR and ΔT distributions.

2.

Since the first implementation of parallel RF transmission in 2004, many studies have utilized parallel transmission as a tool for homogenizing the MR excitation pattern produced at high field strength. However, the markedly increase in degrees of freedom introduced by parallel RF transmission present both opportunities and challenges for SAR management. On the one 3

hand they enable E field tailoring and SAR reduction while facilitating excitation profile control. On the other hand they increase the complexity of SAR behavior and the risk of inadvertently exacerbating SAR by improper design or playout of RF pulses. The substantial subject'dependency of SAR in high field MR can be a compounding factor. Building upon a linear system concept and a calibration scheme involving a finite number of in situ measurements, the work described in Chapter 3 establishes a clinically applicable method for characterizing global SAR behavior as well as channel' by'channel power transmission. The method offers a unique capability of predicting, for any excitation, the SAR and power consequences that are specific to the subject to be scanned and the MRI hardware. The method was validated in simulation and experimental studies, showing promise as the foundation for a prospective paradigm where power and SAR are not only monitored but, through prediction'guided optimization, proactively managed. 3.

As introduced in the previous chapter, total RF energy deposition generated by parallel transmission can be quantified using a global power correlation matrix. The study described in Chapter 4 shows that the information needed to characterize the RF heating effect can be contained within a local power correlation matrix. Building upon a calibration scheme involving a finite number of magnetic resonance thermometry measurements, the work establishes a way of estimating the local power correlation matrix. Determination of the matrix allows prediction of either the local RF power 4

deposition or temperature change for an arbitrary parallel transmit radio frequency pulse. Using this method, antenna array safety may not only be simulated, but also characterized and measured on a phantom in the scanner room. 4.

Radiofrequency/microwave'emitting wireless devices are required to undergo standardized safety testing prior to entering the consumer market. Strict regulations are imposed on the amount of RF energy these devices emit to prevent excessive deposition of RF energy into the body. In chapter 5, the application

of

Magnetic

Resonance

(MR)

temperature

mapping

is

demonstrated for safety evaluation of low power wireless devices. Quantification of the RF power deposition was shown for an MRI'compatible dipole antenna and a non'MRI'compatible GSM cell phone via temperature change measurements inside a phantom. Validation of the MR temperature mapping

method

was

demonstrated

by

comparison

with

physical

temperature probe measurements and electromagnetic field simulations. RF heating induced in the phantom due to a radiating dipole antenna and cell phone was captured using MR temperature mapping. The investigation shows that MR temperature mapping is capable of assessing safety of low power RF emitting devices with the advantage of being noninvasive, with millimeter resolution, high speed and high accuracy. 5.

Studies have shown the feasibility of assessing RF safety via temperature measurements using temperature probes and MR temperature mapping. 5

When evaluating the RF energy deposited from low power transmitting devices, often a long RF heating duration is needed to create an appreciable temperature change that can be detected using MRI; however, temperature change can be biased by diffusion of heat and therefore conversion from temperature change to 10g local SAR is not straightforward. In chapter 6, a demonstration of a method used to convert temperature change induced by heating a phantom for 6.5 minutes to 10g average local SAR is presented. The chapter enables the utilization of information provided by MR temperature mapping to be converted to 10g average local SAR and be used for RF compliance purposes. The method could be beneficial as 10g average local SAR is the metric used by regulatory committees around the world for confirming compliance of RF/microwave emitting devices.

MRI E Historical Perspective Nuclear magnetic resonance (NMR) was first described by Isidor Rabi in 1938 while working on molecular beams. However, the initial steps towards the discovery of NMR began two decades before when in 1922, Stern and Gerlach passed a beam of silver atoms through a non'uniform magnetic field and discovered that the path of the atoms was altered (2). In 1924, Pauli proposed the concept of intrinsic angular momentum, or spin, for the nucleus (3), and, four years later, Dirac developed the theory of the electron’s intrinsic half'integer spin system resulting from its charge (4). With the idea of discrete spin angular momenta in hand, in 1933, 6

Stern applied the method of molecular beams to determine the magnetic moment by measuring a beam’s deflection due to the interaction of the magnetic moments with an inhomogeneous magnetic field (5). Rabi improved the method in 1937, using the magnetic resonance method jointly with the molecular beam technique (6). The molecular beam passed through an area with a homogeneous magnetic field with a weak transverse alternating component. In this experiment, Rabi used electromagnetic (EM) waves in the radio frequency (RF) range (6). After Rabi’s demonstration of the NMR technique, Purcell, Torrey and Pound (7) and Bloch, Hansen and Packard simultaneously demonstrated Nuclear Magnetic Resonance (NMR) in bulk matter (8). Then, in 1950 the chemical shift effect was discovered by Dickson (9) and Proctor and Yu (10) while noticing that the resonance frequency of certain atoms depended on the molecular environment to which the atoms were exposed. Also in 1950, Erwin Hahn discovered the spin echo, showing that a pulse sequence could be used to refocus the signal after excitation (11). Fast forwarding to nearly two decades later, in 1973 a significant transformation occurred, as Lauterbur showed that localization of the NMR signal is made possible by using magnetic field gradients (12). The technique was called “Zeugmatography”, and shortly after it was published, many other innovations followed. In the same year, Mansfield, inspired by optical diffraction experiments, introduced the mathematical basis for k'space (13). In 1974, Garroway, Grannel and 7

Mansfield discovered that applying a RF pulse while utilizing a magnetic field gradient can be used for slice selectivity (14). A year later in 1975, Kumar, Welti and Ernst devised a two'dimensional scan technique which they called Fourier Imaging, now widely used in the clinical setting (15). In 1976, Mansfield and Maudsley published the first in vivo image of a student’s finger (16), and in 1977 Mansfield introduced the Echo Planar Imaging (EPI) technique which scanned multiple k' space lines after each excitation (17). Following the inventions of Lauterbur, Mansfield, Ernst and others, an emphasis has been placed on improving the SNR of MRI. Over the next two decades magnet manufacturing was improved, enabling imaging at higher magnetic field strengths while improved RF and gradient coil construction enabled whole'body MR imaging of patients. Even with these improvements, however, MRI was still a relatively slow technique and there was still a demand for improving the speed of signal acquisition. In 1997, Sodickson introduced a technique called “Simultaneous Acquisition of Spatial Harmonics” (SMASH). SMASH enabled the utilization of multiple coils to receive the MR signal in parallel (18), speeding up the time it takes to acquire MR images. Building upon SMASH, in subsequent years other parallel imaging techniques operating in the spatial (SENSE) (19) and k'space (GRAPPA) (20) domains were developed and have become widely used in the clinical setting today.

8

Overall, on five different occasions, Nobel prizes were awarded for research conducted in the field of NMR/MRI: •

In 1944, Rabi was awarded the Nobel Prize in Physics “for the resonance method for recording the magnetic properties.”

•

In 1952, Felix Bloch and Edward Purcell were awarded the Nobel Prize in Physics “for their development of new methods for nuclear magnetic precision measurements and discoveries therewith.”

•

In 1992, Richard Ernst won the Nobel Prize in Chemistry “for his contributions to the development of nuclear magnetic resonance spectroscopy.”

•

In 2002, Kurt Würthrich won the Nobel Prize in Chemistry “for his developments of nuclear magnetic resonance spectroscopy for determining the three dimensional structure of biological macromolecules in solution”

•

In 2003, Paul Lauterbur and Peter Mansfield won the Nobel Prize in Medicine or Physiology “for their discoveries concerning magnetic resonance imaging”

MRI Basics (21E23) Atomic nuclei with unpaired protons/neutrons contain an inherent nuclear spin. Intuitively, these nuclear spins can be viewed as tiny magnets which, when perturbed, precess around an applied magnetic field. These small magnetic moments, !, are related to the angular momentum, J, by:

9

! = !"

(1.1)

where the gyromagnetic ratio γ is a unique signature constant for every atomic species with a nuclear spin. In magnetic resonance imaging (MRI), typically hydrogen nuclei are imaged, as they contain an intrinsic single spin and are most abundant in the body in the form of water (H2O). In the presence of an external magnetic field (B0), the magnetic moment vectors of the spins align on average in the direction of the B0 field. If perturbed away from their equilibrium orientation, the spins precess around the B0 field at a defined angular frequency called the “larmor frequency” (ω), which linearly relates to the B0 field strength as follows: ! = !!!

(1.2)

For hydrogen the gyromagnetic constant is ~42.58 MHz/T. Therefore, if, for example, water molecules (containing hydrogen) are exposed to a 7T field strength their precession frequency is 42.58 MHz/Tesla * 7 Tesla=298.06MHz.

Figure 1.1. A net magnetization is created when the body is positioned inside a uniform magnetic field

10

Interaction with the B0 field Without an external magnetic field, the spins are randomly oriented and the bulk magnetic moment ! sums to zero. !=

!"#

!=0

(1.3)

When spins are exposed to the B0 field, ! is no longer equal to zero and, in the example of spin ½ systems (e.g. protons), two populations of spins ' one parallel to the field (nup) and one antiparallel to the field (ndown) ' are created (21,22). Since the nup population is a lower energy state than the ndown population, the number of spins in the nup state is slightly higher as shown in the following figure:

Figure 1.2. In the microscopic scale, an increased number of spins pointing up are observed, when the sample is exposed to a magnetic field (B0). In the macroscopic scale, a net magnetization vector M is shown.

The ratio of spin populations is given by the Boltzmann: !!! !!" = !"# !" !!"#$

(1.4)

where k is the Boltzmann constant, T is the temperature, and ΔE is the energy difference between the two state systems (parallel and anti'parallel) defined by 11

Δ! = 2!!! . It can then be derived that the equilibrium magnetization for protons is given by !! =

!! ! ℏ! !(! + 1)!! 4!"

(1.5)

where ! is the number of spins per unit volume, ℏ is the reduced Planck’s constant, and I = ½ is the proton spin number. Interaction with the RF field At equilibrium, the net magnetization ! points in the B0 field direction. An oscillating magnetic field applied at the Larmor frequency in the transverse direction (x'y plane) is used to “excite” the magnetization in the transverse plane, which will be illustrated later in this chapter. In order to excite the magnetization, coils are used carrying current on a conductor such as copper. The current generated on the surface of the conductor creates a magnetic field that can tip the magnetization (22). Since inhomogeneous excitation fields cause an alteration of the contrast seen by MR, ideally, excitation coils are designed such that they produce a homogeneous excitation field, in the x'y plane. Common coils used for MR signal excitation are the birdcage and surface coils (21).

12

Figure 1.3. Common coils used for imaging the body. A. Birdcage coil. B. Surface coil.

The RF magnetic field generated by the MR coils (the so'called B1 field) can be decomposed into three components in a Cartesian coordinate system: !! = Re !!! ! + !!! ! + !!! ! ! !"#

(1.6)

Here, !!! , !!! , and !!! are complex quantities whose magnitude represents the amplitude of field oscillations along each cardinal direction and whose phase represents the delay of these field oscillations with respect to a common Larmor' frequency reference. !, ! and ! are the unit vectors in the x, y and z directions, i is the imaginary unit, −1, and we have used definitions of complex quantities as elaborated by Hoult in (24). The circularly'polarized component of the RF magnetic field rotating in the same sense as the spin would precess (i.e. the stationary transverse field component in the positively rotating frame) is responsible for spin excitation, while the sensitivity to MR signal as a function of position has been shown, by application of the principle of reciprocity, to correspond to the transverse

13

field component in a counter'rotating reference frame (24). The field components in the positively (B!! ) and negatively (B!! ) rotating frames may be written as follows: B!! =

B!!

=

B! ! + !B! ! 2

(B! ! − !B! ! )∗ 2

(1.7)

(1.8)

Since the Bz component of the applied RF magnetic field is aligned parallel to the main B0 field, it has a negligible effect on magnetization. Therefore, RF coils are typically designed such that their largest magnetic field components are in the x and y planes, while the Bz component is minimal. Tipping of the magnetization is typically described in two frames of reference (22): (i) the laboratory frame, stationary with respect to our position on the earth’s surface, and (ii) the (positively) rotating frame – a frame of reference rotating around the z'axis at angular frequency ω.

Figure 1.4 A. An oscillating B!! used to tip the magnetization in the laboratory frame of reference. Once the RF field is turned on, the magnetization M is tipped to the transverse (xy) plane. B. The angle between the z axis and xy plane reaches 90 degrees when the RF is turned on.

14

The Bloch Equations and Relaxation Once tipped toward the xy plane, the magnetization vector ! precesses around the z'axis at a frequency equal to the Larmor frequency. The Bloch equations, first proposed by Felix Bloch in 1946, describe the behavior of the magnetization vector ! when exposed to an external magnetic field and subject to relaxation effects (T1 and T2). A single vector equation describes the spins’ behavior as follows: !! ! + !! ! (!! − !! )! !! = !! ×! − − !" !! !!

(1.9)

where ! is the applied magnetic field, !, !, ! are the unit vectors in the x, y and z directions, respectively, and !! is the equilibrium magnetization generated by the B0 field (23). The two constants T1 and T2, in the Bloch equations represent the longitudinal and transverse relaxation rates, respectively. Signal Acquisition A receive coil is used to detect the signal generated by magnetization throughout the body (22). The receive coil is typically positioned around the area being imaged. The voltage V induced around the coil loop by the changing magnetic flux through the coil is

15

!∝−

!Φ! ! =− !" !"

! !, ! ∙ B! !, ! ! ! ! (1.10)

= 2!Re ! !"#

Here,

!!! !"

!! ! !!!∗ (!)! ! !

is the change in magnetic flux with respect to time, !! is the

complex representation of the transverse magnetization induced by the B!! field in the positively rotating frame (24) and B!!∗ is the complex conjugate of the negatively'rotating'frame field component as defined earlier. The Three Basic Categories of RF Pulses While the B1+ component of the RF field is used to manipulate the magnetization of the spin systems. Meanwhile, a concomitant E field is responsible for the deposition of energy in the patient. In this section, three RF pulses commonly used for clinical imaging will be covered, while subsequent sections will address the safety aspects associated with the concomitant E field produced by the RF pulses. Excitation pulse An excitation pulse is characterized by its waveform, its duration (typically between 100#s − 4000#s ), and the corresponding flip angle by which the magnetization is tipped relative to the z'axis. The flip angle produced when an on resonance pulse is applied is given by !

!(!) = ! !

B!! !′ !"′

16

(1.11)

Thus, a 400#s rectangular pulse used to tip the magnetization by 45 degrees requires B!! =

! !!∗!".!"∗!"! ∗!""∗!"!!

= 7.34#T . This example shows a linear

relationship between the RF pulse and the flip angle; however, this relationship only holds when the excitation is on resonance when a small tip angle (~2mm from a blood supply, making it less effective in dissipating heat than other organs in the body and more susceptible to damage from heating (38). In several experimental studies, exposure of animals to RF at different frequencies resulted in cataract development (50'53). Rabbits were found to be especially susceptible to cataracts when exposed to 2450MHz continuous waves (54,55) with power levels > 200mW/cm2 applied directly to the eye for 30 minutes 26

or more. In 1975, Guy et al (56), expanded the previous work and quantified the threshold for cataract formation in terms of SAR. He found that at SAR levels above 150 mW/cm3 cataracts formed in rabbits. These studies and others were ultimately used to create the local SAR regulatory limits in use today. Since cataracts were not created at SAR levels below 100 W/kg, a 10'fold safety margin was incorporated into these thresholds to account for uncertainty in the studies. Furthermore, a 10 gram averaging volume was used based on the fact that the mass of the eyeball is about 10 grams and the mass average SAR was reported to correlate quite well with temperature change (38). SAR limits in MRI In magnetic resonance imaging (MRI), RF safety guidelines, defined by the International Electrotechnical Commission (IEC), limit localized heating to 39 °C or below in “normal mode” operation (57). SAR at every location, r, in the region of interest is calculated as follows: !"#(!) =

!(!) !(!) 2!(!)

!

(1.12)

Where ! ! and !(!) are the density in kg/m3 and the electric conductivity in units of S/m, respectively and ! is the magnitude of the electric field. SAR metrics are used to regulate the amount of RF energy that is deposited into patients, which are specified by the IEC or the Center for Devices and Radiological Health (CDRH), part of the US Food and Drug Administration (FDA): 27

•

Whole body SAR –the total rate of RF energy deposited into the body, when exposed to a radiating source (in W/kg). This quantity is used to limit total short'term exposure in patients undergoing MRI scanning. Whole body SAR is calculated as follows: !"#!" =

!(!) !(!) ! !" 2!(!) !

(1.13)

where the integral is conducted over the whole volume of the body. •

Local SAR – the local rate of RF energy deposited averaged over 10 grams or 1 gram of tissue. This metric was established based on dosimetry studies showing that a temperature increase in the eye can have adverse health effects (as mentioned above). While the whole body SAR is utilized to reduce total exposure to RF energy, local SAR is used to prevent energy hotspots that may cause local thermal damage. Local SAR is averaged over 10 grams for compliance with IEC standards and 1 gram of tissue for compliance with the FDA, respectively, as follows: !"#!"!/!! (!) =

!(!) !(!) ! !" !(!) !"!/!!

(1.14)

The SAR associated with a certain pulse sequence can be calculated by summing the energy absorbed from the pulses at one repetition time (TR) multiplied by the number of TRs in the sequence. The current normal operation mode standard recommended by the CDRH limits energy deposition to 4 W/kg averaged over any 15 minute period for whole body SAR and 3 W/kg averaged over 28

any 10 minutes for the head SAR. Similarly, the IEC normal operation mode SAR limits are 2 W/kg for whole body SAR average over any 6 minute period, 10 W/kg in any 10 gram averaged region of the head or torso, and 20 W/kg for extremities. IEC SAR values are averaged in time over 6 minute and 10'second exposures, where the 10'second exposure limit is three times as high as the 6'minute exposure. When local RF coils are used to image the body (e.g. knee, torso, etc.), partial body SAR is used to calculate the maximum exposure. Under normal mode conditions the partial body SAR = 10 W/kg – (8 W/kg * exposed mass / total mass of patient). The following table summarizes the existing local, partial body and whole body SAR limits provided by IEC for RF exposure in the MRI environment: Whole body SAR (W/kg)

Head SAR (W/kg)

Body region

Whole body

Head

Normal

2

3.2

1st Level Controlled 2nd Level Controlled

4 >4

Short term

Partial body SAR (W/kg) Exposed body part

Local SAR (W/kg)

Head

Trunk

Extremities

2'10

10 (c)

10

20

3.2

4'10

10 (c)

10

20

3.2

>4'10

>10 (c)

>10

>20

The SAR limit over any 10'second period shall not exceed three times the stated values

Table 1.1. Whole body and local SAR limits provided by the IEC (58). Local SAR is averaged of 10 grams of tissue.

Global RF power deposited in the patient is monitored in all clinical MRI scanners in real'time and if the threshold for whole body SAR is exceeded, scanning halts. Although whole'body SAR is monitored in subjects, measurement of subject' specific local SAR is currently challenging (29) and EM field simulation software is 29

often used to simulate the coil'body setup in the scanner and to help establish local SAR limits for safe scanning of patients. The frequency dependence of SAR The movement to higher B0 field strengths necessitated utilization of higher B1 operating frequencies. SAR typically increases with frequency of the applied RF field due to the following effects: •

Faraday’s law of induction – the electric field along a conducting loop increases linearly with the time derivative of the magnetic field (!"!! ) inside the loop according the Faraday’s law of induction (appendix A). These general arguments would lead one to expect SAR to increase approximately quadratically with frequency, as shown analytically for a spherical phantom (21). Actually SAR distributions are highly dependent upon the details of tissue composition and body geometry, through the effects described below.

