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Statistical coding and decoding of heartbeat intervals.

Lucena F, Barros AK, Príncipe JC, Ohnishi N - PLoS ONE (2011)

Bottom Line: Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm.We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation.Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.

View Article: PubMed Central - PubMed

Affiliation: Biological Information Engineering Laboratory, Nagoya University, Nagoya, Aichi, Japan. lucena@ohnishi.nagoya-u.ac.jp

ABSTRACT
The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.

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Analysis of the filter behavior.Filter characteristics of the population code (red circle) and its best match with the Gabor function (gray circle) according to Eq. 2. The bandwidth (A) was quantified at -3 dB of the power spectrum maximum amplitude. The quality factor or sharpness (B) represents the ratio between the center frequency and bandwidth of the filters. The damping ratio (C) is a measure based on the quality factor and shows that the filters characteristics have underdamped () proprieties. The width of each filter temporal envelope (D) was measured at 3 dB below the peak of the energy power using the Hilbert transform.
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pone-0020227-g006: Analysis of the filter behavior.Filter characteristics of the population code (red circle) and its best match with the Gabor function (gray circle) according to Eq. 2. The bandwidth (A) was quantified at -3 dB of the power spectrum maximum amplitude. The quality factor or sharpness (B) represents the ratio between the center frequency and bandwidth of the filters. The damping ratio (C) is a measure based on the quality factor and shows that the filters characteristics have underdamped () proprieties. The width of each filter temporal envelope (D) was measured at 3 dB below the peak of the energy power using the Hilbert transform.

Mentions: If the cardiac rhythm accuracy depends on the capacity of the heart to decode sympathetic and parasympathetic stimuli, it should be possible to correlate the time and the frequency distribution of the decoding filters to the cardiac responses. According to previous studies [6], [36], [37], the filtering properties of the auditory system can be characterized using the ratio of center frequency over bandwidth of a population code, called the Q factor. In the cardiac case, we conducted a clustering analysis of the filters' quality factors. We selected the Gaussian Mean Shift (GMS) method because it does not require the selection of the number of clusters, once the kernel bandwidth is chosen from the data (see methods). As shown in Fig. 5, we found three different clusters of Q factors that span the 0.01 to 0.5 Hz band, dividing it in regions distinct from the traditional VLF, LF and HF bands. The analysis of the joint decoding population shows that the bandwidth of the filters for VLF and LF increases almost linearly with the center frequency, i.e. a constant Q filter bank that preserves the time resolution (Fig. 6A). For HF, the bandwidth is nearly constant for center frequencies ranging from 0.14 to 0.29 Hz, favoring spectral resolution instead of time resolution. And, it increases gradually with the steepest slope between center frequencies located at 0.29 and 0.5 Hz, again preserving the time resolution (see Fig. 6A). These results suggest that sympathetic and vagal decoding in the heart are compatible with scale base decompositions such as the wavelet and multirate Fourier transforms. But, why did the heart evolve to use multiscale transform properties to decode sympathetic and vagal contributions in this way? One argument to explain the decoding filter characteristics is the fundamental compromise, captured in the Gabor uncertainty relation [38], between time and frequency resolution. For example, a filter with high-frequency selectivity has a poor time resolution, and vice-versa. Choosing between low- and high-frequency selectivity impinges severe limitations between fast and slow autonomic cardiac regulation and it is one of the obstacles to proper processing in biological systems that are subject to real time response requirements [39]–[41]. Moreover, a fast cardiac response tends to cause a broadening of the filter bandwidth, decreasing the capacity of the system to filter environmental noise at the cost of selectivity. This behavior can be observed by analyzing the quality factor or sharpness of the filters through dividing the center frequency by bandwidth. The ICA decomposition also shows (Fig. 6B) that HF have a lower susceptibility to unwanted artifacts than VLF and LF, specifically around 0.14 to 0.29 Hz, where the respiratory sinus arrhythmia (RSA) synchronization is located [42]. This result is consistent with the fact that a sympathetic contribution increases the cardiac rhythm, whereas vagal activity behaves in an opposite way. It is also directly related to the system time response (damping ratio), which is represented by the inverse of the quality factor value multiplied by two. A high-damping ratio means a fast cardiac activity in contrast to low-damping ratio (Fig. 6C). Furthermore, filters with broad envelopes are likely to be optimized to process sinusoidal waveforms. Thus, the analysis of the filter envelope patterns suggests that the RSA frequency contributions are happening more frequently. The frequency region where the envelopes have higher values are concentrated between 0.14 and 0.29 Hz (Fig. 6D), which is consistent with experimental studies that characterize the respiratory components influencing autonomic cardiac regulation [43].


