Effect of Scintillator Crystal Geometry and Surface Finishing on Depth of Interaction Resolution in PET Detectors – Monte Carlo Simulation and Experimental Results using Silicon Photomultipliers Sarah Cuddya,b, Alla Reznikc, John A. Rowlandsa,b,c, Farhad Taghibakhsha,b,c (a) Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada, M4N 3M5, Telephone: 416-8339660, Fax: 416-480-5714, [email protected]; (b) University of Toronto, Ontario, Canada (c) Thunder Bay Health Sciences Center, Ontario, Canada. ABSTRACT Resolution of positron emission tomography (PET) systems benefits from information about depth of interaction (DOI) within scintillation crystals, particularly in small bore scanners or parallel plate detectors. In this investigation, the ability of the dual-ended readout detector module configuration to resolve DOI and crystal index was evaluated for a variety of detector pitches and light guide thicknesses to validate the dual-ended readout method. Experimental results with oneto-one coupling between saw-cut 2mm pitch LYSO scintillation crystals and silicon photomultipliers (SiPMs) achieved 2.1 mm DOI resolution. Monte Carlo simulations were used to investigate the effect of larger detector pitches and varied light guide thickness on the crystal index identification accuracy and DOI resolution for a pixilated crystal array in dual-ended readout configuration. It is reported that the accuracy in identifying a 2 mm scintillation crystal was >80% for detector pitches < 6 mm and that DOI resolution was < 2 mm for all detector pitches and light guide thicknesses.

Keywords: PET, dual-ended readout, depth of interaction, silicon photomultiplier, Detect2000, Scintillator crystal identification

1. INTRODUCTION Positron emission tomography (PET) is a valuable technique in screening for and evaluating neurodegenerative diseases and cancer. It can probe biological processes with high sensitivity and specificity but it lacks a morphological reference frame[1]. The current standard of coupling computed tomography (CT) images to PET images provides an anatomical reference for localizing PET regions of interest. A multitude of research has recently been done to couple PET with magnetic resonance imaging (MRI) for better soft tissue contrast and to reduce patient exposure to ionizing radiation[2]. The multimodality coupling of MRI with PET introduces magnetic and geometric restrictions in addition to previous requirements to be addressed in the detector design for a given PET application. These restrictions provide a need for a compact size and magnetically compatible detector modules to fit and function within the bore field of an MR imager. New developments in photodetection technology have produced silicon photomultipliers (SiPMs): small, compact and rugged solid-state high gain, low voltage and fast devices that are capable of detecting single optical photons and are not sensitive to magnetic fields[3]. All these attributes make SiPMs attractive substitutes for photomultiplier tubes, especially for PET-MRI[4] or high resolution PET[5]. Similar to the degradation of image resolution in small animal PET scanners and parallel plate designs of positron emission mammography (PEM) systems, parallax error also affects the image resolution in detector inserts for PET/MRI[1,6,7]. To compensate for parallax error, it is crucial to design a detector module which accurately resolves depth of interaction (DOI) within a scintillation crystal. Use of multi-layered crystals or Phoswich configuration[8], maximum likelihood estimation (MLE)[9], and dual-ended readout[3] are among common reported methods in the

Medical Imaging 2010: Physics of Medical Imaging, edited by Ehsan Samei, Norbert J. Pelc, Proc. of SPIE Vol. 7622, 76221O · © 2010 SPIE · CCC code: 1605-7422/10/$18 · doi: 10.1117/12.845065

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literature for determining DOI. Dual-ended readout is the method of choice in our research, since it can potentially provide a higher DOI resolution. One consequence of implementing a dual-ended readout detector module is the requirement of additional photodetectors and processing channels. By using detectors with larger pitch, the number of required processing channels can be decreased for a given area. For example, Song et. al. reduced the number of detectors by a factor of 11 by coupling an array of 10×10 scintillator crystals to an array of 3×3 photodetectors, therein reducing the number of processing channels to 4 (as opposed to 9) by multiplexing the output signals using anger logic[10]. However, the mentioned detector design with pixilated crystals and single-sided readout does not resolve DOI. Here we report results of our ongoing research on PET detector design (geometry and configuration) using the dualended readout method. The objective of our research is to investigate the accuracy in determining the position of absorption events within pixilated crystals using the dual-ended readout method, and to evaluate the effect of detector pitch and light guide thickness on resolving the interaction position (crystal index and DOI).

