Heart rate monitoring and therapeutic devices: A wavelet transform based approach for the modeling and classification of congestive heart failure

ISA Transactions xxx (xxxx) xxx–xxx

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Research article

Heart rate monitoring and therapeutic devices: A wavelet transform based approach for the modeling and classification of congestive heart failure Ashish Kumar, Rama Komaragiri, Manjeet Kumar∗ Department of Electronics and Communication Engineering, Bennett University, Greater Noida, Uttar Pradesh, 201310, India

A R T I C LE I N FO

A B S T R A C T

Index terms: Heart rate monitoring Congestive heart failure Electrocardiogram Biorthogonal wavelet transform Wavelet filter bank

Heart rate monitoring and therapeutic devices include real-time sensing capabilities reflecting the state of the heart. Current circuitry can be interpreted as a cardiac electrical signal compression algorithm representing the time signal information into a single event description of the cardiac activity. It is observed that some detection techniques developed for ECG signal detection like artificial neural network, genetic algorithm, Hilbert transform, hidden Markov model are some sophisticated algorithms which provide suitable results but their implementation on a silicon chip is very complicated. Due to less complexity and high performance, wavelet transform based approaches are widely used. In this paper, after a thorough analysis of various wavelet transforms, it is found that Biorthogonal wavelet transform is best suited to detect ECG signal's QRS complex. The main steps involved in ECG detection process consist of de-noising and locating different ECG peaks using adaptive slope prediction thresholding. Furthermore, the significant challenges involved in the wireless transmission of ECG data are data conversion and power consumption. As medical regulatory boards demand a lossless compression technique, lossless compression technique with a high bit compression ratio is highly required. Furthermore, in this work, LZMA based ECG data compression technique is proposed. The proposed methodology achieves the highest signal to noise ratio, and lowest root mean square error. Also, the proposed ECG detection technique is capable of distinguishing accurately between healthy, myocardial infarction, congestive heart failure and coronary artery disease patients with a detection accuracy, sensitivity, specificity, and error of 99.92%, 99.94%, 99.92% and 0.0013, respectively. The use of LZMA data compression of ECG data achieves a high compression ratio of 18.84. The advantages and effectiveness of the proposed algorithm are verified by comparing with the existing methods.

1. Introduction The global increase in the deaths caused by cardiovascular diseases (CVD) is on a rampage and agencies have cited alarming percentages of such deaths [1]. With more hectic lifestyles, rapidly aging population and globally expanding life expectancy, control of CVD require purposeful and consequential healthcare amenities. This increasing problem can be efficiently dealt with the creation of economic, patientcentric and wearable wireless devices for recording and tracking vital signs. Dedicated measures and devices intercepting early signs of CVD can be a better way off in early preventive, diagnostic test models. The big challenge here is to develop self-effacing, humble, patient-friendly wearable device for reading and monitoring electrocardiogram (ECG) data in continual and uninterrupted manner. The next level challenge for such devices is to be light in weight with extended battery life, which requires a substantial integration and simulation of signals and complex data [2]. ∗

The wearable portable device thrives and draws power from wireless transceiver. To increase the efficiency of a wearable heart monitoring device, it is much imperative to decrease or prune the use of transceivers, hence efficaciously lowers the power consumption. Analysis of QRS complex detection and R-R interval estimation as part of ECG signals as shown in Fig. 1, are much advisable and advantageous to be conducted for an ECG sensor. Such analysis facilitates and activates the required transmission when it is adjudged to be of critical importance based on patient's cardiac health, thereby leading to decreased power generated through the system. Additionally, the continuous monitoring of patient's heart thus leads and generates a sizeable and substantial amount of ECG data which requires being accumulated and hosted locally in various formats of memory and data storage. Once reserved appropriately, the data needs further seamless transfer to appropriate channels for meaningful investigation. This series of steps in the data collection, storage, and analysis requires heavy power utilization.

Corresponding author. E-mail addresses: [email protected] (A. Kumar), [email protected] (R. Komaragiri), [email protected] (M. Kumar).

https://doi.org/10.1016/j.isatra.2018.05.003 Received 4 March 2018; Received in revised form 2 May 2018; Accepted 6 May 2018 0019-0578/ © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: Kumar, A., ISA Transactions (2018), https://doi.org/10.1016/j.isatra.2018.05.003

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Fig. 1. Graphical representation of a typical ECG signal.

power dissipation. Lowpass filters realized using wave digital filter structure reduces the multipliers count by 75% and delay elements count by 80%. In the ECG detection block, an adaptive slope predication-based threshold is employed. Furthermore, Lempel–Ziv–Markov chain algorithm (LZMA) data compression technique is used to compress the ECG data. Finally, the efficiency of the proposed design is quantified regarding signal-to-noise ratio, detection accuracy, percentage root mean square difference and compression ratio. The rest of the paper is structured as follows. Following the introduction in Section 1, the methodology used to design the proposed work is discussed in Section 2. The detailed description of the results is provided in Section 3, and the results are discussed in detail in Section 4. Finally, Section 5 concludes the paper.

