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

A. CAPURRO; L. DIAMBRA; C.P. MALTA

Physica A - Statistical and Theoretical Physics

Elsevier

Año: 2005 vol. 355 p. 439 - 460

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