Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 85 (6), 4041-6

Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging

Affiliations

Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging

Jing Z Liu et al. Biophys J.

Abstract

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men and 12 women). CB images were resampled to a series of image sets with different 3D resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57 +/- 0.01. No significant difference in the CB fractal dimension was observed between men and women.

Figures

FIGURE 1
FIGURE 1
A sample slice of CB MR image and its resampling to different resolutions. The spatial resolution (voxel size) is indicated below each image.
FIGURE 2
FIGURE 2
Histogram of the CB image set of a subject. The x axis indicates the intensity of the pixels; the y axis indicates the number of pixels at each intensity value. The threshold for separating the white matter (WM) and gray matter (GM) is indicated by the vertical dashed line between the GM and WM peaks.
FIGURE 3
FIGURE 3
Illustration of the steps to extract the CB skeleton in a sample slice. (a) A contour image was created by thresholding. (b) A binary image was generated by assigning value 1 to the pixels inside the contour. (c) The skeleton of the CB image was produced by thinning the binary image. (d) The CB skeleton was color-washed and overlaid onto the original CB image.
FIGURE 4
FIGURE 4
Illustration of the generated CB skeletons in two sample slices from two subjects. The skeletons were overlaid onto the original CB images in different resolutions. Visual inspection showed that skeletons of the CB WM were reproduced with reasonable accuracy.
FIGURE 5
FIGURE 5
Illustration of the linear fit to obtain the fractal dimension in a single subject. The x axis is image resolution (Δ) and the y axis is number of pixels in the skeleton (N) in logarithmic scale. The data (open circles) were fitted using linear regression. The negative slope of the fitted curve (solid line) represents the fractal dimension. The figure and the high correlation coefficient (R2) show that the data can be fitted by a linear function excellently.

Similar articles

See all similar articles

Cited by 10 PubMed Central articles

See all "Cited by" articles

Publication types

Feedback