•

Dielectric dispersion – dielectric properties of tissues vary with frequency. (59,60). For example, the conductivity and permittivity of muscle going from 1.5T to 7T change 11% and 19%, respectively. Figure 1.7 illustrates the change in conductivity and relative permittivity as a function of the operating frequency. Changes in conductivity directly affect SAR by changing the ohmic response to applied electric fields.

Meanwhile, both conductivity and

permittivity affect the distribution of fields in tissue.

30

Figure 1.7. Conductivity (A) and relative permittivity (B) as a function of frequency (59,60).

•

RF field non'uniformity and field'tissue interactions as operating frequency increases, tissue dielectric properties have an increasingly pronounced perturbing effect on applied RF electric and magnetic fields. As a result, SAR in particular regions of interest may either increase or decrease, depending upon the degree of field focusing in the region. The use of parallel RF transmission at high field strength further increases the complexity of SAR behavior, allowing potentially large local SAR increases due to unwanted constructive interference, 31

or else enabling SAR decreases via engineered destructive interferences.

EM field Simulations The design of early RF antennas for MRI or other applications mostly relied on circuit concepts (61) or transmission line theories (61,62), which in turn rely on quasistatic field approximations (63). However, analytical models break down when the coil structure is loaded with heterogeneous materials (such as a human body). With the failure of these analytical approaches, a computational tool based on full wave electromagnetics became essential in designing and evaluating the performance of high frequency RF antennas (29). Until the mid'1980’s, full wave numerical methods had seldom been used to model the fields in RF antennas for MRI systems, as the operating frequencies of MR systems were mostly below 200MHz. Han and Wright first utilized a 2D FDTD simulation method to model surface MRI coils loaded with phantoms (64). Later, the FDTD method was also used to analyze a TEM resonator (65'67) loaded with a uniform phantom (67,68) and a segmented realistic human head model (69,70). Developing around the same time was the Finite element method (FEM), which was used to estimate the EM fields both in a phantom (71) and a head model (72). Simulation software was also improved to incorporate many human body models (73) and to compute SAR distributions as an input to a temperature simulator that 32

could be used to estimate the resulting temperature distributions in realistic body models (74'76). Although electrodynamic simulation software has become common in recent years for assisting antenna design and setting safety limits for various antennas, there are still challenges associated with utilizing simulations. One major challenge has been confirming that the actual EM fields in the body are accurately simulated. In chapter 2 of the thesis, challenges associated with confirming that the EM field simulations are accurately computed will be addressed. RF Dosimetry and MR Temperature Measurement Temperature probe based RF dosimetry studies Early RF dosimetry experiments relied on either external thermometers that had low sensitivity to temperature change (>0.2°C) or used thermocouples that interfered with the EM radiation pattern of antennas. As result, both measurement tools were limited in their ability to quantify RF power deposition accurately. In the 1970s, temperature probe sensing technology improved with the development of new optical temperature probes that minimally altered the RF radiation pattern of antennas, enabling more accurate dosimetry experiments (44,45). Nonetheless, as in previous temperature measurements, these probes still had to be positioned in a specific location and the ability to probe multiple spatial positions at the same time in a non'invasive fashion was a persistent limiting factor. This ability to probe for

33

temperature changes rapidly, at high resolution and noninvasively was enabled by means of MR temperature mapping, as discussed in the next section. MR Thermometry: T1, T2 and Diffusion NMR researchers first studied the effect of temperature change on the acquired signal as early as the 1940s. Bloembergen et al (77) demonstrated the temperature dependence of T1 relaxation on an NMR signal. Years later, T1 and temperature'related MRI experiments were conducted in 1984 by Parker et al (78), showing that spin'lattice relaxation in tissues resulted from dipolar interactions between macro molecules and water molecules, arising from rotational and translational motion. The motion of these molecules is dependent on temperature and therefore is reflected in the T1 values. This temperature dependence was found to be on the order of 1%/°C in aqueous solutions and fat tissue (79). Even though T1 temperature mapping was highly promising at first, in vivo quantification of temperature change was challenging with this approach, the physiological response of tissue was found to alter the quantification of T1 when heated (80). Additionally, non'linear response of T1 with an increase in temperature has been found to occur at temperatures as low as 43 °C (81). Similar to changes in T1 that occur with temperature, T2 relaxation was also found to change with temperature; however, this change (as for T1) was nonlinear (82) and tissue dependent. Diffusion weighted imaging measuring the apparent diffusion coefficient (ADC) was shown to have a linear dependence with temperature and a temperature sensitivity of ~2%/°C was 34

shown by Zhang et al (83). However, diffusion imaging inherently had lower SNR, which was not optimal for many temperature mapping applications. MR Thermometry: The proton resonance frequency shift (PRF) In contrast to ADC, T1, and T2 mapping, which were challenged by non'linear responses or limited sensitivity to temperature change, the proton resonance frequency (PRF) of water changes roughly linearly with temperature and with much greater sensitivity to temperature change. The phenomenon was first was discovered in 1966 by Hindman (84) when conducting NMR experiments on intermolecular forces and hydrogen bond formation. The technique was later implemented in MRI by Ishihara et al in 1995 (85) and De Poorter (86) the same year. Under the influence of a magnetic field, the precession frequency of protons follows equation 1.2. However, the local magnetic field experienced by the protons (Bloc) may differ from the applied main magnetic field (B0). Electron'generated magnetic fields shield from the main (B0) magnetic field and ultimately cause an individual proton to experience a smaller field (87). As result, the field can be written as: !!"# = !! − !! = (1 − !)!!

(1.15)

where s is the shielding constant, which has been shown to be linearly dependent on temperature (84). As result of equation 1.15, the effective precession frequency of protons is: 35

!!"# = !"! − !"! = (1 − !)!"!

(1.16)

where the average electron'screening constant of pure water, which relates linearly with temperature, is approximately '0.01ppm/°C (84). MRI temperature mapping is commonly performed using spoiled gradient' echo (GRE) imaging sequences and measuring the phase change resulting from temperature related localized frequency shifts (84). To remove the temperature' independent contribution from the external magnetic field inhomogeneities, one image is acquired before RF heating and the second image is acquired after (85). The resulting phase'subtracted images can then be converted to temperature change using the following equation: Δ! =

Δ! !"! !!

(1.17)

where ! is the PRF coefficient (in PPM/°C), TE is the echo time of the acquisition and !! = !"! . The echo time of the acquisition can then be optimized to increase the temperature'to'noise (TNR), which is calculated as follows (87): TNR =

Δ!(Δ!) σ!!

(1.18)

where Δ! is the phase difference of the phase subtracted maps and σ!! is the standard deviation of the phase difference image, which is normalized by the signal !

amplitude as follows: σ!! = (87). As result, the TNR is directly proportional to the !

signal amplitude (87): 36

TNR ∝ Δ!(Δ!) !

(1.19)

The GRE signal decay can be approximated to be exponential in nature, with an exponential time constant of T2*. On the other hand, the phase shift increases linearly with time (87). As a result, the TNR of the temperature measurement can be written as: TNR ∝ TE ∙

!" ! ∗ exp !!

(1.20)

Differentiating equation 4.35 with respect to TE yields the optimal echo time of the phase imaging sequence: TEoptimal= T2* (87).

37

2. EFFECTS OF GEOMETRIC INACCURACIES ON SIMULATED FIELDS, SAR, AND TEMPERATURE PROLOGUE Simulation software is commonly used to assess RF exposure from MR coils. This chapter investigates the effects of geometric inaccuracies on FDTD simulations and assesses the difficulties associated with aligning FDTD simulations and experiments.

AUTHOR CONTRIBUTIONS: Leeor Alon: Study design, data analysis & interpretation, literature research, simulation work, manuscript writing. Cem Murat Deniz: Study concept, result analysis, manuscript editing. Yudong Zhu: Study concept, data interpretation, manuscript editing. Daniel K. Sodickson: Study concept, manuscript editing. Christopher M. Collins: Study concept, study design, data interpretation, manuscript editing.

INTRODUCTION In magnetic resonance imaging (MRI), a radio frequency (RF) magnetic (B1) field is used to excite nuclei inside the body while the concomitant electric (E) field 38

deposits RF energy inside the body (88), causing Joule heating of tissues. RF safety guidelines, defined by the International Electrotechnical Commission (IEC), limit localized heating to < 39 °C for “normal mode” operation and 40 °C for first level operation mode while maintaining body core temperature change less than 1° C (57). Currently, experimental mapping of absolute temperature in vivo using MR' based temperature mapping methods faces significant challenges due to motion, tissue'dependent variation of the proton resonance frequency shift coefficient, limited sensitivity, !!∗ , !! and other factors, limiting the potential for routine use in monitoring patient safety (87). Therefore, limits on the Specific Absorption Rate (SAR) – a measure of the rate at which RF energy is absorbed in tissue when exposed to RF energy – are also provided (57). For local SAR exposure, the IEC recommends 10 W/kg for SAR averaged of 10 grams of tissue for normal mode and 20 W/kg for first level mode, which has been advised to prevent thermal damage to tissue (57). Historically experimental measurement estimation of local SAR or temperature change, albeit desirable, has mostly been accomplished in phantom studies (89,90), or in the case of temperature, in human studies where the temperature change was greater than 2° C (91). Since 2° C of tissue heating is undesirable in routine clinical use and in vivo routine temperature mapping remains challenging, these techniques have not been used in common practice (89,91). As a result, in'vivo local SAR estimation relies heavily on a priori electromagnetic (EM) field simulations, where MRI coils are modeled next to one or 39

more of several pre'existing human body models, such as those of the virtual family (73). Typically, numerical RF coil models are driven with a current or voltage source and the resulting local SAR distribution is assessed. However, because the body models used are typically different than the geometry of the patient being imaged, geometrical inaccuracies associated with the body models may result in inaccurate predictions of local SAR and temperature change (∆T) distributions in the body (92). Recently, experimental techniques for electrical property mapping have attempted to map the in vivo electrical properties of patients scanned and estimate SAR (93,94), however, as of today, these measurements are not capable of robustly estimating the tissue property composition and SAR at tissue boundaries where SAR can be the highest and while the estimation of SAR is highly desirable, it’s estimation often require lengthy experiments rendering it infeasible for routine clinical scanning (93,94). In additional to experimental methods for quantifying SAR, recently, a hybrid experimental and simulation approach has been proposed to simulate patient' specific SAR in the scanner where fat' and water' images are acquired and used to generate a simplistic human body with a few tissue types (95). The simplistic human body model is fed into an FDTD simulation solver to compute the SAR distribution. Since the RF magnetic field (B1+) is readily measurable in MR, a number of studies have used similarities between B1+ fields in simulation and in experiment to indicate accuracy of simulation methods for estimating SAR (95'97). While previous studies have shown that B1+ fields provide vital information for aligning 40

simulations and experiments, this work investigates whether alignment of simulations and experiments can be conducted using the B1+ field information. Simulations were conducted for the abdomen region since it is a region with high variability in anatomy within the population and SAR intensive sequences are often required to image it (98). Evaluations were performed at 3T for a single'coil setup and at 7T for single' and two'coil setups using different body models taken from body model libraries that are commonly used for simulating MR safety settings. Simulations were conducted at different mesh resolutions and variations to subjects’ anatomy were imposed in attempt to assess challenges in simulating subject'specific body models. The overall goal of the study was to: A. Evaluate the safety of transmit surface coil(s) in the presence of different body structures. B. Examine whether correlations in the complex B1+ field imply that the SAR and ΔT maps correlate as presumed in several studies (95'97) .

41

Figure 2.1. A . A. Single- and two coils positioned next to the abdomen of the Hugo body model. Imaging slice is shown in yellow-green. B. An axial slice of the electric conductivity (σ) and permittivity

42

(ε) maps used for the original and altered Hugo simulations. C. Single- and two -coils positioned next to the abdomen of the Duke and Ella body models.

METHODS Using a Finite Difference Time Domain (FDTD) (99) simulation software environment (xFDTD, Remcom, PA, USA) a single surface coil (7cm x 7cm) was placed 1 cm above the abdomen of a Hugo human body mesh model (100) and a conducting layer of the coil was modeled along the faces of the FDTD cells, resembling a thin conductive strip of copper (figure 2.1A, left). The coil was driven with a 1'Ampere current source at 128 and 297 MHz placed at a single gap in the coil, simulating the resonance frequency of MR experiments at 3 and 7T. At each frequency, simulations were conducted at isometric resolution of 5×5×5 mm3. A 7' layer perfectly matched layer (PML) outer boundary condition was used and the convergence criterion was set to '60 dB. For each frequency and specified mesh resolution, the following simulations were conducted (figure 2.1B): 1. The original Hugo human body mesh (“original”) was used. 2. Voxels in the abdominal region of original human body model were replaced with muscle and intestinal tissue (“altered”). The total tissue volume replaced was 141cm3, of which 2.3cm3 was skin, 14.8cm3 was muscle and 123.9cm3 was fat tissues substituted with 45.1cm3 of muscle and 95.9cm3 of intestine tissues, respectively. The abdomen was chosen since it is an area of high variability in the distribution of fat, muscle and intestinal tissue among subjects. This type of change to the abdominal region is also possible in patients that have abdominal abnormalities such as hernias where the small 43

intestine can be outside the abdominal cavity (101). Even during a single study in a patient, bowel motility and respiration can cause significant displacements in this region. For both simulations where the original and altered Hugo human body model were used, an additional two'coil parallel transmit experiment was simulated by adding another surface coil to the 7T simulation model (figure 2.1A, right). Two surface coils of identical size (7 x 7 cm2) were placed 1 cm and 2 cm, respectively, above the abdominal area of the Hugo human body mesh model with a 2 cm overlap between the coils. For the two'coil simulations, three different mesh resolutions, boundary conditions and convergence criterion were the same as for the single'coil case. The two coils were driven using a current source at 297.2MHz with weighting of

!

!

exp!! ! for the first coil, and !

!

!

exp! ! for the second coil, respectively, and as in !

the single'coil case, original and altered tissue simulations were computed for the two'coil setup. In addition to simulations conducted on the Hugo body model, four more simulations were conducted using the Duke and Ella body models (figure 2.1C) from the Virtual Family library (73). These extra simulations were conducted since the body models were segmented in high resolution (2) next to different body geometries on B1+ and MR safety. While the conservative nature of 10g'averaged SAR limits may prevent excessive deposition of RF energy, the results demonstrate that location'specific 10g averaged SAR and temperature change can vary significantly as the result of alteration of the body model and 10g averaged SAR limit can easily be exceeded. Fortunately, the regions of greatest temperature increase are near the surface of the body where the initial absolute temperature was below core body temperature due to the boundary with the air at 23 °C and local temperature was below 38.2 °C, remaining within the IEC temperature threshold limit of 39 °C (57). Even though EM field simulations are often used to arrive at safety limits of MRI coils, this work questions the validity of using B1+ fields as a metric for aligning simulations and experiments as although B1+ fields were relatively aligned, resulting 10g average SAR limits were exceeded up to 3.6 times.

56

3. SYSTEM AND SAR CHARACTERIZATION IN PARALLEL RF TRANSMISSION PROLOGUE In the previous chapter we introduced several challenges associated with aligning results from simulations and experiments, and we explored some of the effects of body composition on RF safety. These results clearly motivate the development of experimental techniques for measuring subject'specific SAR in vivo. In this chapter a novel method for quantifying and predicting in vivo global SAR for parallel transmit systems is introduced. The results presented in this chapter were published in the journal Magnetic Resonance in Medicine in 2012 (112) and were also represented in several conference abstracts/presentations (113,114). Following development of the theory by first author Dr. Yudong Zhu, my contributions to this work, which spanned more than two years, included development of the hardware and software to interface with the MR scanner for the creation of this unique SAR monitoring system. I conducted the simulations for this study and performed experiments in phantoms and humans. This work was presented as 3 separate ISMRM conference abstracts and 2 oral presentations.

57

AUTHOR CONTRIBUTIONS: Yudong Zhu: Theoretical work, study design, hardware configuration, data analysis & interpretation, manuscript writing. Leeor Alon: Study design, hardware configuration, software coding, data analysis & interpretation, simulation work, experimental work, manuscript editing. Cem Murat Deniz: Study concept, experimental work, pulse design, manuscript editing. Ryan Brown: Coil construction, manuscript editing. Daniel K. Sodickson: Study concept, manuscript editing.

INTRODUCTION During RF transmission the B1 field interacts with spins and induces MR signal. The concomitant E field, necessarily accompanying the B1 field by the laws of electrodynamics, deposits RF energy in the subject and dictates SAR. Conventional RF transmission strives for a uniform B1 in a large volume,which tends to cause, regardless of the location or size of the imaged region, broad'reaching E field and unnecessarily high RF energy deposition. Parallel RF transmission brought about a new paradigm. With parallel RF transmission, RF pulses simultaneously drive distributed elements of a multi'port transmit coil to affect both spatial and temporal variations of the B1 and E fields. The much increased degrees of freedom (34,115)

58

were shown to enable tailoring of E field and containment of SAR, while improving flip'angle profile control. For a given coil'subject setup, exploitation of the degrees of freedom for improving flip'angle profile and SAR control is realized through design of RF/gradient pulses. Practice of the former in vivo has been supported by subject' specific B1 calibration, which captures the complex effects of coil'subject interaction, geometry and composition on the B1 maps and provides guidance for the pulse design (based essentially on Bloch equation). However, due to a lack of subject'specific SAR calibration support, a guidance to pulse design for realizing effective SAR control has not been possible in vivo. In fact, the extra degrees of freedom, compounded by a generally poor understanding of SAR in high field MR, often spur concerns that improper design or playout of RF pulses may exacerbate SAR, as opposed to reducing it.

These safety and

performance considerations underscore the importance of a valid SAR prediction method, one that, given any set of RF shimming coefficients or RF excitation pulses, predicts the SAR consequences globally and locally.

To evaluate / predict SAR, a

significant amount of recent efforts have relied on electromagnetic field calculations in numerical simulations or experimental findings in scanning an “average” subject. Yet it remains unclear if it will be feasible to adapt the details of the simulated coil' human setup or to extrapolate the “average” findings such that the separately

59

obtained SAR characteristics could closely track what happens or will happen to a subject undergoing an MR exam. The present work followed the lead of a SAR prediction model (34), which, based on system linearity, relates global or local SAR to parallel RF pulses or RF shimming coefficients with a quadratic function. The model has been used in a number of parallel transmission SAR investigations (34,115'120), which demonstrated that design of RF pulses, when guided by the model prediction, enables the extra degrees of freedom inherent of a parallel transmission system be advantageously exploited, and SAR be reduced. The model has also been a foundational piece for analyzing and approaching ultimate transmit performance (120). The introduction of the model is significant – it indicates that there is a structure to parallel transmission global and local SAR behavior and that the uniqueness of a specific coil'subject setup can be encapsulated by the set of parameters defining the structure. The present work focuses on further devising a clinically applicable method to unveil the structure parameters that are specific to a coil'subject setup, and subsequently establish a SAR tracking and prediction capability that provides valuable guidance to the actual scans of the subject. The method is based on a finite number of in situ measurements instead of using simplifying assumptions about the subject and the scanner setup. Compared to a method relying on simulations or “average” results, this eliminates a major source of 60

error associated with variations of SAR expected from one subject / RF apparatus to another. In this paper the scope of the devised method is limited to global SAR and individual channel characterizations.

