Model for the respiratory modulation of the heart beat-to-beat time interval series

In this study we present a model for the respiratory modulation of the heart beat-to-beat interval series. The model consists of a set of differential equations used to simulate the membrane potential of a single rabbit sinoatrial node cell, excited with a periodic input signal with added correlated noise. This signal, which simulates the input from the autonomous nervous system to the sinoatrial node, was included in the pacemaker equations as a modulation of the iNaK current pump and the potassium current iK. We focus at modeling the heart beat-to-beat time interval series from normal subjects during meditation of the Kundalini Yoga and Chi techniques. The analysis of the experimental data indicates that while the embedding of pre-meditation and control cases have a roughly circular shape, it acquires a polygonal shape during meditation, triangular for the Kundalini Yoga data and quadrangular in the case of Chi data. The model was used to assess the waveshape of the respiratory signals needed to reproduce the trajectory of the experimental data in the phase space. The embedding of the Chi data could be reproduced using a periodic signal obtained by smoothing a square wave. In the case of Kundalini Yoga data, the embedding was reproduced with a periodic signal obtained by smoothing a triangular wave having a rising branch of longer duration than the decreasing branch. Our study provides an estimation of the respiratory signal using only the heart beat-to-beat time interval series.