A new process for modeling heartbeat signals during exhaustive run with an adaptive estimator of its fractal parameters

This paper is devoted to a new study of the fractal behavior of heartbeats during a marathon. Such a case is interesting since it allows the examination of heart behavior during a very long exercise in order to reach reliable conclusions on the long-term properties of heartbeats. Three points of this study can be highlighted. First, the whole race heartbeats of each runner are automatically divided into several stages where the signal is nearly stationary and these stages are detected with an adaptive change points detection method. Secondly, a new process called the locally fractional Gaussian noise (LFGN) is proposed to fit such data. Finally, a wavelet-based method using a specific mother wavelet provides an adaptive procedure for estimating low frequency and high frequency fractal parameters as well as the corresponding frequency bandwidths. Such an estimator is theoretically proved to converge in the case of LFGNs, and simulations confirm this consistency. Moreover, an adaptive chi-squared goodness-of-fit test is also built, using this wavelet-based estimator. The application of this method to marathon heartbeat series indicates that the LFGN fits well data at each stage and that the low frequency fractal parameter increases during the race. A detection of a too large low frequency fractal parameter during the race could help prevent the too frequent heart failures occurring during marathons.