THEORY AND METHOD RF energy dissipation and tissue heating Pennes’ bio'heat equation describes thermal energy balance for perfused tissue: !"

!" !"

= ∇. !∇! + ℎ! + ℎ!

(4.1)

where ρ, C and k refer to tissue density, heat capacity and thermal conductivity respectively, and hb is the blood'to'tissue heat transfer rate. RF energy deposition accompanying RF transmission is a driving force of temperature rise, which is captured in Eqn. 3.1 by he, the local RF energy deposition rate. Note that he is due to Joule heating and polarization damping forces, and is thus proportional to the square of local E field strength: he = ½ σ|E|2, where σ = σtissue+ωε”. Temporal and volume averaging of he, when further scaled by appropriate density or mass measurements, give, for example, head, torso, extremity or whole body average SAR as defined in FDA and IEC guidelines (20). Excessive tissue heating may potentially result from RF energy deposition. This risk tends to weigh in if patient scan involves a high RF duty'cycle sequence /

61

high B0 field, in which case monitoring and optimization of RF transmission become crucial. A linear system perspective An MR scanner commonly modulates both RF and gradient fields when exciting spins. Modulation of the RF field is achieved by updating, as specified by a designed RF pulse waveform, the magnitude and phase of a Larmor'frequency sinusoidal pulse that drives a transmit channel and a transmit coil. The updating happens every Δt, which is typically several micro seconds in practice. This modulation is multiplied in parallel RF transmission, where a plurality of designed waveforms, sinusoidal pulses and transmit channels, as well as a multi'port transmit coil, are employed to provide considerably enhanced support for the RF field modulation, giving rise to an RF field that varies both in space and time. Parallel RF transmission includes RF shimming as a special case. A useful perspective to parallel transmission is to treat the transmit channels, the transmit coil and the subject as a system. For any Δt interval, the magnitude' phase pairs specified by multiple RF pulse waveforms, expressed with complex scalars wp(n) (n = port index and p = interval index), define the inputs to the system – there is one input configuration per Δt interval. The B1+ field and the RF energy deposition are important outputs of the system. During RF transmission the B1+ field interacts with the spins, forming the basis of MR signal induction (spin

62

excitation). The concomitant E field, necessarily accompanying the B1 field by the law of electrodynamics, induces RF energy deposition in the subject (SAR). To address the goal of creating a target excitation profile while keeping SAR low, one needs to design RF pulse waveforms, or system inputs, in an optimal way so that the system will respond with both 1) a properly modulated B1+ field that works with the gradient field in exciting spins, and 2) a properly restrained E field that steers clear of excessive RF energy deposition. This task of maximizing efficiency of spin excitation tends to call for, constructive and destructive interferences of B1+ and E fields. A key prerequisite to the design optimization is accurate prediction of B1+ distribution and E'induced RF energy deposition given any input configuration. This is tractable in practice, and described below. Parallel RF transmission system hardware is normally set up in such a way that the electromagnetic field induced in the subject responds linearly to the inputs. This can be appreciated by considering the subject and the RF transmit coil as a multi'port network that interacts with a plurality of sources through the ports (Fig. 3.1). The RF power amplifiers, each presenting to the multi'port network equivalently a voltage source in series with an output impedance, amplify modulated RF pulses and drive the ports. Provided that the amplifiers satisfy common linearity specs, the voltage sources are related linearly to the modulated RF pulses that are fed to the corresponding amplifiers’ input terminals. In this case linearity of Maxwell equations dictates that the electromagnetic field responds 63

linearly to the voltage sources and, in turn, to the modulated RF pulses. It follows that any electromagnetic field component at a location within the object, as a function of time, can be expressed as: ! ! = !(!

!

! ,!

!

! ,…!

!

(4.2)

! )

where L represents a linear mapping, y(t) denotes the electromagnetic field component, v(n)(t)’s are the modulated RF pulses, and N is the number of Tx ports. The phasor notation is suitable for describing the steady state of a time variable within each Δt interval. For example, at a location r inside the object and within

the

pth

Δt

E(r,t)=[αx(r)cos(ω0t+ϕx(r))

interval,

the

E

field

αy(r)cos(ω0t+ϕy(r))

can

be

expressed

αz(r)cos(ω0t+ϕz(r))].

as The

corresponding phasor notation for E is a complex vector: Ep(r)=[αx(r)exp(jϕx(r)) αy(r)exp(jϕy(r)) αz(r)exp(jϕz(r))]. For the same interval, the phasor notation for the modulated RF pulse for the nth port is the complex scalar w(pn ) .

A linear system

behavior captured by Eqn. 3.2 can thus be expressed in a matrix form for the Δt interval: ! = !!

(4.3)

In Eqn. 3.3, w = [wp(1) wp(2)… wp(N)]T is a vector collecting the definitions for the modulated RF pulses – the nth entry is the complex scalar corresponding to the pair of magnitude and phase values for the Δt interval and the nth port. y = [yp(1) yp(2)… yp(L)]T is a vector collecting phasor representations of the time variables of interest 64

for the same interval (e.g., B1+ field at M spatial locations). A is an L'by'N complex' valued matrix representing the linear mapping. Local and global SAR models Linearity allows decomposition of the net E field as a weighted superposition of E fields corresponding to the N individual sources, with the weights being wp(1), … (!) ! !!! !!

wp(N). In phasor notation !! =

!

!

(!), where !

!

! is the E field (the

response) due to a w (the input) that has its nth entry being one and the rest being zeroes. This leads to the following expression for local RF energy deposition rate: ℎ! ! = ! = 2

= !

! ! 2

!

=

! ! (!)∗ ∙ !! ! 2 ! ∗

!

!!!

!

!

!

!

!!!

(!) !!

!!! ! ! !

∙

(4.4)

!!!

∗

⋯ ! ⋯ ⋯

! (!) ! (!) 2

⋯ ∗

⋯

⋯

∙ !

(!)

(!)

! ⋯ !!(!) ⋯ !

where * denotes complex conjugate, H denotes conjugate transpose and the underscored indices are row or column indices for vector and matrix entries. Eq. 3.4 shows local RF power deposition can be expressed as quadratic functions in wp(1), … and wp(N). In matrix form, he = wH Λ w. It follows that global RF energy deposition rate can also be described by a quadratic model: 65

!! = !

!(!) ! !! (!) !" = 2 ⋯

= ⋯

(!) !!

∗

⋯ !(!) (!) ∗ ! (!) ∙ ! (!) (!) !" 2 ⋯

⋯ ⋯ !

⋯

⋯

⋮ ⋯ ! (!) ! ⋮ ⋯

(4.5)

= !! !! Matrices Λ and Φ are named, respectively, local and global power correlation matrices. Both Λ and Φ are N'by'N, and can be shown to be Hermitian and positive semidefinite. They capture the effects of field interference and tissue conductivity on RF energy deposition at regional and global scales. Total deposited RF energy during RF transmission is a time integral of ξp, expressed as: !

!=

!

Δ! !! = !!!

!

! ! ! !Δt !! !

∗

!!!

!!!

= !!!"## !!"## !!"## !Δt

!ℎ!"! !!"## =

(4.6)

0

0

0

!Δt

!"#!"

where wfull is a vector collects all samples of the RF pulse waveforms. Similarly, !

!=

!

Δ! !! (!) = !!!

!

!!!

∗

!!!

= !!!"##

!(!)Δt

0 0

0 66

! ! ! !(!)Δt !! !

!(!)Δt

!!"## !"#!"

(4.7)

quantifies total deposited RF energy at location x over the course of the RF excitation. It is to be noted that in characterizing SAR, even in the absence of inter'coil coupling, RF energy dissipation locally or averaged over an imaging volume cannot be treated by considering the individual sources in isolation. This can be attributed to the overlapping of E fields. Quantitatively this is reflected in the typically non' zero off'diagonal entries in Λ and Φ – these correlation entries quantify the mutually interfering nature amongst the sources and encapsulate information instrumental for SAR reduction. In practice however, existing RF shimming or RF pulse calculations often resort to sum of squares of the waveform samples when tracking SAR, which is equivalent to using an identity matrix in place of Λ or Φ. Such an approach could be subject to significant error in managing SAR. For instance, given a set of parallel RF pulses, one can add a 180° phase offset to one of the pulses without affecting the evaluation of wH I w – use of identity matrix I is incapable of capturing the SAR effect caused by the constructive or destructive interference of the E fields driven by the pulses. Use of identity matrix I further assumes no response variation to the multiple sources, which is not true in any case where different array elements contribute differently to SAR.

67

Results represented by Eqns. 3.4 and 3.5 indicate that there is a structure to global and local SAR. With a proper measurement scheme (calibration) it is possible to unveil the structure and establish a practical SAR tracking / prediction capability.

Figure 3.1. A system perspective to parallel RF transmission: The transmit channels, the transmit coil and the subject together form a system, with w(n), the parallel RF pulse waveforms, as inputs, and B1+ field and RF energy deposition as outputs. Parallel RF transmission system hardware is normally set up in such a way that the electromagnetic field induced in the subject responds linearly to the inputs.

Calibration method An RF transmit system with linearity adequately maintained, facilitates EM field calibration. Eqn. 3.3 suggests that, based on linearity, EM field responses measured in N experiments that employ N linearly independent input 68

configurations may be sufficient for predicting the EM field response to any input configuration. This is because matrix A can be fully determined from the measured EM field responses and the corresponding inputs: ! ! ! ! …! ! = ! ! ! ! ! …! ! ⇒ ! = ! ! ! ! …! !

! ! ! ! …! !

!!

(4.8)

Eqn. 3.8 pools Eqn. 3.3'type equations together, with the experiment index shown as subscripts. Note that existence of the inverse of matrix [w(1) w(2) … w(N)] is guaranteed due to the linear independence of the input configurations. A simple yet concrete example is calibration of transmit B1 fields with N experiments, where the nth experiment (n=1,2,…N) involves driving the nth port with a unit'amplitude rectangular RF pulse (a sinusoid of unit amplitude and zero initial phase) and the other ports with zero'amplitude RF pulses. In this case [w(1) w(2) … w(N)] is an identity matrix, and [y(1) y(2) … y(N)] = A stores individual channel field maps. For improved robustness in the presence of noise or perturbations, more / tailored calibration experiments could be used, which is the subject of active research especially in the context of transmit B1 field mapping. To illustrate with simpler notations, consider one row of Eqn. 3.8. It deals with EM field at one spatial location and can be rewritten as: ! = !" 69

(4.9)

where W is defined as [w(1) w(2) … w(M)] T, x denotes the transpose of the lth row of A, and for B1 mapping, b is a vector collecting B1+ at the lth location measured in calibration experiment 1 through M (M ≥ N).

If the noise covariance matrix of

measured b is V, the classic solution to x is given by the best linear unbiased estimate(121): ! = (!! !!! !)!! !! !!! !

(4.10)

As is clear, for multi'port parallel RF transmission, calibrating A satisfies one prerequisite of the RF pulse design process – the spatiotemporal variation of the B1+ field, and further, the spin excitation profile, can then be possibly predicted for any set of RF pulses, which enables excitation profile control through the design and use of appropriate RF pulses. This illustrated framework for establishing a model (and determining A) points to a few important considerations, including physical basis of the prediction model, measurement noise handling, tailoring of calibration (specifically, design of the calibration configurations that W captures), and sensing or measurement scheme. These are covered in depth below in the context of power and SAR characterization. An MR system with linearity well maintained has RF power dissipation characterized by Eqns. 3.4 and 3.5, which facilitates RF loss calibration and minimization. By the law of conservation of energy the net RF power injected into the N'port network should be equal to combined RF loss in the subject, in the transmission hardware (including the coil) and through radiation. The latter two are 70

normally related to w in the form of quadratic functions as well, giving rise to the following expression for total RF loss: !"# !"#$%&$' !" !"#$% = !"!#$ !" !"#$% !"##"$%&'! (4.11)

!

= ! !! In Eqn. 3.11 !=Φ+Φ other, where Φ other characterizes RF loss in hardware and through radiation. In general, total RF power dissipation / ! is the upper bound, or, conservative estimate, of RF power deposition in subject / Φ. MR engineering typically strives to set up the transmit system with conductor loss minimized and an effective RF shield implemented. When this is the case RF loss in the subject tends to dominate the total RF loss in the network, and ! becomes a good approximation of Φ. With power sensors at the ports capable of measuring forward and reflected power (Fig. 3.1), Σpfwd ' Σprfl

gives net injected RF power, allowing ! to be

estimated through experiments.

Specifically, given wq, an input configuration for

the qth experiment, forward and reflected power measurements are related to wq by: !!"#,! = !! ! !!!

!!"#,! −

(4.12) =

!"

!"#$ !!

!

!!

!

!!"

Eq. 3.12 is a linear equation with !ij, the entries of!, as the unknowns, and product terms, conj(wq(i)) wq(j), as the coefficients. 71

Carrying out calibration

experiments with at least N2 properly selected input configurations played out one at a time can probe the RF loss characteristic of the multi'port network, allowing Eq. 3.12 'type equations be assembled and all the entries of ! be determined. Since, ! is a hermition'symmetric matrix, determining all the entries of ! involves estimating N2 unknowns. This process does not involve MR imaging and may be completed in a fraction of a second with an automated measuring system. Once the calibration is done, the global SAR model predicts, for the specific subject, the SAR consequence of any input configuration or parallel RF transmit pulses. The above scheme can be adapted to model and predict individual channel forward or reflected power. In this case Eq. 3.12 is modified to assume the form: (!)

!"ℎ !ℎ!""#$ !!"#,! = !! ! !!"# !! =

!"

!"#$ !!

!

(!)

!"ℎ !ℎ!""#$ !!"#,! = !! ! !!"# !! =

!"

!!

!

(4.13)

(!) !!"# !"

!"#$ !!

!

!!

!

(!)

!!"#

!"

With the forward and reflected power measurements used for calibrating !, the individual RF transmit channel’s forward and reflected power transmission are therefore fully characterized – their predicted values for an arbitrary input (!)

(!)

configuration w are wH !!"# w and wH !!"# w, respectively.

72

The forward and reflected power predictions for any RF excitation are expected to be helpful ensuring a smooth scan in practice: 1) Given the peak power rating of the power amplifiers assigned to drive the parallel transmission channels, knowing in advance the peak power requirements for the individual channels allows the user to proactively tailor the excitation pulse (e.g., by applying VERSE) and/or reconfigure the transmit hardware (e.g., by updating the power combination scheme applied to the component amplifier units). 2) Given the reflected power handling capacity of the amplifiers / circulators on the parallel transmission channels, knowing in advance peak reflected power for the individual channels similarly allows the user to implement software' and/or hardware'based mitigation strategies. 3) As a supplement to the global power prediction and monitoring, checking the individual channel forward and reflected power predictions against actual measurements provides diagnostics that promise to detect, reliably and in real'time, system failure and initiate scan suspension.

In other words, using the

power prediction models in planning and monitoring may avert amplifier peak power or VSWR faults, protection hardware breakdown, and system failure'induced excessive SAR. An algorithm was further developed for prescribing input configurations used in the calibration. The algorithm improves the robustness of the solution against perturbation or noise by constructing a complete set of Eq. 3.12 'type equations with a condition number ~ N.

73

There is a link between the global SAR model and S, the scattering matrix of the N'port network (122). Given an S'parameter matrix that is determined from incident and reflected wave measurements (amplitudes and phases) taken at the N directional couplers during a calibration, one can subsequently express total RF power dissipation in the network as aH (I'SHS)a for any a, where a is an N'by'1 vector collecting the instantaneous incident wave measurements taken at the N ports. This leads to != LH (I'SHS) L, where matrix L captures the linear mapping from w to a as well as other scaling in the system. L is fixed for a given hardware' subject setup. An additional link between the global power correlation matrix and parallel receive noise covariance matrix Ψ was suggested in the past, based on the principle of reciprocity (123). In addition to offering alternative ways to calibrating a global SAR model, these links also suggest that the global power correlation matrix provides important information about S and Ψ, and vise versa.

For example,

knowledge of ! and L allows determination of all of S’s eigenvalues. When using measurements to link S or Ψ to !, or to directly establish a global SAR prediction model, maintaining the same measurement condition as that is in place during actual parallel RF transmission is important. In particular, the impedance presented to the ports need to stay the same –likely alteration of RF current and field patterns within the network (including the coil structure and the subject body) due to changes in impedance seen by the ports can result in changes in RF loss characteristics, rendering the SAR model less accurate predicting the RF 74

loss characteristics during actual parallel transmit MRI (when the ports see the output impedance of RF power amplifiers). Simulation studies Parallel RF transmission for MR at 7 Tesla was modeled FDTD calculations (xFDTD, Remcom, State College, PA). The FDTD calculations quantified both EM field and net RF power dissipation corresponding to various input configurations, which allow evaluation of the SAR calibration and prediction method. A first study examined feasibility of the global SAR calibration and prediction in 7T body imaging. The setup involved a human model with heterogeneous electrical and density parameters, and an RF coil composed of 4 loop elements placed about same distance from the back of the human model (Fig. 3.2a). The FDTD calculations used a cell size of 5 x 5 x 5 mm3. A total of thirty'nine simulation experiments were conducted employing the same coil'subject setup but different input configurations. For each input configuration the net power dissipation reading, as generated by the FDTD calculations, was recorded.

To emulate a use scenario of calibration followed by

actual scan, the first twenty of the total of thirty'nine experiments were conducted with input configurations prescribed for SAR model calibration as described above. These twenty input configuration specifications and their resulting net power dissipation values were used to assemble a set of twenty Eqn.'type equations, which was solved with a least squares fit to give an estimate of Φ. Given the estimate of Φ 75

and the specification of any one input configuration, denoted as w, wHΦw provides a prediction of net RF power dissipation. In the remaining nineteen experiments the input configurations were randomly prescribed. Plugging each of these nineteen input configuration specifications into wHΦw gave a predicted net RF power dissipation, which was compared to the corresponding one that was directly quantified by the FDTD calculation. The comparison allowed an assessment of the accuracy of the model'based global SAR predictions and served to check the validness of the prediction model. To investigate impact of coil'subject setup on the global SAR model, in a second study two different setups were modeled each involving four identical loop elements of size 7 x 7 cm2 placed about 1 cm above a uniform water phantom (Fig. 3.3). Overlapping of elements was accommodated by slightly lifting the elements relative to one another. The water phantom had a dimension of 24 x 20 x 24 cm3, with conductivity 0.6 SI/m and relative permittivity 80, mimicking electrical properties of human tissue. With either setups, the set of input configurations included 16 programmed ones for model calibration and 8 randomly generated ones for model validation. Global SAR characteristics exhibited by the two setups were compared. Phantom and in vivo studies On a whole body 7 T scanner (Siemens, Erlangen, Germany) that has a capacity for eight channel parallel RF transmission, experiments were performed to 76

evaluate, under actual MR imaging condition, the global SAR calibration and prediction method. Forward and reflected power on the 8 transmit channels were measured using a power sensor (Rohde & Schwarz NRP'Z11) off directional couplers located at the output ports of the RF power amplifiers. An RF switch (National Instrument Dual 16x1 MUX) and an application software for instrument control and data logging were additionally implemented to automate a sequential collection of all power measurements using the single power sensor. One set of power measurements was collected in parallel Tx MR mode with a cylindrical phantom with half of the rungs of an 8'rung proton Tx'Rx array (Fig. 3.4a). Co'located on the same former was a separate sodium birdcage. Four pre' designed 18 msec'long staircase'shaped parallel RF pulses (Fig. 3.4c) were used to introduce 36 input configurations, including 16 for model calibration and additional 20 randomly generated ones for model validation. The playout of the four parallel pulses were repeated several times to allow a program on the computer enough time for communicating with the RF switch and the power sensor and accomplishing the sequential collection of all power measurements on each of the channels. The study was repeated in a more general coil'object setup, where four loop elements that formed a Tx'Rx array coil were arbitrarily placed on a head shaped phantom (Fig. 3.4b). In vivo evaluations were conducted in human volunteer studies. In one study an 8'channel stripline array was used for parallel transmit MRI of a volunteer’s left 77

knee on the 7T scanner. Eight 40 msec'long staircase'shaped parallel RF pulses were used to introduce 100 input configurations (designed with the algorithm shown in Appendix), including 64 for model calibration and additional 36 randomly generated ones for model validation. The automation program for instrument control and data logging was integrated with a data analysis script written in Matlab (MathWorks, Natick, MA) and C++. It is appropriate to integrate into a scanner’s existing PRESCAN the staircase pulsing scheme. Ahead of the actual MR scan the scheme accomplishes SAR model calibration and validation. The established SAR prediction model is then used to guide pulse design optimization, also ahead of the actual MR scan. This operation mode was followed in an actual imaging experiment. In one example where large' tip'angle parallel excitation was designed for phantom imaging on the 7T scanner, model calibration and validation was first conducted. Pulse designs both with and without the prediction model incorporated were played out, and their corresponding net power as functions of time were recorded. These actual measurements were compared to the predictions given by the model for the two pulse designs, to check how accurate the model guided pulse design optimization (i.e., how well what the design algorithm thinks as the SAR consequence of a given design matches the real SAR consequence).

