Zhang Luduan, Liu Jing Z, Dean David, Sahgal Vinod, Yue Guang H
Department of Biomedical Engineering, The Lerner Research Institute, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, OH 44195, USA.
J Neurosci Methods. 2006 Jan 30;150(2):242-53. doi: 10.1016/j.jneumeth.2005.06.021. Epub 2005 Aug 19.
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.
分形维数（FD）越来越多地用于量化脑结构的复杂性。以往分析人类大脑FD的研究主要集中在二维测量上。在本研究中，我们开发了一种三维（3D）盒计数法，可同时测量人类脑白质（WM）内部结构、WM表面和WM总体结构的FD。该方法首先纳入了一个表示内部结构的形状描述符（3D骨架），并结合了这三个特征，从而对白质结构进行了更全面的表征。计算不同脑段的WM FD以测试该方法的稳健性。计算分形模型的FD以测试该方法的准确性。计算得到的FD值与理论FD值的一致性表明我们的方法在测量分形FD时是准确的。进行统计分析以检验该方法在检测许多年轻和老年受试者的WM结构差异方面的敏感性。WM骨架和表面的FD值在年轻人中显著高于老年人，表明年轻人的WM结构更复杂。这些结果表明，我们的方法在量化三维脑WM结构方面是准确的，并且在检测与年龄相关的结构退化方面是敏感的。
