Leaflet geometry extraction and parametric representation of a pericardial artificial heart valve

Abstract

Reverse engineering technology was used to reconstruct the complex leaflet geometry of a commercial pericardial valve in our study. Results show that the three-dimensional computer-aided design model of the leaflet surface can be rendered by fitting the surface either to cloud points or by a group of B-splines fitted to a set of cloud points that had been obtained by the process of laser-scanning digitizing. However, an acceptable smooth surface is usually not guaranteed and additional manipulation is required. An alternative method is introduced in this paper, which involves the fitting of an equation to the leaflet geometry to create a smooth surface. The geometrical profile of a pericardial artificial heart valve was scanned using a laser digitizing system. The leaflet profile is represented as a set of cloud points. A quadric surface is fitted to a set of unique points, which were located on the set of cloud points. A mathematical equation is obtained by solving a least-squares fit. The geometry of the fitted leaflet surface has been proven to be closely represented by an elliptical hyperboloid. The quadratic equations of the leaflet curvatures, calculated along both the circumferential and the radial directions, resulted in simple hyperbolic curvatures. The advantages of using elliptical hyperboloid geometry for the leaflet surface are discussed and compared with other types of conicoid geometries. The concepts of parametric representation of the leaflet geometry and parametric design for leaflets are discussed. A smooth surface without inflection points and with an adjustable surface area suitable for a series of stent sizes with incremented diameters is created by this method of a single parametric design. Finally, a generic method to apply the geometry extraction and parametric representation to most pericardial heart valve prostheses was discussed. The application to valves with natural shape was introduced, challenges were identified, and a technical solution was proposed.