2. EXPERIMENTAL METHODS 2.1. Detector configuration and experiment strategy The straightforward configuration in the dual-ended readout method is to have two photodetectors for each scintillator crystal. This configuration requires two times more photodetectors and processing channels compared to a generic single-ended readout method with one photodetector per individual crystal. The cost of two-fold photodetectors and electronic processing might be too much for the benefit (DOI), however, one-to-one coupling provides the best detector performances in terms of detection limit, spatial and energy resolution because nearly all available scintillation light photons generated inside a particular crystal are going to be absorbed by the photodetectors assigned to that crystal. In this configuration, only DOI is to be resolved, the crystal index is automatically determined when the photodetector coupled to the crystal is fired as the result of an absorption event. A more economic approach to that is to use fewer numbers of photodetectors, hence processing channels that share the scintillation light. This is usually done by placing a layer of non-scintillating material such as glass (known as the light guide) between scintillator crystal ends and photodetectors to allow light to spread out from one crystal over more than one photodetector. The position index of the crystal is then extracted from the ratio of the signal of photodetectors that share the light (see section 3.2.). Needless to say that the light guide thickness and the photodetector pitch are the key design parameters here that we are to investigate their role in the detector spatial resolution. In our experiments, we used one-to-one coupling configuration to investigate the effect of crystal surface finishing on DOI resolution, and then we used crystal arrays with designated surface finishing to evaluate the effect of light guide thickness and photodetector pitch on accuracy of resolving the position of the event. 2.2. Experimental apparatus and simulation setup Fig. 1.a shows the one-to-one coupling experimental apparatus. We used a lead block to collimate the 511 keV annihilation photons from the 22Na positron source on to a Teflon coated 2×2×20 mm3 polished and saw-cut LYSO scintillator crystal. The crystal was coupled, on polished ends, to two 4.4 mm2 SiPMs (SIPM-0611B4MM from Photonique SA) by optical gel. A custom designed pre-amplifier was used to amplify the SiPMs signal and match it to an ASPEC-927 dual input multichannel analyzer (MCA) for energy spectrum analysis, as well as to a TDS7254 - 2.5 GHz programmable oscilloscope for DOI extraction. We used DETECT2000 software[11] to track photons inside individual crystals both in one-to-one configuration, as well as in an array of ten 2×2×20 mm3 LYSO scintillation crystals (modeled with index of refraction of n = 1.82) to simulate the number of incident photons on each of the photodetectors, from which we resolved the index of the crystal

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Photodetectors … 22Na

2 x 2 x 20 mm3 LYSO scintillation crystals

-9.9 mm

Crystal pitch 2 mm

0.0 mm

Interaction

DOI

A

2x2 mm3

Center

-5.0 mm

B

9.9 mm Light Guide

(a)

Simulated Depth of Interaction

5.0 mm

Processing Electronics A+B: Energy

…

Source

Course of DOI

(20x2x2 mm3)

B2

Optical gel

Lead Collimator Block

LYSO Crystal

B1

A- B : DOI A+B

(b)

2, 3, 4, 5, 6, or 7 mm …

0.5 mm A1

A2

Detector pitch = 3, 4, 5, 6, 7, or 10 mm

Fig. 1. Schematic drawing of: (a) the experimental apparatus used to evaluate energy and DOI resolution in one-to-one configuration, and (b) the detector model for Monte Carlo simulation to evaluate the effect of light guide thickness and detector pitch on accuracy of resolving the position of interaction.

