Abstract
ABSTRACTQuantitative 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.
Highlights
IntroductionFor cerebrovascular blood flow modeling to be successful, clear morphological knowledge of the cerebral arterial tree is needed (Hirsch et al, 2012)
Morphological data confirming that the cerebral arterial tree adheres to this principle of minimum work are, essential and we believe this could aid in optimization of models for the human vasculature and ease hemodynamic flow modeling (Gabrys et al, 2006)
The current study aims to add quantitative data on the branching pattern of the human cerebral arterial tree in the missing range between larger cerebral arteries and the capillary network by applying this new magnetic resonance imaging (MRI) based method using 7 T and 9.4 T MRI
Summary
For cerebrovascular blood flow modeling to be successful, clear morphological knowledge of the cerebral arterial tree is needed (Hirsch et al, 2012) This tree spans from the circle of Willis, which is known to be highly variable, up to the capillary network (Alpers et al, 1959; Hillen, 1986; Hartkamp et al, 1999). It is generally accepted that the morphology of the cerebrovascular tree follows the principle of minimum work as described by Murray (1926a) This principle is expressed by the equation r30 1⁄4 r31 + r32, where according to convention r0 is considered to be the radius of the parent artery and r1 and r2 of both daughter arteries (Murray, 1926b; Sherman, 1981; Zamir, 1999). Morphological data confirming that the cerebral arterial tree adheres to this principle of minimum work are, essential and we believe this could aid in optimization of models for the human vasculature and ease hemodynamic flow modeling (Gabrys et al, 2006)
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