78

Evaluations of support for planning and monitoring Experiments were further conducted to examine potential use of the power prediction models in planning and monitoring of parallel RF transmission on an MR scanner. Some modifications were applied to the phantom experiment setup described above. For this study instead of using the stock directional couplers that are located at the output ports of the power amplifiers, three MR compatible directional couplers were placed near the input ports of three loop elements. The latter formed a three'port Tx'Rx array coil, and were again placed around the head' shaped phantom in an arbitrary fashion. The modified directional coupler (power sensing) locations allowed tighter tracking of power dissipation in the subject as significant RF losses in the long cables linking the amplifiers and the coil are excluded from the power measurements and prediction models. (For instance, RF loss in cables account form over 50% of total RF power delivered by the RF power amplifiers on our 7T system.) Calibration and validation were similarly performed as before. Continued investigations examined diagnostic and monitoring potential of the present method by artificially introducing fault conditions. After calibration and validation under a baseline condition, the system hardware were altered to emulate two system fault scenarios. In Case 1, one capacitor in the loop structure of Element 3 was de'soldered, causing an open condition. In Case 2, an extra segment of coax cable was added to the cable linking Element 2 and its corresponding power 79

amplifier, adding a phase offset of about 45 degrees. The actual measurements taken after the alterations were compared to the baseline measurements and the baseline model predictions, and differences in prediction models were further noted.

RESULTS Results from the first FDTD simulation study are summarized in Fig. 3.2. Based on the net power values quantified by the FDTD calculations for the 20 input' configuration cases prescribed for SAR model calibration, Φ was determined. In each of the additional 19 input'configuration cases Fig. 3.2b shows that net power predicted with wH Φ w, the calibrated global SAR model, was in excellent agreement with net power quantified directly by FDTD. The average percentage difference between predicted and directly quantified net power was 2 percent. In Fig. 3.3c and f, results from the second FDTD simulation study again indicate high accuracy achieved by the calibrated global SAR models. In addition, Fig. 3.3b, magnitude of estimated Φ for Setup 1 (Fig. 3.3a), shows significant power correlations between 1 and 3, and 2 and 4, consistent with the interference patterns expected of the geometrical arrangement of the elements and the object. Similar observations could be made of Fig. 3.3e for Setup 2 (Fig. 3.3d). For each setup the variation of Φ’s diagonal entries correlates with loading difference due to the elements’ varying proximity to the lossy object. In Setup 2 for example, Element 4 was the furthest from the object in the setup while Elements 1 and 2 were the closest. Furthermore, notice that for the two setups the ratios of the largest to the 80

smallest eigenvalues were, respectively, 3.1 and 6.3. These indicate that with either setup, even RF pulses of same sum of magnitude squared could have significantly different SAR consequences (up to a factor of 3.1 and 6.3, respectively). Such differentiation is non'existent with an identity matrix'based SAR model.

Figure 3.2. (a) Global SAR calibration and prediction in a simulation study involving a heterogeneous human model and an RF coil composed of 4 loop elements. (b) Based on the net power values quantified by the FDTD calculations for the 20 input-configuration cases prescribed for calibration, Φ was determined. In each of the additional 19 input-configuration cases the net power predicted with wH Φ w, the calibrated global SAR prediction model, appeared to be in excellent agreement with the net power quantified directly by FDTD, demonstrating the validness of the model.

For each of the two parallel Tx phantom studies, results demonstrated feasibility of the global SAR calibration and prediction method under actual MR imaging condition. The measurement hardware was supportive of providing quality data to global SAR modeling and prediction. For the evaluation setups, including parallel Tx with a somewhat conventional Tx array coil and parallel Tx with a more general Tx array coil, the method handled both very well, producing robust Φ estimates and giving model'based SAR predictions that closely matched actual measurements (results for the 4'loop array coil setup shown in Fig. 3.4d). 81

Figure 3.3. Investigation of impact of coil-subject setup on the global SAR model. Two different setups were simulated each involving four identical loop elements of size 7 x 7 cm2 placed about 1 cm above a uniform water phantom (a,d). With either setup the set of input configurations included 16 programmed ones for model calibration and 8 randomly generated ones for model validation. In b, magnitude of estimated Φ for Setup 1 shows significant power correlations between 1 and 3, and 2 and 4, consistent with the interference patterns expected of the geometrical arrangement of the elements and the object. Similar observations could be made of e for Setup 2. In addition, for each setup the variation of Φ’s diagonal entries correlates with loading difference caused by the elements’ varying proximity to the lossy object.

The measurement automation in the in vivo study streamlined the entire calibration and validation process. From the start of RF pulse playout on the scanner to pop up of estimated Φ and measurement'versus'prediction plots on the screen, the entire process was completed in less than 18 seconds. Fig. 3.5a shows that the predictions given by the calibrated global SAR model were in excellent agreement with direct measurements. Also notice that model calibration was performed at a low power levels, yet the validity of the prediction model held over a considerably wide test range, suggesting robust modeling as well as good system linearity. Similar success was repeated in an additional in vivo study. The mean ± standard deviation of difference between the predicted and measured power were 3.68 ± 82

4.39% and 2.51 ± 3.83% for the two studies respectively. In both studies and in all validation cases the maximum prediction error was less than 11 percent. For the setup using designed large'tip'angle parallel excitation to perform MR on the 7T scanner, Fig. 3.5b shows an example comparison. In general an excellent agreement were observed between predicted and measured global RF power deposition. The measured net power were however somewhat lower than the predicted at sharp peak locations. This were attributed, in part, to the timing offset between power measurement and RF pulse update (every 10 usec). Measurement imperfection was estimated to account for prediction error of up to ~10% (114).

83

Figure 3.4. Global SAR model calibration and validation on a 7T whole body MR scanner. (a) Study involving 4-channel parallel Tx MR of a cylindrical phantom with half of the rungs of an 8-rung TxRx array. (b) Study involving a more general coil-object setup that had four loop elements arbitrarily placed on a head shaped phantom and formed a Tx array coil. (c) Four pre-designed 18 mseclong staircase-shaped parallel RF pulses were used to introduce 36 input configurations, including 16 for model calibration (definitions shown in the table) and additional 20 randomly generated ones for checking the accuracy of the model-based global SAR predictions. (d) For the 4-loop array coil setup, a comparison of model-based SAR predictions with actual measurements.

Fig. 3.6 shows one set of results from the study that evaluated the planning and monitoring potential of the present method.

When applying parallel RF

transmission in practice, coupling and interaction taking place in the array structure 84

and the subject can significantly affect individual channel RF power transmission towards and away from the subject. As discussed earlier tracking/predicting the effects and proactively managing power transmission is important for ensuring a smooth scan. The results shown in Fig. 3.6 demonstrated that the present method was able to accurately predict not only the net power transmission but also the individual channel power transmission in both forward and reflected directions.

Figure 3.5. Streamlined SAR model construction for parallel Tx MR. An automation of data collection shortened the entire calibration and validation process to less than 18 seconds. Results from an in vivo study indicated that the predictions given by the calibrated global SAR model were in excellent agreement with direct measurements (a), with a worst case prediction error of less than 10% (b). Results from a further study on the use of a calibrated SAR prediction model in RF pulse optimization indicated that the model offered reliable guidance to the pulse design algorithm – the predicted net RF power as a function of time was in excellent agreement with that actually measured during the playout of the designed parallel excitation (c).

85

Three additional sets of results were obtained in the study, with setups that included a baseline and two that had artificially introduced fault conditions. For the baseline case, calibration and validation steps were performed. Fig. 3.7a (!)

(!)

shows!!"# , !!"# and ! that were estimated from the nine calibrating steps. For the subsequent nine validating steps (each with an input configuration that was randomly generated). Fig. 3.7b shows a comparison between the model based predictions and the actual measurements. Again, high prediction accuracy was achieved by the present method. Same experiment steps and result displays were performed for Cases 1 and 2. Fig. 3.8b shows that the opening of Element 3 in Case 1 caused significant changes in Channel 3 reflected power measurements from that of baseline, especially for experiment steps whose input configuration significantly engaged Channel 3 (e.g., Steps 14, 16 and 17). Fig. 3.8e shows that the extra phase shift along Channel 2 caused significant changes in Channel 2 power measurements from that of baseline, especially for experiment steps where the input configuration significantly engaged Channel 2 (e.g., Steps 11, 13 and 18). As expected easiness of detecting difference was input configuration'dependent. A more robust detection was possible. In either of Cases 1 and 2, the altered system remained linear, which allowed model update through a simple repeat of the calibration and validation steps. Compared to detection by comparing specific predictions with measurements, a comprehensive power re'characterization leads (!)

(!)

to updated !!"# , !!"# and ! , which may be used to improve sensitivity and 86

reliability in detecting system changes. One example scheme is to detect based on observing pattern change of a power correlation matrix’s eigenvalues. For the baseline, Case 1 and Case 2, the significant eigenvalues of ! were, respectively, (89), (!)

(!)

(40), and (124). In further screening of the spectra of !!"# and !!"# , sharp contrast (!)

(!)

(!)

revealed between Case 1 !!"# and baseline !!"# , and between Case 2 !!"# and (!)

baseline !!"# , especially in terms the largest eigenvalue (Fig. 3.8c and f). Another example scheme is to detect based on eigenvectors. From one case to another in this study significant pattern changes of eigenvecters were noticed. These along with the (!)

(!)

pattern changes of eigenvalues were certainly reflected in !!"# , !!"# and ! (magnitude shown in Fig. 3.8a and d). Given the goal of detecting fault conditions caused by any degradation in system linearity and/or significant system changes over time, this investigation suggests a possible monitoring scheme: (I) The operator positions the subject and the coil for an MR exam. (II) PPM performs calibration and validation steps. The (!)

(!)

calibration steps lead to baseline!!"# , !!"# and !. The validation steps allow prediction'measurement comparisons and a system linearity check.

(III) During

the MR exam and in real'time, PPM continuously compares individual channel power transmission predictions to actual measurements. (IV) Upon detection of significant deviation in III as well as during every PRESCAN, PPM repeats II. This allows a system linearity check as well as a comprehensive power characterization. A positive detection of significant deviation in III / change in power characteristics 87

serves as the indicator of a system change caused by, for example, hardware failure, system instability, or patient position change.

Figure 3.6. Three channel parallel Tx study with a coil-object setup that had three loop elements arbitrarily placed on a head shaped phantom and formed a Tx array coil. Global SAR model calibration and validation was performed, which led to model predictions that accurately matched net power measurements (bottom plot). The power measurement data were further processed to calibrate predictive models of (!) (!) individual channel forward and reflected power, which gave wH !!"# w and wH !!"# w , nth channel forward and reflected power predictions respectively, for any input configuration w. For the randomly prescribed input configurations (Steps 10 through 18), predictions from these models were in excellent agreement with actual measurements (plots labeled Ch n fwd and Ch n rfl).

88

DISCUSSION AND CONCLUSION From the perspective of advancing high field MR, it appears inevitable to perform in vivo SAR model calibration for managing SAR, just as a B1 map calibration is needed for managing excitation profile. Given the task of scanning a specific subject, to maximize performance one uses B1 and SAR calibration results acquired of the subject as key inputs to guide optimization of pulse design or shimming calculations.

Performance aside, to ensure smooth scan it is highly

desirable still to accurately characterize RF power transmission and deposition, and thereby comply with safety and hardware limits.

89

Figure 3.7. Calibration and validation under a baseline setup in a system monitoring study. (!) (!) (a) Magnitude displays of !!"# , !!"# and !, which were calibrated using power measurements corresponding to Input configurations 1 through 9. (b) Comparison of model predictions with power measurements for any of the randomly generated ones of Input configurations 10 through 18 indicated accurate prediction. These models / data may serve as a reference for detecting possible system changes from baseline at a later time.

These considerations on performance and safety point to a sensible in vivo MR paradigm: a PRESCAN process calibrates SAR prediction models specific to the subject and performs model'guided excitation pulse calculations to manage SAR for the intended scans, actual scans then proceed with the operator knowing in advance the SAR consequence, knowing that RF transmit has been performance'optimized for this specific subject and won’t exceed safety limits or hardware capability, and knowing in real'time should any of the transmit chains malfunction. 90

Given that a parallel RF transmission system is commonly set up to be linear, this paper introduced explicitly the concept of a multi'port network and an overall linear system to link designed RF pulses (inputs) directly to EM fields and SAR in the scanned subject (outputs). The appropriate amount of abstraction accomplishes the goal without forcing one to deal with subject, coil, or hardware details. This is in contrast with other possible approaches that rely on intermediate variables (e.g., voltages or currents at the ports or elsewhere in the system).

Dealing with

intermediate variables not only complicates the measurement scheme (e.g., by requiring phase'sensitive detections), but necessities extra calibration in order to complete a full characterization that links RF pulse waveforms (the ones we explicitly design or program) to B1+ and SAR. The paper further presents a method for predicting RF energy transmission and deposition. In a nutshell the method performs a finite number of calibration experiments using judiciously defined input configurations and records the outputs of the overall system. The results from the calibration experiments are then used to build prediction models capable of relating any predetermined RF pulses to the overall system’s outputs. Implementation of the method on a clinical MR scanner does not require special hardware. MR scanners equipped with parallel RF transmission channels already check in real'time, with RF power monitors (20,125), forward power transmission in the individual cables linking the RF power amplifiers and the multi' port transmit coil, and are programmed to stop scan upon detection of an excessive level of total forward power. The implementation entails a straightforward upgrade 91

of the RF power monitors’ capacity to include individual channel reflected power, and a program that processes the forward and reflected power readings according to the descriptions in THEORY AND METHOD. Since the transmit and receive windows of an MR experiment typically don’t overlap, the parallel receive channels on the scanner may also be tapped into (e.g., to demodulate directional coupler outputs and convert the results to power readings, and thereby accomplish parallel power sensing/monitoring) to further simplify the measurement setup employed by the calibration and monitoring scheme. While the built'in RF power monitors / parallel receive channels were not accessible to allow further demonstrations, the present investigation did provide indications of the capacity of a full'fledged implementation: (I) Calibration completed within a second. The total amount of time required for playing out the calibration configurations scales with N2. It can be fit into 1 sec with the staircase' type of pulses and parallel RF power sensing, if N is not much greater than 32. This makes the time cost of performing a calibration after patient positioning negligible. (II) More accurate and tight characterization of global SAR, which can be expected in a new sensing setup that has better controlled RF power sensors and has directional couplers located close to the coil. This improves the guidance provided to pulse design optimization and helps refine the SAR limit setting on the scanner. (III) Real' time monitoring and automatic protection. The individual channel power characterization and prediction capability, when leveraged to check channel integrity during scan, helps ensure real'time detection of hardware failure. Such 92

events as breakdown of components in the transmit hardware, alteration of coil geometry / placement, and subject posture change could all lead to change of the system characteristic, manifesting in a discrepancy between predictions and measurements, or, characterizations done before and after. A system state change is a cause for intervention, including suspension of scan for subject and scanner protection.

Figure 3.8. Cases 1 and 2 in a system monitoring study. The baseline was altered to emulate two system fault scenarios. In Case 1 the baseline setup underwent a system change in which Element 3 was (!) (!) forced to open. Re-characterization was performed. (a) shows updated!!"# , !!"# and !. (b) shows predictions, measurements, as well as predictions from baseline models (circles). (c) shows maximum (!) (!) (!) (!) eigenvalues of Case 1 !!"# and !!"# (solid bars) vs. that of baseline !!"# and !!"# (non-filled bars). In Case 2 the baseline setup underwent a system change in which Channel 2 had an extra phase offset of about 45 degrees. Results are similarly displayed in d-f. Note the pattern change of a power correlation matrix’s eigenvalues: For the baseline, Case 1 and Case 2, the significant eigenvalues of ! were, respectively, [4, 43], [5, 29], and [19, 41]. In terms the largest eigenvalues, further note the sharp contrast between Case 1 (3) (3) (2) (2) !!"# and baseline !!"# , and between Case 2 !!"# and baseline !!"# (c and f).

93

The system perspective described earlier reinforces the rational for the parallel transmission operation mode: calibration + pulse design + transmission. It also helps pinpoint the limitations of some common misconceptions. As a simple example, many believed that they need to detune or deactivate all other coil elements when mapping the B1 of one coil element in an array coil. One issue here is that the detuning or deactivation would modify the configuration of the system, making it a different one than the system actual RF transmission is conducted upon. With schemes that attempt parallel transmission power calibration through simplistic use of a normally measured S'parameter matrix or noise covariance matrix, an analogous limitation exists – the impedance present at the ports during measurement may be quite different from that during actual parallel transmission. In these examples, system alteration invalidates the application of (a linear system’s) superposition principle and causes errors in using calibration data for prediction or for guiding actual MR. Along the same line, the benefits of in situ measurements can be appreciated – for accurate models and results it is most desirable to calibrate the same system as that is in effect during actual MR (Fig. 1). The present work is part of an effort to create a solution that quantitatively track and proactively manage SAR on a subject'specific basis. With the analysis shown and the performance demonstrated, there is the confidence that some significant improvements of high field clinical MR safety and performance are within reach.

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4. METHOD FOR IN SITU CHARACTERIZATION OF RADIOFREQUENCY HEATING IN PARALLEL TRANSMIT MRI PROLOGUE The previous chapter introduced a system and methodology for measuring and predicting global SAR in vivo. In this chapter we describe a related method to measure and predict local SAR, initially in phantoms and perhaps eventually in vivo. This method involves use of MR thermometry to calibrate the electric field correlation matrix, Λ. Calibration of this local matrix enables prediction of the temperature change resulting from any arbitrary pulse. The work described in this chapter was published in Magnetic Resonance in Medicine in 2012 (89).

