Respiratory sinus arrhythmia (RSA) is largely mediated by the autonomic nervous system through its modulating influence on the heart beats. We propose a robust algorithm for quantifying instantaneous RSA as applied to heart beat intervals and respiratory recordings under dynamic breathing patterns. The blood volume pressure derived heart beat series (pulse intervals, PIs) are modeled as an inverse gaussian point process, with the instantaneous mean PI modeled as a bivariate regression incorporating both past PIs and respiration values observed at the beats. A point process maximum likelihood algorithm is used to estimate the model parameters, and instantaneous RSA is estimated via a frequency domain transfer function evaluated at instantaneous respiratory frequency where high coherence between respiration and PIs is observed. The model is statistically validated using Kolmogorov-Smirnov (KS) goodness-of-fit analysis, as well as independence tests. The algorithm is applied to subjects engaged in meditative practice, with distinctive dynamics in the respiration patterns elicited as a result. The presented analysis confirms the ability of the algorithm to track important changes in cardiorespiratory interactions elicited during meditation, otherwise not evidenced in control resting states, reporting statistically significant increase in RSA gain as measured by our paradigm.
We propose a Bessel kernel based time frequency distribution technique for identification and tracking of spectrum of Atrial Fibrillation (AF) in ECG. The algorithm shows a good frequency resolution and a low RMS error even when the noise dominates the signal which is criti- IntroductionAF is the most common sustained cardiac arrhythmia, increasing in prevalence with age, accounting for approximately one third of hospitalizations for cardiac rhythm disturbances [1]. AF is characterized by the replacement of consistent P waves on the ECG by rapid oscillations (fibrillatory waves) that vary in amplitude, frequency, and shape, associated with an irregular ventricular response. AF affects approximately 10% of the population over age of 75 and is associated with an increased risk of stroke [1,2].Previous studies have shown that spectrum of the atrial activity of the ECG under AF has a dominant peak (AF frequency) and there is a significant correlation between spontaneous or drug induced termination of AF and the time variation of AF frequency [3], indicating the importance of accurately tracking the AF frequency in time.Tracking of spectral content of a time signal can be done using STFT, but it has an inherent tradeoff between time and frequency resolution [4]. Stridh et al. [5,6] employed Wigner-Ville and Choi-Williams time frequency distributions for analyzing time variation of spectral content of AF, but the accuracy and noise robustness of the algorithms are inconclusive. As AF activity has a substantially low amplitude in the ECG and almost undistinguishable from noise and other ECG artifacts, it is important that a given method has a significant robustness to noise. Sandberg et al. [7] employed Hidden Markov models for frequency tracking of AF, but the performance at SNR less than 0dB has not been studied. The proposed Bessel kernel based time frequency distribution technique is capable of tracking AF frequency in ECG with a good frequency resolution and a low RMS error even when the noise dominates the signal. System modelAtrial fibrillation was mathematically modeled by a sum of frequency modulated sinusoidals with time varying amplitude and its harmonics [7,8] and is given bywhere a k (t) = e −γ(k−1) (a + ∆a sin(ω a t)), ω 0 is the fundamental AF frequency, ω f is the frequency of frequency modulation, ∆ω is the maximum frequency deviation, M is the number of harmonics excluding the fundamental, γ is the decaying factor of harmonics, a is the average amplitude of the fundamental, ω a is the frequency of amplitude modulation, and ∆a is the maximum amplitude deviation. n(t) represents white Gaussian noise, artifacts from insufficient QRST cancelation, and other ECG artifacts. According to the model, AF frequency is given by ω AF (t) = ω 0 + ∆ω cos(ω f t).The objective is to accurately estimate ω AF (t), especially when n(t) is higher compared to the amplitude of the fundamental a 1 (t). Though this model is an approximation to the real AF signal, it is useful when analyzing the performance of differe...
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