To deal the substantial power requirements of ECG data transmission, efforts are being made to compress the ECG data to minimize the rate at which data is produced for transmission is reduced thus helping in lowering the power requirements of the system. To achieve high compression ratio lossy data compression techniques and procedures are considered, but they have failed to provide required results. The ECG signal reconstructed after lossy data compression results in an ECG signal that contains a sizable amount of noise, due to which crucial diagnostic data gets wasted thus lacking regulatory conformity. For medical applications, the complications in lossy compression techniques used in ECG data compression demand usage of lossless data compression techniques of ECG signals. The world of wearable sensors is experiencing new waves with high-efficiency, decreased power operation and modest convolution in the application. Hence, it is much required to find a better fit and balance between the complexity and compression ratio (CR). The current trends and medical scenario, have given birth to several QRS complex detection algorithms [3,4,60–62]. The striking feature of all these detections algorithms is reduced power consumption which is an enabler of wearable devices. The research in wearable devices has integrated both unified lossy and lossless data compression techniques together. The research advancements in cardiac health monitoring have made it quantifiable to note the reduction in the sensor power by 2–5 times [5]. It is comprehended that implementation and combination of two distinct hardware setups for QRS complex detection and compression lead to increased system computations and power. Therefore, it is of utmost importance to have a joint QRS complex detection and lossless data compression algorithm. In the present work, an improved wavelet transform based joint ECG detection, and data compression algorithm applicable for the modeling and characterization of congestive heart failure is proposed. To decide on congestive heart failure, a detailed analysis and characterization of the ECG signal morphology are required. The biorthogonal wavelet transform is used to design wavelet filter banks (WFBs) due to its higher SNR compared to other wavelet transforms and requires less number of coefficients, and its shape resembles the ECG wave. The proposed wavelet filter bank is different from previously designed WFBs. Instead of using conventional low and high pass filter pairs, the proposed decimated WFB architecture consists of a series combination of three lowpass filters realized using wave digital filter realization. The proposed architecture thus considerably reduces the circuit complexity as less number of gates, and less number of clocks with different frequency at each level are required which results in an advantage of lower dynamic

2. Methodology Different recorded physiologic signals from Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database, PTB diagnostic ECG database, from physionet.org [6] are chosen for the analysis of the proposed method. The MIT-BIH arrhythmia database contains 48 different ECG signals recorded from different subjects. The duration of each record is 30:06 min with a frequency of 360 Hz. The collected data is further classified into five types: normal, atrial premature contraction (APC), premature ventricular contraction (PVC), left bundle branch block and right bundle branch block. Table 1 categorizes different ECG signals available in MIT-BIH database. The methodology used to develop the proposed design is elucidated below. Joint ECG detection and data compression algorithms contain three building blocks, namely, pre-processing, peak detection and Table 1 Detail of different types of ecg signals. Type of ECG Signal

ECG record

Total number of beats

Healthy Atrial Premature Contraction

100, 103, 207, 223, 106,

2000 2000

Premature Ventricular Contraction Right Bundle Branch Block Left Bundle Branch Block

2

101, 108, 112. 121, 124, 200, 201, 202, 205, 209, 213, 215, 219, 220, 222, 228, 231, 232, 233 107, 200, 201

2000

118, 207, 212

2000

109, 111, 207, 214

2000

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classification, and data compression. A detailed discussion of the proposed approaches and their theoretical background is as follows.

ψ (n) =

1 M

∑ s (n) ϕb0,c (n) ∑ s (n) ψb,c (n), b ≥ b0

∑ h ψ (m − 2c )

Wψ (b, c ) =

(7)

j

∑ s (n)2 2 ⎡⎢∑ h ψ (m − 2c ) ⎣

n

m

1 ⎣ M

∑ h ψ (m − 2c ) ⎡⎢ m

⎤ 2 ϕ (2 j + 1n − m) ⎥ ⎦

(8)

∑ s (n)2b+1ϕ (2b+1n − m) ⎤⎥ ⎦

n

(9)

Solving Eq. (9) results in

Wψ (b, c ) =

∑ h ψ (m − 2c ) Wϕ (j + 1, m)

(10)

m

A similar procedure results in

Wϕ (b, c ) =

∑ hϕ (m − 2c ) Wϕ (b + 1, m)

(11)

m

Similarly, transformed signal is reconstructed using inverse DWT. Inverse DWT can be computed using in Eq. (12)

s (n) =

1 M

∞

∑ Wϕ (b0, c ) ϕb0,c (n) + ∑ ∑ Wψ (b, c ) ψb,c (n) B = b0

c

c

(12)

