Modeling active muscle contraction in mitral valve leaflets during systole: a first approach.

The present study addresses the effect of muscle activation contributions to mitral valve leaflet response during systole. State-of-art passive hyperelastic material modeling is employed in combination with a simple active stress part. Fiber families are assumed in the leaflets: one defined by the collagen and one defined by muscle activation. The active part is either assumed to be orthogonal to the collagen fibers or both orthogonal to and parallel with the collagen fibers (i.e. an orthotropic muscle fiber model). Based on data published in the literature and information herein on morphology, the size of the leaflet parts that contain muscle fibers is estimated. These parts have both active and passive materials, the remaining parts consist of passive material only. Several solid finite element analyses with different maximum activation levels are run. The simulation results are compared to corresponding echocardiography at peak systole for a porcine model. The physiologically correct flat shape of the closed valve is approached as the activation levels increase. The non-physiological bulging of the leaflet into the left atrium when using passive material models is reduced significantly. These results contribute to improved understanding of the physiology of the native mitral valve, and add evidence to the hypothesis that the mitral valve leaflets not are just passive elements moving as a result of hemodynamic pressure gradients in the left part of the heart.

On modelling and analysis of healthy and pathological human mitral valves: two case studies.

Biomechanical data and related constitutive modelling of the mitral apparatus served as a basis for finite element analyses to better understand the physiology of mitral valves in health and disease. Human anterior and posterior leaflets and chordae tendinae from an elderly heart showing no disease and a hypertrophic obstructive cardiomyopathic heart (HOCM) were mechanically tested by means of uniaxial cyclic extension tests under quasi-static conditions. Experimental data for the leaflets and the chordae tendinae showed highly nonlinear mechanical behaviours and the leaflets were anisotropic. The mitral valve from the HOCM heart exhibited a significantly softer behaviour than the valve from the healthy one. A comparison with porcine data was included because many previous mitral modelling studies have been based on porcine data. Some differences in mechanical response were observed. Material parameters for hyperelastic, transversely isotropic constitutive laws were determined. The experimental data and the related model parameters were used in two finite element studies to investigate the effects of the material properties on the mitral valve response during systole. The analyses showed that during systole the mitral valve from the HOCM heart bulged into the left atrium by taking on the shape of a balloon, whereas the anterior leaflet of the healthy valve remained in the left ventricle.

Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution.

This study presents a three-dimensional finite element model of the mitral apparatus using a hyperelastic transversely isotropic material model for the leaflets. The objectives of this study are to illustrate the effects of the annulus shape on the chordal force distribution and on the mitral valve response during systole, to investigate the role of the anterior secondary (strut) chordae and to study the influence of thickness of the leaflets on the leaflets stresses. Hence, analyses are conducted with a moving and fixed saddle shaped annulus and with and without anterior secondary chordae. We found that the tension in the secondary chordae represents 31% of the load carried by the papillary muscles. When removing the anterior secondary chordae, the tension in the primary anterior chordae is almost doubled, the displacement of the anterior leaflet toward the left atrium is also increased. The moving annulus configuration with an increasing annulus saddle height does not give significant changes in the chordal force distribution and in the leaflet stress compared to the fixed annulus. The results also show that the maximum principle stresses in the anterior leaflet are carried by the collagen fibers. The stresses calculated in the leaflets are very sensitive to the thickness employed.