Article

# Autonomic function assessment using analysis of heart rate variability

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## Abstract

Analysis of changes in heart rate can be useful in determining the state of various body systems. In particular the analysis of heart rate variability (HRV) is used in the assessment of autonomic function. This paper uses the discrete harmonic wavelet transform for a time-frequency analysis of HRV data to show changes in spectral power over time. Signals representing patient heart rate are presented, and methods for spectral and time-frequency analysis are described. Three sets of patient data are then analysed using these methods. The results show the potential of time-frequency analysis in the assessment of medical disorders, such as the sleep apnoea syndrome, where transient alterations in autonomic function occur.

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... Several approaches have been used to cope with the need to assess a time-varying power spectrum. The short-time Fourier transform (18,47), time-dependent autoregressive models (16,18), Wigner-Ville distribution (18,19,44,46), discrete wavelet transform (DWT; Ref. 21), the Hilbert transform (10,11,22,32,36,41,51,58), and the selective-discrete-Fourier transform algorithm (SDA) (7,34,35) have been used to obtain time-dependent spectral analysis. ...
... s͑m ϩ n͒e 2ifTsm (11) where Ts is the sampling interval. Therefore, the computation of the CWT of a discrete signal should be understood in the following sense: the discrete-time signal represents the samples of a continuous-time signal, and we sample, both in time and in frequency, the CWT of that continuous signal. ...
... Another point to be noticed is that, usually, the analysis of discrete-time signals is performed using the DWT (11,32,36,51,58), which is computationally efficient (21,22). However, the DWT enables the assessment of the spectral power in several predetermined frequency bands. ...
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Myocardial infarction (MI) is known to elicit activation of the autonomic nervous system. Reperfusion, induced by thrombolysis, is thus expected to bring about a shift in the balance between the sympathetic and vagal systems, according to the infarct location. In this study, we explored the correlation between reperfusion and the spectral components of heart rate (HR) variability (HRV), which are associated with autonomic cardiac control. We analyzed the HR of patients during thrombolysis: nine anterior wall MI (AW-MI) and eight inferoposterior wall MI (IW-MI). Reperfusion was determined from changes in ST levels and reported pain. Reocclusion was detected in four patients. HRV was analyzed using a modified continuous wavelet transform, which provided time-dependent versions of the typically used low-frequency (LF) and high-frequency (HF) peaks and of their ratio, LF/HF. Marked alterations in at least one of the HRV parameters was found in all 18 reperfusion events. Patterns of HRV, compatible with a shift toward relative sympathetic enhancement, were found in all of the nine reperfusion events in IW-MI patients and in three AW-MI patients. Patterns of HRV compatible with relative vagal enhancement were found in six AW-MI patients (P < 0.001). Significant changes in HRV parameters were also found after reocclusion. Time-dependent spectral analysis of HRV using the wavelet transform was found to be valuable for explaining the patterns of cardiac rate control during reperfusion. In addition, examination of the entire record revealed epochs of markedly diminished HRV in two patients, which we attribute to vagal saturation.
... Of the various types of wavelets developed over the past decades, the harmonic wavelet possesses compact frequency expression [10], thus can be efficiently implemented through a pair of Fourier and inverse Fourier transform operations. Such feature made it well suited for dynamic modeling of the Burgers equation [11], non-linear partial differential equation solutions [12], heart rate variability analysis [13], particle shape pattern recognition [14], image denoising [15], and surface electromyographic (EMG) signal classification [16]. An overview of applying harmonic wavelet transform for vibration signal analysis was provided in [17], and examples have included vibration analysis of buildings [17], beam structure [18], rotary machines [19], rotor rig testing systems [20,21], helicopter gearbox [22], and rolling bearings [23]. ...
... A combination of the energy and Shannon entropy content of a signal's wavelet transform coefficients, denoted as energy-to-entropy ratio, is thus designed as rðm; nÞ ¼ E energy ðm; nÞ E entropy ðm; nÞ (17) where the energy E energy (m,n) and the entropy E entropy (m,n) are calculated using Eqs. (13) and (14), respectively. ...
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Chapter
Wavelet transform is a mathematical tool that converts a signal into a different form. This conversion has the goal to reveal the characteristics or “features” hidden within the original signal and represent the original signal more succinctly. A base wavelet is needed in order to realize the wavelet transform. The wavelet is a small wave that has an oscillating wavelike characteristic and has its energy concentrated in time. Figure 3.1 illustrates a wave (sinusoidal) and a wavelet (Daubechies 4 wavelet) (Daubechies 1992).
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During obstructive sleep apnea, transient arousal at the resumption of breathing is coincident with a substantial rise in blood pressure. To assess the hemodynamic effect of arousal alone, 149 transient stimuli were administered to five normal subjects. Two electroencephalograms (EEG), an electrooculogram, a submental electromyogram (EMG), and beat-to-beat blood pressure (Finapres, Ohmeda) were recorded in all subjects. Stimulus length was varied to produce a range of cortical EEG arousals that were graded as follows: 0, no increase in high-frequency EEG or EMG; 1, increased high-frequency EEG and/or EMG for < 10 s; 2, increased high-frequency EEG and/or EMG for > 10 s. Overall, compared with control values, average systolic pressure rose [nonrapid-eye-movement (NREM) sleep 10.0 +/- 7.69 (SD) mmHg; rapid-eye-movement (REM) sleep 6.0 +/- 6.73 mmHg] and average diastolic pressure rose (NREM sleep 6.1 +/- 4.43 mmHg; REM sleep 3.7 +/- 3.02 mmHg) over the 10 s following the stimulus (NREM sleep, P < 0.0001; REM sleep, P < 0.002). During NREM sleep, there was a trend toward larger blood pressure rises at larger grades of arousal (systolic: r = 0.22, 95% confidence interval 0.02-0.40; diastolic: r = 0.48, 95% confidence interval 0.31-0.62). The average blood pressure rise in response to the grade 2 arousals was approximately 75% of that during obstructive sleep apnea. Arousal stimuli that did not cause EEG arousal still produced a blood pressure rise (mean systolic rise 8.6 +/- 7.0 mmHg, P < 0.0001).(ABSTRACT TRUNCATED AT 250 WORDS)
• J N Rottman
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• S G Mcnarnara
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McNarnara, S. G., R. R. Grunstein and C. E. Sullivan (1993), Obstructive sleep apnoea, Thorax, 48, 754-764.