where the interaction occurred, as well as the DOI. The modeled detector module is dual-ended with one pair of photodetectors at either end. Crystals of 2 mm pitch were chosen such that up to 1 mm geometric image spatial resolution could be achieved[7]. 2.3. Monte Carlo simulation The Monte Carlo simulation was programmed to generate a mean of 19,000 individual optical photons with a normal distribution (as is the case when a 511 keV annihilation photon is absorbed by the scintillator crystal) at selected DOI positions within one crystal and to track them until they escaped, were absorbed, or were detected by the photodetectors. Optical photons were generated isotropically within the 2×2 mm2 crystal area for specific depths of interaction, and the simulation was repeated 10 times to approximate the absorption of ten 511 keV annihilation photons. Modeling was done to determine geometric resolution, thus detection efficiency is assumed to be 100% for both the scintillator and photodetector[7]. The crystal surface was finished with polished, unreflective surfaces on both ends and “saw-cut” surfaces on the crystal sides. The saw-cut finishing was approximated by simulating a UNIFIED surface[12] for which the angle between microfacets was σ = 90°, the probability of reflection about the normal of a micro-facet was sl = 1.0, and the reflection coefficient was RC = 0.95. This surface was chosen since the light output closely approximates that measured experimentally. A continuous piece of glass for a light guide of varying thickness was simulated between the crystals and photodetectors to enable light sharing. Each of the five layers in the detector module were separated by a 0.01 mm layer of optical coupling gel with refractive index n = 1.46 to minimize reflection and refraction at the interfaces. The photodetectors in the simulated system were discrete detectors of varying pitch with 100% active area on the detecting surface. Each photodetector was modeled as a 0.5 mm thick piece of the same glass as the light guide (n = 1.50). The outside surface of the glass was assigned as the DETECT surface where simulated photons interacted and were readout.

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The simulation was performed for six different pitch sizes of photodetectors, and six different light guide thicknesses for each of the detector pitches (Fig. 1.b). Photons detected by each of the four photodetectors were recorded for events in each of the ten scintillation crystals for all cases. Data was consolidated and analyzed to extract information about the position of the interaction within the crystals.

3. RESULTS AND DISCUSSION 3.1. Effect of crystal surface finishing In the one-to-one coupling configuration, we studied the effect of crystal surface finishing on photon collection yield as a function of DOI using Monte Carlo simulation. Fig. 2.a shows the normalized photon collection yield at one end of the crystal (output A) for different surface finishing varying from σ = 0° (polished crystals) to σ = 90°, sl = 1 (saw-cut crystals). The sensitivity of the output to DOI increases by increasing crystal surface roughness. However, for large values of σ, the output changes nonlinearly with DOI. Linear variations of output A (and hence B) results in insensitivity of the energy signal, A+B, to DOI which is desirable. In other words, non-linear dependency of the output yield on DOI will potentially degrade energy resolution. To demonstrate the effect of crystal surface finishing on energy resolution, we examined the energy spectra obtained from SiPMs coupled to polished and saw-cut LYSO crystals in a single-ended configuration (Fig. 2.b). Polished crystals provided smoother spectra and better energy resolution (14% FWHM) compared to those from saw-cut crystals (19% FWHM), they also resulted in smoother spectra with a few distinguishable peaks in them (including lead fluorescence and Compton back scattering of 511 keV photons) which could be used to evaluate the overall linearity of the SiPM and its electronic processing circuitry. In the one-to-one coupling configuration, DOI is extracted from signal asymmetry as described in Eq. 1, where A and B are the signals generated by SiPMs at the two ends of the scintillator, and k is a calibration factor obtained from calibration plot of signal asymmetry versus DOI[12] A− B . A+ B

DOI = k

(1)

110%

8000

100%

7000

90%

6000

80% 70% 60% 50% 40%

Unified 30

Increasing surface roughness from polished toward saw-cut finishing

Unified 60

30% 20% -12.5 -10

Counts

A (Normalized Light Yield)

Using an event based analysis we experimentally evaluated variations of the signal asymmetry profile with DOI from Lead fluorescence (78 keV) Positron annihilation (511 keV) Compton (170 keV)

5000 Polished, DOI = 0 mm

4000

Saw-cut, DOI = 0 mm

3000

Gamma 1.27 MeV

2000 1000

Unified 90 with sl = 1

0

-7.5

-5

-2.5

0

2.5

5

7.5

10

0

12.5

200

DOI (mm)

(a)

400

600

800

1000 1200 1400 1600 1800

ADC channel number

(b)

Fig. 2. Effect of crystal surface finishing on (a) the normalized light yield (fraction of photons received by the detector) as a function of DOI for different surface finishing obtained from Monte Carlo simulation, and (b) Experimental result of energy spectra for crystals with polished and saw-cut surface finishing.

