Branching Pattern of the Cerebral Arterial Tree

Abstract

Quantitative data on branching patterns of the human cerebral arterial tree are lacking in the 1.0-0.1 mm radius range. We aimed to collect quantitative data in this range, and to study if the cerebral artery tree complies with the principle of minimal work (Law of Murray). To enable easy quantification of branching patterns a semi-automatic method was employed to measure 1,294 bifurcations and 2,031 segments on 7 T-MRI scans of two corrosion casts embedded in a gel. Additionally, to measure segments with a radius smaller than 0.1 mm, 9.4 T-MRI was used on a small cast section to characterize 1,147 bifurcations and 1,150 segments. Besides MRI, traditional methods were employed. Seven hundred thirty-three bifurcations were manually measured on a corrosion cast and 1,808 bifurcations and 1,799 segment lengths were manually measured on a fresh dissected cerebral arterial tree. Data showed a large variation in branching pattern parameters (asymmetry-ratio, area-ratio, length-radius-ratio, tapering). Part of the variation may be explained by the variation in measurement techniques, number of measurements and location of measurement in the vascular tree. This study confirms that the cerebral arterial tree complies with the principle of minimum work. These data are essential in the future development of more accurate mathematical blood flow models. Anat Rec, 302:1434-1446, 2019. © 2018 The Authors. The Anatomical Record published by Wiley Periodicals, Inc. on behalf of American Association of Anatomists.

Keywords: anatomical research; branching patterns; cerebral arterial circulation; high resolution MRI; minimum work.

Figure 1

Examples of the casts: (A) Photograph of one of the plastic casts of the full cerebral arterial circulation, as was used in the 7 T MRI. Different color pigments where used for the six major cerebral arteries. (B) Photograph of a small section of the casts as was used in the 9.4 T MRI. (C) Photograph of the same small section of casts for the 9.4 T MRI placed in the gadolinium‐gelatine solution in a Perspex container.

Figure 2

Example MRI data. (A) Minimum intensity projection of 20 slices (1.95 mm total thickness) of 7 T MRI data. (B) Minimum intensity projection of 100 slices (1.50 mm total thickness) of 9.4 T MRI data.

Figure 3

Dissected cerebral arterial tree of the right middle cerebral artery spread out on the table. Arteries are still partially filled with the gelatine‐red paint solution.

Figure 4

Relative frequencies in percentage (%) of top: parent artery radius in millimeters (mm) for bifurcations, middle: proximal radius in mm for segments, bottom: Length for segments in mm.

Figure 5

Relative frequencies of (A) asymmetry ratio, (B) area ratio, (C) length‐to‐radius‐ratio, (D) tapering.

Figure 6

Area ratio. Scatterplots of squared parent artery radius (r ₀) versus sum of squared radii (r ₁, r ₂) of all daughter arteries for (A) cast, (B) dissection, (C) 7 T MRI, and (D) 9.4 T MRI.

Figure 7

Principle of minimum work according to Murray. Scatterplots of cubed parent artery radius (r₀) versus sum of cubed radii (r ₁, r ₂) of all daughter arteries for (A) cast, (B) dissection, (C) 7 T MRI, and (D) 9.4 T MRI.