I.C. Howard

A THREE-DIMENSIONAL ANALYSIS OF A BIOPROSTHETIC HEART VALVE

A three-dimensional finite element model of the leaflets of a bicuspid bioprosthetic heart valve is presented. The model is based on a non-linear elastic representation of the tissue behaviour which closely simulates that found in experiments. The geometry of the model is based on measurements from a real valve. Shell elements which permit bending have been used in the analysis. The results indicate that bending stresses in the leaflets make a significant contribution to their deformation. This confirms earlier two-dimensional work which had suggested that analyses, where only membrane stresses were modelled, were likely to produce significant errors in the stress states. The analysis also predicts peak stresses close to, but not at, the attachment of the leaflet to the stent post.

A comparative study of linear and nonlinear simulations of the leaflets in a bioprosthetic heart valve during the cardiac cycle

Two geometrically identical models of the leaflets of a bicuspid bioprosthetic heart valve have been constructed using finite elements. The boundary conditions applied to the models were also identical but a linear material model has been used in one and a nonlinear elastic model in the other. The models were fullscale and contained 2600 Belytschko-Lin-Tsai shell elements which allowed the variation of stress through the thickness of the leaflet to be modelled. A time-varying, spatially-uniform pressure differential was applied across the leaflets to model their behaviour during a complete cardiac cycle. The simulation was performed using a dynamic, explicit, time-stepping, finite element code. A comparison of the two models showed that the nonlinear model was more responsive to the time-varying pressure wave, and deformed into more complex shapes during the opening and closing phases which induced lower compressive but higher tensile stresses in the leaflets.

A two-dimensional finite element analysis of a bioprosthetic heart valve

A finite element scheme has been developed using total Lagrangian techniques for the two-dimensional analysis of bioprosthetic heart valve leaflets undergoing large deformation. Two models of a leaflet, namely a radial and a circumferential slice, have been analysed. The attachment of the slice to the stent was simulated by progressive contact on a circular former and the coaptation of the leaflets in the centre of a heart valve by a straight line of contact. For the circumferential model, different initial configurations have been considered. The prolapse pressure under which the heart valve closes has been shown to be small in comparison with the normal pressure a heart valve sustains. The regions of the valve that are most heavily stressed are subjected to a strong component of bending. The amount is sensitive to the details of the boundary conditions and to the initial configuration of the valve. These observations are likely to be significant in the use of this kind of stress analysis to improve the design of this type of valve.

On the opening mechanism of the aortic valve: some observations from simulations

Viewed from the standpoint of mechanical engineering design, the aortic valve is impressive. However, our understanding of its mechanics is limited by our inability to study its in vivo function closely and in detail. Computer simulation methods offer an alternative approach and a first step towards the construction of a more complete cardiac model is described. The model includes the aortic valve, its leaflets and their supporting root, and the sinuses modelled as nonlinear materials. An explicit finite element code has been used to examine the time-varying displacements of the structure that was subject to pressure distributions, which included left ventricular, aortic and thoracic pressures. It was shown that the leaflets of the valve open by a combination of root expansion in a radial direction and leaflet movement in the direction of blood flow. This was compared to a model in which the aortic root was stiffened significantly, and it was found that this modified valve opened by leaflet folding to give a much smaller orifice. These findings, concerning the importance of root expansion, are in agreement with earlier experimental observations.

Influence of anisotropy on the mechanical behaviour of bioprosthetic heart valves

Chemically modified pericardium is commonly used in the fabrication of bioprosthetic heart valves. This material exhibits non-linear elastic behaviour and, as for most other biological soft tissues, it is orthotropic in its extensibility. The influence of the natural orthotropy of pericardium on the mechanical behaviour of pericardial heart valves during the whole cardiac cycle has been studied, using the finite element method. A model of the leaflet of a bicuspid valve has been created, defining the material of the tissue as orthotropic non-linear elastic. Two preferential orthogonal orientations of the tissue have been analysed (axial and circumferential). The results show that even a small amount of orthotropy (an orthotropy index of 1.5 has been used) can significantly affect the mechanical behaviour of the valve, and that an appropriate orientation of the fibres can contribute to optimizing the stress distribution in the leaflets.

Three-dimensional stress analysis of polypropylene leaflets for prosthetic heart valves

The effect of changing the modulus and thickness of the material in the leaflets of an artificial heart valve has been investigated. This has been achieved with a finite element model of the valve having approximately 2300 thin shell elements. The valve motion and the resulting stresses are modelled dynamically during closure, and subsequent pressurisation. The stresses decrease as the leaflets are made thicker and the modulus is increased. Local and global thickening has been investigated. The highest stresses appear at the tops of the stent posts in the regions of the commissures. When the modulus is too low, or the leaflets are too thin, the valve prolapsed.

