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From Newton's equation and the continuity equation, an equivalent analogue circuit model can be derived for each small segment of the coronary arteries. Sapoznikov divided the coronary artery tree into 116 segments. By replacing each segment with its analogue circuit model, a final incremental network model was derived. The model was tested using typical physical parameters under normal conditions, as well as in the presence of coronary artery stenosis. In the case of stenosis, the arteriolar flow with and without autoregulation were compared. The model shows good agreement with the reported effects of stenoses and heart rate on coronary blood flow.

Previous studies done by our group suggest that partially occluded coronary arteries may generate sounds due to turbulent blood flow. To support these previous findings the frequency spectra of diastolic heart sounds are compared before and after angioplastic surgery. Since the low-level sounds associated with partially occluded coronary arteries are contaminated with considerable background noise, traditional FFT analysis may not produce accurate frequency spectra. Indeed, in a previous study using the same data, no significant differences were found in the diastolic heart sounds before and after angioplastic surgery. In this study, three eigenvector methods (Pisarenko, MUSIC, and Minimum-Norm) have been selected to generate the frequency spectra because of their higher resolution, particularly in the presence of noise. Although the Pisarenko method produced spurious zeros and could not be used, the other two methods produced spectra showing, in most cases, a marked decrease in high-frequency spectral components following angioplasty.

Previous studies have indicated that diastolic heart sounds may contain information useful in the detection of occluded coronary arteries. In this study, recordings of diastolic heart sound segments were modeled by autoregressive (AR) methods including the adaptive recursive least-square lattice (RLSL) and the gradient lattice predictor (GAL). Application of the Akaike criterion demonstrated that between 5 and 15 AR coefficients are required to completely describe a diastolic segment. The reflection coefficients, prediction coefficients, zeros of the polynomial of the inverse filter, and the AR spectrum were determined over a number (N = 20-30) of diastolic segments. Preliminary results indicate that the averaged AR spectrum and the zeros of the inverse filter polynomial can be used to distinguish between normal patients and those with coronary artery disease.

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