• the cold pressor test.
• heart rate variability
• inhomogeneous point process
• bivariate model
• Brain-heart interaction

Knowledge of brain-body interaction is important due to various mental effects on the body since these two important systems sophisticatedly interplay through the autonomous nervous system (ANS). Heart rate variability or HRV is an interesting index in studying sympathetic and parasympathetic activities of the ANS. In this project, we tried to address how the brain functions on the heart in terms of directional coupling of the brain to the heart.For this purpose, we chose a dataset including HRV and electroencephalography (EEG) signals of 24 subjects under the cold pressor test. Then, we developed a new bivariate ARX model, taking HRV and the theta-band EEG signal power, employed to define a heartbeat probability model which is necessary for studying R-waves event as a point process model. In the next step, we derived time-varying features from the transfer function between the brain and heart calculated from the ARX coefficients, which are the model outputs to investigate the coupling between these two physiological systems. We represented this coupling by time-varying plots. The final result undergoes a statistical analysis by employing the Wilcoxon signed rank test and the Friedman test, both with p-value <0.05. According to p-value topographical maps,we found that the activated areas are close to regions which are currently known to be the central autonomic network (CAN).