2.1.2. Selection of wavelet transform There are different segments in a typical ECG signal which are indexed by letters, P, Q, R, S, T and U. Accurate analysis of ECG signal with abrupt changes demands a new class of well-localized functions in time and frequency. Wavelet transform which is a rapidly decaying wave-like oscillation which exists for a finite duration having zero mean satisfies this condition. Fourier analysis allows discontinuous, nonsmooth waveforms and convert them into a linear combination of extremely smooth functions, namely, the sine waves. Whereas the wavelet transform coverts smooth functions into a linear combination of effectively jagged or discontinuous functions. So, going from smooth to nonsmooth has its place in modern communication and signal processing. The wavelet transform is used in numerous engineering applications like, telecommunications, signal processing, geophysics, imagery and video coding and astrophysics to name a few. Various wavelet families such as Haar, Daubechies, Coiflet, biorthogonal, reverse biorthogonal, symlet have been used depending on

b

(4)

n

2 ϕ (2b + 1n − m)

By interchange the order of summation in Eq. (8)

(3)

∑ s (n)2 2 ψ (2bn − c )

1 M

Wψ (b, c ) =

Using Eq. (3) in Eq. (2) results in

1 M

(6)

Using Eq. (7) in Eq. (4) results into

b

Wψ (b, c ) =

2 {2(2bn − p)

m

Where, W∅ (b0 , c ) and WΨ (b, c ) are the scaling function and wavelet function, respectively. ψb, c and Φ b0, c are the transformation kernel. b0 and k, are scaling and shifting parameters, respectively.

ψb, c (n) = 2 2 ψ (2bn − c )

and with a shift of c units. Eq.

Let, p = m-2c. substituting in Eq. (6), gets modified as

(2)

n

2b

p

(1)

n

∑ h ψ (p)

ψ (2bn − c ) =

2.1.1. Mathematical background of wavelet transform An ECG signal s(n) is decomposed using forward discrete wavelet transform (DWT). The standard relations for the Forward DWT are as follows.

Wψ (b, c ) =

(5)

Now, if n is multiplied by a factor (5) gets modified into

Both low-frequency noises and high-frequency noises are also recorded during the ECG recording and are an integral part of an ECG signal. Prominent low-frequency noises in an ECG include baseline wander, motion artifact, electrode contact noise while important highfrequency noises are power line interference, Electromyography noise from the chest wall, Burst noises [7]. The proper setting of a recording device leads to a reduction in the noise level due to external noise sources. Whereas, it is challenging to remove internal noise generated due to other physiological signals like electromyography signal and the electrodermal activity signal. In some individual cases, due to the imbrication of power line spectrum over QRS complex spectrum, removing power line interference is difficult. Noise-free ECG signals are required for an accurate feature analysis and diagnosis by the clinicians. In the past few years, various new approaches, namely, digital filtering [8,9,65,66], adaptive filtering [64], Kalman filtering [10,11,58], fractional calculus [12,13], empirical mode decomposition [14] and wavelet transform [15,16] are proposed for the denoising of ECG signal. All these denoising approaches aim to increase the efficiency by filtering several noises present in an ECG signal. Comparison of different ECG detection approaches is shown in Table 2. Considering the tradeoff between robustness and noise, parameter choice and hardware complexity; wavelet transform based techniques are found to be most suitable for ECG denoising [3]. The wavelet transform based denoising algorithms have a medium hardware complexity and very high denoising capability as compared to other existing techniques.

Wϕ (b0 , c ) =

2 ϕ (2n − p)

p

2.1. Pre-processing

1 M

∑ h ψ (p)

but Table 2 Comparison of different ecg detection approaches. Algorithms

Technique

Hardware Complexity

Detection Performance

Filtering

Band pass Filtering [38,40] Digital Filtering [8,9] Adaptive Filtering [64] Kalman Filtering [10,11] ANN [24] Haar Wavelet Biorthogonal Wavelet Symlet Wavelet Daubechies Wavelet Reverse Biorthogonal Wavelet Genetic Algorithm

Simple

96–98%

Complex Medium Medium Medium

99% < 99% < 99% < 99%

Very Complex

∼99.9%

Artificial neural network Wavelet Transform [2,3,5,15–18,20–23,27,45,47]

Genetic Algorithm [14,43]

3

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Fig. 2. Decomposition using wavelets.

sharper. A higher order wavelet results in a large number of coefficients, thus increasing the computational time and power consumption. Hence there is a tradeoff between the order of the filter and frequency response. Quadratic spline wavelet transform is useful in avoiding the tradeoff between the order of the filter and frequency response, but the shape of wavelet function is not suitable for ECG detection. Biorthogonal wavelet transform has a shape that resembles that of an ECG signal when compared to other wavelet transforms. It is observed from Ref. [20] that almost all wavelet transforms have a similar detection accuracy of 90% of the ECG signals available in a database. For the remaining 10% of ECG signals, biorthogonal wavelet transform gives less error compared to other wavelet transforms. Classification of wavelet transforms on their main properties are listed in Table 3. Here, Nd and Nr respectively are decomposition order and reconstruction order. It is evident from Table 3 that biorthogonal wavelet transform satisfies all the criterion required for the ECG signal denoising and detection. Hence, the biorthogonal wavelet transform is selected for the proposed work.

