Multifractal detrended fluctuation analysis and local scale exponents of inter spike intervals

The study presents the analysis of detrended fluctuations (DFA) in inter spike intervals (ISI) of neuronal ensemble from cortex of awake behaving macaque monkeys. The original DFA method was applied to analyze fluctuation of variances from fitted trends of different order. The spectrum of local scale exponent was calculated to investigate the presence of different scaling regions. It was observed that the single scaling exponent is insufficient to describe the firing pattern dynamics, the better fit is achieved using both short-term a₁ and long-term α₂ scaling coefficients. The validation procedure using phase randomized surrogates provided more reliable local scale exponents´ estimates. Generalized DFA analysis revealed the presence of multifractality in ISI time series. Results indicate that multifractality is partly due to the broad probability distribution function and partly due to the presence of long-range correlations. Isodistributional surrogate data were used to test the significance of generalized Hurst exponent spectrum and origin of multifractal behavior. In conclusion, both DFA and its multifractal expansion reveal the presence of long-range correlation in ISI time series indicating the presence of memory in the neuronal firing pattern.