Arbor vitae cerebelli: Fractal properties and their quantitative assessment by novel “contour scaling” fractal analysis method (an anatomical study)

Abstract

Background

Arbor vitae cerebelli (tree-like branching white matter of the cerebellum) has a complex spatial configuration that is challenging to assess using conventional morphometric methods. This study proposes a fractal approach to describe and quantify the anatomy of Arbor vitae cerebelli. For this purpose, a new “contour scaling” method for fractal analysis of cerebellar white matter was developed.

Material and methods

The cerebella of 100 cadavers (50 male and 50 female) who died from causes unrelated to brain pathology, aged 20–95 years, were examined. Mid-sagittal sections of the cerebellar vermis were studied. The fractal dimension values of the cerebellar white matter were determined using both the developed fractal analysis method and the conventional “box counting” method, along with measurements of non-fractal parameters including cerebellar weight, area and perimeter of the vermis cross-section, perimeter-to-area ratio, and circularity.

Results

Considering the cerebellar white matter as a tree-like fractal, it was found to have 7 or 8 primary branches, which subdivide into 10-18 second-iteration branches, 19–38 third-iteration branches, and 34–53 fourth-iteration branches. Females more often had 8 primary branches compared to males, while males had a greater number of branches in the second to fourth iterations. The mean fractal (Hausdorff) dimension was 1.697 (1.721 in males, 1.674 in females, P = 0.01). The fractal dimension correlated most strongly with the perimeter and area of the vermis cross-section and had no significant relationship with age.

Conclusion

The fractal (Hausdorff) dimension, determined using the novel “contour scaling” method, quantitatively assesses the degree of branching of the cerebellar white matter. An increase in the absolute size of the cerebellum leads to a higher degree of branching of its white matter and an increase in the number of its constitutive components – white matter branches and folia.