Composite material homogenization for shear wave elastography of muscle-like fiber-laden viscoelastic waveguides...

The functional role of skeletal muscle and the hierarchal microstructure and arrangement of fibers within it results in anisotropy and inhomogeneity in both material properties and imposed stresses. Dynamic elastography reconstruction methods for estimating muscle tissue viscoelastic properties that are based on assumptions of homogeneity, isotropy and only bulk wave motion may produce inaccurate estimates. Biases may also be introduced in reconstruction by homogenizing muscle, which is inherently heterogeneous due to its fiber structure. The significance of these biases, and their interplay with imposed stresses and potentially confounding waveguide effects, is explored with a series of analytical and numerical finite element elastography studies on computational and physical fiber-laden phantoms. Limited experimental studies validate numerical finite element approaches and analytical methods that then explore a broad range of fiber arrangements, frequencies and prestress effects. The focus of this study is on shear wave propagation that is aligned with the fiber direction. For this case, numerical and analytical approximations based on the Halpin-Tsai homogenization approach are compared against explicit heterogeneous fiber-laden numerical finite element models and shown to be robust over a broad range of parameter values. This study confirms that homogenization for comparison with dynamic elastography measurements is valid. Moreover, this study provides insight into how fiber and extracellular matrix properties - which may be uniquely altered by pathology, trauma and therapy - in turn manifest in alterations in the homogenized properties that are directly estimated based on elastography measurements.