Transformation Elastography: Converting Anisotropy to Isotropy

Abstract

Elastography refers to mapping mechanical properties in a material based on measuring wave motion in it using noninvasive optical, acoustic or magnetic resonance imaging methods. For example, increased stiffness will increase wavelength. Stiffness and viscosity can depend on both location and direction. A material with aligned fibers or layers may have different stiffness and viscosity values along the fibers or layers versus across them. Converting wave measurements into a mechanical property map or image is known as reconstruction. To make the reconstruction problem analytically tractable, isotropy and homogeneity are often assumed, and the effects of finite boundaries are ignored. But, infinite isotropic homogeneity is not the situation in most cases of interest, when there are pathological conditions, material faults or hidden anomalies that are not uniformly distributed in fibrous or layered structures of finite dimension. Introduction of anisotropy, inhomogeneity and finite boundaries complicates the analysis forcing the abandonment of analytically-driven strategies, in favor of numerical approximations that may be computationally expensive and yield less physical insight. A new strategy, Transformation Elastography (TE), is proposed that involves spatial distortion in order to make an anisotropic problem become isotropic. The fundamental underpinnings of TE have been proven in forward simulation problems. In the present paper a TE approach to inversion and reconstruction is introduced and validated based on numerical finite element simulations.