Non-linear and chaos characteristics of heart sound time series

Analysis of chaotic time series is common in many fields of science and engineering. It arises primarily from massive interactions between the many different parts of a non-linear system or in non-linear physical phenomena that are intrinsically complex. It is important to analyse the time series of these non-linear dynamic systems based on chaos theory. In recent years, many researchers on heart dynamics have demonstrated that chaos really exists in heart movements. In this study the non-linear and chaos characteristics are investigated and the fractal dimensions (FDs) and largest Lyapunov exponents (LLE) of the heart sound time series are calculated. First, the C-C method is used to estimate the time delay and embedding dimensions which are used to reconstruct the phase spaces. Then, the FDs and LLEs of the different heart sound signals are calculated and analysed, including the healthy heart sound, splitting of the second heart sound, mitral incompetence, and abnormal aortic shrinkage. From the results, the non-linear and chaotic characteristics in heart dynamic movement are found, and the results of LLEs show that the healthy heart has more obvious chaotic movements than abnormal movements.