Inverse Characterization of Tissue Properties: Investigation of Non-uniqueness

We present an inverse framework for identifying spatially varying tissue material properties and fiber orientations based on known strain (deformation) and loading. Loading, along with the undeformed and deformed configurations, drive a force residual minimization process that circumvents the need of repeated forward simulations. Reconstruction of material properties is performed within a Kirchhoff–Love shell finite element framework with subdivision surfaces. Material parameters are represented using a neural network as a function of spatial location, enabling both smooth and localized variation. We validate the method against synthetic benchmarks with heterogeneous elasticity and fiber architecture and apply it to a bioprosthetic heart valve. Though the solver supports general constitutive laws, we demonstrate it on Neo-Hookean and Fung models. The latter model shows non-uniqueness, where distinct parameter fields yield similar final residuals, revealing challenges in identifiability, while fiber orientation recovery remains more robust. We also develop a companion inverse framework to estimate muscle activation patterns in shell-based tissues using stress/strain-based formulations.