Form from function: generalized anisotropic inverse mechanics for soft tissues.

Abstract

Elastography, the imaging of soft tissues on the basis of elastic modulus has gained popularity in the last few decades and holds promise for application in many medical areas. Most of the attention has focused on heterogeneous materials that are locally isotropic, the intent being to detect a stiff tumor within a compliant tissue. Many tissues of mechanical interest, however, are anisotropic, so a method capable of determining material anisotropy would be attractive. This work presents a method, named GAIM (Generalized Anisotropic Inverse Mechanics), to determine the mechanical anisotropy of heterogeneous, anisotropic tissues, by directly solving the finite-element representation of the stress balance in the tissue. GAIM divides the sample into subdomains assumed to have uniform properties and determines the material constants in each subdomain. Use of a linear material model led to rapid computation with statistical confidence levels as performance metrics. Multiple tests, asymmetric loading and strain heterogeneity are needed to address the ill-posedness of the inverse problem, and represent a paradigm shift in the testing of soft tissues. Simulated experiments of fibrous soft-tissues demonstrated the ability of the method to capture anisotropy qualitatively even though only a linear model is used. Results from the tests on soft-tissue analogs demonstrated the success in identifying regional differences in anisotropy based on full-field displacements and boundary forces obtained from multiple biaxial extension tests. The method’s success in capturing regional anisotropic changes associated with growth and remodelling in fibroblastpopulated cruciforms is a significant achievement, and holds promise for determining structural information of tissues from the mechanical response, since the structural and mechanical anisotropy are correlated. The linear GAIM model can be extended by a second step for nonlinearity with a fiber-based constitutive model. A closedform solution for the latter was developed and provides rapid results for nonlinear regression. In summary, this work has built a novel exploratory tool to extract regionspecific anisotropic properties on intact tissue samples. GAIM can be applied to provide information on the mechanical function of healthy tissue subjected to complex physiologic loads, identify regions within a tissue that exhibit irregular mechanical behavior (possibly due to disease or damage), and provide structural information from the mechanical function of tissues that are not amenable to structural tests.