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![Page 1: Towards implementation of a Digital Volume Correlation method for measurement of displacements and strain in trabecular bone Bryant Roberts, Egon Perilli,](https://reader035.fdocument.org/reader035/viewer/2022062721/56649f265503460f94c3dee5/html5/thumbnails/1.jpg)
Towards implementation of a Digital Volume Correlation method for measurement of displacements
and strain in trabecular bone
Bryant Roberts, Egon Perilli, Karen Reynolds
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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
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Problem
How accurate are these models?
How can we validate these models?
A technique for direct measurement of displacements and strain?
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ProblemTraditional methods…
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Extensometer observes strain across 20mm sample of trabecular bone (Adapted from [1])
[1] Perilli, E et al. 2008 Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur, J Biomech, 41, 438-446
L = 20 mm, Ø = 10 mm
Digital reconstruction of cancellous bone sample pre- and post- loading. Large strain across sample is observed (from [1])
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Problem…impractical for single trabecula
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Single trabecula of ~1mm length within an aluminium foam sample (Adapted from [2])
[1] Verhulp, E et al. 2004 A three-dimensional digital image correlation technique for strain measurements in microstructures, J Biomech, 37, 1313-1320
0.91
mm
1.01 mm
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Proposed SolutionDigital Volume Correlation (DVC)1
– Takes image volumes from micro-CT and tracks displacement of microstructural features within sample
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[1] Bay, B et al. 1999 Digital volume correlation: three-dimensional strain mapping using x-ray tomography, Exp Mech, 39(3), 217-226
5002 pixel μ-CT images of (left) unloaded bone sample and (right) deformed bone sample with feature tracked throughout
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Aim
Identify, and implement a suitable DVC method for measurement of internal displacements and strains
within trabecular bone
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MethodCoarse-Fine search implementation1
1) Global whole pixel search using NCC2
2) Refined sub-pixel computations using Lucas-Kanade algorithm3
Capable of producing displacement measurements in 2D
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[1] Jandejsek et al. 2011 Precise strain measurement in complex materials using DVC and time lapse micro-CT, Procedia Eng, 10, 1730-1735[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), 221-255
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1 Global Search
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• Unloaded subset translated over all possible whole pixel positions of deformed image
mn
n
(m + n) - 1
(m +
n)
- 1
Unloaded image subsetDeformed image
Correlation matrix, stores values [-1, 1]
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1 Global Search
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2 Sub-pixel refinement
• Lucas-Kanade algorithm
Gauss-Newton gradient descent algorithm minimising the sum-of-squared error between the subset and deformed image
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2 Sub-pixel refinement• Lucas-Kanade algorithm
– Warps pixel co-ordinates of the subset to corresponding positions in deformed image
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Displacement Accuracy
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12.5 pix
12.5
pix
Deformed image from digital translationw/ grid of measurement pointsUnloaded image
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Results
Measurement
Points (nr)Accuracy ± Precision*
(pixels)
Computation Time (min:sec)
529x: 12.5074 ± 0.1195
y: 12.4964 ± 0.1091 9:02
1024x: 12.5035 ± 0.1151
y: 12.5007 ± 0.116315:54
2025x: 12.5036 ± 0.1115
y: 12.4984 ± 0.115032:24
*Accuracy reported as the average of displacement measurements and precision reported as the RMSE
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Range of all displacement measurementsx: [11.3440, 13.5290]y: [11.5681, 13.6017]
For displacements of 12.5 pixels along x- and y- axes
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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
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[1] Bay, B et al. 1999 Digital volume correlation: three-dimensional strain mapping using x-ray tomography, Exp Mech, 39(3), 217-226[2] Verhulp, E et al. 2004 A three-dimensional digital image correlation technique for strain measurements in microstructures, J Biomech, 37, 1313-1320
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Future Focus
• Extending function of current program– Computation of strain– Handling undesirable displacements
• For consideration– Handling of 3D images– More efficient Inverse Compositional LK
algorithm for improved performance
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Future Focus
Jandejsek et al. report maximal displacement errors within 0.001 pixel
Acceptable tool for validation of full range of strains in μFEM
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Additional Outcomes
ABEC 2012 Abstract Presentation in Brisbane
Future review article for submission- Journal of Biomechanics
- Computer Methods in Biomechanics and Biomedical Eng.
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Thank You
Questions?