Clinical Accuracy QRS Detector with Automatic Parameter Adjustment in an Autonomous, Real-Time Physiologic Monitor*

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1 Clinical Accuracy QRS Detector with Automatic Parameter Adjustment in an Autonomous, Real-Time Physiologic Monitor* Samuel C. Pinto 1, Christopher L. Felton 2, Lukas Smital 3, Barry K. Gilbert 2, David R. Holmes III 2, Clifton R. Haider 2 1. Technological Institute of Aeronautics, Sao Jose dos Campos, Sao Paulo, Brasil; samcerq@ita.br 2. Mayo Clinic, Rochester, MN, USA; felton.christopher@mayo.edu, holmes.david3@mayo.edu, haider.clifton@mayo.edu 3. Brno University Of Technology, Brno, Czech Republic; smital@feec.vutbr.cz *This work was funded by the following organizations: FNUSA-ICRC, Mayo Clinic, and Office of Naval Research Abstract This paper presents a computationally and temporal data-compact QRS complex detection algorithm useful in embedded real-time electrocardiogram (ECG) waveform analysis. The aim of the compact algorithms is to provide high sensitivity and specificity, i.e. diagnostically useful QRS waveform detection, in a continuous ambulatory monitor setting. The proposed detector uses a multi-level approach: QRS highlighting by means of a Truncated Discrete Time Stockwell Transform (TDTST), peak discrimination, and a trained Neural Network to reduce the number of false positive QRS detections. An optimization method is presented that automatically adjust the detector s parameters to minimize the computational cost. Results demonstrate that the compact TDTST algorithm exhibits high QRS detection accuracy, an error rate of 0.31%, and remains applicable to real-time embedded physiologic ambulatory monitors. Keywords: Compact algorithm, Stockwell transform, Realtime, Physiologic monitoring, QRS detection, Embedded. I. INTRODUCTION QRS complex detection in ECG waveforms continues to play a major role in the evaluation of cardiac health. The demand for continuous remote QRS monitoring continues to grow, which requires the acquisition, processing, and analysis of the ECG signal to be performed in real-time on a embedded platform. A review of QRS methods used for QRS processing in battery operated devices is presented in [1]. These algorithms show variable performance with a limited analysis of computation/power costs associated with them. The main challenges to obtaining a high accuracy continuous real-time QRS monitor lies in the necessity of ensuring enough computing power versus patient comfort, especially in terms of device size versus battery life [2]. In the ambulatory scenario, there are two general options: the data is acquired and immediately transmitted to another station that processes the signal, or, in the other, the embedded platform is responsible for both the acquisition and the processing of the signal. The primary disadvantage for the first option is that wireless transmission of raw data is power intensive. For the second, it is necessary to develop algorithms and devices that permit realtime analysis on simple embedded platforms with low power consumption. Fig. 1. ECG Signal Processing Pipeline. The primary contributions of this work are the presentation of simple but efficient rules for detecting QRS complexes from a form of the time-dependent Fourier transform of the signal and a systematic procedure for lowering the power consumption for a given signal processing algorithm. This paper also presents a systematic methodology to automatically adjusting algorithmic parameters to reduce the total computational cost while maintaining detector accuracy accuracy. The ability to automatically adjust parameters is essential for the portability of the same algorithm to different devices, since each device has its own signal acquisition and data processing characteristics, which may lead to significant differences in the parameters to achieve the same overall power consumption-todetection-accuracy performance. II. QRS DETECTION ALGORITHM In this paper, a multi-level algorithm is presented for detection of QRS complexes. In the first level, the ECG signal is processed using the Truncated Discrete Time Stockwell Transform (TDTST), similar to the work described in [3] and [4]. This first level of processing outputs a time-dependent frequency evaluation of the signal, as discussed in Subsection II-A, in which two moving averages are used to identify possible QRS complexes (named windows) in II-B. However, since very high QRS detection accuracy is required, a machinelearning approach is used to classify which windows are QRS complexes, as further explained in Subsection II-C. Fig. 1 presents the complete pipeline used to process the ECG signal. A. Discrete-Time Stockwell Transform The TDTST is one form of time-dependent Fourier analysis with frequency dependent, time-frequency resolution, as /17/$ IEEE 1005 GlobalSIP 2017

