de J Jürgen Hart

A three-dimensional computational analysis of fluid–structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valves behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.

A two-dimensional fluid–structure interaction model of the aortic value

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increases the durability of these valves by unloading the delicate parts of the leaflets, maintaining their physiological functioning. The interaction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has, so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structure interaction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domain method based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. The model has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed video recordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are well predicted for different leaflet thicknesses.

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.

Finite-element-based computational methods for cardiovascular fluid-structure interaction

In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.

A three-dimensional analysis of a fibre-reinforced aortic valve prosthesis

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. It is postulated that leaflet fibre-reinforcement leads to a decrease of tears and perforations as a result of reduced stresses in the weaker parts of the leaflets. A three-dimensional finite element model of a reinforced three-leaflet valve prosthesis was developed to analyse the stress reduction. Different fibre reinforcements were investigated and the model responses were analysed for stresses that are expected to contribute to failure of fibre-reinforced valve prostheses. Results of these simulations show that, in peak stress areas of reinforced models, up to 60% of the maximum principal stresses is taken over by fibres and that, in some cases of reinforcement, a more homogeneous stress distribution is obtained.

Computational analysis of ventricular valve–valve interaction: Influence of flow conditions

Apart from dependence on the heart muscle contractility, the pumping efficiency of the heart depends on the functioning of its valves. Valve functionality, expressed as 1 minus the ratio between regurgitant and stroke volume, is the result of the motion of the valve depending on local flow phenomena. In this work, the relation between flow conditions and valve functionality was studied by means of a parameter study of the flow and valve dynamics in a two-dimensional computational model of the left ventricle with two rigid valves. It was found that valve functionality depends strongly on the applied flow conditions as expressed by the Strouhal and the Reynolds numbers. Furthermore, it was found that the regurgitant volume can vary from beat-to-beat resulting in a non-periodic pumping efficiency of the heart. These observations are of importance to future research based on simulations of geometrically more realistic heart valve-ventricle configurations as it may not always be taken for granted that beat-to-beat variations of the pumping efficiency are small.