the suitability of various applications. Precise estimation of ECG signal parameters demands a suitable choice of basis function [17]. These wavelet families are further categories into orthogonal, semi orthogonal, shift orthogonal and biorthogonal [18]. For reconstruction of ECG signal from wavelet coefficients and conserving the energy of the ECG signal, valuable property is orthogonality. ECG signal a(k-1, n) is first decomposed (as shown in Fig. 2) using scaling coefficients (h(n)) and wavelet coefficients (g(n)) and then down-sampled by the scaling and wavelet filter banks (coefficients h(n) and g(n)). In the next step, h (n) and g(n) are down-sampled to get a(k, n) and b(k, n) also known as TREND and DETAIL. The trend signal a(k,n) is further downsampled. In each step, the signal TREND is further downsampled till ECG signal in the desired frequency band is obtained. The process to reconstruct the ECG signal is reverse [19]. The orthogonal wavelets are neither regular nor symmetric thus introduces a non-linear phase shift during analysis. Presence of nonlinear phase shift is problematic in case of ECG signal as the temporal shape of the transformed signal is important. The problem of non-linear phase shift is eliminated by using biorthogonal wavelet transform as they are regular as well as symmetric. Besides the symmetry, another valuable property that plays a crucial role while selecting wavelet transform is the time-frequency localization and the ability to localize temporal and spectral information. Time localization is inversely related to frequency localization and the smoothness of the wavelet function. A signal that has events that are separated by narrow frequency margins require frequency localization. The signals where transitory events are important, require time localization. For the selection of a wavelet transform for ECG signal denoising and detection, properties of an ECG signal need to be examined. The three essential properties of an ECG signal which play a vital role in the selection of wavelet transform are (i) slope of QRS signal, (ii) the shape and spectrum of ECG signal [59] and (iii) event localization in time [20]. The wavelet transform on an ECG signal should result in a linear phase. Hence such a wavelet transform is non-orthogonal. Time localization is vital because of the transient nature of ECG events. As biorthogonal wavelets are symmetric, non orthogonal and localized in time, the above-listed criterion is satisfied. With the increase in the order of the wavelet transform based filter, the desired frequency response becomes

2.1.3. Selection of wavelet filter bank architecture ECG signal has both quicker parts and slower parts in the response. The slower parts of the response are likely to last for a more extended region in time hence form the low-frequency components of the ECG signal. The quicker parts in the ECG response are likely to last for a smaller duration in time and thus form the high-frequency components Table 3 Classification of wavelets with their main properties.

4

Wavelet transform

Key properties

Implementation

Orthogonal splines Semi-orthogonal splines Shift-orthogonal splines Biorthogonal Splines

Symmetry and regularity + orthogonality Symmetry and regularity + optimal time-frequency localization Symmetry and regularity + Quasiorthogonality + fast decaying wavelet Symmetry and regularity + compact support

IIR/FIR Recursive IIR/FIR IIR FIR

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Fig. 3. Proposed wavelet filter bank architecture.

proposed architecture for the wavelet filter bank requires ten adders, four multipliers, and three delay elements. It is evident from Table 4 that the proposed filter bank realization uses less hardware compared to the other existing filter bank realizations.

of the ECG signal. Hence, it is desirable to separate the high frequency and low-frequency components of the ECG signal. For that, a system of filters that possess specific individual characteristics as well as collective characteristics is required. Such a system is known as a filter bank. A filter bank, as opposed to a single filter in discrete time signal processing, has a common input or summation output. Two filter banks one for analysis and the other for synthesis form central core to multirate discrete signal processing. For ECG signal denoising different wavelet filter bank architectures namely, two-channel filter bank [21], quadrature mirror filter bank [55], Mallat's wavelet filter bank [21], parallel filter bank, decimator wavelet filter bank [22], undecimator wavelet filter bank [23], and pyramid filter bank [56] are proposed by various practitioners. One of the primary concern with all these filter bank architectures is that they require more hardware which results in increased circuit complexity. Hence, a new wavelet filter bank architecture is proposed for ECG denoising that utilizes a cascade connection of three lowpass filters which requires less hardware with low power consumption. Block diagram representation of the proposed wavelet filter bank is shown in Fig. 3. The proposed wavelet filter bank architecture is capable of detecting all the useful peaks of an ECG signal, namely P, Q, R, S, and T. Aforementioned wavelet filter bank architectures are verified for all wavelet transforms. The efficiency of a filter bank is determined by finding signal-to-noise-ratio (SNR), percent root-mean-square difference (PRD), circuit complexity and root mean square error (RMSE). The transfer function of lowpass filter H(z) and highpass filter G(z) used in the equivalent wavelet filter bank architecture is as follows:

