[IEEE 2012 IEEE EMBS Conference on Biomedical Engineering and Sciences (IECBES 2012) - Langkawi,...

A Novel Algorithm for ECG Parametrization and Synthesis

Emir Turajlic Computer Science Department

Sarajevo School of Science and Technology Sarajevo, Bosnia and Herzegovina

[email protected]

Abstract— Parametrization and modeling of electrocardiogram (ECG) recordings are some of the most challenging areas of biomedical signal processing owing to the fact that ECG signals commonly exhibit complex temporal morphology and contain various artifacts of data collection process. In this paper, we propose a novel and fully automatic framework for highly accurate and robust ECG parametrization and reconstruction. The proposed method facilitates adaptive ECG signal modeling, and as such it is not constrained to an opportune combination of mathematical functions. The method relies on Dynamic Time warping (DTW) algorithm to establish the temporal relationship between the ECG model and the analyzed ECG pulses and to obtain their parametric description. Performance evaluation experiments conducted on a database of 40 one-minute ECG signal recordings, including examples of Normal Sinus Rhythm R Interval ECG record, Arrhythmia, Supraventricular Arrhythmia and Atrial Fibrillation, have shown that the proposed method is able to consistently produce accurate signal parametrization and reconstruction.

Keywords-ECG parametrization; ECG synthesis; dynamic time warping;

I. INTRODUCTION Electrocardiogram (ECG) is a time-varying signal

representing the electrical activity of cardiac muscle and is usually obtained as a recording of the potential difference between two electrodes placed on a surface of the skin.

Analysis of the ECG signal constitutes an important part in the processes of detection, diagnostics and monitoring of heart conditions. However, even after decades of research it remains one of the most challenging problems in modern biomedical signal processing. ECG signal is a non-stationary, quasi-periodic waveform that commonly exhibits complex temporal morphology and contains various artifacts of data collection process, such as the baseline wander (caused by respiration) and the high-frequency electromyography noise arising from muscle activity. Even the basic shape of ECG waveform can not only deviate from idealized model, but can also display a significant amount of time-variance for any given patient [1].

Over the years, various approaches to ECG signal modeling and feature extraction from the ECG signal have been proposed, including Gauss curve modeling via nonlinear optimization algorithms [2], Hilbert Transform based modeling

[3], Mealy and Moore automata model [4], threshold methods [5], continuous wavelet transform and principal component analysis [6], Archetypical Analysis [7], Hidden Markov modeling [8], [9].

In this paper, we propose a novel algorithm that is able to fully automatically, robustly and with high levels of accuracy parameterize, model and reconstruct the recordings of electrocardiogram signal. The proposed method uses Characteristic Waveform (CW) that is estimated as the most representative ECG pulse amongst the observed ECG waveforms to model a fundamental shape of an ECG pulse. Thus, the ECG model is non-deterministic and adaptive in nature. It relies on the Dynamic Time warping (DTW) algorithm to establish the temporal relationship between the proposed ECG model, i.e. Characteristic Waveform, and the analyzed ECG pulses and to provide parametric description for ECG waveform morphology. Specifically, the proposed method uses temporal and spatial parameters to describe the distinguishing features of an ECG pulse, such as P wave, T wave and QRS complex.

The remainder of this paper is organized as follows. The proposed methods for ECG parametrization and ECG synthesis are described in Sections II and III, respectively. Section IV presents and discusses the experimental results. Section V concludes the paper.

II. ECG PARAMETRIZATION A block diagram of the proposed algorithm for ECG signal

parametrization is illustrated in Fig. 1. What follows is a discussion on individual elements of the proposed system.

A. ECG Signal Pre-processing Accurate and robust parametrization of ECG signals

requires reliable pre-processing algorithms. These include R-peak detection, [10], [11], [12], removal of baseline wander (different approaches appear in literature, including FIR filtering [13], adaptive filtering [14], Empirical Mode Decomposition [15], nonlinear filter banks [16]), and removal of high-frequency noise from the ECG signal, where relevant solutions include low pass filtering [17], independent component analysis [18], discrete wavelet transform and Wiener filter [19].

