Estimation of the second heart sound split using windowed sinusoidal models

Knowing the time difference between the onsets of the aortic part (A2) and the pulmonic part (P2) of the second heart sound (S2), also referred to as the time split (TS) of S2, can assist in the diagnosis of a variety of heart diseases. However, estimating the TS is a non-trivial task due to the potential overlap between A2 and P2. In this paper, a model-based approach is proposed where both A2 and P2 are modeled as windowed sinusoids with their sum forming the S2 signal. Estimation of the model parameters and the S2 split form a non-convex optimization problem, where a local minimum is obtained using a sequential optimization procedure. First, the window parameters are found as the solution to a regularized least squares problem. Then, the frequencies and phases of the sinusoids are found by locating the maximal peaks of the heart signals’ frequency magnitudes, and using the corresponding phases. Finally, the TS is estimated as the time difference between the peaks of the cross-correlations between the measured S2 signal and the modeled A2/P2 signals. The algorithm is able to estimate the TS for synthetic signals with a root-mean-square error (RMSE) of 7.6 ms for equidistantly placed TSs between −70 ms and 70 ms. The RMSE increases for small TSs in the interval −30 ms to 10 ms, and at increased noise levels. The algorithm was applied to phonocardiograms recorded from 146 patients, where the average estimated TS was 29.6 ms, in conformance with the average TS of healthy subjects as found in the literature.