Biomechanical Analysis of Bone Properties Using 3-Point Bending and the BoneJ Plug-in in ImageJ Mark Begonia1, Ganesh Thiagarajan1, Amber Rath Stern1,2 1 Department

of Civil and Mechanical Engineering

School of Computing and Engineering University of Missouri-Kansas City 2 Engineering

Systems, Inc., Charlotte, NC

Preliminary Steps: STEP 1A: Download and install ImageJ http://rsbweb.nih.gov/ij/download.html Notes on installation process: 1. Select a computer with sufficient RAM (16 GB used for these analyses) 2. Check the operating system and then download the appropriate version

STEP 1B: Download and install the BoneJ plug-in http://bonej.org/ Notes about the webpage: • Shows how to cite software usage in references/bibliography • Provides directions and tips for installation • Gives basic definitions for each parameter

STEP 2: Review literature on bone biomechanical properties and testing Engineering concepts and relations to bone:

Measurement of various bone properties:

1.

1.

2. 3.

Sharir, A., et al. (2008). "Whole bone mechanics and mechanical testing." The Veterinary Journal 177(1): 8-17. Turner, C. H. (2006). "Bone strength: current concepts." Ann N Y Acad Sci 1068: 429-446. Beaupied, H., et al. (2007). "Evaluation of macrostructural bone biomechanics." Joint Bone Spine 74(3): 233-239.

2. 3.

Schriefer, J. L., et al. (2005). "A comparison of mechanical properties derived from multiple skeletal sites in mice." J Biomech 38(3): 467-475. Akhter, M. P., et al. (2001). "Bone biomechanical properties in prostaglandin EP1 and EP2 knockout mice." Bone 29(2): 121-125. Akhter, M. P., et al. (2004). "Bone biomechanical properties in LRP5 mutant mice." Bone 35(1): 162-169.

Preliminary Steps: STEP 3: Gather and organize all the required data 1. Three point bending test data from the loading system (Bose ElectroForce 3220) 2. Data sheets (PDFs) with specimen information, pre-test measurements, and post-test measurements 3. DICOM files from microCT

SCHEMATIC OF 3-POINT BENDING TEST Left Fracture Distance (Fx-Left)

Right Fracture Distance (Fx-Right)

Distal (Left-Side)

Proximal (Right-Side)

Left Overhang (LO)

Span (7.65 mm)

Length = LO + Span + RO

Right Overhang (RO)

Preliminary Steps: STEP 4: Review the biomechanical parameters to determine which ones are critical to report

Biomechanical Parameters Obtained from BoneJ Ultimate Load (N) Stiffness (N/mm) Work to Failure (mJ = N*mm) Volume (mm3) Minimum Area Moment of Inertia (mm4) Maximum Area Moment of Inertia (mm4) Cross-sectional Area (mm2) Minor Axis Radius (mm) Major Axis Radius (mm) Young’s Modulus (GPa = N/mm2)

These 3 parameters are obtained by analyzing the three point bending test data in either Microsoft Excel or GraphPad PRISM This parameter is obtained by analyzing a range of DICOM images with the BoneJ plug-in. These 5 parameters are obtained by analyzing a single DICOM image with the BoneJ plug-in. This parameter is obtained by using an equation that incorporates the Stiffness parameter, Span, and Area Moment of Inertia (BoneJ result)

Preliminary Steps: STEP 5: Find the Excel template files for organizing results 1. Excel file #1 – Ultimate Load (N) and Stiffness (N/mm) 2. Excel file #2 – Work to Failure (mJ = N*mm) 3. Excel file #3 – DICOM Parameters  Volume (mm3)  Minimum area moment of inertia (mm4)  Maximum area moment of inertia (mm4)  Cross-sectional area (mm)  Minor axis radius (mm)  Major axis radius (mm)  Young’s modulus (GPa = 1000 MPa = 1000 N/mm2) 4. Excel file #4 – Summary

