A three-dimensional fractal analysis method for quantifying white matter structure in human brain

Abstract

Fractal dimension (FD) is increasingly used to quantify complexity of brain structures. Previous research that analyzed FD of human brain mainly focused on two-dimensional measurements. In this study, we developed a three-dimensional (3D) box-counting method to measure FD of human brain white matter (WM) interior structure, WM surface and WM general structure simultaneously. This method, which firstly incorporates a shape descriptor (3D skeleton) representing interior structure and combines the three features, provides a more comprehensive characterization of WM structure. WM FD of different brain segments was computed to test robustness of the method. FDs of fractal phantoms were computed to test the accuracy of the method. The consistency of the computed and theoretical FD values suggests that our method is accurate in measuring FDs of fractals. Statistical analysis was performed to examine sensitivity of the method in detecting WM structure differences in a number of young and old subjects. FD values of the WM skeleton and surface were significantly greater in young than old individuals, indicating more complex WM structures in young people. These results suggest that our method is accurate in quantifying three-dimensional brain WM structures and sensitive in detecting age-related degeneration of the structures.