H (z ) = −0.12 + 0.99z −1 + 0.99z −2 − 0.15z −3 G (z ) = −0.17 + 0.53z −1 − 0.53z −2 + 0.17z −3 −1

−2

2.2. ECG signal detection An adaptive slope prediction-based thresholding is used to detect different peaks of an ECG signal. Two different values of threshold, namely, the downward threshold (Threshold1) and the upward threshold (Threshold2), as given in Eq. (15), are selected with which the denoised ECG signal is compared to detect different peaks in the ECG signal. Both the upward as well as downward threshold values are calculated using continuous assessment of the signal peak and noise peak. The set of thresholds are defined in Eq. (15).

Threshold 1 = NP + 25%(SP − NP ) Threshold 2 = 50%Threshold 1

where NP is the continuous assessment of the noise peak, and SP is the continuous assessment of the signal peak. The continuous assessment of noise peak and signal pear respectively is given by Eq. (16).

NP = 25% of overall peak + 85% of NP , if overall peak is the noise peak SP = 25% of overall peak + 85% of SP, if overall peak is the signal peak (16) Then denoised ECG signal is compared with both the threshold values. If the compared value is higher than Threshold2 value, then a peak is counted and identified as R-peak. Those peaks whose value lies between Threshold1 and Threshold2 are counted as a P-peak. All the other peaks that may occur within the refractory period (0.2s) are disregarded. This procedure is repeated until the end of the ECG signal. By calculating the rising and falling edge of the detected peak, the actual presence of a peak can be determined. The process of proposed adaptive slope prediction threshold-based ECG peak detection is shown in Fig. 6. By calculating the time difference between two successive R peak times, the heart rate in beats per minute (bpm) can be calculated by using Eq. (17).

(13)

−3

where, z , z and z are the delay elements. The decomposition level of the wavelet transform plays a vital role in the detection of number of peaks and their location in an ECG signal. Selecting the desired decomposition level is allied with the frequency components necessary for the ECG signal analysis for a given number of samples. Biorthogonal wavelet transform satisfies the relationship as in Eq. (14).

2N = p

(15)

(14)

Heart Rate =

where p is the number of signal samples, and N is the decomposition level. Since most of the signal energy lies between 0 and 20 Hz [24], the third level of decomposition gives an optimal performance, hence, selected for the proposed work. Mother wavelet can be chosen based on the characteristics of the wavelet transform, namely, the number of wavelet coefficients, and resemblance with ECG signal. In the proposed work, third level decomposition is selected as it has maximum frequency components compared to other decomposition levels as shown in Fig. 4. To further reduce the circuit complexity of proposed filter bank architecture, lowpass filters are realized using wave digital filter (WDF) realization. WDF realization is advantageous regarding number of the multiplier and delay element requirement when compared to other filter realization techniques reported prior [57] thus reducing the overall circuit complexity of the filter bank. Wave digital filter realization of a 3rd order lowpass filter is shown in Fig. 5. Hardware comparison of the proposed wavelet filter bank with the existing ones are listed in Table 4. It is observed from Table 4 that the

60 Average time difference between two successive R − peaks (17)

Physiological condition of a subject is measured using heart rate. If a heart rate regularly exceeds 100 bpm, then the subject is suffering from sinus tachycardia, and if the heart rate is below 50 bpm, then the subject is suffering from sinus bradycardia. This system thus shows the presence of particular sinus arrhythmia disease in the subject. 2.2.1. Lossless data compression Lossy and lossless compression are the two broad categories of datacompression techniques. Medical regulatory boards have not approved lossy compression techniques, hence can't be commercially used. So, lossless compression technique with high bit compression ratio is highly required. Many lossless ECG data compression techniques are reported in the literature [26–31]. Compression ratio (CR), compression speed (CS), and memory usage are the three parameters based on which the proposed compression technique is selected. Comparison of some 5

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Fig. 4. Frequency component at each wavelet filter bank output. Table 4 Hardware comparison of proposed wavelet filter bank with existing ones. Methods

Lowpass filters

Highpass filters

Adders

Multipliers

Delay Elements

Decimator [23] Kumar [3] Kumar et al. [4] Kumar et al. [25] Proposed

3 3 3 3 3

4 4 4 1 0

16 16 16 16 10

13 13 13 16 4

13 13 13 24 3

Fig. 5. Wave digital filter realization of a 3rd order lowpass filter. Fig. 6. Proposed adaptive slope prediction threshold-based ECG detection.

lossless data compression techniques -based on the above three parameters are discussed in Table 5. It is observed from Table 5 that all the three criterion cannot be achieved simultaneously. Considering the tradeoff among the above three criterion, LZMA data compression technique is used for the ECG data compression. LZMA data compression technique used in this work has medium compression speed, high compression ratio, and low memory usage and detailed in Fig. 7. During compression, detected ECG samples are taken. Then, a window of eight ECG samples is selected, and the compression process is applied on the window. The first value of the window is unchanged,

and the next bit value is subtracted from the previous bit value as described below

Delta (0 ) = W (0 ) Delta (i ) = W (i ) − w (i − 1) 1≤i≤7 End For example, a window of input ECG samples “5, 6, 7, 8, 9, 8, 7, 6” is selected, and the encoded output sequence is “5, 1, 1, 1, 1, −1, −1, 6

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Table 5 Comparison of different data compression techniques.

