Single-trabecula building block for large-scale finite element models of cancellous bone

Abstract

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) 'building-block' of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of approximately 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of approximately 30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.

Statistics of Envelope of High-Frequency Ultrasonic Backscatter from Trabecular Bone: Simulation Study

“…The Gauss distribution was assumed for velocity and density values distribution in simulations. Thickness distributions of trabeculae are right-skewed as reported in experimental studies (Dagan et al, 2004;Saha, Wehrli, 2004). The published trabeculae thickness distributions well fit Gamma distribution.…”

How to select the elastic modulus for cancellous bone in patient-specific continuum models of the spine

“…where r(z) is the radius of the trabecula at location z along its length, Tbrh is the mean thickness of the trabecula across its length L, and the constants are a = 1.3736 and/3 = 40.9 bm (DAGAN et al, 2004 To analyse lattices of various sizes and with different trabecular qualities, we developed a custom-made FE code* that solves the apparent elastic modulus Ecb of any cubic orthogonal trabecular lattice under compression loading, depending on three trabecula characteristics: Tbrh, Tbsp and tissue BMD. Being ideally orthogonal and under pure compression loading, these lattices best represent spinal trabeculax bone, which closely follows orthogonal paths (NORDIN and FRANKEL, 1989) and which mostly supports compression (LINDH, 1989).…”

“…To obtain the Ecb regression equations, we developed computational orthogonal lattice models of cancellous bone (Fig. 1) that employed the singletrabecula generic 'building block' (described in detail in DAGAN et aL, (2004)) as the basic structural unit. Briefly, the generic trabecula 'building block' is based on statistical analyses of the dimensions of 200 trabeculae, which led to the profile shape of (Fig.…”

Modeling and calculation of the stress-strain state of trabecular bone fragments

“…The problem was solved within the linear theory of elasticity. The trabeculae material was homogeneous and isotropic, the elastic modulus (E=100 MPa) and Poisson's ratio (ν=0.3) were taken from [8]. The uniaxial compression of the fragments was simulated in the direction of the y-axis.…”