AUTHOR CONTRIBUTIONS: Leeor Alon: Study design, hardware configuration, software coding, data analysis & interpretation, simulation work, experimental work, manuscript writing. Cem Murat Deniz: Study concept, experimental work, manuscript editing. Ryan Brown: Coil construction, manuscript editing. Daniel K. Sodickson: Study concept, manuscript editing.

95

Yudong Zhu: Theoretical work, study design, hardware configuration, data analysis & interpretation, manuscript editing.

INTRODUCTION The advent of parallel RF transmission brought about a new paradigm wherein RF pulses simultaneously drive distributed elements of a multi'port transmit antenna to effect both spatial and temporal variations in the RF magnetic (B1) and electric (E) fields (34,35). The resulting increase in degrees of freedom as compared with traditional RF transmission was shown to enable the tailoring of E fields and the containment of global SAR while improving flip angle profile control (34). For a given coil'subject setup, flip angle profile and global SAR controls are realized through design of the individual RF and gradient pulses. The practical control of flip angle profile in vivo is enabled by subject'specific B1 calibration, which captures the complex effects of coil'subject geometry, composition and interaction on the B1 maps, while information required for global SAR control may be obtained through calibration of a power correlation matrix (126'128). Both the information provided from the B1 maps and E field interference related information can be exploited together to improve flip angle profile while simultaneously reducing SAR (34,129,130). Global and local SAR are measures of the rate at which energy is absorbed by the body when exposed to an RF field and are measures of safety with regard to RF heating. Several schemes were recently proposed for tracking of global power 96

deposition in an imaged body in the scanner (112,126'128). However, experimental quantification of local SAR has continued to pose a fundamental challenge, both for routine scanning and for rigorous evaluation of the safety and suitability of transmit array coils. As a result, excessively restrictive power limits are commonly used, preventing the flexible usage of parallel transmit technology. Efforts to evaluate local SAR have often relied upon electromagnetic field calculations in numerical simulations or experimental findings in "average" subjects (131). Commonly used techniques such as the FDTD method or the finite element method (FEM) have been used as a development platform for evaluating the safety and performance of array coils and/or RF pulse designs. However, it remains unclear to what extent simulation results, even guided to some (112) extent by current experimental measures may be extrapolated to match the true conditions in an individual body in the scanner. This work builds upon a SAR prediction model (34,112), which relates global or local power deposition to RF pulse waveforms or RF shimming coefficients via a quadratic function. The model indicates that local power deposition due to parallel transmission can be characterized by a single mathematical structure called the local power correlation matrix. This matrix provides information about the correlation of local E fields among transmit coils at various locations within the imaged body. In this work, it is demonstrated that measurements of temperature change in response to a set of predesigned RF heating pulses, via a finite number of MR thermometry acquisitions, enable practical calibration of the local power correlation matrix. Once the power 97

correlation matrix is determined for a particular voxel, the local RF heating effect for an arbitrary RF pulse may be predicted for that location. Close agreement between predicted and measured temperature distributions are shown for a variety of RF pulses under experimental and simulated conditions.

THEORY AND METHODS RF energy dissipation and tissue heating Pennes’ bio'heat equation describes the thermal energy balance for perfused tissue (41): !"

!! !"

= ∇. !∇! + ℎ! + ℎ! + ℎ!

(4.1)

where !, ! and ! refer to tissue density, specific heat capacity and thermal conductivity, respectively, ℎ! is the blood'to'tissue heat transfer rate and ℎ! energy transfer due to matabolism. The RF energy deposition rate is expressed by ℎ! , which is a driving force for temperature rise as result of Joule heating and is proportional !

to the square of the local E field strength ℎ! = ! E ! , where ! is the tissue !

conductivity. Temporal and volume averages of ℎ! , when further scaled by appropriate density or mass, constitute SAR as defined in FDA and IEC guidelines (58,132). Linearity allows decomposition of the net E field as a weighted superposition of E fields corresponding to N individual sources effecting weights !!!

⋯

!!! ,

where p represents the time interval that a certain pulse weighting is applied. In 98

phasor notation: !! ! =

! ! !!! !!

! ! ! , where ! ! is the E field resulting from a

unit weight in the nth source and zero weights for all other sources. This leads to the following expression for local RF energy deposition rate (106,133): ℎ! =

!(!) !! (!) 2

!

=

! ! = 2

!(!) ! (!)∗ ∙ !! ! 2 ! ∗

!

!!! ! ! !

(4.2)

!!!

!

!!! ! ! !

∙

= !! ! ! ! !!

!!!

where

*

denotes complex conjugate and

denotes conjugate transpose. Equation

H

(4.2) shows that the local RF energy deposition can be expressed as a quadratic (!)

! function of !! = [!! … !! ]. The matrix !(!) is referred to as the local power

correlation matrix at spatial location r and it captures the effects of E field interference and tissue conductivity on local RF energy deposition. The total local energy deposition by a given parallel transmission pulse can be expressed as: !

!!"#$! (!) =

!" ∗ ℎ!,! ! !!!

! = !!"##

! ! !" ! !

! ⋱ !

! ! ! ! !"

(4.3) !!"## !!"#!

where !!"## is a vector collecting all P sets of the RF pulse weights over the heating duration and !" is the RF pulse waveform sampling interval. Equation (4.3) 99

indicates that there is a compact structure to local energy deposition. With proper calibration of the ! matrix, local energy deposition at any spatial location can be calculated in a deterministic fashion for any RF pulse waveform !!"## . SAR model and temperature change. To spatially resolve RF energy deposition in vivo is a challenging problem. The present method uses MR thermometry to noninvasively map temperature and to further provide inputs for determining Λ(r). This can be explained using the Pennes’ bio'heat equation (Eq. 4.1), which suggests that if an RF transmit experiment is conducted at a time scale short enough compared to that of heat diffusion and at a magnitude overpowering other energy transfer processes, the local RF energy deposition rate is proportional to local temperature rise, ∆! ! (90): ∆! ! =

!!"#$! (!) !"# ! = !(!)!(!) !(!)

(4.4)

where SAR(r) is the local specific absorption rate produced by the parallel RF transmission pulse. Combining equations (4.3) and (4.4) yields:

! !!"##

! ! !" 0 0

0 0 ⋱ 0 0 ! ! !" !(!)!(!)

!!"## !"#!"

(4.5) = ∆! !

Equation (4.5) shows that local temperature change is proportional to local RF energy deposition, where local specific heat capacity and tissue density are the 100

scaling factors between the two. With temperature change from MR thermometry as sensor data, the quadratic model can be determined with a calibration scheme same as that given by Zhu et al. (8). Even though it is difficult to quantify local power deposition without knowing local specific heat capacity or tissue density, calibration of Λ(r)/(! ! ! ! ) and the resulting capability of predicting temperature changes are highly relevant. This is because temperature change is directly correlated with tissue damage (124,134) and is therefore a direct measure of RF safety. For the sake of simplicity the scaling terms ! ! and ! ! are incorporated inside Λ(r) in further discussions of the local power correlation matrix. In the present work MR thermometry employs proton resonance frequency shift (PRF) method (135), which exploits a chemical shift that is linearly proportional to the change in local temperature. Experiments Experiments were performed on a 7T Siemens whole'body MR scanner (Siemens Medical Solutions, Erlangen, Germany) equipped with an 8'channel parallel transmit system (1kW peak power per transmit channel). RF transmission and detection were provided by three 7cm x 7cm transmit/receive coils and one receive'only coil with the same dimensions. An additional receive coil was introduced to improve the receive sensitivity inside the phantom. The coils were placed around a cylindrical former with an 18cm diameter. Two of the transmit coils (TC1 and TC3 in Figure 4.1) were partially overlapped to reduce mutual inductance, 101

while the remaining transmit coil (TC2) and the receive'only coil (RC4) were separated from TC1 and TC3 by ~90 degree arc lengths, allowing independent tuning and matching of all coils. During RF transmission, all transmit coils were connected to independent RF amplifiers. Imaging was conducted on a cylindrical agar phantom of 20cm diameter and 25cm length with the following ingredients: 2300g water, 100g agar, 1600g sugar, 40g NaCl and 1g benzoic acid. The resulting mixture was heated to approximately 85 degrees Celsius and allowed to cool to room temperature to form a stable gel with conductivity and relative permittivity of approximately 0.77 Siemens/meter and 58, respectively, measured using a dielectric probe (Agilent 85070E Dielectric Probe Kit, Agilent Technologies, Germany). These values approximate the dielectric properties of muscle at 297.2MHz (59). Two low'conductivity oil phantoms were placed adjacent to the coils to control for any non'temperature'related phase drift between scans. The T2*of the phantom was measured to be 9.3ms, using a multi'echo gradient echo (GRE) sequence. For an initial validation of the MR thermometry measurements and characterization of the heating of the phantom, four fluoroptic MR'compatible temperature probes (Luxtron) were inserted into the phantom and a high duty cycle RF pulse was played out on all coils. Then at intervals of 5 minutes MR thermometry was performed to confirm that the temperature measured using MR thermometry coincided with the temperature measured using the probes. Additionally, it was confirmed that over a range of 15 degrees Celsius heating increased in a linear fashion with respect to time and was not saturated. 102

The ! matrix was calibrated using the first nine experimental steps, with the transmit coil weights given in Table 4.1 . In addition to the calibration steps, 3 more experimental steps with randomly chosen RF coil weightings ( Table 4.1) were performed to check if the measured temperature change maps matched the maps predicted using the model. Each of the nine calibration steps and three validation steps consisted of four procedures, as illustrated in Figure 4.1A: 1) A phase map was acquired prior to RF heating using a spoiled 2D GRE sequence. 2) RF was applied with weights w in the absence of encoding gradients, to generate heat in the phantom. 3) A post'heating spoiled GRE phase map was acquired with the same sequence as in procedure 1. 4) No RF or gradient pulses were played out for a 10' minute cool down period. The phase difference between the two GRE sequences was used to calculate the temperature change map. The parameters for the 2D spoiled GRE were as follows: TE=7ms (approximately equal to the T2* of the gel phantom), TR=100ms, transmit voltage=13.4volts, matrix size = 128x128, number of slices=3, voxel size=2.5 x 2.5 x 5mm3, acquisition time = 66s and number of averages=5. RF heating corresponding to a unit pulse amplitude was generated by play out, in procedure 2, of a rectangular 4ms pulse with 25% duty cycle, transmit voltage=125V and duration=300s. The parameters for the RF heating pulse were chosen empirically given the coil size, phantom properties, and RF amplifier peak power and duty cycle limitations. Gradients were disabled during the RF heating sequence to eliminate gradient heating. Total time it took to conduct the entire

103

experiment (steps 1'12) was just under 200 minutes. The measured and the predicted temperature change maps were then analyzed and compared.

Figure 4.1 A. Schematic of the experimental calibration and validation procedure. B. Photograph of the transmit-receive coils and agar gel phantom used in the experiments. Transmit-receive elements TC1-3 are shown in the photograph. The receive-only coil (not seen) is opposite to TC2 on the other side of the phantom.

Simulations Numerical simulations were performed to assess the validity of the calibration and prediction method, while accounting for the perfusion, diffusion and metabolic energy terms in the bio'heat equation (Eq 4.1). Commercially available FDTD software (xFDTD, Remcom, PA, USA) was first used to quantify local RF power deposition. Four surface coils measuring 7cm x 7cm were placed on the torso of a 104

simulation was first initialized with no exposure to RF, allowing the temperature of the body model to reach a physiologically realistic temperature steady state (~37 degrees C) with the environment of the scanner room at 23 degrees C. Then each calculated SAR map obtained with different port weights as shown in Table 4.2 was used to calculate the temperature change resulting from RF heating. The RF duration for the simulations was set to 60 seconds. Between any two successive heating periods, a 5 minute cool'down period with no exposure to RF was applied to allow the temperature of the human body model to cool down or return to steady state. This 5 minute cool'down period was chosen empirically. Over the entire course of the 24 steps the maximum local temperature rise in the emulated human body was kept below 1 degree C, as specified by the FDA and IEC safety limits (58,132). Temperature difference maps due to the RF heating in each step were then used for the calibration and validation of the power correlation matrix'based local heating prediction model. In particular, the first sixteen temperature difference maps were used to calibrate the model, and the last 8 temperature difference maps were used to test if the calibrated model was able to predict parallel RF transmission induced temperature change accurately. To examine the effects of the diffusion, perfusion and metabolic energy occurring in the emulated human body on the accuracy of the heating prediction model, a second series of simulations were performed with an identical setup as that of the first except that the RF heating duration was set to 300 seconds and injected RF power was reduced by 80%.

106

Figure 4.2. FDTD model of a human body mesh (Hugo) with four transmit coils (C1-4) shown in black placed on top of the body mesh.

108

Figure 4.3. Results of the experimental calibration procedure. A. Temperature difference maps measured for three slices in each step of the calibration process. Each step (each row of temperature change maps) corresponds to a different set of RF amplitude and phase weightings applied to each coil, as specified in Table 4.1. B. Absolute value of Λ matrix elements for four different voxel positions indicated by the origin of each red arrow.

RESULTS Experiments Results of the experimental calibration procedure are summarized in Figure 4.3. Figure 4.3A shows temperature change maps measured in three axial slices in each step of the calibration process. Distinct spatial variations in the temperature change distribution can be observed between the steps and, to a lesser extent, between nearby slices. The maximal temperature change for the calibration and prediction steps was < 4 degrees C. Each calibration step (each row in Figure 4.3A) corresponds to a set of complex RF weightings applied to the array coil according to Table 4.1. Figure 4.3B shows the absolute value of the Λ matrix at different spatial locations across one axial slice. The origin of the red arrow represent the voxel represented by the corresponding Λ matrix. The top Λ matrix is dominated by heating contributions from coils 1 and 3, with little E field correlation among the coils. In the left Λ matrix, power correlation can be observed among all coils, with the strongest contribution from coil 3. The bottom Λ matrix indicates strong contributions from coils 2 and 3 with some E field correlation between coils 1 and 3. Finally, the right Λ matrix is dominated by coil 1 alone with minor contributions from the other coils.

109

Figure 4.4 illustrates the predictive capability of the power correlation matrix'based local heating prediction model. Temperature change maps measured for each randomly selected set of coil weighting in steps 10'12 of Table 4.1 are juxtaposed with predicted temperature change maps derived by using the same set of weighting as input to the local heating prediction model. The predicted and measured maps show a maximal temperature change of less than 4 degrees C. The root mean squared error between the measured and predicted temperature change maps for the three slices of interest are presented in Table 4.3.

Figure 4.4. A. Results of the experimental prediction and validation procedure, demonstrating the predictive capability of the local SAR model. For each set of the randomly selected coil weightings indicated in steps 10-12 of Table 4.1, and in each of three axial slices, a temperature change map measured using MR thermometry is compared with the predicted temperature change map derived by using the known coil weights as inputs for the local heating prediction model. Good agreement between measurements and predictions is observed, as indicated also by the difference maps beneath each measured/predicted pair.

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Simulations For the simulation study Figure 4.5A shows agreement between eight predicted temperature change maps and corresponding maps calculated directly from simulation software. For a coronal slice of interest, the maximum temperature change and root mean square error between simulated and predicted values for the 60 second heating case was 0.735 and 0.018 degrees, respectively. For the 300 second case the maximum temperature change and root mean square error between simulated and predicted values was 0.47 and 0.04 degrees, respectively. The results from the individual steps showing the root mean squared errors and maximal temperature changes are summarized in Table 4.4. In Figure 4.5B, the absolute values of Λ matrix entries are plotted for different voxel locations, illustrating the spatial dependency of the Λ matrix. The origin of the red arrow indicates the voxel location of the corresponding Λ matrix. The power correlation matrices reflect the complex interaction of electric fields associated with the coil elements and the body. The top Λ matrix is dominated by E fields contributions from coil 2. The left Λ matrix represents a voxel whose local SAR is dominated by the E field from coils 2 and 4, with a strong cross'correlation between the coils. In the bottom Λ matrix, E fields from coils 1 and 3 predominate, and a correlation between these fields is observed. In the right Λ matrix, the E field for coil 1 predominates. Figure 4.5C, compares the simulated (bottom) and predicted (top) temperature change in an axial slice of interest in the human body model, showing heating entering inside the body. 111

Figure 4.5. RF heating in an emulated human body. A. Results of the prediction and validation procedure. Unaveraged SAR maps and directly simulated coronal temperature change maps are juxtaposed next to temperature change maps predicted using the calibrated heating prediction model, for each of the validation experiments 17-24 from Table 4.1. Results shown are for the 60 and 300 second heating cases at a coronal slice of interest. B. Results of the calibration procedure, illustrating the spatial dependency of the power correlation matrix Λ for a coronal slice of interest. 4 x 4 color plots represent the absolute value of Λ matrix entries, and each plot shows Λ at a different voxel position, indicated by the origin of the corresponding red arrows. C. Predicted (top) and directly quantified (bottom) temperature change map for an axial slice of interest, showing the prediction capability of the model in a deeper region inside the human body model, while accounting for perfusion and diffusion effects.

112

elements of the array coil and the subject being imaged. Using a finite number of MR thermometry acquisitions, measuring temperature change in response to a set of predesigned calibration pulses, the present method calibrates the power correlation matrix and further predicts the local RF heating effect of an arbitrary RF pulse for any location of interest in the subject. The method has a potential advantage in that it offers a way of in situ SAR evaluation by characterizing and predicting the RF heating effect for the actual imaging setting, in contrast to SAR evaluation by quantifying EM fields in numerical simulations. With numerical simulations there is no assurance that the EM fields quantified with approximate coil and subject models in simulations match that actually generated in the MR experiments (92) as tissue electrical properties and their distributions are typically unknown and the coil structural details can be differ between experiment and simulation. Both of these factors may affect the local power deposition in the body (92). In addition, since temperature change rather than RF power deposition is directly correlated with tissue damage and safety (136), utilization of temperature change to calibrate and, in turn, to further predict temperature change for an arbitrary RF pulse is another potential advantage of the present method., It is worth noting that the off'diagonal entries of the power correlation matrix, and the underpinning phase relationships between E fields from different coil elements, can have a significant impact on RF heating. Consider the left Λ matrix in Figure 4.3B, for which the off'diagonal Λ2,3 or Λ3,2 entries are larger than the diagonal Λ2,2 entry. For the sake of physical insight, one may construct a similar 114

situation with a simplified illustration in which coil element 2 has an E field vector [ex ey ez]=[1 1 1] and coil element 3 has an E field vector [ex ey ez]=[2 2 2], leading to a Λ matrix with significant off'diagonal entries: Λ2,2= 3 ! !

6

!

! ! !