2 Fig. 2. ECG Signal and the computed Shannon Energy using the TDTST. further discussed in [5]. The advantages of the Stockwell Transform (ST) over the commonly used Short-Time Fourier Transform in the context of QRS complex detection are presented in [3]. The TDTST is defined in Eqs. (1)-(3). S[p, f) = N α(f) n= N α(f) w[p n, f) = x[n]w[p n, f)e j2πfn/fs (1) f 2π e ( f (p n)2 )/2F s (2) N α (f) = (F s / f )invnorm(1 (1 α)/2) (3) In Eq. (1), the index p refers to the sample index, f to the frequency for which the TDTST is being computed and 1 α is area of the windowing function tails truncated, as defined in Eq. (3), and invnorm is the inverse cumulative distribution function of the standard Normal distribution. In the QRS detection pipeline, the TDTST is computed for a set of frequencies f 1 < f 2 <... < f M, which imposes a minimum delay of N α (f M )/2 to maintain causality. In this paper, α will be assumed to be equal to The f 1 < f 2 <... < f M frequency components are then summed using the concept of Shannon Energy, Eq. (4). Se[p] = M (S[p, f i )) 2 log(s[p, f i )) (4) i=1 The Shannon Energy takes advantage of the majority of the QRS complex energy being contained in a limited frequency band, f 1 < f M. Therefore the TDTST is conceptualized as a set of filters with frequency-dependent impulse responses h f [k] = f /2) j2πfk e ( f k2 2π that extract the power of the signal at a given frequency, maintaining a time-frequency resolution that is coherent with natural properties of the QRS complexes, as discussed in [5]. Finally, the energy of different frequencies is grouped to give the notion of total QRS complex energy over time, and by observing peaks in the complex energy, it is possible to identify the QRS complex itself. B. Discriminator The output of the TDTST processing is then presented to a very simple set of rules to improve identify of true versus artifactual QRS complexes, similar to the approach in [6]. An alternative naive empirical approach for identifying QRS complexes would be to define a hard threshold, and when the Fig. 3. Discrimination process for obtaining possible QRS complexes. (a) Comparison of the signal with its long and short time moving averages. (b) Representations of windows (in blue) and their associated peaks. level of the TDTST goes above the set threshold, it would be classified as a QRS complex. However, since the amplitude of the TDTST signal varies over time, an adaptive threshold was implemented by a moving average of the signal over a time period long enough to capture N of the last QRS complexes as compared to a relatively short-time M < N moving average of the signal. These moving averages are presented along with the Shannon Energy of an ECG signal in Fig. 3-(a). When the short-time moving average is greater than the long-time moving average for period k a a peak condition is set corresponds to a QRS complex. Moreover, the peak of the Shannon Energy is used to compute the time instant of the peak of the QRS complex and is also marked on the Fig. 3- (b). The k a time period when the short-time average is greater the long-time average, is named as a window, as illustrated in Fig. 3-(b). It is important to note that the moving average discrimination process described above requires a limited number of basic arithmetic operations as compared to the TDTST computation. Therefore the moving average feature method will have minimal impact on the overall computational cost of the described QRS detection method. C. Classification of Possible QRS Complexes The overall discrimination processes described above extract probable QRS complexes. However, not all of the windows defined using the described methods are true QRS complexes, given physiologic signal components and/or noise. Therefore, several parameters of the window that could assist in this decision were extracted, namely the time-width of the window (W T ), the time difference between the peak of the current window and the previous window ( T ), the ratio between the amplitude of the current peaks compared, and the average amplitude of the previous three peaks (p). We used a Neural Network (NN) as a classifier such that, given these parameters, W T, T and p, the NN produces an output indicating whether the window is likely to have been generated by a QRS complex or is artifactual. 1006

