Modified stability diagram of pulsatile flow through heart valves based on improved spectral estimates of LDA data

The Laser Doppler Anemometry (LDA) measurement technique presents an inherent difficulty when spectral analysis is applied to it. The random nature of the LDA signal prohibits sampling at regular, equi-spaced, time instants. Irregular sampling presents additional variability of the spectral estimator. In order to reduce this variability, spectral analysis of LDA data is performed according to the method of direct Fourier transform of short blocks of data, as suggested by Gaster and Roberts. The LDA data is measured in a flow field distal to prosthetic heart valves with varying degrees of stenosis. Spectral analysis is performed on valvular velocity waveforms at selected spatial and temporal points to produce the power density spectra. The spectral estimates of velocity data sampled during the rapid closure stage of the valve are achieved with excellent frequency resolution. Important and useful information about dominant frequency peaks and preferred modes which exist in the flow, otherwise smeared or concealed in the spectral contents, is derived from the spectral information. These modes are quantitatively analyzed in light of vortex formation and related flow mechanisms, and used for the formulation of a modified stability approach for pulsatile flows through heart valves. The stability of the flow is represented by a cluster of points, each corresponding to a dominant mode apparent in the flow. The results are compared with those achieved by the traditional stability approach. The comparison demonstrates the bias of the traditional stability diagram that leads to unreliable stability criteria. Our stability 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.