Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion

Abstract

Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.

Experimental validation of finite element predicted bone strain in the human metatarsal

“…The elastic moduli for early isotropic models have been homogeneous (171)(172)(173), but more recent studies have used inhomogeneous materials (8,164,165,170,174-178) as they have been found to be more accurate than the models using homogeneous material properties (9,179,180). For inhomogeneous material properties, the elastic modulus is typically estimated using empirical equations that relate the bone density to modulus.…”

“…Density-elasticity relationships have also been developed using optimization techniques for the human femur (8,194,195), tibia (8,196), humerus (8), radius (8), and ulna (197).…”

“…An elastic modulus was subsequently assigned to each element based on 1) a previously published density-elasticity relationship (Figure 3-3a), or 2) density-elasticity relationships obtained through optimization (see Density-Elasticity Equations and Optimization). The Poisson's ratio for all elements was set to 0.3 in accordance with previous FE models of human bone (8,164,207,208). The boundary conditions of the FE models replicated the mechanical tests.…”

“…However, in vivo strain gauge measurement is highly invasive and limited to small, localized regions of the bone surface. As a consequence, computational modeling approaches such as the finite element (FE) method have become increasingly important for strain estimation (8,9).…”

“…As an alternative to experimental testing, density-elasticity equations for the human femur (8,194,195), tibia (8,196), humerus (8), radius (8), and ulna (197) have been developed using optimization techniques. These studies typically assume an equation of the form E=aρ b , where E is the elastic modulus, ρ is the density, and a and b are unknown coefficients determined by minimizing the error between experimental measurements and FE predictions.…”