Constitutive Modeling and Finite Element Analysis of Myxomatous Mitral Leaflet Tissue

Abstract

Although rarely discussed, material modeling of the myxomatous leaflet is considered as the cornerstone of mitral valve finite element analysis. The present study presents an incompressible, hyperelastic constitutive model to characterize myxoid mitral leaflet tissue mechanics. The model incorporates the transversely isotropic response and the layered structure of the tissue. First, an analytical constitutive model for the tissue is developed based on continuum mechanics and layered composites theory. Second, the material constants of the constitutive equation are determined by fitting the model to the experimental data. The analytical material model is then implemented using solid finite element methods by simulating a biaxial tensile test. A numerical simulation of the out-of-plane pressure loading is also conducted. Both the analytical outcomes and the simulated results agree well with experimental data and show good mutual agreement. The calculated strain distribution of the out-of-plane pressure loading simulation indicates myxoid leaflets exhibit enhanced extensibility and decreased stiffness compared to normal valves; the radial direction is more extensible than the circumferential direction. The presented material approximation is able to capture the myxomatous mitral leaflet mechanics. The results of the numerical simulation conform to those of the experimental tests.

In Situ Mechanical Characterization of Multilayer Soft Tissue Using Ultrasound Imaging

“…The ‘trust-region-reflective’ optimization method [58], extensively applied to soft tissue finite strain applications [59]–[61], has been employed in this work. Though the Levenberg-Marquardt algorithm has also been used extensively in soft tissue finite strain material coefficient optimizations [62]–[64], it has known limitations for negative definite Hessian matrices [65], which are overcome when the trust-region-reflective optimization is used.…”

Influence of Annular Dynamics and Material Behavior in Finite Element Analysis of Barlow’s Mitral Valve Disease

“…To our knowledge, only two studies have reported the use of myxomatous leaflet properties in their FE-models [17,24]. In both studies, the mechanical response of myxomatous tissue has been acquired by fitting constitutive models to the experimental data presented by Barber et al [4].…”

“…However, the paper did not include any material parameters for the presented constitutive model. In the paper by Zhong et al [24], the constitutive model that was used to fit the experimental data in Barber et al [4] assumes a two layered composite, each layer being reinforced by one family of fiber orthogonal with respect to each other. In the present paper the myxomatous leaflet properties described by Barber et al [4] are fitted to the constitutive Gasser-Ogden-Holzapfel (GOH) model available in the Abaqus material library [25], accounting for the mean leaflet thickness observed in BD patients [2].…”