Sparse-input Detection Algorithm with Applications in Electrocardiography and Ballistocardiography ;1 ;1 2 1 1 F. Wadehn∗ , L. Bruderer∗ , D. Waltisberg , T. Keresztfalvi and H.-A. Loeliger 1 Signal and Information Processing Laboratory, ETH Zurich, Gloriastrasse 35, Zurich, Switzerland 2 Institut fuer Elektronik, ETH Zurich, Gloriastrasse 35, Zurich, Switzerland Keywords: Ballistocardiography, Heart Rate Estimation, Hypothesis Test, Factor Graphs, System identification, State- space Models, Maximum likelihood, Maximum a posteriori. Abstract: Sparse-input learning, especially of inputs with some form of periodicity, is of major importance in bio- signal processing, including electrocardiography and ballistocardiography. Ballistocardiography (BCG), the measurement of forces on the body, exerted by heart contraction and subsequent blood ejection, allows non- invasive and non-obstructive monitoring of several key biomarkers such as the respiration rate, the heart rate and the cardiac output. In the following we present an efficient online multi-channel algorithm for estimating single heart beat positions and their approximate strength using a statistical hypothesis test. The algorithm was validated with 10 minutes long ballistocardiographic recordings of 12 healthy subjects, comparing it to synchronized surface ECG measurements. The achieved mean error rate for the heart beat detection excluding movement artifacts was 4:7%. 1 INTRODUCTION Early signal-processing methods for BCG signals (Watanabe et al., 2005; Mack et al., 2009) concerned Cardiovascular diseases are among the leading causes estimation of heart rates averaged over a few sec- of death and severe health impairments both in high- onds using frequency-based methods. These meth- income countries with an aging population, as well ods do not provide beat-to-beat resolution or infor- as in developing countries, which are increasingly mation on irregular arrhythmias. Recently, advanced adopting western sedentary lifestyles and diet (Yusuf applications such as heart rate variability analysis or et al., 2001). Cardiac monitoring appliances range sleep staging, have brought up the challenging task from high resolution devices such as multi-lead of detecting individual heart beats in a BCG signal. ECG or the invasive esophageal ECG (Schnittger Schemes that rely on a single peak of a, possibly et al., 1986) to non-invasive, non-obstructive long preprocessed, BCG signal lack robustness for most time monitoring systems among which pulse oxime- applications due to oscillations caused by one heart try (Yelderman and New Jr, 1983) and ballistocardio- beat that decay slowly and overlap with the next heart graphy (BCG) (Alihanka et al., 1981) are the most beat (Bruser et al., 2011). prominent. In ballistocardiography, forces exerted by A variety of methods, proposed for beat-to-beat ventricular blood ejection are measured with force detection are based on, possibly adaptive, template sensors, usually placed below or inside a mattress on matching techniques (Shin et al., 2008; Paalasmaa which patients are lying. These force measurements et al., 2014) or sets of features extracted from the can be used to infer heart rates, heart rate variability BCG signal (Friedrich et al., 2010; Bruser et al., and even for getting indications about the cardiac out- 2011). These approaches have in common that they put (Cathcart et al., 1953; Inan et al., 2009). BCG sig- are not based on a probabilistic framework and their nals can be interpreted as an overlap of several oscilla- performance, which relies on specific patterns of tions of the body-bed-sensors system. Figure 1 shows troughs and peaks, might decrease, if used with stiff a filtered (see Section 3.1) single channel BCG signal systems, where oscillations have not sufficiently de- and heart-beat times (time of R peak in QRS com- cayed and the following impulse might lead to de- plex), extracted from a synchronized surface ECG. structive interference. In addition, these algorithms were developed for single-channel measurement sce- ∗These two authors contributed equally Wadehn F., Bruderer L., Waltisberg D., Keresztfalvi T. and -A. Loeliger H.. 21 Sparse-input Detection Algorithm with Applications in Electrocardiography and Ballistocardiography. DOI: 10.5220/0005186600210030 In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2015), pages 21-30 ISBN: 978-989-758-069-7 Copyright c 2015 SCITEPRESS (Science and Technology Publications, Lda.) BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing BCG BCG a.u. Amplitude a.u. 4-th order 8-th order 14-th order 0 0.5 1 1.5 2 7.6 7.8 8 8.2 8.4 Time [s] Time [s] Figure 1: Filtered single channel BCG signal (solid) with Figure 2: One hearbeat period segment of a measured BCG heart beat positions (red). signal and the estimated state-space model’s outputs, ob- tained with the presented bootstrap system identification narios. Extension of these schemes to process multi- approach. Subspace identification with 4-th, 8-th, and 14- th order model resulted in