Notes for this step: • Create copies of the Excel templates; do not overwrite the existing information • Import data for each sample onto different sheets and label the sheets accordingly • The summary file (#4) should be used to provide collaborators with immediate results • The other files (#1-3) are only needed if someone wishes to know all the details for obtaining a particular parameter

STEP 6: Calculate the Ultimate Load STEP 6A: Import Bose data into Excel file #1 STEP 6B: Keep only the time, displacement, and load values STEP 6C: Create 2 columns for the positive displacement and load values (PDISP, PLOAD) STEP 6D: Create 2 columns for the normalized displacement and load values (NDISP, NLOAD) STEP 6E: Create an xy-scatter plot of load vs displacement (i.e. use the NLOAD and NDISP data) STEP 6F: Use the =MAX() function to find the max NLOAD Notes: 1. X-data = displacements and y-data = loads 2. The terms “Load” and “Force” are the same 3. The terms “Displacement” and “Deflection” are the same 4. The normalized load-displacement plot provides an easier-to-read graph with the data starting at zero

STEP 7: Calculate the Stiffness STEP 7A: Create a copy of the xy-scatter plot for load vs displacement STEP 7B: Change the x-axis to show only the linear region of the curve STEP 7C: Add a trend line and edit the trend line options to show the equation and R2 value STEP 7D: Edit the x and y data ranges so only the linear region of the plot is shown STEP 7E: Repeat steps 7B and 7D until R2 > 0.99 STEP 7F: The value for Stiffness is the number next to the “x” in the trend line equation

STEP 8: Calculate the Work to Failure STEP 8A: Create a copy of Excel file #1 and save it as Excel file #2 (refer to Slide #5) STEP 8B: On the load-displacement plot, identify where fracture occurred (i.e. large drop-off) STEP 8B: Apply this equation to the data range up to the fracture load and displacement ∆𝑥

𝑦1 + 𝑦2 2

where Δx = x2 - x1 = change in displacement where y1 and y2 = load values at t1 and t2

Notes: 1. The first Work to Failure (i.e. WTFAILURE) value will be zero and ensuing values will be either (+) or (-) 2. When reporting results, use the Total Work To Failure (i.e. TOTAL WTF) value 3. TOTAL WTF is the sum of all the WTFAILURE values leading up to the fracture load

Fracture

Shaded Region = Work to Failure

EXTRA: Example Plots from Literature Turner, C. H. (2008). "Bone strength: current concepts." Ann N Y Acad Sci 1088: 429-448.

Beaupied, H., et al. (2008). "Evaluation of macrostructural bone biomechanics." Joint Bone Spine 84(3): 233-239.

Vanleene, M., et al. (2011). "Transplantation of human fetal blood stem cells in the osteogenesis imperfecta mouse leads to improvement in multiscale tissue properties." Blood 118(3): 1053-1080.

STEP 9: Organize Data Sheet Info STEP 9A: Create a table of pre-test measurements for each sample in Excel file #3 Length

Pre-test Measurements Span

Distance between the two bottom supports

Length

Length of the entire bone

Left Overhang

Distance from left support to DISTAL end of bone

Right Overhang

Distance from right support to PROXIMAL end of bone

Fx Le

Fx Right

Le (Distal)

RIGHT (Proximal)

Le Overhang

Span

Right Overhang

STEP 9B: Record additional information included in the three-point bending data sheets Additional Information Caliper at Midpoint – Min. Diameter

Measured at the center of the bone in units of mm

Caliper at Midpoint – Max. Diameter

Measured at the center of the bone in units of mm

Weight

Measured in units of g

Post-test Fracture Location – Fx Left

Measured starting at the DISTAL end of bone in units of mm

Post-test Fracture Location – Fx Right

Measured starting at the PROXIMAL end of bone in units of mm

STEP 9: Organize Slice Info STEP 9C: Create a table for initial slice information for each sample in Excel file #3 Initial Slice Information First DICOM Slice