, Λ3,3 = 12

! ! !

and Λ2,3 =

. The resulting temperature change from a unit pulse driving coil element 2

alone plus the temperature change from a unit pulse driving coil element 3 alone will then be substantially smaller than the temperature change if unit pulse driving is applied to coil elements 2 and 3 simultaneously. The ability to capture the effects of constructive and destructive interference between coil fields is a unique feature of the power correlation matrix model. Characterizing the full interaction effects by calibrating the off'diagonal entries in the power correlation matrix however, causes the total number of calibration steps to scale quadratically with the number of parallel transmit channels driving the array coil, necessitating management of time cost per step in cases involving in vivo use of a large channel'count array coil. Accordingly, one advantage of using simulation software compared to this method is that simulations can be conducted faster, especially for large coil arrays, making simulations software more suited for rapid off'line evaluation of novel coil array designs. Effect of heat transfer and diffusion on calibration accuracy is another factor impacting the timing of calibration steps in practice. The RF heating sequence used in the MR experiment of the present work was arranged to deliver a significant amount of RF energy in a relatively short period of time. Each channel injected an 115

average of ~44 watts of forward power into the sample using a 25% duty cycle in order to facilitate detection of RF heating with MR thermometry. During this time thermal diffusion smoothed the temperature difference over a distance of 2β∆t, where ∆t is the duration of the heating period and β is heat diffusivity. The value of β in our phantom gel is 0.0014 cm! /s, and over a heating period of 300 seconds the characteristic temperature diffusion length was 0.9 cm (90). Utilization of RF amplifiers with higher duty cycles and higher peak power capabilities could allow shortening of the RF heating period further and, as a result reduce the characteristic temperature diffusion length to a sub'voxel size allowing tracking of RF heating effects more closely. With simulations that employ a realistic human body model and solve both Maxwell and bio'heat equations, feasibility of using the present method for in vivo calibration and prediction was assessed. The results were promising '' within the SAR limits per the IEC regulatory restrictions (58), there are various calibration protocols that allow the present method to accurately model local heating. In the presence of perfusion, diffusion and metabolic energy terms in the bio'heat equations (Eq. 4.1), a protocol working with shorter calibration/heating steps tends to give more accurate results. For instance, in the 300 second heating case, the diffusion, perfusion and metabolic energy terms in the bio'heat equation introduced larger errors into the calibrated model than in the 60 second heating case (Table 4.4). Clearly, further optimization of calibration protocols, including the timing of the heating and waiting periods, are necessary for in vivo application of the present 116

method. In terms of accuracy of the method, it relies on sufficient E field magnitude inducing a temperature change, which is detectable by MR thermometry. As result, it is highly desirable to have a robust and sensitive MR thermometry tool that detects small temperature changes while overcoming motion, SNR, phase drift and other challenges in vivo MR presents. Since the SNR of temperature'related phase difference maps is directly proportional to the signal amplitude (137), the transmit (!!! ) and receive (!!! ) sensitivities affect the quality of the MR thermometry measurement and nulls in either can limit accurate detection of temperature changes. One has the option of setting up the transmit or receive coil for MR thermometry entirely independent of the parallel transmit coil array to be calibrated, which facilitates MR thermometry. For instance, during MR thermometry !!! can be shimmed to avoid low !!! regions with a volume transmit coil and good !!! coverage can be achieved with a phased array coil, while during the playout of the calibration pulses, the volume transmit coil and the phased array coil remain deactivated. In the experimental setup employed in this work three transmit'receive coils and one receive'only coil were placed around a phantom to yield an SNR of 331 at the center of the phantom. In this work, a basic MR thermometry sequence was used to sample 3 slices of the phantom volume with 5 averages. In vivo MR thermometry is challenging, yet active research continues to bring about technical advances (137,138). Improved MR thermometry sequences may be leveraged directly by the present method to allow reduction of

117

the RF heating duration/intensity and the wait time between steps, as well as to enable large volume coverage, supporting application of the present method in vivo.

ACKNOWLEDGMENTS The authors thank Drs. Bernd Stoeckel and Hans'Peter Fautz for providing technical support for the experiments conducted on the 7T scanner. The authors also thank Drs. Graham Wiggins and Assaf Tal for useful discussions on coil safety evaluation, and Dr. Christopher Collins for providing his helpful code for simulating temperature changes induced by local energy deposition.

This work was supported in part by NIH grants R01'EB011551 and R01' EB000447.

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5. A METHOD FOR SAFETY TESTING OF WIRELESS DEVICES USING MAGNETIC RESONANCE IMAGING PROLOGUE Having developed the robust temperature mapping tools described in the previous chapter, we realized that the rapid acquisition and the high spatial resolution available using MR technology is highly beneficial for evaluating safety of not only MR coils, but also any arbitrary RF/microwave emitting device. In this chapter we demonstrate the use of MR thermometry to quantify temperature changes from both a dipole antenna, which is MRI compatible, and a mobile phone, which is not MRI compatible.

AUTHOR CONTRIBUTIONS: Leeor Alon: Theoretical work, study design, software coding, data analysis & interpretation, simulation work, experimental work and manuscript writing. Gene Y. Cho: Phantom building, experimental work, manuscript editing. Xing Yang: Hardware construction. Yudong Zhu: Error analysis & interpretation, manuscript editing. Daniel K. Sodickson: Study concept, manuscript editing.

119

Cem Murat Deniz: Study design, data analysis & interpretation, simulation work, experimental work and manuscript writing.

INTRODUCTION During the last decade, there has been rapid development of wireless technology worldwide (139). The rising number of wireless device users has raised concern about the possible health effects of radio frequency (RF)'transmitting devices, especially mobile phones (140). It is known that exposure to RF radiation results in increased heating of tissue via Joule and Dielectric heating mechanisms (141,142). Recently, other physiologic changes have also been reported (143'145); however, their health effects are not yet fully understood. As specified by the Federal Communications Commission (FCC) and other regulatory bodies, SAR from RF emitting devices must be measured prior to entering the consumer market, in order to prevent the deposition of excessive RF energy into the body (146,147). SAR is the rate at which RF energy is absorbed in biological tissue and it depends on several factors including the antenna design, the output power of the wireless device, the distance between the transmitting device and the body, and the morphological features and the electrical property distributions of the body (148). Electromagnetic (EM) field simulations are often used to characterize the interaction between an antenna and a load for safety assessment of the RF antennas. However, modeling of complex antenna'load structures to match realistic physical conditions using EM field simulations is not straightforward (149,150) and possible 120

discrepancies between simulated and manufactured devices may occur (151). In addition to using EM field simulations to evaluate antenna safety, the current standard for experimental measurement of SAR utilizes electric field probes (151) that are mechanically moved in a point'by'point, grid'like fashion in 3D space inside a phantom filled with a liquid mimicking the electrical properties of human tissues. This process can be time consuming because of the need for high experimental resolution. Another limitation is that electric field probes measurements produce large errors when measurements are conducted within a few millimeters of phantom boundary (150,151). Additionally, electric field probes need to be calibrated periodically in order to preserve isotropy of the probe measurements. While the liquid phantom used with electric field probes has electrical properties similar to those of human tissue, it lacks the complex anatomy presented by the human body due to the invasive nature of the electric field probe measurements, which can only be used in simple homogeneous liquid phantoms. A temperature'based method for compliance testing was proposed using an array of optical fiber thermal sensors positioned inside a phantom showing good agreement with electric field probe measurements (152). However, spatial resolution has been limited because of the large number of temperature probes that need to be positioned inside the phantom invasively. Recently, it was shown that magnetic resonance imaging (MRI) temperature change measurement can be used for tracking the RF power deposition from an antenna array (153), in order to ensure RF safety of MR system with multichannel RF power transmission capability. 121

For safety evaluation of low powered transmitting devices (e.g. cell phones), the temperature change induced in a phantom due to RF exposure is small. Therefore high sensitivity to the temperature change is required for accurate RF safety assessment of wireless devices for regulatory compliance testing purposes. Conventionally, both MRI temperature mapping and RF heating were conducted inside the magnet bore (153,154). The work described in this chapter shows that RF heating can be induced outside the magnet bore, enabling testing of wireless devices that are not necessarily MRI compatible, since the thermal diffusivity of the fabricated phantom was 0.129 mm2/sec and imaging can be conducted rapidly.

Figure 5.1 Experimental setup and configuration of matching numerical simulations. (A) Dipole antenna with λ/2 length, (B) FIT simulation setup of the dipole antenna and the gelatin phantom, (C) Gelatin phantom and fluoroptic temperature probes, (D) Experimental setup inside the MR scanner room: the gelatin phantom is positioned inside an MR coil designed for knee imaging, with a mounted GSM mobile phone and surrounding oil phantoms for calibration.

The fundamental phenomenon governing most MR'based temperature mapping is the Proton Resonance Frequency (PRF) shift, which linearly relates the 122

precession frequency of the spins of protons with temperature (87). This temperature'dependent frequency shift is caused by thermal effects on electrons that shield the nuclei from the external applied magnetic field. The shielding effect alters the effective magnetic field, resulting in alteration of the precession frequency of the proton spins (155). The PRF phenomenon enables monitoring of temperature changes during many clinical procedures such as local hyperthermia therapies or RF ablation (87). MR temperature mapping using the PRF method is particularly desirable as it allows imaging of complex in vivo anatomies at high spatial and temporal resolution. In this work, a method for safety assessment of RF emitting devices using MR temperature mapping is proposed for both MR'compatible and non'MR compatible RF emitting devices. The MRI'based method is advantageous for quantification of RF emissions, for a number of reasons. First, it measures temperature change, which is correlated directly with tissue damage (147,156). Second, since MR based measurements allow rapid probing of a multitude of spatial positions, temperature mapping can be conducted in a few seconds. This ability to map small temperature changes rapidly makes MRI a good tool for temperature mapping in RF emitting devices. Third, the noninvasive nature of the MR temperature measurements could enable safety assessment of wireless devices using complex anatomical phantoms (157). The principle of the proposed method is explained in Section II. Numerical simulations and experiments using a dipole antenna and a GSM mobile phone are described in Section III. Safety measurements on a simple dipole antenna with 123

validation

against

numerical

simulation

and

optical

temperature

probe

measurements, and results of the safety evaluation of a GSM mobile phone with validation using temperature probe measurements are presented in Section IV. Safety evaluation results and the proposed method as tool for RF safety assessment are discussed in Section V. Finally, conclusions are presented in Section VI. Temperature Measurement using MRI The heat equation with source term is a parabolic partial differential equation, which captures the behavior of temperature in space and time when a body is exposed to an external energy source. The equation in non'perfused, homogeneous media is expressed as follows (158): !"

!" = ∇ ∙ !∇! + !"#$ !"

(5.1)

where !, !,! and SAR are the tissue density (in kilograms per cubic meter), heat capacity (in Joules per kilogram per degree Celsius), thermal conductivity (in Watts (W) per meter per degree Celsius), and SAR (in Watts per kilogram), respectively. SAR ' the driving force for temperature rise as result of Joule/Dielectric heating mechanisms ' is defined as follows: !"# =

!!! 2!

124

(5.2)

where E is the induced electric field (in Volts per meter) inside the body, and σ is the electrical conductivity (in siemens per meter). In addition, SAR can be defined by means of temperature rate'of'increase:

!"# = !

Δ! Δ!

(5.3)

where ΔT (in degrees Celsius) is the temperature change induced during time' interval Δt (in seconds). If heating time (e. g. due to an external RF source) is short, thermal diffusion can be ignored and integration of equation (5.2) with respect to time results in equation (5.3).

Figure 5.2. Fluoroptic temperature probe locations and temperature measurements. (A) Locations of the fluoroptic probes within the phantom, (B) Setup of dipole antenna circuit, (C) Fluoroptic probe temperature measurements of dipole antenna heating. Heating occurred from 2 minutes 30 seconds to 9 minutes (highlighted in yellow).

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PRF temperature change reconstruction using MRI relies on phase subtractions between two phase images, acquired one before and one after heating. The linear relationship between temperature and phase change is captured in the following equation (87): Δ! =

!! − !! !"!! !"

(5.4)

where φ1 and φ2 are the spatially dependent phases taken from phase images for pre' and post' heating spoiled gradient echo (GRE) imaging sequences, respectively, γ is the gyromagnetic ratio of protons (~42.58×106 in Hertz per Tesla), TE is the echo time of the GRE sequence, B0 is the main magnetic field strength (in Tesla), and α is the temperature dependency of the chemical shift (~0.01 parts per million (PPM) per degree Celsius).

NUMERICAL TECHNIQUES AND EXPERIMENTAL SETUP Simulation Technique Electromagnetic field simulations were performed on the dipole antenna ' phantom setup shown in Figure 5.1B, in order to obtain the SAR distribution induced by the dipole antenna inside the phantom. The commercial Microwave Studio software suite (CST, Framingham, MA, USA) using Finite integration technique (FIT) was used for simulations. The parameters used in the FIT calculations were as follows: 2.7 mm isotropic cell size, mesh size 84 x 83 x 83, feeding with a voltage source operating at 1.96 GHz. A 5 mm separation between the 126

phantom and the dipole antenna was used to simulate the physical setup in the scanner room. The net input power used was 0.65W, similar to the output power of the dipole antenna measured in the scanner room. The computed SAR distribution alongside the measured thermal properties (shown in Table 5.1) of the phantom were fed into a temperature simulator (159) to calculate the temperature change in the phantom following exposure to RF from the dipole antenna (Eq. 5.1). The boundary conditions around the phantom in the thermal simulations were the room temperature at 21 degrees Celsius. Temperature maps and numerical SAR simulations were compared to MR temperature measurements and SAR estimation conducted on the physical dipole antenna positioned in the scanner room. Phantom A cylindrical gelatin'based phantom was used for safety assessment of a dipole antenna and a GSM phone. The phantom was constructed using an acrylic former with a diameter of 10.2 cm and a height of 11 cm, as show in Figure 5.1C. The dielectric properties of the phantom approximated the properties defined in IEEE std 1528'2003 (160) for 1.96GHz RF frequency. The specific composition of the phantom is shown in Table 5.2. Sucrose (>99% Sigma'Aldrich, St. 54.4 Louis, MO) Water (Sigma, St. Louis, MO)

40.7

Gelatin

4.9

127

(Kraft, Northfield, IL)

Table 5.2A dielectric probe was used to measure the conductivity and relative permittivity of the phantom (Agilent 85070E, Santa Clra, CA, USA), which were σ = 1.5 S/m and εr = 36, respectively, emulating the electrical properties of the average human brain at 1.96 GHz. The thermal properties of the phantom (see Table 5.1) were measured using a thermal property analyzer (KD2 Pro, Pullman, WA, USA). Furthermore, since the compounds used to create the phantom can effect α' the proton frequency shift coefficient; the phantom’s sensitivity to temperature change had to be calibrated. The proton frequency shift coefficient was experimentally measured to be 0.009 PPM/ degree C. Measurements were performed by exposing the phantom to a different power levels of RF energy and aligning the MR temperature measurements with optical temperature probe measurements.

Symbol

Physical properties

Values

ρ

Density [kg/m3]

1272

C

Heat capacity [J/kg·°C]

3543

D

Heat diffusivity [mm2/sec]

0.129

k

Thermal conductivity [W/m·°C]

0.457

Table 5.1. Physical properties of the gel phantom

Material

Weight Ratio (%)

Sucrose (>99% Sigma'Aldrich, St.

54.4

128

Louis, MO) Water (Sigma, St. Louis, MO)

40.7

Gelatin 4.9 (Kraft, Northfield, IL)

Table 5.2. Components of the Gel Phantom

MRI Compatible Dipole Antenna and Power Measurement System A half wavelength (λ/2) dipole antenna was constructed using non' ferromagnetic 0.47'mm'diameter semi'grid coaxial cable (Haverhill Cable and Manufacturing Corporation, Haverhill, MA, USA) and a 50 ohm characteristic impedance coaxial balun was used to drive the dipole antenna in the vicinity of 1.96GHz. The dipole antenna (Figure 5.1A) was matched for maximum efficiency with S11 < '15 dB. The high operating frequency resulted in minimal distortion at the 3 Tesla (T) MR Larmor frequency of 123.2MHz. The antenna was connected to an RF transmitter placed outside the Faraday cage of the MRI scan room via a 10'm' long non'ferromagnetic low'loss RF transport cable with an a 0.9 dB insertion loss at 1.96 GHz. The RF transmitter consisted of two stages of amplifiers. A Triquint Semiconductor AH212 1'Watt High Linearity, High Gain, InGaP, HBT Amplifier (Triquint Semiconductor, Oregon, USA) was used for the drive stage, and a Triquint Semiconductor AH420 4W High linearity, InGaP, HBT Amplifier was used for the final stage. A high power directional coupler (Agilent Technologies, 778D) was connected between the transmitter and the long non'ferromagnetic low'loss cable, to monitor the forward and reflected power from the coupling port and the isolation 129

port. The total loss of the components between the amplifier output and the antenna input, including the directional coupler, cables, connectors and coaxial balun (Figure 5.2B) was 3.2 dB at 1.96 GHz. A network analyzer (Agilent Technologies, E5070B) located outside the MRI Faraday cage was used as the RF signal generator. During the RF heating period, the antenna was operated in continuous wave mode (CW) for 6 minutes and 30 seconds with a net output power of 0.65W (as in the simulations) measured using a power sensor (NRP'Z11, Rhode & Schwarz) connected to the directional coupler. The dipole antenna was positioned inside the bore of the magnet and connected to a network analyzer confirming matching and tuning of the dipole was not altered relative to the bench test. Optical temperature probes were used to measure the RF heating produced by driving the dipole antenna, confirming that RF heating was identical for the bench test setup and the setup inside the magnet bore. Dipole Antenna Experiments Prior to the dipole antenna RF heating experiment, the phantom was positioned inside the MR scanner room for 24 hours, allowing the phantom to reach room temperature. After the phantom reached room temperature, RF heating produced by the dipole antenna was measured using a 3T MR scanner and head and neck coil (Siemens Medical Solutions, Erlangen, Germany) with 20 receive channels. A gel'oil phantom set up was used where cylindrical oil phantoms were placed around the phantom to estimate the non'heat'related main magnetic field drift [15]. 130

Airflow inside the magnet bore was turned off to prevent cooling down of the phantom by forced convection of air. Multi'slice, interleaved, spoiled gradient'echo (GRE) measurements of the phantom before and after a heating period of 6 minutes and 30 seconds were acquired with the following parameters: repetition time (TR) = 244 ms, echo time (TE) = 17 ms, voxel dimension = 2.7 mm x 2.7 mm x 5 mm, number of slices = 11 and total acquisition time = 31 s. The PRF method (Eq. 5.4) was used to convert multi'slice, multi'coil GRE phase measurements into a temperature difference map of the heating caused by the dipole antenna [24]. The accuracy of the MR thermometry was assessed via dipole heating experiments, which were run multiple times and compared with results from the optical temperature probe measurements. The location of the optical temperature probes was identified using a 3D high resolution MR image of 1mm x 1mm x 1mm. The high'resolution image was registered with the MR phase image for precise comparison of the MR temperature and optical temperature measurements. Additionally, RF heating solely from the MRI pulse sequences was evaluated independently. MR thermometry measurements were acquired while the dipole antenna was not driven and thus no RF heating was induced by the dipole antenna, confirming that RF heating from the imaging sequences and its contribution to the overall temperature change was minimal.

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Figure 5.3. Temperature and SAR maps of the dipole antenna-phantom setup from MR experiments and FIT simulations. Net input RF power to the dipole antenna was scaled to the measured value in FIT simulations. (A) MR thermometry measurement of the phantom. (B) Temperature change maps from FIT simulations (C) Experimental SAR maps obtained from Eq. 5.3 using phantom properties and MR thermometry maps. (D) SAR map from FIT simulation. Blue circles represent the phantom boundary. (E) Temperature change from the phantom (left-to-right), red indicates MR thermometry experiments and blue indicates FIT simulations.

