Carotid Arterial Wall Shear Stress

Non-invasive 3D Assessment of Wall Shear Stress Profiles in Carotid Arteries for Cardiovascular Risk

Dutch Heart Foundation (Grant 2000.119)
Frieke M.A. Box


An hypothesized relation exists between the presence of atherosclerosis and Wall Shear Stress (WSS) in arteries. WSS is the mechanical force exerted by the flowing blood on the vessel wall. It is defined as the Wall Shear Rate (WSR) multiplied by the dynamic viscosity h. Near the wall the WSR is expressed as the velocity gradient with respect to the outward normal n of the wall.

WSR = dv/dn,

where v is the fluid velocity.

WSS = hdv/dn


To demonstrate that the velocity profiles and derived indices of WSS and WSR in carotid arteries can be obtained with small systematic and random errors from MRI acquisitions, and that differences in these parameters can be observed in groups of individuals with different risk profiles for atherosclerosis and stroke.


Phase contrast MRI can be used to map velocity profiles within vascular structures. The 3D-morphology of these structures can be assessed with Magnetic Resonance Angiography (MRA). The Finite Element Method (FEM) allows the investigation of the relations between calculated velocity profiles, measured blood viscosity and vessel morphology. In this pilot project the systematic and random errors of this technique will be studied using in vitro models and in vivo materials of carotid arteries. In addition, after the validation has been carried out, the techniques will be applied to different patient groups.


Currently the focus is on automating the conversion of the geometric information from MRA data and flow information form velocity-encoded MRI scans into a mesh-representation that is suitable for computational fluid dynamics calculations using the Sepran software environment. The accuracy and precision of the developed techniques are being investigated using MRI studies of phantom data and human volunteers.


  1. Box FMA, Rutten MCM, van Buchem M, Doornbos J, van der Geest RJ, de Koning PJH, Schaap J, van de Vosse FN, Reiber JHC. Quantitative methods for comparisons between velocity encoded MR-measurements and Finite Element Modeling in phantom models. In: “Lecture Notes on Computer Science” Computational Science – ICCS 2002, Amsterdam , April 2002. 255-264.
  2. Spilt A, Box FMA, van der Geest RJ, Reiber JHC, Kunz P, Kamper AM, Blauw GJ, van Buchem MA. Reproducibility of total cerebral blood flow measurements using phase contrast Magnetic Resonance Imaging (MRI). J Magn Reson Imaging 2002;16:1-5
  3. Box FMA, Spilt A, Van Buchem MA, van der Geest RJ, Reiber JHC. Automatic model-based contour detection and blood flow quantification in small vessels with velocity encoded magnetic resonance imaging Invest Radiol. 2003;38 (9): 567-577.
  4. Box FM, van der Geest RJ, Rutten MC, Reiber JHC. The Influence of flow, vessel diameter, and non-Newtonian blood viscosity on the wall shear stress in a carotid bifurcation model for unsteady flow. Invest Radiol. 2005;40(5):277-294.
  5. ten Dam VH, Box FM, de Craen AJ, van den Heuvel DM, Bollen EL, Murray HM, van Buchem MA, Westendorp RG, Blauw GJ; PROSPER Study Group. Lack of effect of pravastatin on cerebral blood flow or parenchymal volume loss in elderly at risk for vascular disease. Stroke. 2005 Aug;36(8):1633-6.
  6. Box FMA, van der Grond J, de Craen AJ, Palm-Meinders IH, van der Geest RJ, Reiber JHC, van Buchem MA, Blauw GJ. Pravastatin decreases wall shear stress and blood velocity in the internal carotid artery without affecting flow volume. Results from the PROSPER MRI Study. Stroke 2007.
  7. Box FM, van der Geest RJ, van der Grond J, van Osch MJ, Zwinderman AH, Palm-Meinders IH, Doornbos J, Blauw GJ, van Buchem MA, Reiber JHC. Reproducibility of wall shear stress assessment with the paraboloid method in the internal carotid artery with velocity encoded MRI in healthy young individuals. J Magn Reson Imaging. 2007 Sep;26(3):598-605.


  1. Box FMA, Spilt A, van Buchem MA et al. Automatic model Based contour detection and flow quantification of blood flow in small vessels with velocity encoded MRI. Proc. ISMRM 7 Philadelphia , 1999: 571
  2. Spilt A, Box FMA, van der Geest RJ, van Buchem MA. Quantitative flow mapping of total cerebral blood flow: what causes variation? Proc. ISMRM 7 Philadelphia , 1999: 2014


The carotid artery is the largest artery for blood supply to the brain. The major advantages of the MRI-measuring technique are the non-invasiveness, and the fact that acquisitions can be made from all parts of the body. The major drawback of MRI is the resolution, especially when little scan time is available. To assess the Wall Shear Stress (WSS) precise knowledge of the velocity profile is essential. Therefore FEM simulations are combined with MRI-measurements. A basic 3-D model of a bifurcation is used to start-off. The flow-volume as a function of time flow(t) is measured in the MRI scanner. The measurements are analyzed by using the package FLOW®. In the simulation flow(t) is taken as inlet flow into the entrance of the mesh. In an intersection the results of the simulation shown as velocity vectors can be visualized as function of time.

MRI Measurement   Extracted Geometry   Matched Mesh
MRI measurement   Extracted Geometry   Matched Mesh

 The basic 3-D model can be transformed to a more realistic geometry. The geometry data are extracted by Magnetic Resonance Angiography.Velocity Vector Movie

 Click on the image to start the movie.


Frieke M.A.Box, PhD.
Division of Image Processing
Department of Radiology, 1-C2S
Leiden University Medical Center
P.O. Box 9600
2300 RC Leiden
The Netherlands
Tel. +31 (0)71 526 2137
Fax. +31 (0)71 526 6801