Mathematical modeling of the cardiovascular autonomic control in healthy subjects during a passive head-up tilt test

Yurii M Ishbulatov,Sergey A Mironov,Anatoly S Karavaev,Boris P Bezruchko,Mikhail D Prokhorov,Anton R Kiselev,Vladimir I Ponomarenko,Margarita A Simonyan,Vladimir A Shvartz,Vladimir I Gridnev

doi:10.1038/s41598-020-71532-7

Abstract

A mathematical model is proposed for the autonomic control of cardiovascular system, which takes into account two separated self-exciting sympathetic control loops of heart rate and peripheral vascular tone. The control loops are represented by self-exciting time-delay systems and their tone depends on activity of the aortic, carotid, and lower-body baroreceptors. The model is used to study the dynamics of the adaptive processes that manifest in a healthy cardiovascular system during the passive head-up tilt test. Computer simulation provides continuous observation of the dynamics of the indexes and variables that cannot be measured in the direct experiment, including the noradrenaline concentration in vessel wall and heart muscle, tone of the sympathetic and parasympathetic control, peripheral vascular resistance, and blood pressure. In the supine and upright positions, we estimated the spectral characteristics of the model variables, especially in the low-frequency band, and the original index of total percent of phase synchronization between the low-frequency oscillations in heart rate and blood pressure signals. The model demonstrates good quantitative agreement with the dynamics of the experimentally observed indexes of cardiovascular system that were averaged for 50 healthy subjects.

Highlights

A mathematical model is proposed for the autonomic control of cardiovascular system, which takes into account two separated self-exciting sympathetic control loops of heart rate and peripheral vascular tone
The development of complex mathematical models from the first principles that simulate individual and collective dynamics of autonomic control loops can benefit the advancement of personalized medicine, computer simulation of various tests without a risk for the patient’s health, and approbation of new methods for the analysis of biological data
We propose a modification of the well-established model of autonomic control of circulation[14] with the self-exciting loops of heart rate and arterial pressure (AP) autonomic control

Summary

Introduction

A mathematical model is proposed for the autonomic control of cardiovascular system, which takes into account two separated self-exciting sympathetic control loops of heart rate and peripheral vascular tone. Dynamics of the two loops cannot be separated via spectral analysis and their individual input in the circulation control is hard to e stimate[6,7] This problem cannot be fully solved even by carrying out the active tests with the selective sympathetic or parasympathetic blockers such as propranolol, arfonad, and atropine, since the blockade of one regulatory loop inevitably leads to changes in the dynamics of another loop. The development of complex mathematical models from the first principles that simulate individual and collective dynamics of autonomic control loops can benefit the advancement of personalized medicine, computer simulation of various tests without a risk for the patient’s health, and approbation of new methods for the analysis of biological data. There are a number of cardiovascular m odels[26,27,28,29] capable of precise simulation of arterial pressure (AP) and heart rate dynamics during a passive tilt test

Results

Discussion

Conclusion