Fractal dimension analysis of grey matter in multiple sclerosis

Abstract

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.

Fractal Structure and Entropy Production within the Central Nervous System

“…Moreover, fractal studies have demonstrated a decrease in fractal dimension of the CNS with illness (i.e., Alzheimer's [42], epilepsy [23,24], MS [45], stroke [49]) which correlates with metabolic studies demonstrating a decline in glucose metabolism with illness [83,85,88,[90][91][92][93][94][95][96][97][101][102][103]. Conversely, there are diseases which demonstrate an increase in fractal dimension including cancer [50][51][52][53][54][55] and grey matter structural changes in MS [46]. Of significance, these diseases which demonstrate an increase in fractal dimension also demonstrate an increase in glucose metabolism.…”

“…Compared to normal healthy subjects, patients with MS have been shown to have a significant decrease in white matter fractal dimension in both sections with MS lesions and sections with normal appearing white matter [45]. Conversely, one study of the fractal dimension of grey matter has shown that MS patients have a significant increase in grey matter fractal dimension compared to controls and such differences were apparent even in patients with first attacks of MS and patients with relapsing-remitting MS [46]. The difference in the structural changes in the white matter vs. grey matter suggests that different pathological processes are taking place.…”

“…Conversely, research has revealed regions of increased cerebral glucose metabolism in MS patients in both the parietal and frontal cortex, suggesting a cortical compensatory mechanism and regional cortical reorganization as these areas of higher metabolism were close to cortical areas of hypometabolism [89]. Like the MS fractal studies which demonstrate a decrease in white matter fractal dimension [45] and an increase grey matter fractal dimension [46], the metabolic studies are reflective of these results with concomitant increases and decreases in glucose metabolism, suggesting again a link between fractal structure and metabolism.…”

“…Aging  FD of the cortex early in fetal life and childhood into adulthood [39][40][41]  human entropy production from birth to age 18 [77]  human entropy production after early adulthood [77]  and  entropy production correlates with and  in VO 2 max in childhood and early adulthood, respectively [80]  entropy production-decreased glucose metabolism in frontal and temporal lobes with normal healthy aging [72,81,82]  FD of the cortex and white matter in late adulthood [28,42,43] Epilepsy  FD of white matter in half the patients with frontal lobe epilepsy [24] Abnormal FD of the cortex in half the patients with cryptogenic epilepsy [23]  entropy production -interictal glucose hypometabolism correlates with epileptogenic region [83,85]  entropy production-glucose hypometabolism of the cerebral cortex, subcortical nuclei, supratentorial white matter, infratentorial structures, superior mesial frontal cortex, superior dorsolateral frontal cortex, mesial occipital cortex, lateral occipital cortex, deep parietal white matter and pons [86,87] Degree of cerebral hypometabolism  number of relapses [88] Thalamic and cerebellar glucose hypometabolism  total lesion volume [89]  entropy production-increased cerebral glucose metabolism in the parietal and frontal cortex located close to areas of hypometabolism [89]  FD of grey matter [46] Alzheimer's  FD of anterior tip of the temporal lobe, mammillary bodies, superior colliculus, posterior edge of the corpus callosum, inferior colliculus and midthalamus [42] FD of cortical ribbon significantly different from control subjects [48]  entropy production-cerebral glucose hypometabolism including the posterior cingulate cortex, parieto-temporal lobe and prefrontal cortex [90][91][92][93][94][95][96]…”

Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

“…FD analysis can also quantify dynamic changes of the structural or functional complexity of the neural system during the process of brain development or degeneration [10][11][12]. Researchers have also applied FD measurement in many image analyses of central nervous system disorders such as schizophrenia [13], tumor detection [14], multiple sclerosis [15], obsessivecompulsive disorder [16], and age-related WM abnormalities [17].…”