Computational Mechanics

1
Multi-scale modeling of the carotid artery Gerk
Rozema, Natasha Maurits, Arthur Veldman
Introduction
Wall elasticity model
Atherosclerosis is a disease in which gradual
thickening of the vessel wall occurs due to the
accumulation of fatty plaques. Atherosclerosis of
the carotid arteries is a major cause of ischemic
strokes. Therefore the department of Neurology
(UMCG) hopes to be able to use CFD models in the
future to predict atherosclerotic risk profiles.
The vessel wall is modeled as a linear elastic
membrane circumferential and longitudinal stress
and strain are calculated using the generalized
Hookes law for isotropic materials. The model
can be seen as a new implementation of the well
established Navier equations.
Carotidbifurcation
Circulation model
To reflect the dependence on the rest of the
cardiovascular system, an electric network model
for the global circulation is coupled to the 3D
model of the carotid artery. This allows
(pathological) characteristics of individual
patients to be taken into account.
Multi-scale computational model
The computational model consists of several
submodels The fluid and wall submodels
are combined using a strong coupling method the
equations are solved in an iterative manner
within one time step. This method is stable for
arbitrary fluid-structure mass ratios.

• A model for the blood flow in the carotid
  bifurcation

• A model for the wall elasticity in the carotid
  bifurcation

Carotid bifurcation

• A model for the global cardiovascular
  circulation

heart
Results Future
Ultrasound measurements were used to scan the
carotid artery of a human volunteer. Preliminary
comparison between measured and calculated flow
wave forms shows that elasticity and peripheral
resistance must both be taken into account 1.
The latter will be improved upon by the above
circulation model.
CFD model of carotid bifurcation
The blood flow in the carotid bifurcation is
modeled with the CFD program ComFlo. It employs a
finite-volume discretization of the Navier-Stokes
equations on a rectilinear Cartesian grid. The
boundary of the domain (the vessel wall) is
described using the Cartesian Cut Cells method
the vessel wall is allowed to cut computational
cells, i.e. it does not necessarily need to
coincide with the grid lines, hereby avoiding
frequent regridding.
Ultrasound measurement
CFD calculation
1. N.M. Maurits, E. Loots, A.E.P. Veldman. J.
Biomech. 40 (2007) 427-436.
Computational Mechanics Numerical Mathematics
University of Groningen
P.O. Box 800, 9700 AV
Groningen
University Medical Center GroningenDepartment of
NeurologyP.O. Box 30.001, 9700 RB Groningen