Fractal dimension of skeletonized MR images as a measure of cerebral hemispheres spatial complexity

Abstract

In recent decades, fractal analysis has been increasingly used in various scientific fields, including neuroscience; this method of mathematical analysis allows you to quantify the space filling degree of the studied object and the degree of its spatial configuration complexity. The aim of the study was to determine the values of the fractal dimension of the cerebral hemispheres using fractal analysis of skeletonized magnetic resonance brain images. The present study used magnetic resonance brain images of 100 relatively healthy individuals (who had no structural changes in the brain) of both sexes (56 women, 44 men) aged 18-86 years (mean age 41.72±1.58 years). 5 tomographic sections of each brain were studied. The 1st coronal tomographic section was located at the level of the most anterior points of the temporal lobes, the 2nd – at the level of the mammillary bodies, the 3rd – at the level of the quadrigeminal plate, the 4th – at the level of the splenium of corpus callosum. The axial tomographic section was located at the level of the thalamus. Fractal analysis of skeletonized images was performed using box counting method. The obtained data were processed using generally accepted statistical methods. The average, minimum and maximum values of the fractal dimension of different tomographic sections were the following: 1st coronal section – 1.207±0.003 (1.147÷1.277), 2nd coronal section – 1.162±0.003 (1.077÷1.243), 3rd coronal section – 1.156±0.003 (1.094÷1.224), 4th coronal section – 1.158±0.003 (1.109÷1.218), axial section – 1.138±0.002 (1.079÷1.194). The average value of the fractal dimension of the five tomographic sections was 1.164±0.002 (1.126÷1.209), and the average value of the fractal dimension of the four coronal sections was 1.171±0.002 (1.122÷1.219). Fractal analysis of skeletonized images of the cerebral hemispheres allows to quantify the features of the topology and complexity of the spatial configuration of the cerebral hemispheres. The value of the fractal dimension can be influenced by the anatomical features of the studied areas of the brain, individual anatomical features, as well as atrophic and other pathological changes that lead to changes in the shape of the cerebral hemispheres. The values of the fractal dimension of skeletonized brain images tend to decrease with age. Coronal tomographic sections are the most representative for characterizing age-related atrophic changes. Fractal analysis of skeletonized images of the cerebral hemispheres can be used to diagnose diseases of the nervous system, and the results of the present study can be used as norm criteria.