On dynamics of heart rate variability

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.