Cardiorespiratory synchronization, a mathematical model
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This thesis examines the relationship of the human cardiovascular system and the human respiratory system. It is understood that these systems experience synchronization. In other words, the heart rate and the respiratory rate often vary concurrently. For example, during exercise, the heart rate and the respiratory rate increase simultaneously. Numerous examples of mathematical models of this phenomenon are found in previous research. Some utilize a large body of equations to describe the many aspects that affect this relationship. In this research, Van der Pol equations are introduced as models of thecardiovascular system and the respiratory system. The proposed model is then analyzed in MATLAB and examined for certain desired properties. Ultimately, a controller emulating the central chemoreceptors of the brain is included in this model. This model allows for the variation of the amplitude and the frequency of the oscillators and the levels of carbon dioxide and oxygen within the blood. The resulting model allows for observation of behaviors of cardiorespiratory synchronization during different levels of carbon dioxide deficiency and oxygen deficiency. Therefore, the model may be used to draw certain conclusions about how the human body responds to different conditions such as hypocapnia and hypercapnia.