Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

Abstract

This study aims to investigate the complexity of the developing fetal cortical surface based on the notion of fractal dimension (FD). Forty-four fetal MR images were selected at 22-36 weeks of gestational age (GA) and distributed between two groups: 32 normal fetal brains (excluding twins) and 12 abnormal fetal brains, including twins, mild ventricular dilata-ROC tion, Cornelia de Lange syndrome (small brain), and cortical dysplasia (developmental delay). We adopted the commonly used box-counting (BC) method to estimate the FD of the developing fetal cortical surface. Results from normal fetal brains show that the increase of cortical complexity is highly correlated with fetal developing weeks of GA. In addition, after 28 weeks of GA, the value of FD increases more rapidly because of the faster development of convolved folds. In comparison with results from the normal fetal group, the abnormal fetal brains were examined and the results show that: (1) mild ventricular dilatation has no significant developing difference compared with normal fetal brains; (2) twins had lower FD than that of normal fetal brains, which may be a delay of 2-3 weeks;(3) the case of cortical dysplasia also had low FD, indicating that developing delay may mean less cortical complexity. The results of the normal group are in good agreement with fetal brain development and demonstrate the effectiveness of FD as a promising means for the quantification of complexity of the fetal cortical surface.

Thermodynamics: The Unique Universal Science

“…Brain imaging studies have found increasing cortical complexity in early life, throughout childhood, and into adulthood [237][238][239], and then followed by decreasing complexity in the later stages of life [240,241]. Similarly, a rapid rise in entropy production [242] from early life, throughout childhood, and into early adulthood is also seen, followed by a slow decline thereafter [243].…”

Fractal Structure and Entropy Production within the Central Nervous System

“…Fractal studies on the development and aging of the human brain have shown increasing cortical complexity in early fetal life [39,40], and throughout childhood into adulthood [41] with decreasing complexity later in life [28,42,43]. In fact in 2001, Blanton and colleagues demonstrated that the complexity of the cortex folding characterized by fractal dimension increases with normal brain development over the first two decades of life in normal children [41].…”

“…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]…”

Studying a Chaotic Spiking Neural Model

“…Biologists suggest that chaos may play an important role in human brain [1][2][3][4][5][6][7][8]. Chaos has many interesting properties that might be exploited in carrying out information processing tasks.…”