Slice # for the first image of DICOM stack

Last DICOM Slice

Slice # for the last image of DICOM stack

First Bone Slice

Slice # for the first image that bone is shown

Last Bone Slice

Slice # for the last image that bone is shown

Middle Bone Slice

= (Last Bone Slice # - First Bone Slice #)/2 + First Bone Slice # 10.5 µm

Slice Thickness 0.0105 mm

Notes: 1. For Slice Thickness, either calculate the value in units of (mm) or simply type in the value 2. Do not type in the units of the slice thickness because ensuing equations will not calculate properly

STEP 10: Import DICOMs into ImageJ STEP 10A: Drag-and-drop the folder of DICOM images for an individual specimen into ImageJ STEP 10B: Leave the checkboxes unmarked in the Open Folder and then select Yes

STEP 11: Optimize Threshold STEP 11A: Select the Optimise Threshold option STEP 11B: Mark the checkboxes in the Options window and then select OK Notes on Optimise Threshold: 1. This procedure converts the DICOM stack from grayscale to binary (i.e. black & white) 2. Bone should appear black on a white background 3. Manual thresholding may be necessary for some DICOM stacks

STEP 12: Remove Artifacts Automatically STEP 12A: To automatically remove some artifacts, use the Despeckle command STEP 12B: Select Yes when asked to process the entire DICOM stack, Notes on automated artifact removal: 1. Despeckle will also smooth the edges of the bone surfaces 2. Check the trabecular bone regions to see if Despeckle removed too many details 3. Despeckle does not remove all artifacts; therefore, resort to other automated and manual methods

Rougher Bone Surface Cluster of artifacts

Large artifact

Smaller artifacts still present

Smoother Bone Surface

Cluster removed

Larger artifact still present

STEP 12: Remove Artifacts Automatically STEP 12C: To automatically remove slightly larger artifacts, use the Remove Outliers command STEP 12D: Keep the default values for Radius, Threshold, and Which outliers and then select OK Notes on automated artifact removal: 1. Select the Preview option to see how many artifacts can be removed using this option 2. Some artifacts may still be present; therefore, proceed with manual removal of artifacts

Smaller artifacts completely removed

Larger artifact reduced significantly

STEP 12: Remove Artifacts Manually STEP 12E: To manually remove artifacts, draw a selection on a slice (default shape is rectangular) STEP 12F: If needed, change the selection Properties to adjust the boundary color, thickness, etc. Rectangular selected

Artifact

Boundary of Rectangular section

Keyboard Shortcuts:  CTRL + Y = Change the properties of the selection (e.g. color, thickness)

STEP 12: Remove Artifacts Manually STEP 12G: For larger artifacts outside the bone, use the rectangular selection Keyboard Shortcuts: STEP 12H: Select the Fill option  Backspace = Delete contents of Notes on editing selections: the selection 1. When switching between different slices, the selection does not move  CTRL + F = Fill in the selection 2. To move a selection, left-click inside it and drag the mouse 3. To draw a different selection, left-click outside the existing selection

STEP 12: Remove Artifacts Manually STEP 12I: For artifacts inside or close to the bone, use a selection that has a different shape Notes selection shapes: 1. Circular selections are better for removing internal artifacts 2. Rectangular selections are better for larger artifacts outside the bone

STEP 13: Save a New DICOM Stack STEP 13A: When artifact removal is complete, save the edited DICOM stack STEP 13B: Create a New Folder for storing the new DICOM stack STEP 13C: For the File name, insert a space between the slice name and 4-digit number

Notes on saving a new DICOM stack: 1. The space between the slice name and 4-digit number makes it easier to read sample names 2. Saving a new DICOM stack saves time since artifacts will not have to be removed again

STEP 14: Realign Bone Slices STEP 14A: Select the Moments of Inertia command STEP 14B: Enter the values for the Start Slice and End Slice STEP 14C: Deselect the option to Show axes (3D) and then click OK Notes on Moments of Inertia: 1. Start Slice and End Slice should show bone 2. Bone will now appear white on a black background

