Mathematical modelling of heart rate and blood pressure regulation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics, School of Natural and Computational Sciences, Massey University

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Massey University
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A mathematical model of Heart Rate (HR) control has been expanded to include a mechanical model of the heart. The aim is to better understand the significance of Respiratory Sinus Arrhythmia (RSA), a variation of HR with respiration. RSA is found in several species but the physiological benefits and source of it are still under debate. A recently developed model of heart dynamics has been integrated into a model of HR control and gas exchange. HR is assumed to be primarily affected by the parasympathetic signal, with the sympathetic signal taken as a constant in the model. The parasympathetic signal is assumed to be affected by mechanical feedback from the lungs, direct modulation by the respiratory drive, and feedback from the baroreceptors (blood pressure sensors). The inclusion of a mechanical heart model allowed us to better represent the blood pressure in the HR control model and test two hypotheses regarding the function and source of RSA. Our study confirms that the main source of RSA is central modulation of heart rate. However, more work is needed to confirm using this model the hypothesis that RSA minimizes the work done by the heart while maintaining physiological levels of CO2.