Measuring complexity of fetal cortical surface from MR images using 3-D modified box-counting method

Although fractal analyses of adult human brain complexity have been performed for several years, the use of fractal dimension (FD) to measure complexity of the developing fetal cortical surface has not been extensively investigated. This study attempts to measure the complexity of the developing fetal cortical surface using the concept of FD. As has been done by others, the commonly used box-counting (BC) method was herein extended from 2-D to 3-D to quantify the FD of fetal cortical complexity. The primary theoretical contribution of this work is the modification of the 3-D BC method using a local FD measure to yield an accurate FD that elucidates the fractal characteristics of the cortical surface. The proposed 3-D modified BC (MBC) method was then adopted to estimate the FD to measure the complexity of the cortical surface of 32 normal and six test fetal brains at a gestational age (GA) of 2737 weeks. The results for normal brains reveal that the increase in cortical complexity is correlated with the GA of the fetus. Observations of test brains indicate that the twins and cortical dysplasia are associated with lower FD than that of normal fetuses. These results suggest that the proposed 3-D MBC method is an effective means of measuring the complexity of the fetal cortical surface.