SNR = 10 × log10

Compression technique

Compression speed

Compression ratio

Memory usage

Lempel–Ziv–Welch (LZW) Lempel–Ziv–Oberhumer (LZO) Lempel–Ziv–Markov chain algorithm (LZMA) LZFX

Medium Fast

Medium Low

Medium Low

Bzip2 LZ4 Run length encoding (RLE) Huffman coding

Medium

High

Low

Fast

Low

Medium Fast Medium High

High Low High Medium

Not Reported High Low Medium High

(denoised ECG signal − original ECG signal)2 N pi − ⌢ p ) ∑iN= 1 (pi − p )(⌢ 2 p −⌢ p ) ∑N (p − p )2 ∑N (⌢ N

RMSE = CC =

∑nN= 1 (original ECG signal)2 ∑nN= 1 (denoised ECG signal − original ECG signal)2

∑n = 1

i=1

PRD = 100

i

i=1

i

N 2 ⎧ ∑n = 1 [original ECG signal − denoised ECG signal] ⎫ N 2 [ original ECG signal ] ∑ ⎨ ⎬ n=1 ⎩ ⎭

(18)

Where N is the number of samples. The proposed technique is compared with the existing literature [32–38] to validate the denoising capabilities. To ensure a fair comparison between various ECG denoising methods given in Refs. [32–38], all these methods are implemented under same conditions using Matlab R2017a. Performance of the proposed work is evaluated in five different conditions, namely, normal ECG signal, ECG signal with random noise, ECG signal with white Gaussian noise (WGN), ECG signal with baseline wandering noise (BWN) and ECG signal with power line interference noise (PLI). All the above four noises are generated and added to the raw ECG signal using MATLAB R2017a environment. Table 6 presents the performance comparison of the proposed technique with the existing techniques. It is evident from Table 6 that the proposed technique achieves highest SNR and lowest MSE as compared to the previously designed techniques. Also, the proposed technique delivers a higher average value of CC which is 0.9723 and smaller average value of PRD which is 12.141%. Comparison chart of SNR and MSE of the proposed algorithm with existing algorithms is shown in Fig. 8. Detection accuracy (DA), specificity (SP), overall detection error (error), and sensitivity (SE) are the four performance evaluation indexes of the proposed ECG detector. All the four performance evaluation indexes are mathematically expressed as in Eq. (19):

−1”. The delta encoding provides encoded output sequences in the form of differences from previous data as shown in the example. Then the sliding dictionary algorithm is applied to the encoded output sequence of the delta encoding. Finally, the sliding dictionary output is used as an input of a range encoder which encodes the symbols of the ECG data into numbers based on the frequency at which the symbols occur.

3. Experiment results The proposed design is implemented using Matlab R2017a and tested amongst various ECG signal from different databases, namely, MIT-BIH database, BIDMC congestive heart failure database, PTB diagnostic ECG database, and St.-Petersburg Institute of Cardiological Techniques 12-lead arrhythmia database [63]. The frequency range of raw ECG data taken from these databases lies between 250 Hz and 1000 Hz.

DA = SP =

3.1. The performance measures

Number of correctly detected ECG peaks Total number of ECG peaks Number of correctly detected ECG peaks Number of correctly detected ECG peaks + incorrectly detected ECG peaks

Error = The proposed work is divided into three parts, namely, ECG signal denoising, peak detection and data compression. Signal-to-noise ratio (SNR), root mean square error (RMSE), correlation coefficient (CC) and percent root mean square difference (PRD) are the four performance evaluation indexes of the proposed ECG signal denoising technique. All the four performance evaluation indexes are mathematically expressed as in Eq. (18):

SE =

incorrectly detected ECG peaks + missed ECG peaks total number of ECG peaks

number of correctly detected ECG peaks number of correctly detected ECG peaks + missed ECG peaks

(19)

Initially, four different types of ECG data, namely, healthy, coronary artery disease, congestive heart failure, and myocardial infarction is taken from open access databases. Here, sixteen healthy subjects from MIT-BIH arrhythmia database, 52 healthy subjects from PTB database,

Fig. 7. Block diagram representation of LZMA compression scheme. 7

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Table 6 Performance comparison of proposed technique with the existing techniques. Reference

