Related Experiment Video

Updated: Feb 21, 2026

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis
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A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

721

Vessel calibre and flow splitting relationships at the internal carotid artery terminal bifurcation

C Chnafa1, P Bouillot2, O Brina2,3

  • 1Biomedical Simulation Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, ON, Canada.

Physiological Measurement
|October 12, 2017
PubMed

Insights

Blood flow in cerebral arteries follows a power law related to vessel size, but closer to a square law than the assumed cube law. This relationship shows significant individual variation and a correlation with age.

Area of Science:

  • Cardiovascular research
  • Biomedical engineering
  • Neurovascular imaging

Background:

  • Mathematical power laws are theorized to govern vessel lumen calibres and flow rates, optimizing cardiac and metabolic work.
  • Previous studies indirectly confirmed these laws by measuring branch calibres, but direct evidence at individual bifurcations is limited.

Purpose of the Study:

  • To investigate the power law relationship between flow distribution and vessel calibres at individual bifurcations in the internal carotid artery terminal bifurcation.
  • To compare measured exponents with theoretical optima and assess correlations with patient age and measurement methods.

Main Methods:

  • Utilized 4D phase-contrast magnetic resonance imaging and 3D rotational angiography in 31 patients.
  • Employed robust and automated methods to determine flow rates and diameters of parent and daughter vessels at the internal carotid artery terminal bifurcation.

Main Results:

  • Junction exponents for diameter-diameter and diameter-flow relationships were approximately 2.06 and 2.45, respectively, deviating from the theoretical optimum of 3.
  • Significant inter- and intra-individual variations were observed, with a negative correlation between age and the geometrical exponent (r = -0.55, p = 0.003).
  • Results demonstrated a dependence on lumen diameter measurement techniques, potentially explaining literature variability.

Conclusions:

  • The study confirms a power law relationship between middle and anterior cerebral artery flow division and vessel calibre.
  • The observed relationship is closer to a square law than the commonly assumed cube law.
  • Findings highlight significant individual variability and age-related changes in cerebrovascular flow dynamics.
Abstract

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