Homogeneity versus inhomogeneity in muscle elastography

Abstract

The hierarchal microstructure and arrangement of skeletal muscle fibers results in both anisotropy and inhomogeneity. Most elastography reconstruction methods assume homogeneity and many also assume isotropy. In this computational (finite element) and experimental (MR) elastography study we investigate the impact of assuming homogeneity as muscle architecture dimensions and property differences are varied. This analysis also takes into consideration the inherent anisotropy (transverse isotropy) created by homogenization of the fiber structure, and the added complication ofnonhomogeneous (pre-stress) boundary conditions. Specifically, the computational harmonic analysis uses a parametric sweep across 200 Hz to 2000Hz applied to 4-, 40- and 400-fiber models with the aligned fiber cross-sectional area fixed (reduced fiber diameter as fiber count increases) and comprising 50% of the circular cross-sectional area in the fixed diameter cylindrical phantom. Fiber elastic moduli two to five times that of connective tissue are considered. This phantom also undergoes tensile axial pre-loading simultaneous to elastography studies. Predicted results are compared to a homogeneous transverse isotropic model that is reached in the limit as the fiber count increases to infinity while still summing to 50% of the cross-sectional area. Selected cases, such as the 4-fiber model are also evaluated experimentally using MR elastography.