SUMMARYThe present study addresses constitutive modelling and implementation of transversely isotropic hyperelastic material models for the analysis of the mitral valve. This valve separates the left atrium and left ventricle in the heart. Two convex strain energy potentials are employed in derivation of stress tensors and elasticity tensors. The plane stress and incompressibility conditions are accounted for directly. The relationships are implemented in an implicit code (ABAQUS) via the user-defined interface. Numerical simulations of the valve motion during a part of the heart cycle are carried out and compared to ultrasound measurements of a healthy human valve. The significance of placement of chordae tendinae is illustrated. The implementation provides a tool for simulations of both healthy and pathological mitral valve conditions.

Despite observations of massive methane release and geohazards associated with gas hydrate instability in nature, as well as ductile flow accompanying hydrate dissociation in artificial polycrystalline methane hydrates in the laboratory, the destabilising mechanisms of gas hydrates under deformation and their grain-boundary structures have not yet been elucidated at the molecular level. Here we report direct molecular dynamics simulations of the material instability of monocrystalline and polycrystalline methane hydrates under mechanical loading. The results show dislocation-free brittle failure in monocrystalline hydrates and an unexpected crossover from strengthening to weakening in polycrystals. Upon uniaxial depressurisation, strain-induced hydrate dissociation accompanied by grain-boundary decohesion and sliding destabilises the polycrystals. In contrast, upon compression, appreciable solid-state structural transformation dominates the response. These findings provide molecular insight not only into the metastable structures of grain boundaries, but also into unusual ductile flow with hydrate dissociation as observed during macroscopic compression experiments.

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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.

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Further investigations utilizing a larger range of object weight and velocities are required to be able to fully classify minor traumatic injuries. Preliminary results indicate that this can be achieved by controlled experiments using a porcine model. Reflectance spectroscopy was found to be a useful tool to study immediate skin reactions to the trauma.

An incompressible transversely isotropic hyperelastic material for solid finite element analysis of a porcine mitral valve response is described. The material model implementation is checked in single element tests and compared with a membrane implementation in an out-of-plane loading test to study how the layered structures modify the stress response for a simple geometry. Three different collagen layer arrangements are used in finite element analysis of the mitral valve. When the leaflets are arranged in two layers with the collagen on the ventricular side, the stress in the fibre direction through the thickness in the central part of the anterior leaflet is homogenized and the peak stress is reduced. A simulation using membrane elements is also carried out for comparison with the solid finite element results. Compared to echocardiographic measurements, the finite element models bulge too much in the left atrium. This may be due to evidence of active muscle fibres in some parts of the anterior leaflet, whereas our constitutive modelling is based on passive material.

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.