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Complexity in the brain has been well-documented at both neuronal and hemodynamic scales, with increasing evidence supporting its use in sensitively differentiating between mental states and disorders. However, application of complexity measures to fMRI time-series, which are short, sparse, and have low signal/noise, requires careful modality-specific optimization.    Methods  Here we use both simulated and real data to address two fundamental issues: choice of algorithm and degree/type of signal processing.  Methods  were evaluated with regard to resilience to acquisition artifacts common to fMRI as well as detection sensitivity. Detection sensitivity was quantified in terms of grey-white matter contrast and overlap with activation. We additionally investigated the variation of complexity with activation and emotional content, optimal task length, and the degree to which results scaled with scanner using the same paradigm with two 3T magnets made by different manufacturers.  Methods  for evaluating complexity were:  power spectrum ,  structure function ,  wavelet decomposition ,  second derivative ,  rescaled range ,  Higuchi’s estimate of fractal dimension ,  aggregated variance,  and  detrended fluctuation analysis . To permit direct comparison across methods, all results were normalized to Hurst exponents.    Results  Power-spectrum, Higuchi’s fractal dimension, and generalized Hurst exponent based estimates were most successful by all criteria; the poorest-performing measures were wavelet, detrended fluctuation analysis, aggregated variance, and rescaled range.    Conclusions  Functional MRI data have artifacts that interact with complexity calculations in nontrivially distinct ways compared to other physiological data (such as EKG, EEG) for which these measures are typically used. Our results clearly demonstrate that decisions regarding choice of algorithm, signal processing, time-series length, and scanner have a significant impact on the reliability and sensitivity of complexity estimates.

Optimizing Complexity Measures for fMRI Data: Algorithm, Artifact, and Sensitivity