[32] [33] [34] [35] [36] [37] Proposed

Random noise

WGN

BWN

PLI

SNR

MSE

SNR

MSE

SNR

MSE

SNR

MSE

NA NA 10.0102 9.1269 NA 9.0021 30.0051

NA NA 0.0020 0.0011 NA 0.0026 0.0008

1.2189 6.8530 8.1230 NA NA 6.1834 32.6583

NA NA 0.00028 0.0020 0.00390 0.00160 0.0003

NA NA 14.0250 11.5000 8.5146 12.9826 28.3821

0.0218 0.0025 0.0039 NA NA 0.0028 0.0029

NA NA 10.0102 9.1269 NA 9.0021 30.0051

NA NA 0.0020 0.0011 NA 0.0026 0.0008

Fig. 8. Comparison of SNR and MSE of the proposed algorithm with the existing algorithms.

Table 7 Detail of ecg data used in the proposed work. ECG database

Type of data

Records

Length of data

Frequency

Leads

MIT-BIH database PTB database BIDMC database PTB database St. database

Healthy Healthy Congestive Heart Failure myocardial infarction coronary artery disease

16 records of 16 subjects 80 records of 52 subjects 15 records of 15 subjects 365 records of 148 subjects 17 records of 7 subjects

≅ 30.06 minutes variable 20 hours variable 30 minutes

360 Hz 1 kHz 250 Hz 1 kHz 257 Hz

2 12 2 12 12

Table 8 performance evaluation of the proposed ECG detector. Type of ECG beat

Number of beats

TP

FP

FN

DA (%)

SP (%)

Error

SE (%)

Healthy Myocardial infarction Coronary artery disease Congestive Heart Failure Total

104363 40182 41545 89237 275327

104296 40150 41496 89177 275119

67 32 49 60 208

42 25 36 51 154

99.93 99.92 99.88 99.93 99.92

99.93 99.92 99.88 99.93 99.92

0.001 0.0014 0.0020 0.0012 0.0013

99.95 99.93 99.91 99.94 99.94

Table 9 Performance evaluation of the proposed ecg compression technique. ECG database

Length of data

Compression ratio

MAE

Compression time

MIT-BIH database PTB database BIDMC database St. database

≅ 30.06 minutes Variable 20 hours 30 minutes

18.92 18.39 19.87 19.71

0 0 0 0.0002

317.29 ms 409.52 ms 640.24 ms 609.83 ms

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Fig. 9. output of the proposed heart rate monitoring and Therapeutic Devices, (a) input ECG signal, (b) noise source, (c) noise added ECG signal, (d) Denoised ECG signal, (e) detected ECG peaks, (f) compressed ECG signal.

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Fig. 10. Reconstructed ECG signal. Table 10 Comparison of the proposed detector with the existing detectors.

Compression ratio =

MAE = Max (original signal − reconstructed signal )

Method

SE (%)

SP (%)

Error

Reference

Proposed Pan tompkins Cvikl et al. Iliev et al. Faezipour et al. Pulse train approach Genetic algorithm Search-back Quadratic spline wavelet Wavelet denoising

99.94 99.74 99.81 99.16 99.79 99.57 99.61 99.72 99.29 99.56

99.92 99.60 99.79 99.53 99.78 99.56 99.52 99.79 99.72 99.53

0.0013 NR NR NR 0.4000 NR NR NR NR NR

[38] [39] [40] [41] [42] [43] [44] [45] [46]

Quality score =

Compression ratio

Quality score

Reference

m-AZTEC 5.8 Mukhopadhyay et al. 15.83 Mukhopadhyay et al. 22.81 Near-lossless compression technique

0.30 2.0 3.10

[47] [48] [49]

USZZQ and Huffman coding of DSM SPIHIT Lossless compression technique

11.09

4.16

[50]

8.06

6.78

[51]

Rice Golomb Coding Sang Joon Lee et al. JPEG2000 Proposed

2.38 16.5 8.05 18.89

NR 27.15 9.29 2047

[52] [53] [54] –

Compression ratio Percentage Root − mean − square Difference

(20)

Performance evaluation of the proposed ECG compression technique is depicted in Table 9. It is evident from Table 9 that the proposed ECG compression technique achieves an average compression ratio of about 19.22:1 and an average compression time of 494.22 ms. 3.2. Results The output of the proposed heart rate monitoring and Therapeutic Devices is shown in Fig. 9. Fig. 9(a) contains input ECG signal with a sampling frequency of 360 Hz taken from MIT-BIH arrhythmia database. Random noise is generated and added to the original ECG signal so that the worst case can be considered which is represented in Fig. 9(b). Fig. 9(c) represents the noise added ECG signal. Fig. 9(d) represents the denoised ECG signal. Whereas the detected ECG peaks and the compressed ECG signal is shown in Fig. 9(e) and (f) respectively. Finally, the reconstructed ECG signal is shown in Fig. 10.

