Separating the influence of Brain Signals from the Dynamics of Heart

Abstract

ECG signals appear to be quite complex. In this paper, we present results, which show that a normal ECG signal, which is a function of time can be transformed into a relatively simpler signal by stretching the time in a predetermined way. Before such a transformation, if you were to analyze various packets of the data for the Trans-Spectral Coherence (TSC) you could confirm that the signal indeed is very complicated. This is because the TSC gives us an idea of how various harmonics in a spectrum are related to one another. The coherence dramatically improved once we found an intermediate variable.. However, there was one hurdle. To find this variable, we needed to postulate that the complexified data lies on a 4-sheeted Riemann-Surface. With this insight, we could identify a proper time transformation which led to extremely high TSC. The transformed signal is quite simple. We can now rearrange the ECG data in terms of a set of functions in an affine space, which we can explicitly calculate from the data. This reveals that the dynamics of the heart, if freed from the external influence is quite simple.