Department of Radiology, MR-Physics, Medical University of Graz, Graz, Austria.
PLoS One. 2012;7(7):e41148. doi: 10.1371/journal.pone.0041148. Epub 2012 Jul 18.
The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.
分形维数（FD）可作为生物系统形态复杂性的度量。本研究旨在测试该定量参数在脑血管复杂性方面的有效性。对 10 例脑动静脉畸形（AVM）患者和 10 例健康对照者的 TOF-MRI 扫描最大强度投影进行分形分析。采用 Box 计数维数、Minkowski 维数和多重分形分析评估的广义维数等不同 FD 测量方法进行分析。通过将 FD 值与动态对比增强 MRI 数据中获得的对比剂传输最大斜率以及 X 射线血管造影数据中获得的病灶大小进行比较，探讨了该参数的生理意义。结果表明，对于所有方法，AVM 半球的 Box 计数维数、Minkowski 维数和广义维数 FD 均显著高于无 AVM 半球，表明 FD 是一种敏感的捕捉血管复杂性的参数。此外，我们还发现 FD 与对比剂传输最大斜率之间以及 FD 与中央病灶大小之间具有高度相关性，表明 FD 具有生理相关性。因此，该方法可以作为一种附加的客观参数，自动评估并可能有助于 AVM 的复杂检查。