STEP 14: Calculate the Volume STEP 14D: Copy the contents of the Results file into Excel file #3 Notes on Moments of Inertia: 1. The volume (mm3) can be found in the 4th column of the Results file 2. Refer to the BoneJ website for definitions on the other parameters shown below (which have not been reported by this group)

STEP 15: Calculate the Young’s Modulus STEP 15A: First identify the 10 Mid-Span Slices that need to be analyzed

STEP 15: Calculate the Young’s Modulus STEP 15B: Then calculate the Area Moment of Inertia Notes on the area moment of inertia used for this analysis: 1. This value is a weighted average that is calculated using 10 total slices across the mid-span a) 5 slices are distal to the central slice in the mid-span b) 5 slices are proximal to the central slice in the mid-span 2. Higher weighting is assigned to the slices that are closer to the mid-span Area Moment of Inertia

𝐼𝐷−𝑀𝑆 = 0.20 𝐼𝐷10 + 0.10 𝐼𝐷20 + 0.10 𝐼𝐷30 + 0.05 𝐼𝐷40 + 0.05 𝐼𝐷50

𝐼 = 𝐼𝐷−𝑀𝑆 + 𝐼𝑃−𝑀𝑆

𝐼𝑃−𝑀𝑆 = 0.20 𝐼𝑃10 + 0.10 𝐼𝑃20 + 0.10 𝐼𝑃30 + 0.05 𝐼𝑃40 + 0.05 𝐼𝑃50 where ID-MS = weighted area moment of inertia for slices Distal to the Mid-Span where IP-MS = weighted area moment of inertia for slices Proximal to the Mid-Span where #’s 10-50 represent the slice #’s distal or proximal to the Mid-Span Span MidSpan

Young’s Modulus

Distal

5 Distal Slices

5 Proximal Slices Central Slice

Proximal

𝑆𝑙 3 𝐸= 48𝐼 where S = elastic stiffness where l (cursive lowercase “L”) = span where I (uppercase “i”) = area moment of inertia

STEP 15A: Identify the 10 Mid-Span Slices STEP 15A-1: Copy the Stiffness and Span values into the SUMMARY sheet in Excel file #3 STEP 15A-2: Record information from 3-point bending data sheets into Excel file #3

STEP 15A: Identify the 10 Mid-Span Slices STEP 15A-3: Identify the first and last DICOM slices that show bone Notes on specifying the range of bone slices: 1. The First/Last Bone Slice will not always be the same as the First/Last DICOM Slice 2. Realignment of slices (STEP 14) often changes the total number of DICOM images for a sample

First bone slice is Slice #77, not Slice #1

Last bone slice is Slice #1672, not Slice #1674

STEP 15A: Identify the 10 Mid-Span Slices STEP 15A-4: Determine the bone orientation (Distal vs Proximal) for the slices at the beginning Notes on identifying the proper bone orientation: 1. There is no standard orientation in the microCT (i.e. distal-proximal or proximal-distal are possible) 2. Proximal end marked by the femur head and greater trochanter (i.e. two structures in the DICOM stack) 3. Distal end marked by the epiphysis (i.e. one structure in the DICOM stack)

Slices at the beginning of this stack show the epiphysis of the femur

Slices at the end of this stack show both the femur head and greater trochanter

STEP 15A: Identify the 10 Mid-Span Slices STEP 15A-5: Select the corresponding table of slices for analysis Notes on using the correct table: 1. After selecting the correct table, black out the other one 2. The Excel formulas and values will still remain intact 3. Slices are spaced apart in increments of 10, but this can be modified to higher increments to analyze a larger range of slices across the mid-span