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120

γ

Saw-cut

LYSO

90

γ

80

Polished

100 80 60 40

DOI = 0

60 50 40 30 20

20 0 -100%

DOI = 4 mm

70 511 keV counts

Normalized counts

LYSO

10 0

-75%

-50%

-25%

0%

25%

50%

75%

100%

-0.8

-0.6

-0.4

(A-B) / (A+B)

-0.2

0.0

0.2

0.4

0.6

0.8

Signal asymetry

(a)

(b)

Fig. 3. Experimental results showing (a) profile of signal asymmetry, (A-B)/(A+B), for polished and saw-cut crystals when annihilation photons enter form either side of the scintillator crystal, and (b) histogram of signal asymmetry for saw-cut crystal when DOI changes 4 mm to the right.

absorption events of annihilation photons from a 22Na source on saw-cut and polished scintillator crystals. Two extreme cases are shown in Fig. 3.a when annihilation photons enter the scintillator crystal from the front- and back-faces of the crystal through either of the SiPM detectors. The profile is plotted for the events with energy (A+B) within the main peak of the 511 keV events. The wide range of signal asymmetry of the saw-cut crystal indicates higher sensitivity to DOI compared to the polished crystal that has a narrow range of variations. Fig. 3.b shows the histograms of signal asymmetry measured at two different DOIs, 0.0 and 4.0 mm, for the scintillator crystal with saw-cut surface finishing. The DOI resolution is estimated to be (2.1 ± 0.6) mm for saw-cut scintillator crystal. Our previous results showed DOI resolution of (9.0 ± 1.5) mm for polished crystals[13]. This shows that using dual-ended readout method polished crystals can detect if the interaction happened in the left side or right side of the crystal only, while with saw-cut surface finishing it is effectively possible to resolve interactions down to slightly more than 2 mm. While increasing crystal surface roughness improves DOI resolution, it causes increased light loss for interactions taken place in the middle of long crystals resulting in degraded overall energy resolution, and excessive degradation in timing resolution[12]. 3.2. Determining Crystal Index In crystal arrays with fewer numbers of photodetectors than individual scintillator crystals, such as the one depicted in Fig 1.b, we used asymmetry of signals between neighboring detectors to determine the crystal index, i.e., the crystal in which the interaction occurs. In the dual-ended readout method, the signals of the detectors on two ends of the crystal are first added together in order for the result of asymmetry to be independent of the DOI. Equation 2 which might be viewed as a condensed form of Anger logic, describes asymmetry between neighboring detectors in dual-ended readout to identify crystal index of a detector module shown in Fig. 1.b. The asymmetry is converted to a physical position in millimeters using the conversion factor c, and the histogram of identified crystal indices was made using a bin size of 2.0 mm, matching the crystal pitch. The accuracy in resolving the correct crystal index was determined from the normalized histogram, i.e., the number times (in percent) the correct crystal was indexed.

Crystal Index Position = c

( A2 + B2 ) − ( A1 + B1 ) . A1 + A2 + B1 + B2

(2)

detector pitch of ~5.5 mm, where the accuracy of crystal identification is independent of light guide thickness. Fig. 4.a also indicates that the variation in crystal identification accuracy becomes very small for small pitch detectors. This is better illustrated in Fig. 4.b, where the accuracy is plotted against the light guide thickness for different detector pitch

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Crystal Identification Accuracy

Crystal Identification Accuracy

100% 80% 60% 40%

Light Guide Thickness (mm): 3.5 4.5 5.5 6.5 7.5

20% 0% 2

4

6

8

100% 80% 60% 40%

Detector Pitch (mm): 3 4 5 6 7 10

20% 0%

10

2

Detector Pitch (mm)

(a)

4

6

8

Light Guide Thickness (mm)

(b)

Fig. 4. Simulated accuracy in identifying scintillation crystal position index. (a) Calculated accuracy plotted as a function of detector pitch for different light guide thicknesses. (b) A plot demonstrating the effect of change in light guide thickness on crystal.

