1. Bryant Roberts, Egon Perilli, Karen Reynolds
Towards implementation of a Digital Volume Correlation method for measurement of displacements and strain in trabecular bone
Bryant Roberts, Egon Perilli, Karen Reynolds

2. Project Context
A focus of MDRI research towards development of μFEM from micro-CT
Projects include
orthopaedic screw insertion into the trabecular bone of the human femoral head; and
human vertebral body under compressive load

3. Problem
How accurate are these models? How can we validate these models? A technique for direct measurement of displacements and strain?

4. Problem Traditional methods… L = 20 mm, Ø = 10 mm
Digital reconstruction of cancellous bone sample pre- and post- loading. Large strain across sample is observed (from [1])
L = 20 mm, Ø = 10 mm
Extensometer observes strain across 20mm sample of trabecular bone (Adapted from [1])
[1] Perilli, E et al Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur, J Biomech, 41,

5. …impractical for single trabecula
Problem
…impractical for single trabecula
0.91 mm
1.01 mm
Single trabecula of ~1mm length within an aluminium foam sample (Adapted from [2])
[1] Verhulp, E et al A three-dimensional digital image correlation technique for strain measurements in microstructures, J Biomech, 37,

6. Proposed Solution Digital Volume Correlation (DVC)1
Takes image volumes from micro-CT and tracks displacement of microstructural features within sample
5002 pixel μ-CT images of (left) unloaded bone sample and (right) deformed bone sample with feature tracked throughout
[1] Bay, B et al Digital volume correlation: three-dimensional strain mapping using x-ray tomography, Exp Mech, 39(3),

7. Aim
Identify, and implement a suitable DVC method for measurement of internal displacements and strains within trabecular bone

8. Method Coarse-Fine search implementation1
Global whole pixel search using NCC2
Refined sub-pixel computations using Lucas-Kanade algorithm3
Capable of producing displacement measurements in 2D
[1] Jandejsek et al Precise strain measurement in complex materials using DVC and time lapse micro-CT, Procedia Eng, 10,
[2] Lewis, J.P. n.d., Fast Normalized Cross-Correlation, Industrial Light & Magic
[3] Baker, S. & Matthews, I. 2004, Lucas-Kanade 20 years on: a unifying framework, Int J Comput Vision, 56(3),

9. 1 Global Search
Unloaded subset translated over all possible whole pixel positions of deformed image m n
(m + n) - 1
Unloaded image subset
Deformed image
Correlation matrix, stores values [-1, 1]

10. 1 Global Search

11. 2 Sub-pixel refinement Lucas-Kanade algorithm
Gauss-Newton gradient descent algorithm minimising the sum-of-squared error between the subset and deformed image

12. 2 Sub-pixel refinement Lucas-Kanade algorithm
Warps pixel co-ordinates of the subset to corresponding positions in deformed image 12

13. Displacement Accuracy
12.5 pix
Deformed image from digital translation
w/ grid of measurement points
Unloaded image

14. Computation Time (min:sec)
Results
For displacements of 12.5 pixels along x- and y- axes
Measurement
Points (nr)
Accuracy ± Precision*
(pixels)
Computation Time (min:sec)
529
x: ±
y: ±
9:02
1024
x: ±
y: ±
15:54
2025
x: ±
y: ±
32:24
*Accuracy reported as the average of displacement measurements and precision reported as the RMSE
Range of all displacement measurements
x: [ , ]
y: [ , ]

15. Conclusions Measurements precision 0.11 pixels (1.914 μm)
1.23 μm error is reliable for mapping of elastic strain across whole sample1
2.0 μm error useful for strain in single trabecula beyond yield strain2
Time linearly increasing with number of points
Hours/days required to compute dense fields
[1] Bay, B et al Digital volume correlation: three-dimensional strain mapping using x-ray tomography, Exp Mech, 39(3),
[2] Verhulp, E et al A three-dimensional digital image correlation technique for strain measurements in microstructures, J Biomech, 37,

16. Future Focus Extending function of current program For consideration
Computation of strain
Handling undesirable displacements
For consideration
Handling of 3D images
More efficient Inverse Compositional LK algorithm for improved performance

17. Future Focus
Jandejsek et al. report maximal displacement errors within pixel Acceptable tool for validation of full range of strains in μFEM

18. Additional Outcomes ABEC 2012 Abstract Presentation in Brisbane
Future review article for submission
- Journal of Biomechanics
- Computer Methods in Biomechanics and Biomedical Eng.

19. Thank You
Questions?