Lossless compression technique for real time Photoplethysmographic measurements Rajarshi Gupta, Sr. Member, IEEE
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diastolic time (ts and td), pulse width (tw) and pulse height or amplitude (hp). The AC component consists of two phases, namely, rising part or the anacrotic phase, indicating ventricular contraction or systole and the falling part or catacrotic phase, indicating ventricular relaxation or the diastole and wave reflections from the boundary. Computerized measurement techniques have enabled the researchers to analyze the PPG signals to assess important physiological parameters like heart rate, blood oxygen saturation, blood pressure, vascular assessment, cardiac output and respiration etc. As these measurements are sensitive to motion artifacts and power line interferences, filtering and preprocessing is necessary for the accurate detection of clinical features [5]-[6]. A vast literature is available in measurement science and physiology exploring application of PPG for indirect assessment of these parameters. The pulsatile component of PPG is synchronous with the heart rate. The distance of the consecutive systolic peaks has been used as an alternative measure for rhythm analysis and measurement heart rate variability [7]-[9]. In [7] and [9] investigation was done to compare the reliability of heart rate measurement against the same measured from ECG signal, taken as gold standard. Pulse oximetry is perhaps the most common clinical parameter monitored under critical care units and surgery in hospital settings. It utilizes PPG principle to compute the difference of light absorbance at the wavelengths 660 nm and 940 nm (generated by alternate excitation of two photodiodes) by HbO2 and Hb at the arterial blood to measure SpO2 [10][11]. Due to the similarity of the blood pressure wave and PPG, non-invasive measurement of arterial blood pressure (BP) using PPG signal (or using ECG and PPG) is another area which has been explored by researchers in the last decade. In many of the works, PTTf (or pulse wave velocity) was used as potential indicator of systolic BP measurement [12]-[15]. The SBP and DBP were estimated using linear regression models, where the regression coefficients were calculated using a known standard, like cuff sphygmomanometer. Multi body site PPG measurement has also been used for assessment of vascular diseases like arterial occlusive disease, vascular ageing, tissue perfusion etc. The deviation from the bilateral symmetry of the PPG a collected from the lower limbs has been utilized for arterial disease assessment. The asymmetries are visible in PPG features like reduction of peak amplitude, rise time etc. [16]-[18]. PPG has also been used for indirect measurement of cardiac output and respiration [19]-[20].
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Abstract— Photoplethysmogram (PPG) signal can provide vital diagnostic information on cardiovascular functions of human body. In this paper, a lossless, real time compression technique based on combination of second order delta and Huffman encoding is proposed for the PPG signal. The algorithm was validated with 10-bit quantized PPG data collected from MIMIC-II database under Physionet and healthy volunteers using Biopac Systems® at 125 Hz sampling frequency. Using a block size of 48 samples, the average compression ratio (CR), percentage root mean squared difference (PRD) and PRD normalized achieved was 2.223, 0.127 and 0.187 respectively with 30 sets of volunteers’ data. Three prime clinical features, systolic amplitude, systolic upstroke time and pulse width from the decompressed PPG waveform were evaluated with less than 1% distortion on the diagnostic measures. Study was also done to estimate the compression efficiency for different sample block size, wave morphology and sampling frequency of raw data. The low time complexity of the proposed algorithm encourages its implementation for development low cost real time PPG measurement application in patient monitoring. Index Terms— PPG measurement, Lossless compression, delta encoding, Huffman coding.
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I. INTRODUCTION
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HOTOPLETHYSMOGRAM (PPG) represents volume changes in the blood vessels. This provides valuable information on the blood circulation system as well as cardiac functions. Photoplethysmography is a popular non-invasive technique to collect the pulse signal from the extremities of the body organs, typically fingers or toes. It employs a matched pair of LED and photodiode operating in the red and/or near IR region (0.8 to 1 µm wavelength) to collect the information from the microvascular bed of tissue beneath the body surface through modulation or absorption of light wave in reflective mode or transmission mode respectively[1]-[2]. In the recent years, there has been an increase in interest on PPG signal as a powerful diagnostic tool due to simple, portable and low-cost technology available for its fast, easy and reliable acquisition [3]-[4]. PPG is a low frequency (around 1 Hz) waveform that consists of a pulsatile AC component (representing average blood volume changes) superimposed on a DC part (representing respiration and sympathetic nervous activity). Figure 1 represents a typical PPG waveform collected from fingertip along with principal wave features like systolic and Rajarshi Gupta is currently with Instrumentation Engg. Section, Department of Applied Physics, University of Calcutta, 92 APC Road, Kolkata-700009. (e-mail:
[email protected]).
td
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Dicrotic notch Pulsatile component
tw ts : systolic time td : diastolic time ph : pulse height/ amplitude tw : pulse width
ph Steady component
layout of the paper is as follows. The Methodology section provides a brief description of the algorithm development logic. In the Testing and Results section, performance of the compression-decompression logic is illustrated using finger PPG data collected from healthy volunteers as well as Multiparameter Intelligent Monitoring in Intensive Care (MIMIC)-II data base under Physionet [35]. The effect of the compression on diagnostic measure of the PPG as well as influence by other factors like sampling frequency and wave morphology of the signal is discussed in the Discussion section. Finally, the conclusion section summarizes the main merits and demerits of the proposed approach. The compression results were clinically validated with cardiologists.
