Dimensional analysis of nonlinear oscillations in brain, heart, and muscle

We present some numerical studies on the dimensional analysis of temporal oscillations observed in human electroencephalograms (EEG), heart rates, and muscle tremors. We show that it is insufficient to characterize the individual system by a single dimension value alone. We also present some detailed numerical analysis of the scaling structure of the attractors reconstructed from the time signal. Our methods are based on the concept of local gauge functions, which we derive from the raw signals and from transformed signals obtained through singular value decomposition. We are able to confirm and improve earlier results on the change of dimensionality of EEG signals. For heart rates we observe an increase of the dimensional complexity during sleep, and for muscle tremor data we find significant changes in the dimensionality depending on the isometrical contraction of the muscle. We attempt to indicate which factors are important in determining dimension estimates and where specific problems lie in each of the examples.