Analysis of Rhythmic Patterns Produced by Spinal Neural Networks

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Abstract
A network of spinal neurons known as central pattern generator (CPG) produces the rhythmic motor patterns required for coordinated swimming, walking, and running in mammals. Because the output of this network varies with time, its analysis cannot be performed by statistical methods that assume data stationarity. The present work uses short-time Fourier (STFT) and wavelet-transform (WT) algorithms to analyze the nonstationary rhythmic signals produced in isolated spinal cords of neonatal rats during activation of the CPGs. The STFT algorithm divides the time series into consecutive overlapping or nonoverlapping windows and repeatedly applies the Fourier transform across the signal. The WT algorithm decomposes the signal using a family of wavelets varying in scale, resulting in a set of wavelet coefficients presented onto a continuous frequency range over time. Our studies revealed that a Morlet WT algorithm was the tool of choice for analyzing the CPG output. Cross-WT and wavelet coherence were used to determine interrelations between pairs of time series in time and frequency domain, while determining the critical values for statistical significance of the coherence spectra using Monte Carlo simulations of white-noise series. The ability of the cross-Morlet WT and cross-WT coherence algorithms to efficiently extract the rhythmic parameters of complex nonstationary output of spinal pattern generators over a wide range of frequencies with time is demonstrated in this work under different experimental conditions. This ability can be exploited to create a quantitative dynamic portrait of experimental and clinical data under various physiological and pathological conditions.