Long-Range Temporal Correlations, Multifractality, and the Causal Relation Between Neural Inputs and Movements

Understanding the causal relation between neural inputs and movements is very important for the success of brain machine interfaces (BMIs). In this study, we perform systematic statistical and information theoretical analysis of neuronal firings of 104 neurons, and employ three different types of fractal and multifractal techniques (including Fano factor analysis, multifractal detrended fluctuation analysis (MF-DFA), and wavelet multifractal analysis) to examine whether neuronal firings related to movements may have long-range temporal correlations. We find that MF-DFA and wavelet multifractal analysis (but not Fano factor analysis) clearly indicate that when neuronal firings are not well correlated with movement trajectory, they do not have or only have weak temporal correlations. When neuronal firings are well correlated with movements, they are characterized by very strong temporal correlations, up to a time scale comparable to the average time between two successive reaching tasks. This suggests that neurons well correlated with hand trajectory experienced a “re-setting” effect at the start of each reaching task. We further discuss the significance of the coalition of those important neurons in executing cortical control of prostheses.