Nonlinear micro‐CT based FE modeling of trabecular bone—Sensitivity of apparent response to tissue constitutive law and bone volume fraction

Abstract

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

Damage Function of a Quasi-Brittle Material, Damage Rate, Acceleration and Jerk during Uniaxial Compression: Model and Application to Analysis of Trabecular Bone Tissue Destruction

“…In experiments, only part of the damage is visible on the surface of the sample, and although more complete data on the structure and properties of the material can be obtained, for example, using tomography, experimental data alone are not sufficient to better understand the process of damage accumulation [24][25][26]. Additional data can be obtained using mathematical modeling [27].…”

“…The samples were loaded until destruction a = 0.005 mm/s that, according to (20), corresponds to ,ε = 0.000625 1 0.0625% strain per second). The experimental curve from [26]…”

“…Let us consider the application of Equations ( 10)- (26) to the modeling of a sample of trabecular bone tissue. As the initial data, we used the results of experiments published in [26].…”

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

“…Parallel to the work conducted on modelling human bone, there have been efforts to model bone of several animals. Studies range from small animals such as mice [287,[329][330][331][332][333][334][335][336], rats [288,[337][338][339][340][341][342][343] and zebrafish [344], to medium-sized animals such as dogs [345], as well as large animals such as pigs [346][347][348][349][350][351][352], sheep [353][354][355], bovine [220,[356][357][358][359][360][361][362][363] and horses [273,364].…”

“…Research directives within the field of animal bone modelling and analysis include 12A 1 -12A 3 . 12A 1 : Usage of animal bone experimental data to estimate mechanical properties [220,287,288,330,331,340,342,347,363,369] and conception of animal bone failure models [331,338,349,351,356,358,362] that may be similar to human bone failure models [342,344,370]. This directive includes studies in which pathological changes to the skeleton are purposefully induced in test animals by genetic manipulation [371] or malnutrition [332,338,354] in order to create models to study osteoporosis [338,354].…”