An Octahedral Fibrous Constitutive Model for Heart Valve Mechanics and Function

Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers. The organization of fibers and their load-bearing characteristics give rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. The model uses an octahedral arrangement of fibers embedded in a ground matrix, allowing anisotropy, volume fraction, and pre-stretch to influence the material response. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. The calibrated model reproduces responses across biaxial, pure-shear, and constrained-uniaxial tests, while separate numerical tests demonstrate its ability to represent substantial volume reduction and the reverse Poynting effect. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Widespread reversal of the preferred material directions, by contrast, prevents closure in the simulated valve. Finally, we examine how fiber pre-stretch and collagen volume fraction affect leaflet strain and contact, finding a stronger response to changes in pre-stretch over the parameter ranges studied.