(same dataset). For 3.0 mm detector pitch, the correct crystal is detected independent of the light guide thickness, similar to one-to-one coupling. Also, it clearly shows that the trend in variation of accuracy for small detectors (up to 5 mm pitch) is decreasing with light guide thickness, and but for large detectors (greater than 6 mm pitch) the accuracy improves for thicker light guides. We understood that detectors with 5.0 mm pitch are the largest detectors that when coupled to crystals with light guide thickness of 3.5 mm result in an acceptable accuracy of 99%. 3.3. Extraction of DOI in crystal arrays using dual-ended readout method To determine the depth of interaction (DOI) within a scintillation crystal we used the asymmetry of the signals from detectors on opposite ends of the photodetector module. In order to determine DOI independent of crystal index, Equation 1 was modified to use asymmetric ratio of the sums of neighboring signals from pairs of photodetectors at ends A and B as depicted in Fig. 1b. In Equation 3, the ratio was converted to a physical measurement of the depth of interaction in millimeters by a calibration factor, k.

DOI = k

( A1 + A2 ) − (B1 + B2 ) . A1 + A2 + B1 + B2

(3)

A data set for each case of 500 error values (the difference between calculated and known DOIs) was used to plot a histogram with bin widths of 0.5 mm from which the full-width half-maxima (FWHM) were extracted to obtain the DOI resolution for each design of the detector module. These FWHM DOI resolutions were plotted in Fig. 5.a as a function of detector pitch where the general trend indicates that DOI resolution worsens with increasing light guide thickness. It can be seen that there is very little variation in resolution for changing detector pitch suggesting that the resolution may be independent of pitch. Fig. 5.b supports the trend that as light guide thickness increases, DOI resolution worsens, however this resolution is never worse than 1.9 mm ranging from 1.2 mm to 1.9 mm. The FWHM resolution is (1.5 ± 0.4) mm for any simulated dual-ended readout detector module design.

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Light Guide Thickness (mm):

3.5 5.5 7.5 2

(a)

4

6 8 Detector Pitch (mm)

4.5 6.5

DOI FWHM Resolution (mm)

DOI FWHM Resolution (mm)

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

2 1.5 1 Detector Pitch (mm): 3 4 5 6 7

0.5 0 2

10

4

6

8

Light Guide Thickness (mm)

(b)

Fig. 5. Simulated measurements of the ability of the detector module to resolve depth of interaction (DOI) within a 2 x 2 x 20 mm scintillation crystal. (a) DOI resolution as a function of detector pitch for a series of light guide thicknesses. (b) Plotted DOI resolution for increasing light guide thickness with a variety of detector pitch sizes.

4. CONCLUSIONS We achieved DOI resolution of 2.1 mm with individual scintillator crystals of 2.0 mm pitch and saw-cut surface finishing using dual-ended readout method with silicon photomultipliers in one-to-one coupling configuration. This configuration can be used to realize a detector module with isotropic detector resolution of 2 mm. Simulation of detector modules using dual-ended readout method not in one-to-one configuration showed that the accuracy in positioning the interaction in 2×2×20 mm3 scintillation crystals decreased with increasing detector pitch. Detector pitches of 6 mm and less were able to resolve the crystal index with at least 80% accuracy. Additionally, the full-width half-maximum depth of interaction resolution decreased when light guide thickness was increased. In spite of this, DOI resolution was always better than 1.9 mm with a range of 1.2 mm to 1.9 mm for all simulated cases. This suggests that dual-ended readout method in not one-to-one configuration is applicable to pixilated scintillator blocks for DOI-PET, possibly for multimodality PET/MRI applications. Results from this study will aid in the optimization of our detector module performance and design.

5. ACKNOWLEDGEMENTS AND AFFILIATION This research was supported in part by the Canadian Institutes of Health Research (CIHR) Strategic Research Training Fellowship, the Sunnybrook Health Sciences Centre, Thunder Bay Regional Research Institute, and the Ontario Graduate Student Scholarship. Sarah Cuddy is a graduate student in the Department of Medical Biophysics at the University of Toronto and Sunnybrook Health Science Centre. Farhad Taghibakhsh is a post-doctoral research fellow at Department of Medical Biophysics, University of Toronto. He is also a CIHR Strategic Research Training Fellow at Department of Radiation Oncology, University of Toronto.

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