Fractal analysis of the boundary between white matter and cerebral cortex in magnetic resonance images: a controlled study of schizophrenic and manic-depressive patients

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Abstract
This paper reports development of a computerized (‘box-counting’) method for estimation of fractal dimension (FD) of the magnetic resonance image (MRI) boundary between cerebral cortex and white matter; and the application of this method to MRIs of 39 schizophrenics (SZs), 23 manic-depressives (MDs) and 31 controls (CONs). Mean FD across all diagnostic groups was 1·402; 95% confidence interval (CI) 1·399 to 1·406. Mean FD was greater in boundaries extracted from manic-depressive patients than in boundaries extracted from controls (difference between MD and CON mean FDs = 0·008; 95% CI −0·002 to +0·018); and less in schizophrenics than in controls (difference between SZ and CON mean FDs = −0·003; 95% CI −0·011 to +0·005). Mean FD was positively correlated with subcortical volume and anterior cerebral volume, and negatively correlated with sulcal cerebrospinal fluid volume. Significant differences in mean FD between diagnostic groups were demonstrated by analysis of covariance (ANCOVA; P < 0·01), with age and volumetric measures of brain size as covariates; and manic-depressive boundaries were shown to have significantly greater values for residual FD (after controlling for effects of brain size) than boundaries extracted from controls (t test; P < 0·05). It is proposed that FD is a useful measure of clinically relevant differences in the complexity of MRI boundaries.