IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 64, NO. 10, OCTOBER 2017 2361 A Hidden Markov Model for Seismocardiography Johan Wahlstr¨ om ∗ , Isaac Skog, Member, IEEE, Peter H¨ andel, Senior Member, IEEE, Farzad Khosrow-khavar, Member, IEEE, Kouhyar Tavakolian, Member, IEEE, Phyllis K. Stein, and Arye Nehorai, Fellow, IEEE Abstract—We propose a hidden Markov model approach for processing seismocardiograms. The seismocardiogram morphology is learned using the expectation-maximization algorithm, and the state of the heart at a given time instant is estimated by the Viterbi algorithm. From the obtained Viterbi sequence, it is then straightforward to estimate instantaneous heart rate, heart rate variability measures, and cardiac time intervals (the latter requiring a small num- ber of manual annotations). As is shown in the conducted experimental study, the presented algorithm outperforms the state-of-the-art in seismocardiogram-based heart rate and heart rate variability estimation. Moreover, the isovolumic contraction time and the left ventricular ejection time are estimated with mean absolute errors of about 5 [ms] and 9 [ms], respectively. The proposed algorithm can be applied to any set of inertial sensors; does not require access to any additional sensor modalities; does not make any assumptions on the seismocardiogram morphology; and explicitly models sensor noise and beat-to-beat variations (both in amplitude and temporal scaling) in the seismocardiogram morphology. As such, it is well suited for low-cost implementations using off-the-shelf inertial sensors and targeting, e.g., at-home medical services. Index Terms—Cardiac time intervals, heart rate variabil- ity (HRV), hidden Markov model (HMM), seismocardiogram (SCG). I. INTRODUCTION C ARDIOVASCULAR disease is the leading global cause of death, accounting for about 17 million deaths per year and with estimated annual costs of $320 billion [1]. The most commonly employed modality for assessing cardiac function is the electrocardiogram (ECG), which is a recording of the time-dependent voltage measured by electrodes placed on the body. In each cardiac cycle, the ECG demonstrates a distinctive waveform whose largest deflections can be found in the QRS Manuscript received October 7, 2016; revised December 27, 2016; accepted December 28, 2016. Date of publication January 9, 2017; date of current version September 18, 2017. Asterisk indicates corresponding author. ∗ J. Wahlstr¨ om is with the ACCESS Linnaeus Center, Department of Signal Processing, KTH Royal Institute of Technology, Stockholm 114 28, Sweden (e-mail: jwahlst@kth.se). I. Skog and P. H¨ andel are with the ACCESS Linnaeus Center, Depart- ment of Signal Processing, KTH Royal Institute of Technology. F. Khosrow-khavar is with the MENRVA Research Group, School of Engineering Science, Simon Fraser University. K. Tavakolian is with the Department of Electrical Engineering, University of North Dakota. P. K. Stein is with the School of Medicine, Washington University in St. Louis. A. Nehorai is with the Preston M. Green Department of Electrical and Systems Engineering, Washington University. Digital Object Identifier 10.1109/TBME.2017.2648741 complex. Often, the beat-to-beat interval is estimated as the time interval between two successive R peaks, the so called RR- interval. Later, we will also make use of the term NN-interval, referring to the RR-interval between two successive beats pro- duced by sinus node depolarizations, i.e., excluding intervals affected by ectopic beats [2]. Although the ECG remains the standard diagnostic tool for cardiovascular disease, there is an increasing interest in alternative methods based on, e.g., the pho- toplethysmogram (PPG) [3], the impedance cardiogram (ICG) [4], the phonocardiogram (PCG) [5], or the ballistocardiogram (BCG) [6]. In this study, our primary concern is the seismo- cardiogram (SCG) 1 [8]. Although SCGs traditionally have been recorded using accelerometers, recent studies have also em- ployed gyroscopes [9], [10]. The vibrations can be studied along the superior-inferior axis (head-to-foot), the sinistro-dexter axis (left-to-right), and the dorsoventral axis (back-to-front). Most of the translational vibrations are concentrated along the dorsoven- tral axis, and hence, this has been considered the most important axis in accelerometer-based SCGs 2 [11]. SCGs offer several advantages over competing sensor modalities. These include the possibility of utilizing sensors embedded into personal de- vices such as smartphones (enabling a variety of at-home med- ical services) [12], the noninvasive nature of the method, and the low development cost of the sensors. The cost of a mass- produced inertial measurement unit (IMU), comprising three accelerometers and three gyroscopes, can be expected to be less than $1 [13]. To conclude, the SCG compares favorably to the ECG in terms of both availability and cost (but typically not in terms of accuracy), and can to some extent also be said to provide a different type of information (mechanical rather than electrical). Normally, the data recorded from IMUs fixed to the sternum will reflect both respiratory motions and cardiac vibrations. This is exemplified in Fig. 1, which shows accelerometer and gyro- scope measurements along the dorsoventral and sinistro-dexter axes, respectively. The measurements were recorded over two respiratory cycles. As should be intuitive, the respiratory con- tribution in Fig. 1(a) bears close resemblance to a sine wave. Moreover, each heartbeat in Fig. 1 can be seen to generate a characteristic wave pattern. While several attempts have been 1 While some studies use the terms BCG and SCG somewhat interchangeably, the general agreement is that the BCG represents recoil forces of the body to blood ejected by the heart, while the SCG represents local vibrations caused by the heart’s contractions and relaxations [7]. 2 On the other hand, the data collected in this study indicates that the rotational vibrations are primarily concentrated along the superior-inferior and sinistro- dexter axes. 0018-9294 © 2017 Canadian Crown Copyright