Modeling the dynamics of blood pressure under the sleep apnea effect

Abstract

In this study, a dynamic system modeling to analyze blood pressure disorders under the sleep apnea effect is carried out. As a first step, the basic variables of the blood pressure system and the causal relationship between these variables are determined with the help of previous scientific literature. Through modeling steps, these relationships are presented in a simulation environment by writing the related mathematical equations. After the equations are determined and the model is constructed, we first try to deduce the dynamics of the basic variables of blood pressure system for a healthy human. The model should generate the dynamics of the basic variables of the blood pressure system for a healthy human body, as suggested in the corresponding literature. The model indeed passes this basic test of model validity. Thereby, the model can provide insights to investigate the medical disorder scenarios such as sleep apnea, without experimenting on human beings. Increased blood pressure, hypertension, a known problem of the blood pressure system caused by sleep apnea, is obtained by simulation runs. The reason of this particular hypertension is that the sleep apnea causes oxygen deficiency in the tissues during and after apnea periods, leading to structural changes in the function of sensory cells. These changes are obtained in the simulation results. Next, by the scenario analysis, the dynamics of the fundamental variables in the blood pressure system under different intensity, frequency or distribution of the sleep apnea have been analyzed. Simulation results show that the increase in the intensity or frequency of apnea leads to more severe hypertension. Finally, receptor blocker drugs, like alpha 1 and beta 1 blockers typically used as a treatment of hypertension are also modeled and experimented with. The effect of different usage times of these drugs on the treatment of the disease has been simulated. Simulation results show that the timing of medication is important for effective control the of the hypertension associated with the sleep apnea, if drug usage time is optimal.