Heart rate variability refers to the variations in time interval between successive heart beats. An understanding of its dynamics can have clinical importance since it can help distinguish persons with healthy heart beats from those without. Our aim in this thesis was to characterise the dynamics of the human heart rate variabilty from three different groups: normal, heart failure and atrial fibrillation subjects. In particular, we wanted to establish if the dynamics of heart rate variability from these groups are stationary, nonlinear and/or chaotic. We used recurrence analysis to explore the stationarity of heart rate variability using time series provided, breaking it into epochs within which the dynamics were stationary. We then used the technique of surrogate data testing to determine nonlinearity. The technique involves generating several artificial time series similar to the original time series but consistent with a specified hypothesis and the computation of a discriminating statistic. A discriminating statistic is computed for the original time series as well as all its surrogates and it provides guidance in accepting or rejecting the hypothesis. Finally we computed the maximal Lyapunov exponent and the correlation dimension from time series to determine the chaotic nature and dimensionality respectively. The maximal Lyapunov exponent quantifies the average rate of divergence of two trajectories that are initially close to each other. Correlation dimension on the other hand quantifies the number of degrees of freedom that govern the observed dynamics of the system. Our results indicate that the dynamics of human heart rate variability are generally nonstationary. In some cases, we were able to establish stationary epochs thought to correspond to abrupt changes in the dynamics. We found the dynamics from the normal group to be nonlinear. Some of the dynamics from the atrial fibrillation and heartfailuregroupswerefoundtobenonlinearwhileotherscouldnotbecharacterised by the technique used. Finally, the maximal Lyaponov exponents computed from our various time series seem to converge to positive numbers at both low and high dimensions. The correlation dimensions computed point to high dimensional systems.

Theses(Msc Applied Mathematics)-----Botswana International University Science and Technology,2018