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For the last few decades, information and communication technology, backed by development of low power and high speed processors have revolutionized health monitoring of patients with disorders like arrhythmia, high blood pressure, diabetes etc. in clinical or home environment [21]-[22]. ECG and PPG are the primary signals which are routinely measured in cardiovascular function assessment. Miniaturization of sensors and fabrication of compact RF modules has enabled wireless collection of biomedical signals [23]-[24]. Compression of medical signals can provide two-fold benefits in physiological parameter monitoring; first, less memory to store (or buffer) the data before the transmission and second, enhanced channel efficiency of the communication link. An important aspect of compression in biomedical signals is preservation of diagnostic measures. Although a lot of research is already available for Electrocardiogram (ECG) signal compression [25]-[26], the area of PPG compression is largely unexplored till date by the research community. Use of cycle to cycle Fourier series for PPG signal compression is described in [27]. Here, the period of each cycle of the PPG signal was identified and Fourier series was applied to compute the Fourier coefficients. The signal was reconstructed using reduced set of coefficients, thus achieving data reduction without significant loss of information. Application of delta modulation for PPG signal compression was investigated in [28]. The optimum step size for implementing delta modulation for PPG signal, with and without motion artifact, was studied in [29]. Although there have been some discrete attempts in wireless PPG acquisition as reported in [30]-[31], these works did not involve any compression technique. The chief motivation of this work is to propose a lossless compression technique for continuous measurement of PPG in patient monitoring applications. Huffman encoding [32]-[33] is a popular technique that uses a Huffman table to assign fewer bits to more frequently occurring ‘symbols’ and more bits to less frequently occurring ‘symbols’, to achieve low code length per encoded character. Whilst finding limited application in ECG compression [34], Huffman coding remains largely unutilized in PPG signal compression methodologies. In this work, the lossless compression algorithm is based on combination of second order delta and Huffman encoding. The chief outcome of the work is achieving a low-complexity algorithm with moderate level of compression efficiency. The
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Fig.1: A typical PPG waveform with clinical signatures
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II. METHODOLOGY In the proposed compression algorithm, second order difference (delta) of the PPG sample array was used for encoding. The delta values represent the difference between consecutive samples, and normally defined as: Δ1 (i ) = x (i + 1) − x(i) (1) Δ 2 (i) = Δ1 (i + 1) − Δ1 (i ) where, x(i) = PPG samples; Δ1 is the first difference and Δ2 is the second difference. In the proposed compression algorithm, the first delta (Δ1) and the second delta (Δ2) array was suitably biased to get rid of negative elements, so that efficient compression could be achieved in the Huffman coding stage. The compression process is illustrated through the following steps: A. Modification of the first and second difference array The first delta array was computed using equation (1). The difference array elements were modified using equation (2) to avoid biasing negative values. bΔ1 = Δ1 ; if abs(mΔ1 ) > abs(nΔ1 ) (2) bΔ1 = abs ( nΔ1 ) + Δ1 ; if abs(nΔ1 ) > abs(mΔ1 ) where, bΔ1 is the modified first delta array; mΔ1: max(Δ1) and nΔ1: min(Δ1).The second delta array Δ2 was computed from bΔ1 was follows: (3) Δ 2 = b Δ1 (i + 1) − b Δ1 (i ) The array Δ2 was modified in a similar way to equation (2)
Number of occurrences
bΔ2 elements (symbols) 5 4 3 0 2 6
18 15 12 1 1 1 Σ = 48(*) (*: sample block size considered)
Probability
Codes
0.375 0.312 0.250 0.021 0.021 0.021
0 10 110 1110 11110 11111
543026 1 43026
D. Compression of Huffman bit stream for bΔ2 array
0.625
1
0
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1
0.313
026 0.063
1
0
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by either no biasing or with nΔ2 to generate bΔ2 array, the biased second delta, where mΔ2: max(Δ2) and nΔ2: min(Δ2). This process ensured that all elements in Δ2 are positive and minimum biasing is done. The bias information for first and second difference array and signs of mΔ1, nΔ1, mΔ2, and nΔ2 were separately stored.
For even number of Huffman symbols if hs[k]
