Error Estimation in Whole Bone Microstrain Measurement When Using Digital Volume Correlation

Micro-CT scanning of murine femurs before and after uniaxial compression produce 3- dimensional images detailing changes within the bone micro-architecture. Digital volume correlation (DVC) is a mathematical technique used to determine strain within the bone volume, by tracing the dislocation of a pattern between the 3-dimensional images. Uncertainty in the microstrain calculated arises due to limitations in microscopy, the absence of a homogeneously distributed pattern within the bone volume, and inconsistency the methodology used to process the micro-CT scans and microstrain data.

The uncertainty in strain was quantified as strain error (SE), measured by analyzing repeated micro-CT scans of an uncompressed bone. The Minimum SE quantified was ±180- 225µϵ in accuracy (mean), with a 1100-2100µϵ precision (standard deviation)in rats; ±10- 150µϵ in accuracy, with a 1100-1700µϵ precision in mice. SE displays a regular random distribution throughout the bone volume, centered about 0µϵ and showing strain in both tension and compression.

The minimum SE is obtained by optimizing the DVC input parameters using a design of experiments (D0E). A sub-volume size of 43-55 voxels with a 50-75% volume overlap between consecutive steps of the DVC yielded the lowest SE at the highest strain resolution within the bone sub-volume. A strain error resolution (SER) of ±2500µϵ encapsulates over 90% of the SE, and is chosen as the minimum strain value that is viable when evaluating microstrain from a compression test of the bone. Any strain within the SER limits are eliminated from a viable set of microstrain value, believed to either be error or minimally contributing to the macroscopic properties of the bone.

SER of ±2500µϵ results in a displacement uncertainty of 9-11mum within the bone subvolume. A visual inspection of the repeated scans shows an uncertainty of 2.5 voxels between the 2 images when imaged at a nominal resolution of 4-5µm. The use of monochromatic x-rays (such synchrotron x rays) can increase resolution and reduce the signal-to-noise ratio in the CT scanning process, thus reducing the SE calculated by DVC.

Year	Entry
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2017	Bakalova LP. Relating Cortical Bone Mechanics to Intracortical Pore Morphology, Distribution and Remodeling History Within the Fibula Diaphysis [Master's thesis]. Urbana, IL: University of Illinois at Urbana-Champaign; 2017.
2014	Roberts BC, Perilli E, Reynolds KJ. Application of the digital volume correlation technique for the measurement of displacement and strain fields in bone: a literature review. J Biomech. March 21, 2014;47(5):923-934.
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Year

Entry

2017

Tozzi G, Dall’Ara E, Palanca M, Curto M, Innocente F, Cristofolini L. Strain uncertainties from two digital volume correlation approaches in prophylactically augmented vertebrae: local analysis on bone and cement-bone microstructures. J Mech Behav Biomed Mater. March 2017;67:117-126.

2016

Currier EJ. Predicting Peak Load of the Femoral Neck Using Structural Parameters [Master's thesis]. University of Illinois at Urbana-Champaign; 2016.

2008

Keaveny TM, Hoffmann PF, Singh M, Palermo L, Bilezikian JP, Greenspan SL, Black DM. Femoral bone strength and its relation to cortical and trabecular changes after treatment with PTH, alendronate, and their combination as assessed by finite element analysis of quantitative CT scans. J Bone Miner Res. December 2008;23(12):1974-1982.

2017

Bakalova LP. Relating Cortical Bone Mechanics to Intracortical Pore Morphology, Distribution and Remodeling History Within the Fibula Diaphysis [Master's thesis]. Urbana, IL: University of Illinois at Urbana-Champaign; 2017.

2014

Roberts BC, Perilli E, Reynolds KJ. Application of the digital volume correlation technique for the measurement of displacement and strain fields in bone: a literature review. J Biomech. March 21, 2014;47(5):923-934.