Pointwise Estimation of Material Parameters for Heterogeneous Nonlinear Hyperelastic Membranes: Computational Development

Material parameter estimation plays a crucial role in the physical characterization of biological structures. However, identification of parameters in living organs presents considerable challenge. Take for example human aneurysms. Aneurysmal tissues are anisotropic, heterogeneous and most notably, patient-specific. More often than not, methods of characterizing the tissues need to be non-invasive. Obviously, the traditional controlled specimen experiments (e.g. uni-axial and bi-axial tests) are not suited to such applications. In this presentation, we introduce a methodology that can sharply characterize the heterogeneous properties of nonlinear membranes. The method builds on a unique feature of the membrane equilibrium problem, that is, the wall stress is static-determinate. We devised a numerical method to determine the membrane stress without knowing the true material properties. Given a series of deformed configurations, we can determine the stress distribution in each of the configuration independent of material model and thus, obtain pointwise stress-strain data. With theses data, we can characterize the pointwise material property by way of constitutive regression. Unlike the inverse finite element method [1] which extracts material properties indirectly, here, the regress is performed directly at the constitutive level. In addition, the computations for parameter regression and field solution are completely decoupled. If the initial configuration is unknown, it can also be considered, at least locally, in the identification process. The method builds a solid ground for the material parameter estimation using in vivo medical images. We verified the methodology using numerical simulations. An inflation experiment was simulated for a cerebral aneurysm model reconstructed from medical images. The subsequent application of proposed method rendered an accurate estimation of the assumed heterogeneous property.