3 The choice for using a NN is based on the fact that there is not a linear mapping between the parameters derived from the TDTST and the actual QRS complex. Moreover, the propogation of noise through the frequency analysis yields false positive peaks. Therefore, the NN approach is a suitable technique since NN s are able to approximate any arbitrary non-linear function and are efficient methods for training these networks on large ground-truth annotated ECG databases, such as described in [7]. It is important to note that the NN will be executed when a possible QRS complex, i.e. a window, is identified. Therefore, the NN firing rate will be approximately equal to the individual s heart rate (HR). A NN firing rate equal to the HR implies that the NN will contribute minimally to the total computational cost of our method, as the filter bank for the TDTST computation runs closer to the the ECG waveform sampling rate than to the HR. III. ALGORITHM OPTIMIZATION For QRS detection, the data and computational resources required by the embedded algorithm tend to scale with the requirement to generate accurate findings. For wearable devices, data and computational compactness are critical, since the resources are fixed and any computation increase leads to a larger device or a shorter battery life. The goal of this section is to present a method to address the maximum detection accuracy of the algorithm for a given resource set versus the highest level of QRS detection performance in terms of resource usage. Initially, it is necessary to identify the parameters that influence both the computational cost and the QRS detection accuracy. In the QRS detection, it is necessary to identify which frequencies f 1,..., f M the TDTST will be computed. At the windowing operation, it is necessary to relate the amount of time required to compute the short and the long term averages and the factor k a. For the QRS classification, there are no parameters to be identified. A. Computational Cost Analysis In order to reduce the power consumption of the device, it is necessary to lower the algorithm s computational cost. However, a generic, yet precise, measure of algorithmic computational complexity, i.e. compactness, remains difficult. Herein, each of the steps in the processing pipeline will be analyzed in terms of computational resource usage to develop a figure of merit. For the TDTST computation, M convolutions with impulse responses with lengths N α (f i ), i = 1,..., M are calculated for each input sample, which leads to M k=1 N α(f i ) multiplications and M k=1 N α(f i ) M additions. The Shannon Energy can be cached in memory, since it takes a single variable as its argument. In the windowing operation, 4 additions and 2 multiplications per input sample are employed, and the classifier is activated only at approximately the individual s HR, which is much lower than the sampling rate. Therefore, the computational impact of the classifier is negligible. Moreover, it is important to notice that the detection algorithm is desired for low power embedded devices. Given the fact that ambulatory devices often do not have dedicated hardware for efficient multiplication, the power cost of multiplications is much larger than the cost of additions. Further, since the total number of multiplications and additions for one clock cycle are similar, the computation cost of the algorithm presented in this paper is almost entirely due to the multiplications in the TDTST computation. Note that in devices with dedicated hardware multiplies the algorithm could also include additions the optimization formulation. However, herein, the hardware-specific measure of computational cost will be the number of multiplications per TDTST computation N m : N m = M (F s / f k )invnorm(1 (1 α)/2) (5) k=1 B. Optimization Of The Discrimination Process For each subset of frequencies in the calculation of the TDTST there may be different optimal parameters that lead to maximum accuracy. Therefore we used optimization as a way to compute for each extracted feature the best configuration. In this optimization setup, the decision variables will be the amount of time that the short and long averages are computed, T l and T s respectively, and the factor k a. Since the cost function should express the accuracy of the detector, it was chosen as in Eq. (6), where FP means False Positive and FN, False Negative. C = F P + F N (6) The optimization algorithm works in the following way: the user defines a range of possible values and an initial value for each parameter. The optimization algorithm then iteratively selects values for each of the parameters and evaluates their cost. The algorithm is responsible for guiding the choice of parameters such that moves the cost towards the global minimum. Having identified the cost function and the optimization parameters, it is necessary to define an algorithm for conducting the optimization. The optimization is nonlinear, due to the way that the QRS detector is framed. Therefore, algorithms for nonlinear optimization usually do not have guarantees of convergence to a global minimum. The optimization algorithm used in this work is the Particle Swarm Optimization [8], which has demonstrated efficiency in exploring the described solution space, if carefully adjusted. IV. RESULTS A. Evaluation of the algorithm against the MIT-BIH database The MIT-BIH [7] ECG dataset was used both for the optimization of the discrimination process and the NN training. In this process, α was set to 0.97, the set of frequencies f 1,..., f M were chosen such that f k = f 1 + (k 1) f, and 1007

