Fractal analysis of resting state fMRI signals in adults with ADHD
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Abstract
The fractal concept developed by Mandelbrot provides a useful tool for examining a variety of naturally occurring phenomena. Fractals are signals that display scale-invariant or self-similar behaviour. They can be found everywhere in nature including fractional Gaussian noise (fGn). Resting state fMRI signals can be modelled as fGn which makes them appropriate for fractal analysis. The Hurst exponent, H, is a measure of fractal processes and has values ranging between 0 and 1. Fractional Gaussian noise with 0<H<0.5 demonstrates negatively autocorrelated or antipersistent behaviour; fGn with 0.5<H<1 demonstrates a positively correlated, relatively persistent, predictable, long memory behaviour; and fGn with H = 0.5 corresponds to classical Gaussian white noise. In the present study, we aim to estimate the fractal behaviour of adult ADHD patients when compared to age-matched healthy controls using dispersional analysis. We hypothesize that ADHD patients will demonstrate more predictable (higher H values) fractal behaviour. Ten ADHD patients (5 female, mean age (32.60±10.46)) and ten controls (7 female, mean age (30.10±8.49)) were brain imaged by 3T MRI scanner. All patients and control participants completed the Conners’ Adult ADHD Rating Scales (ADHD scores). Our analysis shows that the ADHD patients demonstrate more positively correlated, relatively persistent, predictable and longer memory fractal behaviour in regards to healthy controls. The discriminated brain regions are part of the frontal-striatal-cerebellar circuits and are consistent with the hypothesis of abnormal frontal-striatal-cerebellar circuits in ADHD. We have shown that the analysis of fractal behaviour may be a useful tool in revealing abnormalities in ADHD brain dynamics.