Mathematical modelling of the cardiovascular system to study the effects of respiratory sinus arrhythmia and heart failure : this dissertation is submitted for the degree of Doctor of Philosophy, School of Natural and Computational Science, Massey University

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Massey University
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This thesis presents the development of lumped parameter models of the cardiovascular system with a specific aim of simulating the system dynamics over a range of heart rates. The models contain several new modelling features that have been introduced progressively throughout the thesis starting with isolated models and continuing with closed loop models of the circulation. Specifically, the contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameters were taken from the literature and experimental data. Sensitivity analysis was performed on one of the models outputs by changing one parameter at a time; this analysis indicated that the total blood volume is the most influential parameter in the model. The developed models were used to study the effects of Respiratory Sinus Arrhythmia (RSA), variability in heart rate at the frequency of breathing. RSA is an indicator of good health but the mechanism that gives rise to RSA and its function are still debatable. Two potential sources of RSA were incorporated: periodic heart rate that mimics the central regulation of heart rate which originates in the brainstem, and periodic systemic veins resistance that mimics one possible effect of the pleural pressure which drives breathing. The effects of RSA on cardiac output were then studied. The simulations suggest that the mean cardiac output does not change significantly due to RSA at either low or high heart rates. Two types of heart failure were simulated using the new models by changing certain model parameters: systolic and diastolic. Both the systolic and diastolic heart failures caused an accumulation of blood in the lungs. The ejection fraction for diastolic heart failure remained within the normal physiological range while in the case of systolic heart failure the ejection fraction reduced rapidly. These results are consistent with physiological observations.
Arrhythmia, Cardiovascular system, Heart failure, Heart, Contraction, Respiration, Mathematical models