A Model of the Geometrical Changes in Aortic Valve Leaflets in Response to Leaflet Extension and Variable Boundary Conditions

Abstract

The function, deformation and performance of heart valve leaflets are dependent on the material properties and the geometry of the leaflet. As the leaflet acts as a constrained membrane the geometry is dependent on the boundary condition applied to the leaflet and any permanent extension of the leaflet. Both of these factors are varied during the preparation of frame-mounted porcine bioprosthetic heart valves and surgical insertion of free-sewn valves. This can result in abnormal geometry and function. A mathematical model has been developed which describes these changes in geometry of a cylindrical leaflet as a function of the diameter of the aortic root (boundary conditions) and the length (or permanent extension) of the leaflet. Both the angle of inclination and the radius of curvature of the cylindrical leaflet were reduced with increased leaflet length or decreased aortic diameter. Agreement was found between the model predictions and experimental observations in porcine bioprosthetic heart valves, where abnormal leaflet geometries are produced by non-physiological boundary conditions and permanent set of the leaflets by fixation with glutaraldehyde. The general solutions developed in this model allow leaflet geometries to be predicted for a range of conditions in free-sewn and frame-mounted valves.