Detection of body position changes from the ECG using a Laplacian noise model
Introduction
A change in body position causes a change in the position of the heart, manifested in the ECG as a change in morphology of the QRS complex and the ST–T segment [1], [2]. Such changes are particularly problematic in ambulatory ST monitoring since they may cause false ischemia alarms [3]. Hence, it is important to develop techniques which discriminate body position changes (BPCs) from true ischemic episodes. Such techniques will not only improve the reliability of ST monitoring, but they will also be useful in polysomnographic signal analysis where a BPC may be misclassified as an apneic event [4].
An early attempt to address the BPC problem was based on the Karhunen–Lòeve transform (KLT) and the pattern of coefficients in the KLT domain, defined both for the QRS complex and the ST–T segment [5]. Based on the assumption that the QRS-related coefficients change more rapidly during a BPC than during an ischemic episode, the results suggested that ischemic episodes can be distinguished from non-ischemic ones in the European ST–T Database. However, detection performance was not explicitly evaluated since BPCs were not annotated [5].
More recently, another KLT-based approach has been proposed and evaluated for detecting BPCs [6]. At the same time, a novel approach was proposed that explores changes in the orientation of the heart's electrical axis as reflected by the rotation angles of the vectorcardiographic loop [7]. For both approaches, a Bayesian-type detector was developed based on the assumption that a BPC is manifested as a step change in Gaussian noise [6], [7], see also [8]. The input signal to the detector was a time series defined either by KLT coefficients or rotation angles. The results indicated that both approaches performed relatively well, but signal segments with impulsive noise, baseline wander, and ectopic beats were all found to impair performance and produced high false alarm rates. In such noisy situations, it is advisable to replace the Gaussian noise model with another that better accounts for outlier samples.
A Laplacian noise model has been successfully employed in other biomedical applications [9], [10], [11], [12], [13], and is therefore investigated in the present paper for BPC detection. The main novelty is the development of the generalized likelihood ratio test (GLRT) for this particular model. The GLRT involves an alternating optimization procedure for estimating interdependent statistical parameters. Since the noise level of the observations may change considerably from one patient to another, the standard deviation of the noise model is treated as an unknown parameter which is subjected to maximum likelihood (ML) estimation.
The paper is organized as follows. Section 2 describes the model-based approach to BPC detection. The performance is assessed on two different databases: one with healthy subjects performing BPCs, and another with patients undergoing percutaneous transluminal coronary angiography (PTCA), see Section 3. In Section 5, the performance is compared to that of the Bayesian detector based on the Gaussian model [6]. The paper concludes with a discussion in Section 6.
Section snippets
Methods
The proposed BPC detector comprises the steps displayed in Fig. 1, and is described in the following.
Materials
The performance of the GLRT-based detector was evaluated on two databases: one with healthy subjects performing BPCs to assess the detector performance in terms of sensitivity and positive predictivity value, and another from patients with induced ischemia to assess specificity by setting the probability of false alarm. In both cases, the standard 12-lead ECG was acquired at a sampling rate of 1 kHz and an amplitude resolution of 0.6 μV.
The BPC database consists of 20 healthy subjects who
Calculation
The computation of the GLRT in (8) requires that the three ML estimators , , and have been determined – an issue which is addressed in this section. When hypothesis is assumed, is found by maximizing the related log-likelihood function with respect to ml,0, i.e.,
Inserting the Laplacian noise model, it is easily shown that the maximization in (20) is equivalent to minimizing the cost function:
Its minimum
Results
The following parameter setup was used when evaluating detector performance: λQRS = 0.8, N = 44 s, Nσ = 50 s, Wmin = 15 s, Wmax = 50 s, K = 4, and γ′ = 1800.
The histogram of the noise samples , resulting from the subjects of the BPC database, is displayed in Fig. 5. The preprocessing makes it permissible to merge all the data after subtracting the median, and the resulting histogram may also be relevant for individual subjects. The shape of the histogram suggests that the Laplacian PDF is better as a
Discussion
This study shows that the Laplacian noise model is better for representing the impulsive nature of the noise observed in the KLT domain. This finding implies that there is no longer a need for robustifying ad hoc measures such as the median absolute deviation filter which was previously employed for the purpose of rejecting outliers in the detector based on the Gaussian noise model.
The present detector includes a test whose aim is to discard detections caused by ischemic episodes. Since such
Conclusions
The problem of BPC detection was addressed by investigating a Laplacian noise model of the KLT coefficient series which characterize the QRS complex and the ST–T segment. The GLRT-based detector was derived, embracing the estimation of a time-varying BPC amplitude as well as the mean and standard deviation of the Laplacian noise. The noise in the KLT domain was found to be better characterized by the Laplacian noise model than the Gaussian one. Furthermore, the performance achieved by the
Acknowledgements
AM is supported by a Marie Curie Intra-European Fellowship (FP7-PEOPLE-2011-IEF). This work was supported by the grants TEC2010-19410 and TEC2010-21703-C03-02 from MINECO, Spain, and by Grupo Consolidado GTC from DGA, Spain.
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