Cell Phone Experiments During a bench test, communication between a LG'CU920c cell phone (LG Electronics, Seoul, Korea) and a MD8475A base station emulator (Anritsu, Kanagawa, Japan) was established to emulate a phone call, with the cell phone programmed to transmit at maximum power in the 1900 MHz GSM band. The phone was positioned on the phantom’s acrylic cylindrical former for 15 minutes and heating produced by the cell phone was measured using three fluoroptic MR' 132

compatible optical temperature probes (LumaSense, Santa Clara, CA) inserted ~4cm into the phantom at different positions (Figure 5.2C). In order to confirm the normal operation of the cellular phone inside the MR Faraday cage, the experimental setup used in bench test was brought to the MR scanner room. The phantom and cell phone were positioned on the MR scanner patient table ~2 meters away from the magnet. Temperature change resulting from the cell phone RF heating was measured while the cell phone was programmed to transmit maximum power. It was confirmed that the distance from the magnet bore was sufficient for the phone's operation to be unaltered via comparing to bench test temperature results.

P robe

MR

|

Measured thermometry ( C)

Error| ( C)

ΔT ( C) A 0.980

1.003

.023

B 0.820

0.863

0.043

C 0.134

0.179

0.045

Table 5.3. Dipole Antenna Experiment. Probe Temperature Measurements and Errors in MR Thermometry

133

Figure 5.4. Error of MR thermometry measurements compared to fluoroptic temperature probe measurements from Probes A-C in different experiments.

The RF heating experiment was performed using a 3T whole body scanner and a closely fitting birdcage knee coil (Siemens Medical Solutions, Erlangen, Germany). Two cylindrical oil phantoms were placed around the gelatin phantom to estimate the non'heat'related main magnetic field drift (Figure 5.1D). An axial interleaved spoiled 2D GRE imaging sequence was used to image the phantom pre' and post' RF heating. The following sequence parameters were used: TE = 17 ms, TR = 330 ms, matrix size = 64 x 64 x 16, voxel dimension = 4 mm x 4 mm x 5 mm, flip angle = 20 degrees and total acquisition time = 21.1 seconds. TE of the sequence was set to equal the T2* ' the transverse magnetization relaxation time ' of the phantom to improve the signal'to'noise ratio (SNR) of the temperature measurement (87). The phase images were subtracted and a phase correction was applied using the oil phantoms as a phase reference. For the phase correction, a 2D second order polynomial fit was used to characterize the phase drift associated with the main magnetic field. Oil phantoms were used as they have a conductivity of ~0.04 siemens/meter (at 128MHz) and heating of the oil is negligible when exposed to RF energy from the imaging coils. Between the imaging sequences, the phantom was withdrawn and positioned ~2 meters away from the magnet bore. The cell phone programmed to transmit at maximum power at the 1900 MHz GSM band using a MD8475A base station emulator. The mobile phone was placed on the phantom (Figure 5.1D) and RF heating was induced for 15 minutes. After the RF heating was conducted the phone was removed and the table was retracted inside the magnet 134

bore. Removal of the phone and movement of the table took under 10 seconds. Additionally, temperature change was monitored during the experiment using three fluoroptic MR'compatible optical temperature probes (Figure 5.2A). The fluoroptic probes were used to provide an external reference and a validation for MR thermometry measurements. The location of the probes was registered in the same manner as in the dipole experiment.

Figure 5.5. MR-based temperature maps along with fluoroptic probe temperature measurements in the phantom heated by the mobile phone. (A) Locations of slices for the temperature maps. The green arrows indicate the position of the fluoroptic probes. (B) Fluoroptic temperature probe measurements. Heating occurred during minutes 24-39 (highlighted in yellow).

135

MR Temperature Mapping Error Analysis Temperature simulations were conducted to estimate the error associated with the lead'time between RF heating and MR acquisition. During MR thermometry experiments, removing the cell phone from the phantom and moving the patient table back into the scanner bore for a second phase image acquisition took under 10 seconds. In temperature simulations, a phantom with the same structure and thermal properties (measured using a thermal properties analyzer) was used. After RF heating was simulated, 10 seconds of cool'down effect with no external energy source was computed using finite difference solver for the heat equation (159). The effect of the time delay between heating and imaging was quantified by plotting the errors between the two. For evaluation of the MR temperature mapping error, an identical gel'oil set up was used. This gel'oil phantom setup was placed inside the magnet bore and a gradient echo phase image was acquired by imaging the 3D volume of the phantom. The patient table was retracted multiple times from the bore for different time periods, varying between 1 (Experiment 1) and 8 (Experiment 4) minutes, during which there was no induced RF heating, either by a cell phone or by a dipole antenna. Thereafter, the table was positioned back inside the magnet bore and a second gradient echo phase image was acquired. Similar post processing algorithms were used, as explained in Section F, to obtain temperature maps.

136

Figure 5.6. Simulated temperature maps of post-heating (A), and after waiting 10 seconds postheating (B). Temperature error associated with waiting 10 seconds till the MR imaging sequence started (C). Maximum error was 0.074 °C at the surface of the phantom. Experimental temperature acquisition was performed with no external source emitting RF, but the imaging sequence itself (D). The maximum error = 0.069 °C.

RESULTS DipoleEantenna Simulation and Experimental Results Figure 5.2C shows temperature measurements inside the phantom acquired using three fluoroptic probes. The maximum heating captured from the probe measurements was 0.98 °C (Probe A) as a result of 6 minutes and 30 seconds RF heating period (minutes 1.5 to 9 in Figure 5.2). MR thermometry results show good agreement with the optical temperature measurement, as shown in Table 5.3. Figure 5.3B shows the temperature simulation results using the SAR map generated by the FIT simulation as an input to a finite'difference temperature simulator solving the heat'equation (Eq. 5.1). In FIT simulations, net RF power injected to the dipole antenna was scaled with the measured net RF power injected from the dipole 137

antenna (0.65W) during experiments. The temperature measurements and SAR results from the simulated dipole antenna match the experimental results both in pattern and magnitude (Figure 5.3 A and B). Location of the maximum temperature change within the axial slice captured in experiments was in good agreement with the temperature change obtained using FIT simulations with 4% difference in the absolute temperature (Figure 5.3B). The maximum temperature change observed over the whole phantom was 1.62 °C. Figure 5.4 shows the validation of MR thermometry results against temperature probe measurements. The measurement error of less than 0.15 °C was achieved from experiments conducted at different times. The standard deviation and the mean of the measurement error were 0.07 °C and 0.006 °C, respectively.

Probe

Measured MR thermometry ( C)

|Error| ( C)

ΔT ( C) A

0.423

0.370

0.053

B

0.23

0.225

0.005

C

0.111

0.124

0.013

Table 5.4. Mobile Phone Experiment. Probe Temperature Measurements and Errors in MR Thermometry.

Mobile Phone Experimental Results Temperature change resulting from the mobile phone heating was calculated in accordance with the PRF approach. Temperature difference maps for axial, sagittal and coronal slices inside the phantom are presented in Figure 5.5A. These maps match the temperature measured using the fluoroptic probes in magnitude 138

and location, as shown in Figure 5.5B and in Table 5.4. The maximum temperature change generated by the phone over the RF heating duration was 0.943 °C in close proximity to the cell phone. MR Temperature Mapping Error Analysis Results Figure 5.6A'C indicates that the maximum error associated with the wait' time was 0.074 °C. This accounts for 7.8% error of the maximal temperature change. Additionally, experiments evaluating the error associated with the imaging sequence and table/phantom misregistration are summarized for the entire field of view in Table 5.5. The maximum error in a slice of interest was 0.069 °C, which accounts for 7.3% error of the maximum temperature change in the cell phone experiment.

DISCUSSION This work shows that MR temperature mapping can be used to map small temperature changes with a standard deviation of error of 0.07 °C relative to the optical temperature probes. It is shown that temperature maps generated from a dipole antenna are in good agreement with the FIT simulation with regard to the magnitude and pattern of the temperature change and SAR. The ability to map small temperature changes using the presented method enables the use of three' dimensional MRI'based temperature mapping for safety and compliance evaluations of wireless devices, which are not necessarily MRI compatible.

139

With regard to the accuracy of the MR thermometry measurements, the SNR of temperature'related phase difference maps is directly proportional to the signal amplitude (87). Since this work was conducted in a phantom, a wide variety of single' and multi'channel MR coils can provide high SNR for the temperature measurement, enabling the detection of small temperature changes. In the experimental setup, for both the dipole and the cell phone, the SNR was higher than 200 using a closely fitting coil. Fabrication of a phantom with long T2* was also desirable as longer TEs are beneficial for observing small frequency shifts. An effort was made to minimize the presence of bubbles in the phantom gelatin; therefore, minimizing main magnetic field susceptibility. In order to optimize the pulse sequence parameter, the TE of the sequence was set equal to the T2* of the phantom, thereby maximizing the sensitivity of the temperature measurement. Standard Experiment

Mean Error

Deviation of Error

1

'0.008

0.039

2

'0.002

0.024

3

'0.003

0.023

4

0.008

0.036

Table 5.5. MR Temperature Mapping - Error Analysis

Challenges inherent in the proposed technique include compensation for non'heat'related B0 field changes that depend on the magnet, field'of'view, shim, sequences, the shape of the scanned object and other factors. These B0 field changes 140

are mitigated using oil phantoms positioned around the object being scanned, combined with 2D field extrapolation technique (161). Since the resonant frequency of oil changes by a negligible amount with heating, non'temperature'related magnetic field variations which resulted in a phase change between the pre' and post' RF heating were mapped using these phantoms. Additionally, other metabolites can be added to the phantom to provide a frequency reference (162). Even with these challenges, it is shown that the MR temperature mapping error is well below the uncertainty budget that was reported for electric field based measurements systems (152). It should be noted that the largest errors associated with the cooling period between the end of the RF heating and the start of the MR scanning is located at the phantom'air boundary ' a region where traditional electric field based methods are not capable of providing accurate measurements. The effect of heat transfer and diffusion on calibration accuracy is another factor impacting the accuracy of the SAR estimation from the temperature change, as the RF heating time smoothed the temperature distribution. For the experiments presented, the duration of the RF heating stage was 6 minutes and 30 seconds for the dipole experiment and 15 minutes for the cell phone experiment, respectively. Temperature change smoothing occurs over a distance of 2!∆!, where ∆! is the duration of the heating period and ! is heat diffusivity The measured value of ! in the phantom gel was 0.129 mm! /s. Therefore, over a heating period of 390 and 900 seconds, the characteristic temperature diffusion length was 1 cm and 1.52 cm,

141

respectively. This corresponds to 3.7 / 3.8 voxels within the slice plane and 2 / 3.1 voxels in the slice direction for dipole/cell phone experiment (90). Although heat diffusion over time disrupts the conversion of temperature change to SAR, it has recently been shown that averaged 10g SAR can be calculated from temperature change based on MR temperature measurements and physical measurements of the thermal properties of the phantom (163). In addition to conversions between temperature change and SAR, measuring the temperature change itself has its own merits for the following reasons: First, temperature change correlates with tissue damage (164) and therefore is an ideal measure of RF safety. Second, the temperature'based measurements using gel phantom resemble real'life conditions where non'perfused tissue is being exposed to RF waves. Thus, the temperature change measured in this study is an upper bound for possible overall temperature change in perfused'tissue, such as human brain. Although this study has not been verified for in vivo experiments, regulatory bodies (supported by some studies) assert that limits on peak 10g SAR or temperature change in a phantom provide overestimation for the RF heating induced in living sample (146,147). This assertion has not been conclusive and using MR for mapping accurately temperature changes in vivo remains an ongoing active topic for research. Third, it has been shown that electrical conductivity changes as a function of temperature. For example, the conductivity of water has been reported to change ~2% per degree Celsius (165). Since the proposed method relies on temperature measurements, conductivity changes are captured by temperature measurement. 142

As many wireless technologies exist in mobile devices (i.e. Wi'Fi, Bluetooth, etc.), the ability to test RF safety from multiple frequency bands at once could be useful since temperature measurement is RF frequency'independent. Conversely, for the E field probe measurement systems, multiple probes may have to be calibrated to the different frequencies and SAR testing from each of these frequencies would be conducted independently. Additionally, as many wireless devices operate at frequencies that are far from the operating frequencies of MR scanners, their transmission does not significantly deteriorate the quality of the MR measurement. As a result, it is possible to simultaneously measure the heat produced by a dipole antenna while conducting MRI scans; thus, creating a framework for in vivo scanning to investigate the effects of RF on the body. Another benefit of the method is that many spatial locations can be probed accurately, non' invasively, and within several seconds at high resolution using conventional clinical or animal MRI scanners. The process of cell phone compliance testing can also be parallelized using the proposed method. Multiple phantoms can be initially scanned as several model copies of the wireless device can be placed on the phantoms and set to transmit at maximum power output at a few seconds apart from each other. After heating is induced, the phantoms can be scanned again, sequentially at intervals of a few seconds, thereby significantly improving the speed of RF safety testing of wireless devices.

143

CONCLUSION In this paper, a novel measurement method for low power wireless device safety evaluation is presented. The measurement method is robust for imaging small temperature change in phantoms with millimeter resolution. The proposed method has shown excellent reproducibility and agreement with simulation and temperature probe measurements. The ability of the method to assess RF safety rapidly makes it especially well'suited for compliance testing of handheld or body' mounted wireless devices with specific safety standards.

Acknowledgements The authors would like to thank Dr. Christopher M. Collins for his input regarding electromagnetic field simulations.

144

6. WIRELESS DEVICE 10g SAR CALCULATION FROM 3D MRI TEMPERATURE MEASUREMENTS PROLOGUE Deposition of RF energy can be quantified via local SAR and temperature' change measurements. MRI provides a tool to measure small temperature changes in phantoms being exposed to RF radiation. Conversion from temperature'change to SAR is nontrivial when heating duration is long, since the heat'diffusion effect is prominent. In this work, a method for 3D calculation of 10g SAR is shown via inversion of the heat equation using high'resolution 3D temperature maps and measured thermal properties.

AUTHOR CONTRIBUTIONS: Leeor Alon: Theory development, study design, software coding, data analysis & interpretation, simulation work, experimental work and manuscript writing. Gene Y. Cho: Phantom building, experimental work, manuscript editing. Leslie F. Greengard: Theory development. Daniel K. Sodickson: Study concept, manuscript editing. Cem Murat Deniz: Theory development, study design, software coding, data analysis & interpretation, simulation work, experimental work and manuscript writing. 145

INTRODUCTION Exposure to RF radiation results in increased heating of tissue via Joule and Dielectric heating mechanisms (142). In order to prevent the deposition of excessive RF energy into the body, maximum allowed temperature increase during RF heating is regulated (166,167) by means of measuring SAR, the rate at which energy is deposited inside the body. SAR is conventionally measured in the wireless industry using electric (E) field probes (168) that are mechanically moved in a point'by' point, grid'like fashion in 3D space inside a phantom filled with a liquid mimicking the electrical properties of human tissues. Recently, several studies have shown the feasibility of assessing the RF safety via temperature measurements using temperature probes (152) and magnetic resonance (MR) temperature mapping (169). In temperature'based methods, heating duration plays an important role in estimating SAR. Keeping the duration of heating small requires sufficient device output RF power in order to minimize the heat diffusion, while being able to accurately measure a temperature change. Temperature based RF safety assessment of low power RF emitting devices requires the heating duration to be sufficiently long in order to get detectable temperature change within the phantom. Thus, heat diffusion cannot be ignored and inversion of the heat equation is needed to estimate the local SAR distribution. In this work, we take advantage of MR temperature mapping to measure small temperature changes with a resolution of a few millimeters, to invert the heat 146

equation and calculate the local SAR distribution. It is shown that by combining the information provided by MR temperature mapping with physical measurement of thermal properties of the phantom, the inversion of the heat equation reveals the local SAR distribution. Results are shown 1) using Electromagnetic (EM) field simulations, where the true simulated SAR (which is not known in experiments) is recovered from temperature with realistic noise addition, and 2) using MR based temperature measurement experiments.

THEORY The heat equation with source term is a parabolic partial differential equation, which captures the behavior of temperature in space and time when a body is exposed to an external energy source. The equation in non'perfused, homogeneous media is expressed as follows: !"

!" = ∇ ∙ !∇! + !"#$ !"

(6.1)

where ρ, C, k, and SAR are the tissue density (in kilograms per cubic meter), heat capacity (in Joules per kilogram per degree Celsius), thermal conductivity (in Watts (W) per meter per degree Celsius), and SAR (in Watts per kilogram), respectively. If the heating time (e. g. due to an external RF source) is short and thermal diffusion is negligible, Eq. (6.1) can be integrated in time and simplified to: !"# = !

Δ! Δ!

147

(6.2)

where (in degrees Celsius) is the temperature change induced during time'interval (in seconds). However, when heating occurs over a sufficiently long period, heat diffusion cannot be ignored (i.e. using Eq. (6.2) results in high errors) and SAR needs to be determined by inversion of the heat equation. There are several methods available to extract the source term in parabolic partial differential equations (170,171). In this current implementation, we choose to use a finite difference approximation to the heat equation and using the following linear polynomial equation (171): !!! !

(1 + !)! !

!! = (1 + !) !! +

(6.3)

!!!

where f is the source term defined as: ! = ∆! ∗ !"# ∗ ! !! , !! and !! are the initial and final temperature of the sample, respectively, and L is a linear Laplace operator defined as: ! = ∆! ∗ ! ∗ ∇! . Since all the terms in Eq. (6.3) except f are measurable quantities (k and C can be measured using a thermal probe, and ∆! = !! − !! using MR), Eq. (6.3) can be written as a linear matrix equation and f can be calculated using the following L1 norm weighted least squares minimization, which has been shown to be robust with respect to noise for sparse representations (172): !"#$%&! { !" − ! where ! = !! − (1 + !)!!! !! , ! =

!!! !!! (1

!

+! !

!

+ !)! , and λ is the regularization

parameter that was set to 1.5 in this study. This value was chosen using by 148

(6.4)

conducting an L'curve analysis on simulations with realistic noise in the temperature maps.

METHODS EM field simulations were performed on the dipole antenna ' phantom setup shown in Figure 6.1A, in order to obtain the SAR distribution induced by the dipole antenna inside the phantom and validate that the heat equation inversion problem can be solved accurately. Commercial Microwave Studio software (CST, Framingham, MA, USA) using finite integration technique (FIT) was used for the simulations. The parameters used in the FIT calculations were as follows: 2.7 mm isotropic cell size, mesh dimensions 84 x 83 x 83, feeding with a voltage source operating at 1.96 GHz. A 5 mm separation between the phantom and the dipole antenna was used to simulate the physical setup in the scanner room. The net input power used was 0.65W. The simulated SAR distribution was used along with the thermal properties of the phantom to model the temperature distribution in the phantom numerically by solving the Heat equation (Eq. 6.1) as result of 6.5 minutes of heating (159). Gaussian noise (similar in mean and standard deviation of the MR temperature maps) with standard deviation of 0.1°C was added to the simulated temperature maps. Inversion of the heat equation was then conducted using L1 weighted norm minimization, where a non'linear conjugate gradient was used for the optimization (173)(Eq. 6.4) in order to estimate the unaveraged local SAR. The 10g SAR, which is regulated for RF safety by the international standard committees 149

[3], was calculated from the unaveraged local SAR and compared with the original, "true" 10g SAR distribution that was computed in simulation. A flow chart of the procedure described above is shown in Figure 6.1A. The mean, standard deviation and maximum error between the true and reconstructed 10g SAR was calculated to evaluate the inverse heat equation solution.

Figure 6.1. A. Phantom-dipole antenna setup and flow chart of the process used for the solution of the inverse heat problem. The phantom dimensions were 10.2 cm in diameter and 11 cm in height. B. Gel phantom used in MR temperature mapping experiments. The phantom properties were as follows: ρ = 1272(kg/m3), C=3543(J/kg·°C) and k=0.457(W/m·°C). C. Dipole antenna used in the MR experiments. D. Schematic representation of the experiment setup used to drive the dipole antenna while measuring the net output power.

