### Article

## Continuous time-variant parametric estimation of transient quadratic phase couplings between heart rate components in healthy neonates

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Published: | September 14, 2004 |
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### Outline

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#### Introduction

Generally, the heart rate variability (HRV) can be taken as an indicator of the co-ordination of the cardio-respiratory rhythms. Quadratic phase couplings (QPC) in the HRV are associated to amplitude modulation effects. At least three main rhythms can be distinguished in short-term recordings of the neonatal HRV: (i) the respiratory sinus arrhythmia (RSA) - a high frequency (HF) component between 0.4 and 1.5 Hz, (ii) nonrespiratory cardiovascular rhythms - a low frequency (LF) component around 0.1 Hz, and (iii) very low frequency components - e.g. movement related heart rate fluctuations (lower than 0.1 Hz) and other fluctuations of longer wavelength (0.04 Hz). These components are not independent of each other. Non-linear interrelations within the cardio-respiratory system could be identified applying complex analysis strategies like spectral and bispectral approaches and time-variant quantification of QPC using Hilbert transformation and coherence profiles on the neonatal HRV [Ref. 1]. Significant QPC between the LF component (0.04-0.25 Hz) and the HF component (>0.25 Hz) could be shown.

The bispectral analysis was performed using a direct (fast Fourier transform based) and time-invariant approach. Continuous (time-variant) parametric estimation of the bispectrum implies the possibility to quantify and to detect the occurrence and changes of non-linear couplings in their time course.

Therefore, the aim of this work was a continuous time-variant, parametric bispectral analysis of the neonatal HRV in the same neonates used in the direct, time-invariant approach [Ref. 1]. For the first time changes and rhythms in the time-course of QPC between the RSA component and the LF component constituted by the nonrespiratory cardiovascular rhythms could be shown in the neonatal HRV.

#### Subjects and Methods

The investigation was carried out in a group of 6 clinically and neurologically normal, full-term neonates (gestational age: 39+0.6 weeks; postnatal age: 4.0+0.6 day; birth weight: 3157+272g). The recordings were performed during sleep between 09.00 and 12.00h. Behavioural states were defined on the basis of the EEG and the EOG. Only the quite sleep periods were taken into consideration. The ECG was available with a sampling frequency of 1024 Hz and the HRV with a sampling frequency of 8.5 Hz. For each neonate one continuous HRV recording with a duration between 420 to 1325 seconds was analysed.

A continuous parametric bispectral approach requires a time-variant estimation of AR model parameters considering third or higher order moments to preserve phase information, which is essential to characterize quadratic phase relations. Such an approach was established by Swami [Ref. 2]. The adaptation of an AR model leads to a parametric bispectrum by using the transfer function of the estimated AR filter [Ref. 3]. The quality of the estimation (time- and frequency resolution of the bispectrum) depends strongly on the used AR model order and a forgetting factor. Data driven simulations were performed to find an appropriate parameter constellation. Using a two-dimensional approach of Schlögl [Ref. 4] an optimal AR model order of 50 and an optimal forgetting factor of 0.95 was identified.

The parametric biamplitude was calculated for each time point. A frequency resolution of 0.25 Hz was used. According to the presumed frequency components (HF, LF) phase-coupling phenomena were examined in a region of interest (ROI) [0.05 Hz, 0.25 Hz] x [0.45 Hz, 0.65 Hz]. For a better representation of the assumed phase-coupling phenomena the mean biamplitude in the ROI was calculated. For an optimal smoothing of the mean biamplitude course a radial basis functions network (RBFN) was used [Ref. 5].

#### Results

Generally, rhythmic fluctuations of the mean biamplitude in the ROI could be shown in all investigated neonates with a more or less distinct characteristic. A more accurate description of rhythms in the time course of the mean biamplitude were achieved by means of the RBFN. Maximums in the mean biamplitude in the ROI seems to occur in a distinct rhythms of approximately 10 seconds.

An exploratory data analysis (boxplot) of the time differences of peaks (TDP) extracted from the RBFN in all neonates demonstrated the existence of a 10-seconds-rhythm in the time course of QPC [Fig. 1]. The median of the TDP was between 8.6 and 11.1 seconds, the quartiles between 6.6 and 9.1 sec and 10.1 and 13.3 seconds accordingly for all neonates [Fig. 1].

#### Discussion

The aim of this work was a continuous investigation of quadratic phase couplings in the neonatal HRV. Until now, only direct (based on fast Fourier transformation) and time-invariant estimation of quadratic phase couplings were used to quantify QPC in the neonatal HRV.

The investigated 10-seconds-rhythms of QPC between the nonrespiratory cardiovascular rhythms (=LF) and the respiratory sinus arrhythmia (RSA=HF) yields to the question whether these are characteristics of a superordinated process. The LF component is related to cardiovascular control, and the RSA is related to the neural generation of the respiration rhythm (and mechanical couplings between lung and heart). Their neural control structures are located close together in almost identical regions of the brain stem. However, these are speculations based on a purely phenomenological investigations and have to be proved by experimental results.

#### Acknowledgment

This study was supported by the Deutsche Forschungsgemeinschaft (DFG grant Wi 1166/2-3/4).

### References

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