Determination of the flow diseases in the vessels using the chaos theory

The cardiovascular system is a complex physical system that transports the blood to each cell of the body. The blood flow is laminar in the healthy vessel. The vascular diseases e.g. stenosis, occlusion frequently appear and turbulent blood flow occurs in this conditions. In addition, the turbulence rate of fluid regime increases while degree of the stenosis is increased. An arterial stenosis induces to a turbulence as chaotic blood flow. Chaotic analysis (nonlinear analysis) can characterize the complexity of chaotic or turbulent flow in an artery caused by vascular disease and can detect the degree of turbulence for clinical purposes. The goal of this research is examination of the vascular diseases using the nonlinear analysis methods. In this study, the Doppler signals obtained from Doppler ultrasonography that is a reliable technique to determine the flow characteristics of vessels, were evaluated using by chaotic analysis. The chaotic behaviour of the blood flow in healthy and diseased vessels was examined with the largest Lyapunov exponent, correlation dimension, Renyi dimension spectrum methods. The Lyapunov exponent quantifies the sensitivity to the initial conditions of a dynamic system and it?s value is positive for the chaotic systems. The correlation dimension gives the minimum number of independent variables that manages the system behaviour in the chaotic systems. The each chaotic invariant indicates the system?s complexity by different meanings. The Doppler signals obtained from the internal carotid artery that belong to healthy and various degree stenosed case and the Doppler signals obtained from aortic valve for healthy case, aortic stenosis and aortic insufficiency diseases were examined. The second-order statistical test was applied to the results obtained from chaotic analysis and the significantly differences were found for healthy and disease conditions. The effective chaotic analysis methods through used in this study were determined to establishing the disease conditions. In this study, it has been determined that the largest Lyapunov exponent and correlation dimension analysis made by using the Grasberger-Procaccia algorithm are distinctive methods for determining the complex behaviour in the blood flow such as disease case and degree of stenosis. The results have shown that the chaotic analysis methods give effective and useful results for detection the vessel disorders.