Estimation of the Rotational Undamped Natural Frequency of Bileaflet Cardiac Valve Prostheses

Abstract

The angular momentum balance is solved numerically for a size 29 mm CarboMedics prosthetic heart valve. The lift force is estimated from potential flow theory, while the drag force is estimated from the lift force and a blunt body empiricism. Buoyancy and gravitational effects are calculated based on the assumption of homogeneous leaflets. Other assumptions include uniform flow, negligible friction at the pivot axis, negligible viscous damping and fluid inertance, and a symmetry flow condition. Oscillations are predicted in the opening dynamics in the range of 2-25 Hz, for flow rates through one-half of the orifice in the range of 0.1-10.0 l/min. The frequency of these oscillations is dependent upon the orientation of the leaflet in relation to the gravitational field and the magnitude of the flow rate. In vivo and in vitro measurements by other investigators demonstrate similar effects of gravity and flow rate, with flutter frequencies of the order of 10-100 Hz. Excitation frequencies, based on vortex shedding, are estimated to be of the order 2-200 Hz, for the range of flow rates of the theoretical model. These results suggest that the natural frequency of this rotational second order system may, in theory, be a contributing factor to the flutter observed in bileaflet cardiac valve prostheses. The clinical significance of this finding is yet to be established.