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, whose organization gives 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. 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. 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. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence.