Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Abstract

Blood flow rate (trueQ˙) in relation to arterial lumen radius (ri) is commonly modelled according to theoretical equations and paradigms, including Murray’s Law (trueQ˙ ∝ ri3) and da Vinci’s Rule (trueQ˙ ∝ ri2). Wall shear stress (τ) is independent of ri with Murray’s Law (τ ∝ ri0) and decreases with da Vinci’s Rule (τ ∝ ri-1). These paradigms are tested empirically with a meta‐analysis of the relationships between trueQ˙ and ri in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that trueQ˙ ∝ ri2.16 and τ ∝ ri-1.02, more consistent with da Vinci’s Rule than Murray’s Law. This meta‐analysis provides standard values for trueQ˙, ri and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

Development of a dual-flow tissue perfusion device for modeling the gastrointestinal tract–brain axis

“…Using the devices in series allowed modeling of multiple tissue barriers in a connected system. To further assess the device flow, sheer stress was calculated using the Navier–Stokes equation ( Seymour et al , 2020 ). At a flow rate of 2.94 μ l min −1 , the cells were subjected to 4.0 × 10 −3 dyn cm −2 shear stress.…”

Analysis of Intracranial Aneurysm Haemodynamics Altered by Wall Movement

“…In the fluid, inlet velocities and outlet pressure conditions were prescribed as follows: where was built based on the waveform plotted in Figure 2 , corresponding to an averaged internal carotid pulse reported by [ 38 ]. It was prefixed with a s linear ramp for a smoother initialization and scaled to reach an average flow rate of 4 mL·s −1 , which correponded to the mean ICA flow measured among 13 studies, as reported in a recent review [ 39 ].…”

“…where V(t) was built based on the waveform plotted in Figure 2, corresponding to an averaged internal carotid pulse reported by [38]. It was prefixed with a 0.2 s linear ramp for a smoother initialization and scaled to reach an average flow rate of 4 mL•s −1 , which correponded to the mean ICA flow measured among 13 studies, as reported in a recent review [39]. At the outflow, unlike in typical CFD simulations, the absolute value of the pressure was of major importance.…”

Cerebral blood flow rates in recent great apes are greater than in Australopithecus species that had equal or larger brains

“…(Online version in colour.) [25]. Thus, the ICAs account for 88%, and the VAs account for 12%, of total cerebral perfusion.…”

“…Although the ICAs supply approximately 75%, and the VAs 25%, of total brain perfusion ð _ Q TOTAL Þ in humans [25][26][27][28][29][30][31], these proportions approach each other in extant haplorhine species with smaller brains until they become approximately equal in brains smaller than 10 ml. (See the electronic supplementary material, including figure S5, for a detailed analysis of the roles of the VAs and ICAs in extant haplorhines.)…”