Master thesis : Exploring the Fractal Dynamics of the Heart Rate: Modeling and Analysis of Components in Health and Disease

Abstract

The presence of a fractal pattern, characterized by self-similarity at various scales, has been observed in numerous biological signals. This thesis specifically investigates the fractal pattern of the heart rate. The main objective of this project is to analyze the underlying mechanisms that contribute to this complex structure, aiming to gain a deeper understanding of its nature and how it is influenced by different diseases. The study focused on three distinct groups which included healthy subjects, individuals with congestive heart failure, and those with atrial fibrillation. The study aimed to adapt and expand a stochastic model proposed by Ivanov et al. (1998), which originally focused on modeling the fractal dynamics of heart rate in healthy individuals. The model assumes that the heart rate is influenced by the parasympathetic and sympathetic systems. In this project, the model was re-implemented and extended to incorporate diseased subjects. The extended stochastic model accurately represented the fractal dynamics of the heart rate, showing strong correlation with observed patterns. Atrial fibrillation resulted in a complete loss of fractal dynamics at low scales, replaced by a random signal. Congestive heart failure had a lesser impact but showed a reduction in the influence of the sympathetic and parasympathetic systems. These findings highlight the model’s strength in elucidating complex physiological processes. Looking ahead, further advancements can be made by incorporating additional factors, paving the way for even more comprehensive understanding.