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2012 IEEE EMBS International Conference on Biomedical Engineering and Sciences | Langkawi | 17th - 19th December 2012

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R-peak amplitude trajectory

Waveform Normalization and Alignment

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CW EstimationECG

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Figure 1. A block diagram of the proposed Characteristic Waveform ECG parametrization method

DTW

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Figure 2. A block diagram of the proposed Characteristic Waveform ECG synthesis method

Amplitude Modified CW

Amplitude Function Synthesis

R-peak time instant trajectory

The proposed algorithm relies on the following pre-processing techniques: a robust R-peak detection algorithm presented in [10], Empirical Mode Decomposition removal of baseline wander [15], and translation invariant hard thresholding, based on Daubechies wavelets ‘db4’ and decomposition level 4, for denoising of ECG signals.

B. Waveform Normalization and Alignment Waveform normalization and alignment provides a

platform for voice source parametrization independent of R-peak strength and heart rate fluctuations. The amplitude normalization uses the R-peak amplitude envelope, obtained via monotone piecewise cubic interpolation [20] of R-peak values over the entire duration of pre-processed ECG signal, to scale the ECG signal so that the normalized pulses have unity R-Peak amplitude. The temporal normalization is achieved using the estimate of ECG period trajectory, from R-peak instants, to re-sample the individual ECG pulses to a normalized ECG period length, TN=100. ECG matrix is formed by aligning the amplitude-scaled and temporally-normalized pulses. Here, R-peak instants are used to align the ECG pulses. In ECG matrix, each ECG pulse occupies one matrix row and represents a part of the signal in-between successive R-peak instants. ECG matrix is a construct that retains the chronological appearance of the individual ECG pulses in the ECG recordings.

The matrix is subsequently extended to include δ=10 samples of the neighboring pulses on either side of each pulse. Thus, each ECG matrix, E, raw has a length of L=120 samples and the ith normalized ECG pulse, ei is defined as follows.

Ni Tnnin <≤++= 0),1,()( δEe (1)

Here, the normalized period length value, TN =100, represents a compromise between the desired temporal resolution of the electrocardiogram waveforms and the computational efficiency requirements, limited by DTW block. Fig. 3 shows an ECG example matrix, obtained from an Arrhythmia ECG signal.

C. Characteristic Waveform Estimation Characteristic Waveform (CW) constitutes a most

representative ECG waveform amongst the entire set of waveforms present in an ECG matrix and is estimated as a waveform that attains the minimum cumulative Euclidian distance across the candidate waveforms, as in (2).

NikT

kN

ki≤≤−−== ∑

=1,)(*)(minCW

1argeeeee iii (2)

Here, N denotes a total number of waveforms in an ECG matrix.


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Figure 4. Parametrization of a particular ECG matrix (left) pulse via mapping of CW parameters (bottom) with an optimal alignment function

(solid line). The solid and the dashed line (center) correspond to the actual and synthesized optimal alignment functions. Darker colors in a center

graph indicate a lower cost in the DTW cost matrix. The ECG data corresponds to a file from a Normal Sinus Rhythm R Interval database.

D. Dynamic Time Warping- DTW Dynamic Time Warping (DTW) algorithm [21] is

employed to automatically estimate optimal temporal alignment between the Characteristic Waveform and other ECG matrix waveforms. In addition to local constraints, namely, boundary, monotonicity, and continuity constraint, the alignment is subjected to a global constraint in form of Sakoe-Chiba Band [22] to preclude pathological alignments and to increase the computational efficiency of DTW. An example of CW and a particular ECG matrix waveform alignment is given in Fig. 4.

E. ECG Matrix Parametrization The first step in the process of ECG parametrization is

obtaining the parametric description for the Characteristic Waveform. To that end, a pre-stored and normalized waveform corresponding to an ideal representation of ECG pulse with a known parametric description, represented by a vector tI is employed. Vector tI consists of elements that denote significant temporal instants in the ECG waveform. DTW is used to establish a temporal relationship between the idealized model and the Characteristic Waveform and thus, parametrize the Characteristic Waveform. The obtained optimal alignment function W, is used to map the time instant parameters from the idealized waveform to the Characteristic Waveform according to (3).

}{ ),( ONPONOFFPON , Q, P, P, P, T, TS, T== ttWt IICW (3)

Here, Q and S denote the time instant boundaries of the QRS complex associated with ventricular depolarization; TON, TP, TOFF, respectively, describe the time instants related to the onset, peak and the offset of the T-wave associated with the ventricular re-polarization; and finally PON, PP, POFF, respectively, describe the time instants related to the onset, peak and the offset of the P-wave, which is associated with the atrial depolarization in the heart. Each waveform in the ECG matrix is parameterized in a similar manner, using mapping procedure described in (3). However, instead of the idealized ECG waveform, Characteristic waveform is used as a reference signal for parametrization as the accuracy and computational efficiency of alignment process is improved when alignment involves similar waveforms. Consequently, a Characteristic Waveform that is estimated directly from the observable signal is used as a model for the entire ECG recording. In this way, ECG model is adaptable and non-deterministic. The role of the dynamic time warping algorithm is to facilitate tracking of non-linear temporal morphology of this adaptable model.