Statistical coding and decoding of heartbeat intervals.

Lucena F, Barros AK, Príncipe JC, Ohnishi N - PLoS ONE (2011)

Analysis of the filter behavior.Filter characteristics of the population code (red circle) and its best match with the Gabor function (gray circle) according to Eq. 2. The bandwidth (A) was quantified at -3 dB of the power spectrum maximum amplitude. The quality factor or sharpness (B) represents the ratio between the center frequency and bandwidth of the filters. The damping ratio (C) is a measure based on the quality factor and shows that the filters characteristics have underdamped () proprieties. The width of each filter temporal envelope (D) was measured at 3 dB below the peak of the energy power using the Hilbert transform.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3111410&req=5

pone-0020227-g006: Analysis of the filter behavior.Filter characteristics of the population code (red circle) and its best match with the Gabor function (gray circle) according to Eq. 2. The bandwidth (A) was quantified at -3 dB of the power spectrum maximum amplitude. The quality factor or sharpness (B) represents the ratio between the center frequency and bandwidth of the filters. The damping ratio (C) is a measure based on the quality factor and shows that the filters characteristics have underdamped () proprieties. The width of each filter temporal envelope (D) was measured at 3 dB below the peak of the energy power using the Hilbert transform.
Mentions: If the cardiac rhythm accuracy depends on the capacity of the heart to decode sympathetic and parasympathetic stimuli, it should be possible to correlate the time and the frequency distribution of the decoding filters to the cardiac responses. According to previous studies [6], [36], [37], the filtering properties of the auditory system can be characterized using the ratio of center frequency over bandwidth of a population code, called the Q factor. In the cardiac case, we conducted a clustering analysis of the filters' quality factors. We selected the Gaussian Mean Shift (GMS) method because it does not require the selection of the number of clusters, once the kernel bandwidth is chosen from the data (see methods). As shown in Fig. 5, we found three different clusters of Q factors that span the 0.01 to 0.5 Hz band, dividing it in regions distinct from the traditional VLF, LF and HF bands. The analysis of the joint decoding population shows that the bandwidth of the filters for VLF and LF increases almost linearly with the center frequency, i.e. a constant Q filter bank that preserves the time resolution (Fig. 6A). For HF, the bandwidth is nearly constant for center frequencies ranging from 0.14 to 0.29 Hz, favoring spectral resolution instead of time resolution. And, it increases gradually with the steepest slope between center frequencies located at 0.29 and 0.5 Hz, again preserving the time resolution (see Fig. 6A). These results suggest that sympathetic and vagal decoding in the heart are compatible with scale base decompositions such as the wavelet and multirate Fourier transforms. But, why did the heart evolve to use multiscale transform properties to decode sympathetic and vagal contributions in this way? One argument to explain the decoding filter characteristics is the fundamental compromise, captured in the Gabor uncertainty relation [38], between time and frequency resolution. For example, a filter with high-frequency selectivity has a poor time resolution, and vice-versa. Choosing between low- and high-frequency selectivity impinges severe limitations between fast and slow autonomic cardiac regulation and it is one of the obstacles to proper processing in biological systems that are subject to real time response requirements [39]–[41]. Moreover, a fast cardiac response tends to cause a broadening of the filter bandwidth, decreasing the capacity of the system to filter environmental noise at the cost of selectivity. This behavior can be observed by analyzing the quality factor or sharpness of the filters through dividing the center frequency by bandwidth. The ICA decomposition also shows (Fig. 6B) that HF have a lower susceptibility to unwanted artifacts than VLF and LF, specifically around 0.14 to 0.29 Hz, where the respiratory sinus arrhythmia (RSA) synchronization is located [42]. This result is consistent with the fact that a sympathetic contribution increases the cardiac rhythm, whereas vagal activity behaves in an opposite way. It is also directly related to the system time response (damping ratio), which is represented by the inverse of the quality factor value multiplied by two. A high-damping ratio means a fast cardiac activity in contrast to low-damping ratio (Fig. 6C). Furthermore, filters with broad envelopes are likely to be optimized to process sinusoidal waveforms. Thus, the analysis of the filter envelope patterns suggests that the RSA frequency contributions are happening more frequently. The frequency region where the envelopes have higher values are concentrated between 0.14 and 0.29 Hz (Fig. 6D), which is consistent with experimental studies that characterize the respiratory components influencing autonomic cardiac regulation [43].

Bottom Line: Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm.We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation.Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.

View Article: PubMed Central - PubMed

Affiliation: Biological Information Engineering Laboratory, Nagoya University, Nagoya, Aichi, Japan. lucena@ohnishi.nagoya-u.ac.jp

ABSTRACT
The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.

Show MeSH