To verify the couplings and synchronization among the oscillators of the cardiovascular system and interaction of brain with cardiovascular system

Abstract

In this report, we have analyzed the phase synchronization, directionality and newlinevariability aspects from the experimental data. The results obtained on these data newlinesets have been presented and discussed. The results from experimental data verified newlinethe synchronization of the order of n: m and also the directionality from lungs to newlineheart. The synchronization regimes were not continuous but were present in epochs. newlineAlso, the time periods of synchronization were not constant. We have modeled newlineheartbeat, respiration, myogenic activity of smooth muscles, control of ANS over newlinethe Cardiovascular System (CVS) and endothelial related metabolic activity as newlineindependent oscillators. We have considered Phenomenological models to capture newlinethe behavior of a system as a whole and avoided modeling the different parts of a newlinesystem in great detail. The advantage of considering these models were that we newlinecould use lower dimensions and could exploit wider range of mathematical tools, newlinethus a better understanding of the system could be achieved. We have considered newlinePhenomenological models for CVS as Poincare oscillator and for the better newlineunderstanding of heart and lungs interaction, we have considered Van der Pol newlineoscillator. In the Poincare oscillator model, we have taken heartbeat, respiration, newlinemyogenic activity of smooth muscles, ANS s control over the CVS and endothelial newlinerelated metabolic activity as autonomous Poincare oscillators and the interactions newlinebetween the subsystems as couplings between the oscillators. We concluded from newlinethe experimental data and Poincare oscillator model that the direction of coupling is newlinefrom lungs to heart. It was shown that there was presence of linear coupling as well newlineas parametric coupling, however, linear coupling dominated. Linear coupling in the newlinepresence of fluctuations resulted in epochs of synchronization; hence, the fluctuation newlineterm was taken into account for modeling purpose. The synchronization was not newlinecontinuous, it was present in epochs and the time periods of epochs were not fixed. newlineFurther the effects of Electromagnetic Radiations (EMRs) were considered. The newlineEMRs effects resulted in increased endothelial related metabolic activity; this in turn newlineaffected the coupling term of the cardiac oscillator and thereby resulted in the newlinealteration of the blood flow. We concluded that the effects of EMRs would lead toiii newlinefluctuating blood pressure, irregularity of heart beats and breathing pattern. Thus the newlinenormal functioning of CVS system was affected by the EMRs. newlineSubsequently, we have chosen Van der Pol Oscillator as a mathematical newlinemodel to represent the cardiorespiratory synchronization and brain was added as a newlinesensor to this model. We concluded that the Van der Pol model resembled the newlineexperimentally obtained data when the direction of coupling was from lungs to newlineheart. For phase locking, the frequency ratio of external force and oscillator were newlinetaken in the ratio of 3: 1 to 4: 1. It was demonstrated that the amplitude of the newlineexternal force had to be greater than certain threshold for proper functioning of the newlinemodel. The model worked under real world situation, where the natural frequency newlinecould be greater than 1. It was established that the increase in natural frequency newlineresulted in increase of heart rate and the breathing rate. Further, the Van der Pol newlineequations used for representing heart and lungs were modified by introducing brain newlineas a sensor, to simulate the adverse effects of EMRs on CVS. It was shown that if newlinethe levels of oxygen/ carbondioxide changed in the body as a result of the effects of newlineEMRs, the brain sensed it and accordingly increased the heart rate and breathing newlinerate. If the levels were normal, then there were no changes in the heart rate and newlinebreathing rate. To verify the resonance effect of EMRs, we considered the range of newlineRF frequencies (30 MHz 3000MHz), at this range of frequencies, we considered newlinethat the specific parts of the body resonated and there was higher absorption of the newlineinterfering signal. Thus the signals from the brain (sensor for radiation) to heart were newlineinterfered signals which resulted in fluctuation of the blood pressure. With the help newlineof this model we investigated the variation of the amplitude and the frequency of the newlineoscillators and the effects of EMRs on cardiorespiratory system. newlinePreliminary analysis suggested that human CVS is affected by EMRs, even if newlinethe radiations are below the threshold specific absorption rate (SAR) limits specified newlineby ANSI. newline