Fig. 4 illustrates the parameter mapping process between Characteristic waveform and a particular pulse in an ECG matrix. In this manner, Q, R, S, instants and the onset, peak and offset instants related to P-wave and T-waves are obtained for each pulse in the ECG matrix. Subsequently, these parameters are used to derive the familiar ECG pulse description, in terms of the following intervals: 'QT, 'ST', 'PR', 'P', 'QRS'. The true values of these intervals are obtained after they are adequately re-scaled using the ECG cycle duration trajectory. On the other hand, the amplitude parameters, 'T-peak' and 'P-peak' are estimated from ECG matrix using the associated time instant parameter values.

The reason for extending the ECG matrix to include 10% of waveforms on either side of any given pulse is to allow warping of R-peaks. Thus, the alignment function can indicate any error in R-peak instant estimation.


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III. ECG SYNTHESIS Fig. 2 shows a schematic diagram of a proposed ECG

synthesis system. The main principle behind the synthesis process is to use the ECG parameters, obtained during the ECG parametrization stage, and the Characteristic Waveform estimate to obtain an estimate of ECG matrix. Subsequently, the individual ECG pulses from the ECG matrix estimate are temporally scaled according to heart rate trajectory estimates, and arranged in a sequence according to R-peak instant estimates. Finally, the ECG pulse sequence is scaled in amplitude with the synthesized R-peak amplitude trajectory to produce the reconstructed ECG signal.

The first stage of ECG matrix estimation involves the amplitude modification of Characteristic Waveform, via a set of synthesized amplitude alignment functions to take into account spatial morphology of the electrocardiogram waveform. In the subsequent stage of the ECG matrix estimation, the amplitude modified CW waveform is temporally and non-linearly warped via a set of synthesized alignment functions to obtain ECG matrix estimate.

In case of each ECG matrix pulse, the Characteristic Waveform amplitude is modified to account for varying P and T wave peak values. For a particular pulse, the ratio of P and T wave peak values compared to the P and T wave peak values of the Characteristic Waveform, along with the unity values associated with R-peaks and boundaries of the waveforms are used to generate an amplitude alignment curve. Here, a cubic interpolation algorithm is used to interpolate the values of amplitude modification curve over the entire duration of CW. Each ECG matrix pulse is associated with a particular amplitude alignment curve that is used to scale the CW amplitude, such that the resulting amplitude modified CW has exactly the same T-wave and P-wave peak values as the corresponding ECG matrix pulse.

Temporal alignment function synthesis involves reconstruction of the temporal alignment functions that relate CW to other ECG matrix pulses. For a particular ECG pulse, the temporal alignment function synthesis involves the time instant parameters associated with that particular pulse and time instant parameters associated with Characteristic Waveform. Again, the monotone piecewise cubic interpolation algorithm is used to interpolate the values over the entire duration of CW. Fig. 4 illustrates the process of alignment function synthesis. Note that the parameters {1, δ+1, 120-δ+1, L} are added to the ECG parameter set to ensure that the boundary constraint that was originally imposed on Dynamic Time Warping algorithm is satisfied and to prevent R-peak distortion.

IV. RESULTS AND DISCUSSION The performance of the proposed Characteristic Waveform

based ECG parametrization, modeling and synthesis algorithm is evaluated on a database of 40 one-minute recordings of ECG signal[23], including 10 one-minute-long samples from each of the following databases: Normal Sinus Rhythm R Interval Database-sampled at 128 Hz, Arrhythmia Database, sampled at 360 Hz, Supraventricular Arrhythmia Database, sampled at 200 Hz, Atrial Fibrillation Database, sampled at 250 Hz. The

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Figure 5. Examples of denoised ECG signal with base wander removed and the corresponding synthesized signals for a) Normal Sinus Rhythm R Interval database; b) Arrhythmia database; c) Atrial Fibrillation database;

d) Supraventricular Arrhythmia database


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Figure 6. Temporal parameter trajectories and b) Amplitude parameter trajectories for a file 105m in Arrhythmia database

quality of both ECG parametrization and ECG synthesis is evaluated using the Percentage Root-mean-square Difference (PRD) measure between the pre-processed ECG signals and the reconstructed waveforms, as in (4).

