Evaluation of an Inverse Method for Quantifying Spatially Variable Mechanics

Abstract

Soft biological tissues often function as highly deformable membranes in vivo and exhibit impressive mechanical behavior effectively characterized by planar biaxial testing. The Generalized Anisotropic Inverse Mechanics (GAIM) method links full-field deformations and boundary forces from mechanical testing to quantify material properties of soft, anisotropic, heterogeneous tissues. In this study, we introduced an orthotropic constraint to GAIM to improve the quality and physical significance of its mechanical characterizations. We evaluated the updated GAIM method using simulated and experimental biaxial testing datasets obtained from soft tissue analogs (PDMS and TissueMend) with well-defined mechanical properties. GAIM produced stiffnesses (first Kelvin moduli, K1) that agreed well with previously published Young's moduli of PDMS samples. It also matched the stiffness moduli determined via uniaxial testing for TissueMend, a collagen-rich patch intended for tendon repair. We then conducted the first biaxial testing of TissueMend and confirmed that the sample was mechanically anisotropic via a relative anisotropy metric produced by GAIM. Next, we demonstrated the benefits of full-field laser micrometry in distinguishing between spatial variations in thickness and stiffness. Finally, we conducted an analysis to verify that results were independent of partitioning scheme. The success of the newly implemented constraints on GAIM suggests notable potential for applying this tool to soft tissues, particularly following the onset of pathologies that induce mechanical and structural heterogeneities.