For the experiments, a half wavelength (λ/2) dipole antenna (Figure 6.1B) was constructed to operate at 1.96GHz and matched for maximum efficiency with S11 < '15 dB. The schematic of the experimental setup used to drive the antenna is shown in Figure 6.1D. During the RF heating period, the antenna was 150

operated in continuous wave mode for 6.5 minutes and net injected RF power was monitored using a directional coupler (Agilent Technologies 778D) and a power sensor (NRP'Z11, Rhode&Schwarz). RF heating was detected using a 3T MR scanner and head and neck coil (Siemens Medical Solutions, Erlangen, Germany) with 20 receive elements. Multi'slice, interleaved, spoiled gradient'echo (GRE) images of the phantom before and after RF heating were acquired with the following parameters: repetition time (TR) = 244 ms, echo time (TE) = 17 ms, voxel dimension = 2.7 mm x 2.7 mm x 5 mm, number of slices = 11 and total acquisition time = 31s. The PRF shift method was used to convert multi'coil GRE phase measurements into a temperature difference map. The temperature difference map and the thermal properties of the phantom, measured using a thermal property analyzer (KD2 Pro, Pullman, WA, USA), were used to invert the heat equation and compute the unaveraged local SAR. After computing the unaveraged local SAR a 10g SAR average was computed as defined in ref (174).

RESULTS Figure 6.2A shows an EM field simulation comparison between the reconstructed and “true” 10g SAR results for five slices in the middle of the phantom. The mean, standard deviation and maximum error between the reconstructed and “true” 10g SAR distributions over the entire volume of the phantom was 0.1 W/kg, 0.14 W/kg and 1.42 W/kg, respectively. Simulation results show that the 10g SAR can be reconstructed within 8.8% of maximum value using a 151

finite difference approximation solution to an inverse heat diffusion problem. The error reported was due to noise propagation in the inversion process and other reconstruction methods for minimizing the error propagation are under investigation. Preliminary experimental 10g SAR results are shown in Figure 6.2B, where temperature maps of RF heating from a dipole antenna positioned inside the MR scanner room were used in solving the inverse heat problem.

152

Figure 6.2. A. Simulated ΔT and 10g SAR maps (coronal slices) at 5 slices inside the phantom, comparing the “true” simulated 10g SAR distribution and the reconstructed 10g SAR distribution using inversion of the heat equation. B. Experimentally measured ΔT maps and reconstructed 10g SAR maps at 5 slices inside the phantom.

CONCLUSION In summary, a method for computing 10g SAR generated from low power RF devices is presented in this work. High resolution MRI temperature mapping provided a metric related to health risk, while the combination of the temperature 153

mapping with thermal property measurements enabled 10g SAR calculation' a metric used as a standard for safety evaluation of wireless devices.

154

7. SUMMARY Chapter summaries The

present

thesis

embodies

novel

approaches

for

experimental

quantification of RF energy deposition. About 51/2 years ago when I embarked in my doctoral studies, I had the goal of enabling in vivo local SAR quantification. At the time, this goal seemed challenging and valuable, as local quantification of RF deposition has been problematic for over 50 years. While in achieving this lofty goal I have not been entirely successful, the work has significantly improved the way in which global and local SAR are evaluated experimentally. Chapter 2 of this thesis focused on the challenges associated with aligning simulation and experiments. In the MRI field, simulation software is often used to assess the exposure of tissues to RF energy. However, it was shown in Chapter 2 that results computed from simulations are difficult to align with arbitrary subjects, and may be problematic for deriving thresholds for safety in patients. This suggested that when the subject anatomy or coil structure changed, B!! fields, which are measureable in MR, tended to have smaller errors than 10g average SAR and ΔT, and that relative agreement between simulated B!! fields did not guarantee agreement in 10g'average SAR and ΔT distributions. In view of these findings, the focus of my work has been mainly on the development of experimental techniques for quantifying global and local RF power deposition.

155

Chapter 3 of this thesis describes our work on developing a global SAR monitoring system that was the first to be built for parallel transmit MRI, and that was based on directional couplers that measured the forward and reflected power at each channel. The hardware and software developed by our group was highly successful and was later adopted by Siemens and others to measure and predict global SAR in parallel transmit systems. Based on the same quadratic model presented in chapter 3, we demonstrated in chapter 4 that local RF power deposition can be computed and predicted for parallel transmit systems. This was the first time temperature mapping was used to quantify how much energy is delivered into a tissue'mimicking phantom from a parallel transmit setup. The framework presented in chapter 4 also enabled the prediction of local RF power deposition for an arbitrary pulse shape. As a result of the work, we also developed “GLACIUS,” a software tool for the reconstruction of MR thermometry acquisitions (appendix C). I was pleased that the tool became widely useful for evaluating novel coil designs such as those constructed at the Bernard and Irene Schwartz Center for Biomedical Imaging at New York University School of Medicine. Chapters 5 and 6 of this dissertation paved the way for utilizing MRI temperature mapping techniques for safety evaluation of RF/microwave emitting devices. In these chapters, quantification of the RF power deposition was made possible for both MRI compatible and non'MRI'compatible devices, while having the 156

advantage of being noninvasive (traditional SAR measurement systems are invasive), and of providing millimeter resolution and high accuracy. The work in chapters 5 and 6 was presented to worldwide regulatory committees including the International Committee on Electromagnetic Safety (ICES), IEEE Technical Committee 34 on Wireless Handset SAR Certification and IEEE Technical Committee 95 on electromagnetic safety. We hope that MRI based temperature mapping techniques may one day become the gold standard for evaluating RF/microwave emitting devices at various frequencies.

An outlook for the future The ability to use MR to map small temperature changes has been a monumental step in improving RF energy quantification. In a large portion of this thesis work, MR temperature mapping was used to quantify local RF energy deposited by RF/microwave antennas' mostly in phantoms; however, in the future, these methodologies could possibly be applied for in vivo imaging. Robust in vivo temperature mapping techniques have mostly been used in HIFU and hypothermia applications, where the temperature change was significantly higher than in clinical MR exposures. Improvement of current MR thermometry tools used to track small in vivo temperature changes with an error smaller than 0.3° C would be an important step for utilizing MR as a modality to track patient'specific RF power deposition. We have seen in recent years accelerated MR thermometry acquisitions being developed, which if proven robust, 157

could be used for rapid real time MR thermometry that can be incorporated into clinical MRI exams. If these thermometry tools become effective, it is probable that temperature or “cumulative equivalent minutes” (CEM) at 43° C, not SAR, will be adopted as the prominent safety metric utilized by regulatory committees. While the field of MR thermometry is in development, another area of potential impact on the field is the generation of anatomically accurate body models that resemble the patient being scanned. Thus far, reliable modeling has been challenging since patients vary in size and body composition. Simulations have mostly been conducted on a limited number of body models positioned at different locations next to an antenna; however, it has been shown that the use of a restricted number of body models may not be sufficient for safety assurance. We recently showed that deformations applied to a segmented body model could be used to create patient'specific body models, which better pertain the patient being scanned (175). These types of approaches can incrementally improve the accuracy of simulation used for RF/microwave safety evaluations. In addition to deformation'based approaches for accurate body model generation, another potential impactful method for estimating patient safety has recently been shown in the work on electrical property mapping of tissues (94), where measurable magnetic fields are used to estimate the electrical properties in a patient and could possibly be used to compute the E field and SAR in a subject. Currently, electrical property mapping techniques are time consuming and inverting 158

Maxwell’s equations at tissue boundaries still remains challenging, but this is an area of active research that is promising. Even though significant progress has been made in the last several years, more work is necessary in order to provide in vivo quantification of RF energy deposition. In general, continued advancements in some of the areas outlined above may enable not only better understandings of current safety limits, but also safe delivery of increased power levels, which have in the past been constrained by conventional SAR estimation techniques. Both enhanced safety and improved capabilities may in turn help to enable clinical utilization of ultrahigh field MR.

159

8. PUBLICATIONS RESULTING FROM THE DISSERTATION WORK Accepted Peer reviewed papers •

Zhu, Y., Alon, L., Deniz, C. M., Brown, R. and Sodickson, D. K., System and SAR characterization in parallel RF transmission. Magn Reson Med, 67: 1367– 1378. doi: 10.1002/mrm.23126, 2012.

•

Alon L., Deniz C. M., Brown R., Sodickson D. K., and Zhu Y., "Method for in situ characterization of radiofrequency heating in parallel transmit MRI," Magn Reson Med, Jun 19 2012.

•

Deniz C. M., Alon L., Brown R., Sodickson D. K., Zhu Y. Specific absorption rate benefits of including measured electric field interactions in parallel excitation pulse

design.

Magn

Reson

Med.

2012

Jan;67(1):164'74.

doi:

10.1002/mrm.23004. Epub 2011 Aug 29.

In review •

Alon L., Cho G. Y., Yang X., Zhu Y., Sodickson D. K., Deniz C. M. A Method for Safety Testing of RF Emitting Devices using Magnetic Resonance Imaging.

•

Alon L., Deniz C. M., Zhu Y., Sodickson D. K., Collins C. M. Effects of Anatomical Inaccuracies on Simulated Fields, SAR, and Temperature for Surface Coils Near the Abdomen.

160

•

Alon L., Cho G. Y., Greengard F. S., Sodickson D. K., Deniz C. M. Calculation of 10g average SAR via inversion of the heat equation using MRI Thermometry and Thermal Property Measurements.

Selected Conference Abstracts 2010 •

Alon L., Deniz C. M., Lattanzi R., Wiggins G., Brown R., Sodickson D. K., Zhu Y. An Automated Method for Subject Specific Global SAR Prediction in Parallel Transmission. Proc. Intl. Soc. Mag. Reson. Med. 18 (2010), P. 780 (Oral presentation).

•

Deniz C. M., Alon L., Brown R., Fautz H. P., Sodickson D. K., Zhu Y. Real Time RF Power Prediction of Parallel Transmission RF Pulse Design at 7T. Proc. Intl. Soc. Mag. Reson. Med. 18 (2010), P. 1454.

•

Zhu Y., Deniz C. M., Alon L., Fautz H. P., Sodickson D. K. Understanding Parallel Transmit Array Efficiency. Proc. Intl. Soc. Mag. Reson. Med. 18 (2010), P. 1518.

•

Alon L., Deniz C. M., Lattanzi R., Wiggins G., Brown R., Sodickson D. K., Zhu Y. Local SAR Calibration and Prediction Model in Parallel Transmit MRI. Proc. Intl. Soc. Mag. Reson. Med. 18 (2010), P. 3869.

161

2011 •

Deniz C. M., Alon L., Brown R., Fautz H. P., Zhu Y., Sodickson D. K. Parallel RF Pulse Design with Subject'Specific Global SAR Supervision. Proc. Intl. Soc. Mag. Reson. Med. 19 (2011), P. 210 (Oral presentation).

•

Alon L., Deniz C. M., Sodickson D. K., Zhu Y. Do Constraints On |B1+| Also Constrain |E| & SAR in High Field MR? Proc. Intl. Soc. Mag. Reson. Med. 19 (2011), P. 3854 (Oral presentation).

•

Alon L., Deniz C. M., Xu J., Brown R., Sodickson D. K., Zhu Y. Volumetric Local SAR Mapping for Parallel Transmission. Proc. Intl. Soc. Mag. Reson. Med. 19 (2011), P. 491.

2012 •

Alon L., Deniz C. M., Brown R., Sodickson D. K., Zhu Y. Difficulties Associated with Aligning Simulated and Constructed Coils. Proc. Intl. Soc. Mag. Reson. Med. 20 (2012), P. 2772.

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Sodickson D. K., Alon L., Deniz C. M. Brown R., Zhang B., Wiggins G., Cho G. Y., Ben'Eliezer N., Novikov D. Lattanzi R., Duan Q., Sodickson L. A., Zhu Y. Local Maxwell Tomography Using Transmit'Receive Coil Arrays for Contact'Free Mapping of Tissue Electrical Properties and Determination of Absolute RF Phase. Proc. Intl. Soc. Mag. Reson. Med. 20 (2012), P. 387. (Oral presentation).

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Alon L., Tal A., Deniz C. M., Cho G. Y., Sodickson D. K., Zhu Y. RF Coil Local Power Deposition and Efficiency Evaluation Using a Phantom with High 162

Sensitivity to Temperature Change. Proc. Intl. Soc. Mag. Reson. Med. 20 (2012), P. 2736. 2013 •

Sodickson D. K., Alon L., Deniz C. M. Ben'Eliezer N., Cloos M., Sodickson L. A., Collins C. M., Wiggins G., Novikov D. Generalized Local Maxwell Tomography for Mapping of Electrical Property Gradients and Tensors. Proc. Intl. Soc. Mag. Reson. Med. 21 (2013), P. 4175.

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Alon L., Deniz C. M., Cho G. Y., Yang X., Collins C. M., Zhu Y., Sodickson D. K. Mobile Phone RF Safety Testing Using Magnetic Resonance Imaging. Proc. Intl. Soc. Mag. Reson. Med. 21 (2013), P. 3593.

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Deniz C. M., Alon L., Yang X. Cho G. Y., Collins C. M., Brown R., Sodickson D. K., Zhu Y. Novel Method for Experimental Assessment of Antenna Safety Using MR Thermometry. Proc. Intl. Soc. Mag. Reson. Med. 21 (2013), P. 4424. (1st place MR safety poster presentation).

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Alon L., Collins C. M., Giuseppe C., Novikov D., Zhu Y. Tissue Thermal Property Tomography. Proc. Intl. Soc. Mag. Reson. Med. 21 (2013), P. 2519.

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Alon L., Cho Y. G, Sodickson D. K., Deniz C.M. Wireless Device 10g SAR Calculation from 3D MRI Temperature Measurements. Bioelectromagnetics 2013. PA'75. (Student oral).

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2014 •

Alon L., Cho Y. G, Sodickson D. K., Deniz C.M. Calculation of 10g Average SAR via Inversion of the Heat Equation using MRI Thermometry and Thermal Property Measurements. Proc. Intl. Soc. Mag. Reson. Med. 22 (2014).

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Alon L., Tal A., Giuseppe C., Deniz C. M., Sodickson D. K., Collins C. M. Rapid, Direct Measurement of Bulk RF Power Deposition using Free Induction Decay Acquisitions. Proc. Intl. Soc. Mag. Reson. Med. 22 (2014).

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Deniz C. M., Alon L., Cho G. Y., Brown R., Sodickson D. K. Investigation of Different RF Coil Safety Assessment Techniques: E'field Measurements, EM Field Simulations and MR Thermometry. Proc. Intl. Soc. Mag. Reson. Med. 22 (2014).

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Alon L., Deniz C. M., Bruno M., Sodickson D. K., Collins C. M. A Method For Subject'Specific Body Models using Affine And Non'Linear Transformations. Proc. Intl. Soc. Mag. Reson. Med. 22 (2014). (Power poster).

Pending Patents •

Alon L., Sodickson D. K., System, method and computer accessible medium for determining tissue thermal properties. Docket No.: 237237.US.01 – 475396'00368.

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Alon L. Systems and methods based on magnetic resonance imaging for safety evaluation of energy emitting devices. Docket No.: 239307.US.01' 475396'00388. 164

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Alon L., Deniz C. M., Cho G. Y. Apparatus, systems and methods which are based on magnetic resonance imaging for safety evaluation of radio frequency emitting devices. Docket No.: 229837.US.01'475396'00317.

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Zhu Y., Alon L. Apparatus, systems, computer'accessible medium and methods for facilitating radio frequency hyperthermia and thermal contrast in a magnetic resonance imaging system. Docket No. 216013.US.02'475396' 357.

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Alon L., Sodickson D. K. System and method for providing magnetic resonance temperature measurement for radiative heating applications. Docket No.: 242838.US.01 – 475396'00411

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Alon L., Deniz C. M., Cho G. Y., Greengard L. F. Local sar calculation from 3d MRI temperature measurements. Docket No.: 238679.US.01 – 475396' 00381.

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Alon L., Tal A., Collins C. M., Rapid, direct measurement of bulk RF power deposition using free induction decay acquisitions. Docket No.: 242840.US.01 – 475396'00410.

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9. APPENDICES APPENDIX A – MAXWELL’S EQUATIONS Maxwell’s biggest contribution to science lies in the adaptation made to Ampere’s circuit law where he realized that a displacement current term in Ampere’s law was missing and that four modified equations can model the behavior of electromagnetic waves. He published these results in his 1861 paper “on physical lines of force.” Following that, in 1865 he published “a dynamical theory of electromagnetic fields” where he demonstrated his corrected theory alongside the fact that light was an electromagnetic wave. Heinrich Hertz confirmed Maxwell’s findings, in 1887. Maxwell postulated that a current density J streaming into an electrode system is equal to the change in true charge stored between the plates: ! ⋅ !"# = !

!" !" = ! !"

!" ⋅ !"# ! !"

(7.1)

where ! is the surface charge, ! is time and ! is the area of the plate and !" is equal to the electric flux density ! ⋅ !. The current density can then be measured as the time derivative of the electric flux at the electrode surface. The field current, which extends though the dielectric material, was named the displacement current. Adding the displacement current into Ampere’s original circuit law yielded Maxwell’s first equation in integral form: 166

! ⋅ !" =

! ⋅ !"# + !

!" ⋅ !"# ! !"

(7.2)

where ! is the complex magnetic field strength vector. Using Stoke’s theorem, the equation above was transformed into differential form yielding: ∇×! = ! +

!" !" =! !" !"

(7.3)

The current density J generally represents a lossy conduction current obeying Ohm’s law, where ! = !". Maxwell’s second field equation is a generalization of Faraday’s law of induction, asserting that the change of magnetic flux density creates an electromotive force (EMF) in integral form as follows: ! ⋅ !" = − !

!" ⋅ !"# ! !"

(7.4)

Similar to the first equation, this equation can be written in differential form: ∇×! = −

!" !"

(7.5)

The third Maxwell equation is Gauss’s law for electric charge affirming that the divergence of the E field is related to the total electric change density (in differential form only): ∇ ∙ ! = !!"##

167

(7.6)

where !!"## is the charge density. The fourth and final Maxwell equation is Gauss’s law for magnetism, which states that the magnetic field divergence must be equal to zero. In this equation, Maxwell postulated that there is electric charge, but no magnetic charge or “magnetic monopole.” This basically states that whenever a surface encloses a magnetic moment, the magnetic field flux entering the surface must equal the flux leaving the surface, defined by the following equation (again, in differential form): ∇∙! =0

168

(7.7)

APPENDIX B: MATLAB ALGORITHM FOR SYSTEM AND SAR CHARACTERIZATION FOR PARALLEL RF TRANSMISSION In chapter 2, a minimization is performed in order to compute the electric field correlation matrix, Φ (see “calibration method”). The following matlab code generates the weightings matrix, which can be used to pulse on individual channels and responsible for estimation of the electric field correlation matrix. “n_ports” is the number of ports in the system.

experiment_config=10*sqrt(2)*eye(n_ports); for id=1:n_ports-1 two_lines=zeros(2,n_ports); two_lines(:,1)=[10; 10]; two_lines(:,id+1)=[10; 10j]; tmp=two_lines; for shift=1:n_ports-1-id tmp=[tmp; circshift(two_lines,[2 shift])]; end experiment_config=[experiment_config; tmp]; end

m_4calc=n_ports^2;

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