Table 11 Performance comparison of proposed ecg compression technique with existing techniques. Method

number of bits in the original file number of bits in the compressed file

Lossy compression Techniques

4. Discussion The proposed joint ECG detection and data compression technique are evaluated against the robustness to noise, numerical efficiency, and parameter choice, targeting a universal fast and robust heart rate monitoring and therapeutic device. As the ECG signal can get corrupted with various noises, namely, muscle noise, baseline wandering, motion artifacts to name a few, therefore, the designed technique should be robust to these noises. It is evident from Table 6 that the proposed technique achieves highest SNR and lowest MSE as compared to the previously designed techniques. Also, the proposed technique achieves a higher average value of CC which is 0.9723 and smaller average value of PRD which is 12.141%. The intensity of algorithms from being complex to simple is becoming obsolete. Researchers are striving on delivering simpler algorithms through several computer-aided programs and software's to supplement for further evaluations. It is imperative to have numerical efficiency in the algorithms developed for methodical and logical usage. The use of modified biorthogonal wavelet transform based filter bank and its wave digital filter realization makes the proposed design area efficient. It is evident from Table 4 that the proposed wavelet filter bank requires only ten adders, four multipliers and three delay elements which are nearly 65% less compared to the previously designed filter banks. Table 10 compares the peak detection performance of the proposed detector with the existing detectors. It is evident from Table 10 that the proposed detector with an adaptive slope prediction threshold is capable of distinguishing accurately between healthy, myocardial infarction, congestive heart failure and coronary artery disease subjects with a detection accuracy, sensitivity, specificity, and error of 99.92%, 99.94%, 99.92% and 0.0013 respectively. The key benefit of adaptive slope predication threshold-

fifteen congestive heart failure subjects from BIDMC database, 148 myocardial infarction subjects from PTB database and seven coronary artery disease subjects from St. database are considered to evaluate the proposed ECG detector. Only lead-II ECG data from each type of open access databases are considered in this work. Table 7 summarizes the details of ECG data used in this work. Performance evaluation of the proposed ECG detector is depicted in Table 8. Total 275327 ECG beats out of which 104363 healthy beats, 41545 coronary artery disease beats, 89237 Congestive Heart Failure beats and 40182 myocardial infarction beats are used to evaluate the performance of proposed ECG detector. It is observed from Table 8 that the proposed ECG detection technique achieves a higher detection accuracy of 99.92%, sensitivity of 99.94% and lower overall error of 0.0013. Compression ratio, maximum absolute error, and quality score are the three performance evaluation indexes of the proposed ECG compression technique. All the four performance evaluation indexes are mathematically expressed in Eq. (20).

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based detector is that the false peak detection is controlled by comparing the rising and falling edge of the ECG peak. Also, wireless transmission of ECG signals is an active area of cutting-edge-pacing research. The significant challenges involved in the wireless transmission is data conversion and power consumption. Medical regulatory boards have not approved lossy compression techniques, hence can't be commercially used. So, lossless compression technique with high bit compression ratio is highly required. Here in the proposed work, LZMA lossless data compression technique is used, and comparison of the proposed data compression technique with the existing techniques is presented in Table 11. It is evident from Table 11 that the proposed ECG data compression technique has a high compression ratio, the quality score of 18.89 and 2047 respectively. Compare to existing techniques, the novelty of the proposed work is the use of modified biorthogonal wavelet transform based wavelet filter bank with a wave digital filter realization. The use of adaptive slope prediction threshold-based peak detector distinguishes accurately between normal, myocardial infarction, congestive heart failure and coronary artery disease patients with a higher detection accuracy, sensitivity, specificity, and error. Also, the LZMA based ECG data compression technique achieves a high compression ratio and quality score.

[9] [10]

[11]

[12] [13] [14]

[15]

[16] [17] [18]

[19]

[20]

5. Conclusion [21]

In this work, peak detection and lossless data compression of an ECG signal are studied using adaptive slope prediction thresholding and LZMA compression. The proposed technique is validated using various ECG signal databases. Using the proposed adaptive slope prediction technique, sensitivity, specificity and, overall detection error, respectively, are found to be 99.94% 99.92%, and 0.0013. Further, using LZMA compression technique, a compression ratio of 18.89 is achieved when compared to 16.5 using the existing real-time ECG data compression method [53]. Thus, it can be concluded that the combination of ECG peak detection and lossless ECG data compression not only reduces the false peak detection but also increases the ECG data compression ratio thus facilitating a speedy transmission and efficient bandwidth utilization. This proposed methodology can be further extended to analyze various biomedical signals.

[22]

[23]

[24] [25]

[26] [27]

[28] [29]

Compliance with ethical standards

[30]

Conflict of Interest: Author Ashish Kumar declares that he has no conflict of interest. Author Rama Komaragiri declares that he has no conflict of interest. Author Manjeet Kumar declares that he has no conflict of interest. Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

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