STEP 15B: Calculate the Moment of Inertia STEP 15B-1: Move the slider to locate the desired slice STEP 15B-2: Select the Slice Geometry command STEP 15B-3: Select the type of bone and then click OK Notes on using Slice Geometry: 1. If needed, an annotated slice can be saved (Annotated_Aligned_) 2. Always perform Slice Geometry in ascending order (i.e. Slice D10-D50 or Slice P10-P50) 3. Otherwise, the wrong weightings will be assigned

STEP 15B: Calculate the Moment of Inertia STEP 15B-4: Store the results in the Slice Geometry Results sheet of Excel file #3 Notes on using Slice Geometry: 1. Perform Slice Geometry on all 10 slices before transferring the results to Excel 2. The minimum area moment of inertia values (i.e. Imin) are used to calculate a weighted average (IW-AVG)

Area Moment of Inertia 𝐼 = 𝐼𝑊−𝐴𝑉𝐺 = 𝐼𝐷−𝑀𝑆 + 𝐼𝑃−𝑀𝑆

𝐼𝐷−𝑀𝑆 = 0.20 𝐼𝐷10 + 0.10 𝐼𝐷20 + 0.10 𝐼𝐷30 + 0.05 𝐼𝐷40 + 0.05 𝐼𝐷50 𝐼𝑃−𝑀𝑆 = 0.20 𝐼𝑃10 + 0.10 𝐼𝑃20 + 0.10 𝐼𝑃30 + 0.05 𝐼𝑃40 + 0.05 𝐼𝑃50

Unweighted Calculation Javaheri, B. et al. (2014). “Deletion of a Single β-Catenin Allele in Osteocytes Abolishes the Bone Anabolic Response to Loading." Journal of Bone and Mineral Research 29(3): 705-715.

where ID-MS = weighted area moment of inertia for slices Distal to the Mid-Span where IP-MS = weighted area moment of inertia for slices Proximal to the Mid-Span where #’s 10-50 represent the slice #’s distal or proximal to the Mid-Span

STEP 15B: Calculate the Moment of Inertia STEP 15B-5: Save DICOM parameters (Imin, Imax, CSA, R1, and R2) in another sheet in Excel file #3 STEP 15B-6: Calculate the weighted average for all DICOM parameters Notes on calculating weighted averages: 1. Excel file #3 will already have the weighted formula built in for Imin 2. Copy the equation in IMIN WTD AVG over to the other cells to calculate the remaining weighted averages

STEP 15: Calculate the Young’s Modulus STEP 15C: Use the summary sheet in Excel file #3 and the equation below to calculate the modulus Notes on calculating Young’s Modulus: 1. In general, the units should be in N/mm2 or MPa 2. If the modulus is a 4-digit number or larger (e.g. 4730 MPa), divide by 1000 and report 4.73 GPa instead

Young’s Modulus

𝑆𝑙 3 𝐸= 48𝐼

where S = elastic stiffness where l (cursive lowercase “L”) = span where I (uppercase “i”) = area moment of inertia

EXTRA: Effects of Contouring DICOMs Notes on the benefits of analyzing contoured DICOM images:  “Contouring” DICOM images in the microCT software will remove x-ray artifacts and generate a DICOM stack using a volume of interest (VOI) that mainly consists of the bone

Without contouring, artifacts from the microCT scanner could still appear

With contouring, artifacts from the microCT scanner should be removed

EXTRA: Effects of Contouring DICOMs

With contouring, the field of view diminishes but removes artifacts in the process

Without contouring, the field of view is larger and could still contain artifacts

Acknowledgments BoneJ developers Doube, M., et al. (2010). "BoneJ: Free and extensible bone image analysis in ImageJ." Bone 47(6): 1076-1079.

Mark Dallas Department of Oral and Craniofacial Sciences, School of Dentistry University of Missouri-Kansas City

Mark L. Johnson Department of Oral and Craniofacial Sciences, School of Dentistry University of Missouri-Kansas City

Dan Nicolella Materials Engineering Department, Mechanical Engineering Division Southwest Research Institute