Linear and Non-linear Quantification of the Respiratory Sinus Arrhythmia Using Support Vector Machines

Respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling. It is observed as changes in the heart rate in synchrony with the respiration. RSA has been hypothesized to be due to a combination of linear and nonlinear effects. The quantification of the latter, in turn, has been suggested as a biomarker to improve the assessment of several conditions and diseases. In this study, a framework to quantify RSA using support vector machines is presented. The methods are based on multivariate autoregressive models, in which the present samples of the heart rate variability are predicted as combinations of past samples of the respiration. The selection and tuning of a kernel in these models allows to solve the regression problem taking into account only the linear components, or both the linear and the nonlinear ones. The methods are tested in simulated data as well as in a dataset of polysomnographic studies taken from 110 obstructive sleep apnea patients. In the simulation, the methods were able to capture the nonlinear components when a weak cardiorespiratory coupling occurs. When the coupling increases, the nonlinear part of the coupling is not detected and the interaction is found to be of linear nature. The trends observed in the application in real data show that, in the studied dataset, the proposed methods captured a more prominent linear interaction than the nonlinear one.