Nonlinear and Fractal Analysis

There are many complex systems in nature that can be explained by nonlinear interactions of its main components. The heart rate regulation is one of the most complex systems in the human body. Heart rhythm is innervated by both the parasympathetic and sympathetic branches of the ANS. At the same time, the autonomic nervous system is influenced by humoral effects, hemodynamic variables, respiratory rhythm, and stroke volume, among others. Furthermore, there exist feedback loops among these mechanisms influencing each other in a nonlinear way. A consequence of these nonlinear interactions is that heart rate modulation cannot be fully understood by studying its components in isolation. However, the study of the heart rhythm modulation as a whole is a formidable task. A more common approach in the literature, more modest than the full comprehension of the heart rate regulation system, is trying to quantify the complexity of heart rate using nonlinear statistics derived from the chaos theory or from fractal processes. In this chapter, we summarize the most widely used statistics based on nonlinear and fractal dynamics, and we show how to compute them with RHRV.