Fractal Analysis of Blood Flow Based on Heart Valve Dynamics

Introduction. This article develops a mathematical model and algorithms of blood flow taking into account the dynamics of heart valves. The main goal of the research is to determine the nonlinear and complex dynamics of heart activity.
Methods. The model considers the heart chambers as elastic reservoirs that can deform to a certain volume. A point dynamic model is used to represent the dynamics of blood flow. The movement of the valves follows a specific dynamic equation, and valve function is expressed as a smoothly transitioning monotonic function. The complex dynamic characteristics of heart signals are determined using the MFDFA (Multifractal Detrended Fluctuation Analysis) method..
Results. The proposed model allows for the differential analysis of healthy and pathological signals. The main advantages of the model are: low demand for computational resources, a relatively small number of parameters, and the fact that most of them are practically measurable quantities. The results were implemented in the Python environment and the solutions were presented in a visual format.
Conclusion. The mathematical model has made it possible to gain a deeper understanding of the normal and pathological states of the heart. This, in turn, provides practical assistance in developing new diagnostic and treatment methods in medicine. The parameters of the model can be assessed in medical practice through indirectly measurable quantities (dynamics of chamber volume, ejection fraction, and changes in pressures).