normalized root-mean-squared- channel measurements, thus taking advantage of more error (NRMSE) fits1of 32%, 44%, and 52% respectively information, is not readily possible. In addition the evaluted on the training data. aforementioned algorithms are tailored to extract in- stantaneous heart rates from the BCG signals, but do not recover estimates of the relative strength of heart 2 ALGORITHM DESCRIPTION beats. In this paper, we present a robust heart-beat detec- We model BCG signals as a time-shifted sum of beats. tion algorithm, which can be used to extract beat-to- Each beat in turn is modeled as a linear combina- beat estimates (e.g., heart rate or the heart rate vari- tion of exponentially-decaying oscillations with addi- ability) from ballistocardiogram measurements. By tive white Gaussian noise. Using linear discrete-time means of an initial training step the method adapts state-space models these signals are described as fol- itself to the present BCG data. Individual heart- lows beat then detects beats in a recursive window-based Xk = AXk 1 + BUk − (1) fashion, using a probabilistic model of the BCG sig- Yk = CXk + Zk; nal. Core of the model is a state-space model rep- where the input signal U represents the heart beat resentation of the BCG signal and an computation- k train, Y models the measured BCG signal, and Z ally efficient method for performing hypothesis test- k k N (0;V) is the observation noise. The heart beat train∼ ing (Reller, 2012). Owing to the explicit modeling of is modeled as a scaled non-uniformly spaced Kro- the BCG heart beat pulses our method is thus robust necker comb when dealing with beat-to-beat interference in the measurements. Furthermore, the probabilistic treat- N Uk = ∑ d[k Tn] an; Tn N; (2) ment allows to quantify the reliability of a poten- n=0 − · 2 tial heart beat detection and is leveraged for removal of small artifacts in the signal. Lastly, the estima- with N heart beats and scaling factors an, which serve tion algorithm being based on a maximum likelihood as indication for the instantaneous cardiac output. hypothesis-testing procedure, apart from estimates of The heart-beat times Tn and the scaling factors an are heart-beat time also infers the relative magnitude of unknown and estimated from the BCG signal. beats. Information on the heart beat’s relative magni- The proposed method used to infer the temporal tude might be useful to get indications on the cardiac pattern of heart-beats, consists of a model-estimation output (Kurumaddali et al., 2014). step, followed by a robust beat-detection algorithm. The paper is structured as follows. At first the The purpose of the model-estimation step is to iden- BCG signal’s is presented along with our algorithm to tify a suitable state-space model representation in detect individual heart beats and estimate their magni- 1NRMS is computed as follows tude (Section 2). The employed validation dataset and ! ~Y ~Yˆ necessary pre-processing are then discussed (Section 1 k − k 100%; 3), followed by the results (Section 4). − ~Y 1=K ∑K Y k − k=1 kk where Y and Yˆ represent the stacked BCG measurements and predictions of the estimated model. 22 Sparse-inputDetectionAlgorithmwithApplicationsinElectrocardiographyandBallistocardiography Algorithm 1: Sparse-input detection. U1 U2 U3 1: Pre-processing (Section 3.1) 2: 6s artifact labeling (Section 2.4) X0 X1 X2 X3 3: Bootstrapped state-space model identification p0 p1 p2 p3 4: Robust heart-beat detection (Sections 2.2-2.4) ··· 5: Outlier rejection (Section 2.5) Y1 Y2 Y3 (1) of the current BCG signal. To this end, sub- Figure 3: Factor graph of initial part of the BCG signal space methods were selected, due to their efficiency model. and their numerical stability (Van Overschee and De Moor, 1996). Subspace methods (e.g., 4SID) are performed by means of message passing on fac- based on the idea that an estimate of the state se- tor graphs. Factor graphs describe factorizations of quencex ˆ can be directly estimated from input/output multi-variable functions(Kschischang et al., 2001). data. Once the state-space sequence is estimated, the As shown in (Loeliger et al., 2007), state-space mod- system matrices A;B;C are retrieved using a linear els can also be represented with factor graphs and ef- least squares fit (Ljung, 1998). The covariance V of ficient algorithms for probabilistic inference, such as the observation noise Zk can be estimated from data maximum likelihood estimation and maximum a pos- as described in (Van Overschee and De Moor, 1994). teriori estimation can then be derived. As in our BCG signal model measurements of the In Forney-style factor-graph (FFG) nota- input, the heart-beat times and forces, are not avail- tion (Kschischang et al., 2001), boxes represent able, we use a bootstrap method for approximate sys- factors, whereas edges represent variables. A node tem identification: Heart beat excitations are approx- connected to several edges describes a function de- imated with a signal derived from surface ECG mea- pending on these variables.