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.
|2016||Currier EJ. Predicting Peak Load of the Femoral Neck Using Structural Parameters [Master's thesis]. Urbana, IL: 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.|
|2009||Pan B, Qian K, Xie H, Asundi A. Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol. June 2009;20(6):062001.|
|1999||Bay BK, Smith TS, Fyhrie DP, Saad M. Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech. September 1999;39(3):217-226.|
|2011||Donnelly E. Methods for assessing bone quality: a review. Clin Orthop Relat Res. August 2011;469:2128-2138.|
|1989||Kuhn JL, Goldstein SA, Ciarelli MJ, Matthews LS. The limitations of canine trabecular bone as a model for human: a biomechanical study. J Biomech. 1989;22(2):95-107.|
|1999||Bell KL, Loveridge N, Power J, Garrahan N, Meggitt BF, Reeve J. Regional differences in cortical porosity in the fractured femoral neck. Bone. January 1999;24(1):57-64.|
|2014||Gillard F, Boardman R, Mavrogordato M, Hollis D, Sinclair I, Pierron F, Browne M. The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression. J Mech Behav Biomed Mater. January 2014;29:480-499.|
|2007||Liu L, Morgan EF. Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomech. 2007;40(15):3516-3520.|
|2010||Bouxsein ML, Boyd SK, Christiansen BA, Guldberg RE, Jepsen KJ, Müller R. Guidelines for assessment of bone microstructure in rodents using micro-computed tomography. J Bone Miner Res. July 2010;25(7):1468-1486.|
|2003||Cooper DML, Turinsky AL, Sensen CW, Hallgrímsson B. Quantitative 3D analysis of the canal network in cortical bone by micro-computed tomography. Anat Rec. September 2003;274B(1):169-179.|
|2006||Augat P, Schorlemmer S. The role of cortical bone and its microstructure in bone strength. Age Ageing. September 2006;35(suppl 2):ii27-ii31.|
|1997||Silva MJ, Gibson LJ. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone. 1997;21(2):191-199.|
|1970||Galante J, Rostoker W, Ray RD. Physical properties of trabecular bone. Calcif Tiss Res. 1970;5(1):236-246.|
|1974||Bargren JH, Bassett CAL, Gjelsvik A. Mechanical properties of hydrated cortical bone. J Biomech. May 1974;7(3):239-245.|
|2010||Cory E, Nazarian A, Entezari V, Vartanians V, Müller R, Snyder BD. Compressive axial mechanical properties of rat bone as functions of bone volume fraction, apparent density and micro-CT based mineral density. J Biomech. 2010;43(5):953-960.|
|2012||Abdel-Wahab AA, Maligno AR, Silberschmidt VV. Micro-scale modelling of bovine cortical bone fracture: analysis of crack propagation and microstructure using X-FEM. Comp Mater Sci. February 2012;52(1):128-135.|
|2006||Seeman E, Delmas PD. Bone quality: the material and structural basis of bone strength and fragility. NEJM. May 25, 2006;354(21):2250-2261.|
|2004||Riggs BL, Melton LJ III, Robb RA, Camp JJ, Atkinson EJ, Peterson JM, Rouleau PA, McCollough CH, Bouxsein ML, Khosla S. Population-based study of age and sex differences in bone volumetricdensity, size, geometry, and structure at different skeletal sites. J Bone Miner Res. December 2004;19(12):1945-1954.|
|2013||Kersh ME, Pandy MG, Bui QM, Jones AC, Arns CH, Knackstedt MA, Seeman E, Zebaze RMD. The heterogeneity in femoral neck structure and strength. J Bone Miner Res. May 2013;28(5):1022-1028.|
|2004||Hellmich C, Ulm F-J, Dormieux L. Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? arguments from a multiscale approach. Biomech Model Mechanobiol. June 2004;2(4):219-238.|
|2015||Palanca M, Tozzi G, Cristofolini L, Viceconti M, Dall'Ara E. Three-dimensional local measurements of bone strain and displacement: comparison of three digital volume correlation approaches. J Biomech Eng. July 2015;137(7):071006.|
|1998||Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.|