Separation of Aortic and Pulmonary Components from Second Heart Sounds without an Assumption of Statistical Independence

A novel algorithm to separate aortic (A2) and pulmonary (P2) components from the second heart sound (S2) without assuming that A2 and P2 are statistically independent, and with optimizing demixing vectors using root-mean-square error (RMSE) between outputs and signal models as cost function is successfully demonstrated. Conventional methods to estimate the A2-P2 splitting interval (SI) based on the separation of A2 and P2 using independent component analysis (ICA) are subject to distortions due to the fact that A2 and P2 are not strictly statistically independent. Therefore, we propose an algorithm to separate A2 and P2 without assuming their independence. In the proposed algorithm, a nonlinear transient chirp signal model is introduced as the proper models of A2 and P2, and the separated sound is optimized to be closest to the A2/ P2-like model. To evaluate the proposed algorithm, SI estimation was performed for S2 simulated with 60 common SI patterns. The results show that the proposed algorithm can estimate SI stably regardless of the independence of A2 and P2, and can estimate SI with 95% limits of agreement of -0.305 ± 2.15 ms, which is about 69% smaller as the error range than ICA.