Simulation of damage in a porcine prosthetic heart valve

A model of a bioprosthetic porcine valve has been produced which simulates the non-linear elastic behaviour of the fixed tissue and the re-inforcement of the leaflets by collagen fibre bundles. The loading on the model is a spatially uniform but temporally varying distribution of pressure. Bending is allowed in the tissue of the leaflets and is shown to be significant in determining the behaviour and failure modes of the leaflets. The simulation of the undamaged valve is validated against in vitro pulse duplicator studies and a simple fluid--solid interaction simulation. Progressive damage is introduced into three models of the valve at a location where tears have been commonly found in vivo. It was found that during the opening and closing of the valve the tip of the tears were subject to mode III or tearing displacements, but that in the fully closed or diastolic state the tear tip was subject to mode I or opening displacements such that it would be expected to propagate parallel to the line of attachment to the stent. The tear tip stresses increased with the length of the tear so that the rate of tearing would be expected to increase with length.

Study of an infant brain subjected to periodic motion via a custom experimental apparatus design and finite element modelling

This paper presents a rig that was specifically designed to simulate the shaking of mechanical models of biological systems, especially those related to shaken baby syndrome (SBS). The scope of this paper includes the testing of an anthropomorphic model that simulates an infant head and provides validation data for complex finite element (FE) modelling using three numerical methods (Lagrangian, Arbitrary-Lagrangian-Eulerian (ALE) and Eulerian method) for fluid structure coupling. The experiments for this study aim to provide an understanding of the influence of two factors on intracranial brain movement of the infant head during violent shaking: (1) the specific paediatric head structure: the anterior fontanelle and (2) the brain-skull interface. The results show that the Eulerian analysis method has significant advantages for the FSI modelling of brain-CSF-skull interactions over the more commonly used methods, e.g. the Lagrangian method. To the knowledge of the authors, this methodology has not been discussed in previous publication. The results indicate that the biomechanical investigation of SBS can provide more accurate results only if the skull with paediatric features and the brain-skull interface are correctly represented, which were overlooked in previous SBS studies.

Non-linear finite element modelling of porcine bioprosthetic valves

Abstract There are two major types of artificial heart valves in use, namely mechanical valves and bioprosthetic valves. Mechanical valves last longer but require the recipient to undergo long-term anticoagulant therapy. Bioprosthetic valves are more biocompatible than the mechanical valves and long-term anticoagulant theraphy is not necessary. The major mode of failure of mechanical valves is through fatigue. This type of valve failure is catastrohic. Death is certain if the failed valve is not replaced immediately. The bioprosthetic valves normally fail by tearing of the leaflet. Many workers in this field believe that the tearing of the leaflet is associated with accumulated calcium deposits on the leaflets which makes the leaflet less flexible. A bioprosthetic valve usually has a soft failure path, with the leaflet tearing gradually. As the valve becomes less effective, the heart weakens slowly and there is time for diagnosis, treatment and valve replacement. Since there is a strong relationship between areas of high engineering stresses and calcification, engineering stress analysis and design studies offer the possibility of increasing the lifetime of the valve. The aims of the current research are to identify the areas of high stressesin the leaflets of bioprosthetic porcine valves and the ways of reducing these stresses. The stress distribution on the leaflets varies significantly as the leaflets cycle between the open and the closed positions. Thus, a time-stepping finite element code which is capable of non-linear stress analysis was needed to analyse the leaflets. The finite element package currently in use is the OASYSDYNA3D package. It is capable of non-linear geometrical modelling. A non-linear material model for the porcine valve is currently under development. Once the OASYS-DYNA3D package is capable of both non-linear geometrical and material modelling, the porcine valve leaflets can be fully analysed and the areas of high stresses be identifiedso that the design of the valve can be improved.

On the presence of bending stresses in inflated thin-walled structures

Abstract It is proposed that, in appropriate circumstances, membrane structures can experience bending moments. On uniformly inflating a thin sheet structure, which has a shape consisting of multiple curvatures, the structure will deform in such a way that the final shape will have a single radius of curvature, assuming that failure does not occur. It is the large change of shape from a multicurvature surface to a single curvature surface that causes bending moments to exist within a membrane. The validity of the hypothesis has been demonstrated using four finite element models, including an elliptical cylinder, an ellipsoid, a ‘double’ cone and a trileaflet heart valve.