Time-varying cardiovascular complexity with focus on entropy and lyapunov exponents

Measures of nonlinearity and complexity, such as entropy measures and Lyapunov exponents, have been increasingly employed to characterize dynamical properties in a wide range of biological nonlinear systems, including cardiovascular control. In this chapter, we present recent methodological advances allowing to effectively estimate instantaneous approximate and sample entropy measures, as well as the instantaneous Lyapunov spectrum of a series of stochastic events, i.e., the heartbeats. Because the proposed measures are instantaneously defined by means of probability functions defined within a point-process framework, these indices are able to provide instantaneous tracking of the degree of complexity associated with the physiological system in question. Long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications on experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure) are reported.