Transition to Turbulence in Pulsatile Flow Through Heart Valves—A Modified Stability Approach

Abstract

The presence of turbulence in the cardiovascular system is generally an indication of some type of abnormality. Most cardiologists agree that turbulence near a valve indicates either valvular stenosis or regurgitation, depending on the phase of its occurrence during the cardiac cycle. As no satisfying analytical solutions of the stability of turbulent pulsatile flow exist, accurate, unbiased flow stability criteria are needed for the identification of turbulence initiation. The traditional approach uses a stability diagram based upon the stability of a plane Stokes layer where a (the Womersley parameter) is defined by the fundamental heart rate. We suggest a modified approach that involves the decomposition of α into its frequency components, where α is derived from the preferred modes induced on the flow by interaction between flow pulsation and the valve. Transition to turbulence in pulsatile flow through heart values was investigated in a pulse duplicator system using three polymer aortic valve models representing a normal aortic valve, a 65 percent stenosed valve and a 90 percent severely stenosed valve, and two mitral valve models representing a normal mitral valve and a 65 percent stenosed valve. Valve characteristics were closely simulated as to mimic the conditions that alter flow stability and initiate turbulent flow conditions. Valvular velocity waveforms were measured by laser Doppler anemometry (LDA). Spectral analysis was performed on velocity signals at selected spatial and temporal points to produce the power density spectra, in which the preferred frequency modes were identified. The spectra obtained during the rapid closure stage of the valves were found to be governed by the stenosis geometry. A shift toward higher dominant frequencies was correlated with the severity of the stenosis. According to the modified approach, stability of the flow is represented by a cluster of points, each corresponding to a specific dominant mode apparent in the flow. In order to compare our results with those obtained by the traditional approach, the cluster of points was averaged to collapse into a single point that represents the flow stability. The comparison demonstrates the bias of the traditional stability diagram that leads to unreliable stability criteria. Our approach derives the stability information from measured flow phenomena known to initiate flow instabilities. It differentiates between stabilizing and destabilizing modes and depicts an unbiased and explicit stability diagram of the flow, thus offering a more reliable stability criteria.