Heart Rate Variability Analysis Using the Lomb-Scargle Periodogram Simulated ECG Analysis

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1 Page 1 of 7 Heart Rate Variability Analysis Using the Lomb-Scargle Periodogram Simulated ECG Analysis In a preceding analysis, our focus was on the use of signal processing methods detect power spectral density versus frequency in time-domain signals. 1 The purpose of that analysis was to illustrate the identification of power spectral density associated with time domain signals using a signal processing method known as the Lomb-Scargle Periodogram (LSP). The LSP is deemed a better method for evaluating power spectral density in time-varying signals where there may be missing or data gaps, or irregular measurements. For this reason, it is deemed superior to the discrete Fourier transform for power spectral analysis related to signals processing involving unevenly sample data, which is frequently the case in biology and medicine. 2 The Heart Rate Variability (HRV) is a measure of the beat-to-beat intervals of the heart, measured between the R-R intervals of a standard ECG, as in the following figure, which shows and ECG over time in seconds. These waveforms illustrate the occurrence of the R wave. The peak-to-peak measurement of time interval of the R wave from beat to beat has been analyzed statistically. One measure that has been applied is the standard deviation of the NN (or normal-tonormal) intervals, or the intervals of the instantaneous heart rate. The standard deviation of the normal RR interval (SDNN) captured over an ensemble of, say, 24 hours has a significance, as well as shorter recordings of 5 minutes in length or so. 3 The key issue with the SDNN is that measurements need to be made under physiologically stable conditions, prompting shorter time measurements (5 minutes) in which processing of these shorter intervals is performed after each batch. Studies have shown that an SDNN of less than 50 ms is considered indicative of high risk; a SDNN of between 50 and 200 indicates moderate risk; while a value over 100 ms is considered normal. 4 1 Zaleski, JR, Investigating the use of the Lomb-Scargle Periodogram for Heart Rate Variability Quantification. 2 Ruf, T. The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series. Biological Rhythm Research, 1999, Vol. 30, No. 2, pp Malik, M., Heart Rate Variability: Standards of Measurement, Physiologic Interpretation, and Clinical Use. Writing Committee of the Task Force, Department of Cardiological Sciences, St George s Hospital Medical School, Cranmer Terrace, London SW17 0RE, UK. Accessed 21-April Corrales, MM, Torres, B de la Cruz, Esquival, AL, Salazar, MAG, Orellana, JN, Normal values of heart rate variability at rest in a young, healthy and active Mexican population. SciRes, Vol. 4, No. 7, (2012).

2 Page 2 of 7 HRV is affected by aerobic fitness. HRV of a well-conditioned heart is generally large at rest. Other factors that affect HRV are age, genetics, body position, time of day, and health status. During exercise, HRV decreases as heart rate and exercise intensity increase. HRV also decreases during periods of mental stress. HRV is regulated by the autonomic nervous system. Parasympathetic activity decreases heart rate and increases HRV, whereas sympathetic activity increases heart rate and decreases HRV. 5 Furthermore, In patients with chronic heart failure (CHF) and acute myocardial infarction (AMI) it is accepted that the best prognostic information is provided by two methods in the time domain: the standard deviation of the intervals between normal beats (SDNN) and the pnn50 (a measure of the number of adjacent NN intervals which differ by more than 50 ms) HRV_ Accessed 23-April Corrales, MM, Torres, B de la Cruz, Esquival, AL, Salazar, MAG, Orellana, JN, Normal values of heart rate variability at rest in a young, healthy and active Mexican population. SciRes, Vol. 4, No. 7, (2012).

3 Page 3 of 7 The following figure 7 shows high frequency and low frequency spectral densities for different patient attitudes (rest and 90 degree head-up tilt). The relative magnitude of the power of the two spectral densities shifts from predominantly high frequency to low frequency during the process, signaling a discriminator for heart rate variability for these two attitudes. Figure 1: Spectral analysis (autoregressive model, order 12) of RR interval variability in a healthy subject at rest and during 90 head-up tilt. Task Force of the European Society of Cardiology the North American Society of Pacing Electrophysiology Circulation. 1996;93: Copyright American Heart Association, Inc. All rights reserved. To evaluate, some sample simulated data were employed from Physionet. 8 The following figure illustrates the RR intervals of a sample signal (from file ECGSYN.DAT). 7 Malik, M., Heart Rate Variability: Standards of Measurement, Physiologic Interpretation, and Clinical Use.: Writing Committee of the Task Force, Department of Cardiological Sciences, St George s Hospital Medical School, Cranmer Terrace, London SW17 0RE, UK. Accessed 21-April Accessed 23-April-2015

4 Page 4 of 7 The signal is synthesized using a user-definable mean heart rate, number of beats, and sampling frequency, as well as a definable waveform morphology: P, Q, R, S, and T timing, amplitude, and duration), standard deviation of the RR interval, and LF/HF ratio (a measure of the relative contributions of the low and high frequency components of the RR time series to total heart rate variability). 9 The plot in the figure above shows the beat-to-beat variability, with the mean and the mean +/- the sample standard deviation overlaid. The LSP illustrates the principal frequency of the ECG (R-R interval), associated with the highest power, which is 1 second, as shown in the following figure. This corresponds to a frequency of 60 beats per minute: 9 Accessed 23-April-2015

5 Page 5 of 7 Testing the LSP Algorithm As a side note, when validating the LSP, it is useful to employ a known simulated signal so as to validate and verify the output. Consider a test run of the LSP with a simulated signal, given by the following expression: y( t) sin(2 f1t) sin(2 f 2t), where f1 20Hz and f 2 40Hz. The corresponding LSP spreadsheet and Periodogram output for this time signal is given in the following two figures:

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7 Page 7 of 7 Summary The Lomb-Scargle Periodogram is an effective tool for classifying frequencies of unevenly-sampled time-varying signals. These characteristics apply to data collected from medical devices at the point of care, where gaps in data can occur frequently. The use of the LSP for discriminating on signal frequencies is shown to be effective, and bears further investigation with periodic signal analysis, such as heart rate variability, wherein frequency and temporal changes are correlated to decompensating condition.