Volume-Based Fabric Tensors through Lattice-Boltzmann Simulations

This paper introduces a new methodology to compute fabric tensors from computational fluid dynamics simulations performed through the lattice-Boltzmann method. Trabecular bone is modeled as a pipeline where a synthetic viscous fluid can flow from a single source located at the center of a spherical region of interest toward its boundaries. Two fabric tensors are computed from local velocities at the steady state estimated from the simulations, a tortuosity and a normalized tortuosity tensor. The main advantage of the proposed fabric tensors is that, unlike previous approaches, they intentionally disregard the trabecular termini in the computations, which do not play an important role in the estimation of trabecular bone quality. Thus, the proposed fabric tensors are less prone than previously proposed ones to unnecessary reductions of anisotropy related to the the presence of trabecular termini. The results of experiments conducted on synthetic and micro-computed tomography data in 2D and 3D show the artificial fluid flowing inside the trabecular bone has negligible velocities at trabecular termini, reducing in that way their influence in the estimation of the proposed fabric tensors.

I. Introduction

Bone in humans is mainly composed by cortical and trabecular bone (cf. Fig. 1). As a matter of fact, skeletal sites that are more prone to osteoporosis-related fractures such as vertebrae the femoral neck or the radius have a relatively thin layer of cortical bone. Thus, the mechanical competence of bone in those sites mainly relies on the quality of trabecular bone. One of the ultimate goals of trabecular bone research in medicine is to determine the effect of pathological conditions, such as osteoporosis and osteoarthritis, and their treatments on the quality of trabecular bone. One of the parameters that can be used to evaluate the quality of trabecular bone is its anisotropy. For example, evidence supporting that changes in the anisotropy and orientation of trabecular bone are associated with osteoporosis has been reported [1], [2], [3].