4 TABLE III QRS DETECTOR ACCURACY COMPARISON Method Real Time S e (%) P + (%) e (%) Proposed Yes Chaitanya et al. [9] Yes Zidelmal et al. [4] No Smital et al. [3] No Chiarugi et al. [1] Yes Elgendi [1] Yes Pan et al. [4] Yes Ravanshad et al. [10] Yes Fig. 4. The error rate as a function of the number of multiplies per TDTST computation using the approach proposed in this work. f 1 = 10 Hz. The NN had 6 layers with 6 perceptrons in each layer and the Levenberg-Marquardt algorithm was used for the training. The results obtained using the procedure described in Section III are shown in Table I. In this table, e stands for the total error rate, i.e., F P + F N divided by the total number of beats, and NN r for the total reduction in the number of misclassified beats due to the NN classifier. Figure 4 shows the trade-off between computation cost and performance. Some of the optimized detector parameters are shown in Table II. TABLE I RESULTS AFTER TRAINING IN THE MIT-BIH DATABASE M f N m F P F N e NN r 16 1Hz % Hz % Hz % Hz % Hz % Hz % 112 TABLE II OPTIMIZED DETECTION PARAMETERS M f N m k a T l T s 16 1Hz s 0.17s 8 2Hz s 0.17s It is worth emphasizing that all of the 109,494 beats in the database were used for performance evaluation. Hence, no beats were excluded in estimating performance. In the reviewed work [1], the obtained error rate for the results that considered at least 100,000 beats ranged between 0.3% and 1.41%. In [4], an error rate of 0.25% was achieved with no beat exclusion, but the algorithm is not real-time. Table III provides a sensitivity, positive predictive value, and error rate comparison of various QRS detectors. B. Implementation in real hardware The proposed feature computation was implemented and evaluated in real-time embedded on an ambulatory physio- logical recording device based on the 16 bit MSP430 F5528 microcontroller [11] and compiled with the IAR Embedded Workbench C compiler. The compact algorithm used f = 1Hz and M = 16. The execution time of the algorithm was measured via an instruction-set-simulator, the number of clock cycles, and the processing time measured on the hardware while connected to an ECG emulator and recording the ECG waveform and QRS feature. The MSP430 was 43% and 53% utilized at 360 samples per second (SPS) and 400 SPS, respectively. The device consumed roughly 2 ma average current at 400 SPS. The proposed algorithm has proven to be compact, power efficient, and accurate. V. DISCUSSION AND FUTURE WORK This paper has introduced a novel technique for QRS detection in ECG waveforms that combines important properties, such as high accuracy, simplicity, flexibility and the ability to function on embedded devices. More specifically, the main features of this detector are: 1) Detection accuracy is as good as the performance of other, state-of-the-art algorithms. 2) A systematic procedure has been developed to adjust the limited set of detector parameters to extract the maximum performance of the algorithm. 3) Computation intensity of the algorithm has been referenced to the algorithm parameters to simplify the process of balancing computation power and detection accuracy. 4) Algorithmic compactness permits implementation on simple, low-power embedded processors. The time-frequency dependency of the filter can be exploited in a multi-rate structure, in a similar fashion to wavelets, and thereby reducing the total computation (i.e. the limited bandwidth of each filter can be computed at a lower rate), which significantly reduces the total computation, therefore allowing even more computationally limited embedded hardware to be utilized. REFERENCES [1] M. Elgendi, B. Eskofier, S. Dokos, and D. Abbott, Revisiting QRS Detection Methodologies for Portable, Wearable, Battery-Operated, and Wireless ECG Systems, PloS one, vol. 9, no. 1, p. e84018, [2] H. Kalantarian, C. Sideris, B. Mortazavi, N. Alshurafa, and M. Sarrafzadeh, Dynamic Computation Offloading for Low-Power Wearable Health Monitoring Systems, IEEE Transactions on Biomedical Engineering, vol. 64, no. 3, pp ,

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