Evidence for non-Newtonian behavior of intracranial blood flow from Doppler ultrasonography measurements

  • Khalid M. SaqrEmail author
  • Ossama Mansour
  • Simon Tupin
  • Tamer Hassan
  • Makoto Ohta
Original Article


Computational fluid dynamics (CFD) studies of intracranial hemodynamics often use Newtonian viscosity model to close the shear rate term in the Navier-Stokes equation. This is based on a commonly accepted hypothesis which state that non-Newtonian effects can be neglected in intracranial blood flow. This study aims to examine the validity of such hypothesis to guide future CFD studies of intracranial hemodynamics. Doppler ultrasonography (DUS) measurements of systolic and diastolic vessel diameter and blood velocity were conducted on 16 subjects (mean age 50.6). The measurements were conducted on the internal carotid (ICA), middle cerebral (MCA), and anterior communicating (AComA) arteries. Systolic and diastolic wall shear stress (WSS) values were calculated via the Hagen-Poiseuille exact solution using Newtonian and three different non-Newtonian models: namely Carreau, power-law and Herschel-Bulkley models. The Weissenberg-Rabinowitsch correction for blood shear-thinning viscosity was applied to the non-Newtonian models. The error percentage between the two sets of models was calculated and discussed. The Newtonian hypothesis was tested statistically and discussed using paired t tests. Significant differences (P < 0.0001) were found between the Newtonian and non-Newtonian WSS in ICA. In MCA and AComA, similar differences were found except in the systole and diastole for the Herschel-Bulkley and power-law models (P = 0.0669, P = 0.7298), respectively. The error between the Newtonian and non-Newtonian models ranged from − 27 to 30% (0.2 to 2.2 Pa). These values could affect the physical interpretation of IA CFD studies. Evidence suggests that the Newtonian assumption may be inappropriate to investigate intracranial hemodynamics.

Graphical abstract

The WSS estimation error resulting from using the Newtonian assumption compared to three non-Newtonian models for ICA, MCA, and AComA in systole and diastole conditions, based on TCCD measurements of 16 subjects. The error due to the Newtonian assumption ranged from 0.2 to 2.2 Pa (− 27 to 30%). These values could affect the physical interpretation of IA CFD studies.


Doppler ultrasound Non-Newtonian flow Blood viscosity Intracranial hemodynamics Blood rheology 



anterior communicating artery


computational fluid dynamics


Doppler ultrasonography


internal carotid artery


middle cerebral artery


transcranial color-coded Doppler


wall shear stress


normalized wall shear stress


time-averaged wall shear stress



Ohta, Saqr and Tupin acknowledge the support from IFS, Tohoku University, JAPAN. Mansour acknowledges the support from Alexandria University hospital for conducting the ultrasonography measurements.

Funding information

Saqr and Hassan acknowledge the support of the Science and Technology Development Fund (STDF), Egypt, under project (Project ID: 5219)

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© International Federation for Medical and Biological Engineering 2018

Authors and Affiliations

  1. 1.Biomedical Flow Dynamics Laboratory, Institute of Fluid ScienceTohoku UniversitySendaiJapan
  2. 2.College of Engineering and TechnologyArab Academy for Science, Technology and Maritime Transport (AASTMT)AlexandriaEgypt
  3. 3.Research Center for Computational Neurovascular Biomechanics (RCCNB), Smouha University HospitalAlexandria UniversityAlexandriaEgypt
  4. 4.Department of Neurology, Stroke UnitAlexandria University School of MedicineAlexandriaEgypt
  5. 5.Department of NeurosurgeryAlexandria University School of MedicineAlexandriaEgypt

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