[ ] [ ]( )[ ]( )

%100ˆ

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xxnx

nxnxPRD N

n

Nn

∑∑

=

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Here, ][nx and x denotes the pre-processed ECG signal with the baseline wander and noise removed, and its corresponding mean value, respectively. ][ˆ nx denotes the reconstructed ECG signal.

Fig. 5 illustrates the ECG synthesis performance using one example from each of the following conditions: normal sinus rhythm R interval, arrhythmia, supraventricular arrhythmia and atrial fibrillation. The results demonstrate that the proposed method is able to cope with a wide range of different ECG waveforms. Whereas, the normal sinus rhythm and supraventricular arrhythmia have close to an ideal basic waveform shape, examples of atrial fibrillation and arrhythmia have much more irregular shapes. Furthermore, the atrial fibrillation example displays a very jittery heart rate and almost a non-existing P-wave interval, while the two examples of arrhythmia have instantaneous changes in ECG waveform shape, R-peak amplitude and ECG pulse duration.

Nevertheless, the proposed method is able to overcome all of these challenges related to tracking of ECG waveform morphology and produce faithful reconstruction of all considered signals. Since the ECG model is derived from the observed signal, it inherently contains those temporal features that cannot be, practically, represented by a deterministic model. The proposed ECG model is able to adopt all those features that might differ from the ideal notion of ECG pulse, but are consistently present in the observe ECG signal. Furthermore, the nonlinear temporal warping of ECG model along with the non-linear amplitude scaling of the Characteristic Waveform allows the ECG pulse model to take very complex forms, and thus, to accurately adapt to the observed signal.

Table I provides a summary of reconstruction performances for each ECG signal database. Although the reconstruction performance is fairly consistent across databases, as expected, on average, a slightly better performance is achieved on a Normal Sinus Rhythm database. It is important to note that observations ECG reconstruction results have indicated that the error energy is primarily localized around the S and Q instant, where the amplitude of the signal is very irregular. For the vast majority of the ECG signal duration, excluding the QRS complex, the errors are significantly lower than the results from Table I would indicate.

Nevertheless, the results demonstrate that the proposed method consistently offers high levels of accuracy in signal reconstruction and thus, they also validate the quality of ECG signal parametrization.

TABLE I. MODELING ACCURACY - AVERAGE PRD

Accuracy measure

ECG Database

Normal Arrhythmia Atrial Fibrillation

Supraventricular Arrhythmia

PRD 9.5 % 14.3 % 18.9 % 22.1 %

Fig. 6 shows the trajectories of the ECG parameters for an approximately one minute duration of an Arrhythmia ECG example. The graphs show the morphology of temporal parameters, including the following intervals 'QT, 'ST', 'PR', 'P wave width', 'QRS width' and ECG pulse duration. In addition, Fig. 6 shows the dynamic of QRS, T-wave-peak, and P-wave-peak amplitudes. The parameter estimation is robust and accurate as indicated by the quality of ECG synthesis results. The ability of the proposed method to reliably produce this type of ECG parameter trajectories provides evidence that the proposed method could be used as a part of the process for detection, diagnostics and monitoring of heart conditions.

V. CONCLUSION In this paper, a novel method for parametrization and

synthesis of electrocardiogram signals is proposed. The proposed method relies on an adaptive, non-deterministic model to describe a basic shape of the ECG pulse waveform. Dynamic Time Warping algorithm is employed to establish the temporal relationships between the model waveform and other


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waveforms in the ECG signal, independently of heart rate and R-peak amplitudes. The estimated optimal alignment functions are employed to accurately parameterize ECG signal. The ECG synthesis relies on the results of parameterization to temporally and spatially warp the adopted ECG model, in a nonlinear manner, and faithfully reconstruct the observed ECG recordings. Performance of the proposed method is evaluated on a database of 40 1-min-long ECG signals, that includes examples from normal sinus rhythm R interval, arrhythmia, supraventricular arrhythmia and atrial fibrillation databases. The results demonstrate that the proposed method can consistently provide high levels of accuracy in both signal parametrization and signal synthesis, and thus it could be used as part of the processes for detection, diagnostics and monitoring of heart conditions.

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