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.

Coupling one-dimensional arterial blood flow to three-dimensional tissue perfusion models for in silico trials of acute ischaemic stroke

“…It would be interesting to see the effect of different scaling laws. Murray's Law is used in this paper as it seems to be a good fit for the cerebral vasculature [ 48 ].…”

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

“…Although the application of Strahler's [ 130 – 132 ] and Horsfield's ordering methods [ 68 , 69 , 138 , 139 ] could have reduced the variability between the measurements which were made on the branches in this study, for the reasons given below, the morphogenetic ordering method was preferred. We subscribed to the consideration of Weibel [ 95 ] and Hsia et al [ 129 ] that for the human lung, the morphogenetic ordering method provides more instructive data for understanding physiological processes such as flow dynamics [ 95 , 138 , 140 , 141 ] and particle deposition [ 142 , 143 ], while Strahler's ordering method yields more meaningful data for the pathologists [ 129 , 138 ]. Furthermore, Horsfield [ 138 ] cautioned that a great deal of information is lost in the simplification inherent in Strahler's ordering method, especially with regard to the connectivity of the branches.…”

“…In biological structures, there is lack of unanimity on what constitutes optimization [150,151,165,171,172,190,191] and whether the state/condition is achievable or even desirable [121,[173][174][175][176][177]. Regarding the H-ML, some of the views of concern that have been expressed are the following: 'perhaps Murray's law should be viewed as more of what you would call "guidelines" than actual rules' [20]; 'optimum models are abstractions of biological systems and they are not expected to fit these systems with absolute accuracy' [140]; and 'there is a large spread between different parts of the circulation and possibly between different subjects in regard to the principal of minimum work' [141]. In complete departure from the orthodox thinking that optimization is an adaptive (i.e.…”

Imaging of the pial arterial vasculature of the human brain in vivo using high-resolution 7T time-of-flight angiography

“…As indispensable as this dataset has been, 3D reconstructions of the vascular network and surrounding anatomy were not provided in this study. A second recent analysis performed by Helthuis et al (2019) used corrosion casts from four brain specimens and provided valuable insights into the branching pattern of the arterial vasculature.…”

“…Although extensive anatomical studies have described topological properties and the relevant constituents of the pial arterial vasculature (Pfeifer, 1930; Szikla et al, 1977), quantitative data of the human pial arterial vasculature remain scarce (Cassot et al, 2006; Helthuis et al, 2019; Hirsch et al, 2012; Payne, 2017; Schmid et al, 2019). The by far still ‘most comprehensive and influential work’ (Hirsch et al, 2012) is the detailed description of the pial vasculature by Duvernoy et al (1981), which examined 25 brains using intravascular ink injections.…”