Biomedical Signal Processing and Control 44 (2018) 229–236 Contents lists available at ScienceDirect Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc Estimation of the second heart sound split using windowed sinusoidal models Rasmus G. Sæderup a,∗ , Poul Hoang a,∗ , Simon Winther c,d , Morten Bøttcher d , Johannes Struijk b , Samuel Schmidt b , Jan Østergaard a a Department of Electronic Systems, Aalborg University, Fredrik Bajers Vej 7B, 9220 Aalborg Øst, Denmark b Department of Health Science and Technology, Aalborg University, Fredrik Bajers Vej 7D, 9220 Aalborg Øst, Denmark c Department of Internal Medicine, Hospital Unit West, Gl. Landevej 61, 7400 Herning, Denmark d Department of Cardiology, Aarhus University Hospital, Aarhus, Denmark a r t i c l e i n f o Article history: Received 17 October 2017 Received in revised form 19 March 2018 Accepted 9 April 2018 a b s t r a c t 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. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction The second heart sound, also known as the S2 sound, is com- prised of two sounds, namely the sound from the aortic valve closure (A2) and the sound from the pulmonary valve closure (P2). The time difference between the onsets of A2 and P2 is referred to as the S2 split [1] or the time split (TS). Determining the TS is of great importance, as it can assist in the diagnosis of a wide variety of heart diseases such as left bundle branch block (LBBB), right bundle branch block (RBBB), severe congestive heart failure, atrial septal defect or pulmonic stenosis [2]. Pulmonary hypertension (PH) is a disease where the patient has an increased pulmonary arterial pressure (PAP) and it is difficult to diagnose non-invasively [3]. A strong relation between the normalized splitting interval of S2 and ∗ Corresponding authors. E-mail addresses: rsader13@student.aau.dk (R.G. Sæderup), phoang13@student.aau.dk (P. Hoang). the systolic PAP has been found, hence making it possible to esti- mate the PAP non-invasively by estimating the TS using acoustical recordings of the heart also known as phonocardiograms (PCG) [4]. A measured S2 signal from a PCG recording is shown in Fig. 1, having a TS of ≈38 ms. Normally, A2 precedes P2 by 20–80 ms (30–40 ms on average) when inhaling [2], which means that A2 and P2 can be distinguished as two separate sounds. When exhaling, P2 rarely occurs after A2 by more than 30 ms, often yielding that the A2 and P2 sounds are perceived as occurring simultaneously and can therefore not be distinguished by humans [5]. Various methods related to estimation of the TS have been found in the literature, and can overall be put in three categories: model- ing the S2 sound, estimating the TS directly using signal processing methods, and source separating S2 into A2 and P2. For S2 modeling, the methods used include nonlinear chirps [6] and exponentially decaying sinusoids [7]. Estimating the TS directly from the data can be done by using the Hilbert transform to find the envelope of the signal [1], and https://doi.org/10.1016/j.bspc.2018.04.006 1746-8094/© 2018 Elsevier Ltd. All rights reserved.