Medicine (Austin & Northern Health) - Theses
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ItemThe mathematical analysis of heart rate variability( 1998)This thesis examines various mathematical approaches, including conventional statistical descriptions and nonlinear mathematical methods of measuring short term heart rate variability (HRV). The observation that the heart beat is not precisely regular was made nearly 400 years ago by Dr Thomas Willis. This physiological phenomena was not fully appreciated until relatively recently when computer based methods to accurately measure the heart rate became readily available. Since the first contemporary scientific papers describing this natural fluctuation in heart rate started to appear in 1964, there has been an ever increasing number of publications evaluating the use of HRV analysis in various areas of clinical medicine. Although modern signal processing techniques provide a means of analysing beat to beat functions in heart rate there still remain many problems in developing suitable practical techniques which can be used in the clinical setting. Most commonly, HRV analysis is performed using data collected from 24-hour ambulatory electrocardiograms, however the attendant logistic and technical difficulties make long term HRV analysis impractical as a routine clinical investigation. To address this problem, short term analysis of HRV using geometric methods based on the Poincaré plot are examined in detail in this thesis. Issues relating to time series analysis including stationarity, artefact and filtering methodology are also explored. Using health volunteers and subjecting them to various autonomic perturbations it was demonstrated that the width of the Poincaré plot as quantified by SD delta RR (r-MSSD) is a measure of parasympathetic nervous system activity. The autonomic effect of various doses of captopril in patients with left ventricular dysfunction and heart failure was shown to be dose responsive with an increase in cardiac vagal activity occurring at low dose captopril (12.5 mg BD) and a reduction in vagal activity to baseline levels at the highest dose (50 mg BD). The implication of this study suggests that careful dosing of captopril is required in patients with heart failure to optimise cardiac autonomic activity. Reduced HRV has also been shown to be a consistent feature in patients with hypertension and it was demonstrated that increasing doses of enalapril result in an increase in cardiac parasympathetic nervous system activity. The implication being that increasing doses of enalapril provide beneficial autonomic changes in these patients. Mathematical models enable theoretical explorations of physiological control systems too complex for complete understanding. It is with this principle in mind that a simple mathematical model of the baroreflex loop is developed and used to generate some of the characteristic Poincaré plot patterns produced in the various studies presented in this thesis. The implications of the mathematical model have relevance to the nonlinear mathematical methods of HRV analysis and provide theoretical structure with which to interpret the nonlinear parameters used to quantify HRV.