The determination of the generalized fractal dimensions (FDs) from MRI tractograms is affected by image resolution and the number of fiber tracts. In this work, we demonstrate that only certain combinations of image resolution, number of fiber tracts and exponent of the generalized dimensions are able to capture structural changes in human cerebral white matter. MRI tractography was carried out for a different number of fiber tracts and was discretized on different grid sizes. Generalized FDs were evaluated for two groups of healthy subjects with different age distribution. For the box-counting dimension (q = 0) the highest difference between two age groups was found for a matrix size of 2048³ pixel with a strong dependence on the number of fiber tracts. The correlation dimension found the highest differences for a resolution of 1024³ pixel, largely independent of the number of fiber tracts. The correlation dimension evaluated for tractograms discretized on a 1024³ grid is a robust measurement to capture structural changes in human cerebral white matter by means of FD.

中文翻译：

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空间分辨率和纤维密度对大脑纤维束分形维数的影响

从 MRI 纤维束图中确定广义分形维数 (FD) 受图像分辨率和纤维束数量的影响。在这项工作中，我们证明只有图像分辨率、纤维束数量和广义维度指数的某些组合才能捕捉到人类大脑白质的结构变化。对不同数量的纤维束进行 MRI 纤维束成像，并在不同的网格尺寸上进行离散化。对具有不同年龄分布的两组健康受试者评估广义FD。对于计箱维度 (q = 0^{) 对于 2048 3}像素的矩阵大小，两个年龄组之间的差异最大，并且强烈依赖于纤维束的数量。相关维度发现分辨率为 1024 ³像素的差异最大，很大程度上与纤维束的数量无关。^{在 1024 3}网格上离散化的牵引图评估的相关维度是通过 FD 捕捉人类大脑白质结构变化的稳健测量。