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The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of a complex object. Among other applications, FD has been used to identify abnormalities of the human brain in conventional magnetic resonance imaging (MRI), including white matter abnormalities in patients with Multiple Sclerosis (MS). Extensive grey matter (GM) pathology has been recently identified in MS and it appears to be a key factor in long-term disability. The aim of the present work was to assess whether FD measurement of GM in T1 MRI sequences can identify GM abnormalities in patients with MS in the early phase of the disease. A voxel-based morphometry approach optimized for MS was used to obtain the segmented brain, where we later calculated the three-dimensional FD of the GM in MS patients and healthy controls. We found that patients with MS had a significant increase in the FD of the GM compared to controls. Such differences were present even in patients with short disease durations, including patients with first attacks of MS. In addition, the FD of the GM correlated with T1 and T2 lesion load, but not with GM atrophy or disability. The FD abnormalities of the GM here detected differed from the previously published FD of the white matter in MS, suggesting that different pathological processes were taking place in each structure. These results indicate that GM morphology is abnormal in patients with MS and that this alteration appears early in the course of the disease.

Alzheimer's disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study we investigate spherical harmonic-based FD (SHFD), thickness and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI-converters and 29 MCI-non converters) and 32 healthy controls (HC). SHFD, thickness and LGI methodology allowed us to perform not only global but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI-converters compared to HC, and in MCI-converters compared to MCI-non-converters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white matter SHFD was significantly reduced in MCI-converters compared to MCI-non-converters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI-converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next four years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD.