1. Multi-scale modeling of the carotid artery
G. Rozema, A.E.P. Veldman, N.M. Maurits
University of Groningen, University Medical Center Groningen
The Netherlands

2. Area of interest
Atherosclerosis in the carotid arteries is a major cause of ischemic strokes!
distal
proximal
ACI: internal carotid artery
ACE: external carotid artery
ACC: common carotid artery

3. A multi-scale computational model: Several submodels of different length- and timescales:
Carotid bifurcation
A model for the local blood flow
in the region of interest:
A model for the fluid dynamics: ComFlo
A model for the wall dynamics
A model for the global cardiovascular
circulation outside the region of interest
(better boundary conditions)
Fluid dynamics
Wall dynamics
Global
Cardiovascular
Circulation

4. Computational fluid dynamics: ComFlo
Finite-volume discretization of Navier-Stokes equations
Cartesian Cut Cells method
Domain covered with Cartesian grid
Elastic wall moves freely through grid
Discretization using apertures in cut cells
Example:
Continuity equation  Conservation of mass:

5. Boundary conditions Simple boundary conditions:
Future work: Deriving boundary conditions from lumped parameter models, i.e. modeling the cardiovascular circulation as an electric network (ODE)
Outflow
Outflow
Inflow

6. The wall dynamics (1) Simple algebraic law: Independent rings model:
wr(z,t) and wz(z,t): displacement of vessel wall in radial and longitudinal direction
Simple algebraic law:
Independent rings model:
Elasticity
Pressure
Inertia
Elasticity
Pressure

7. Wall dynamics (2) Generalized string model: Navier equations: Inertia
Shear
Elasticity
Damping
Pressure
Pressure
Shear
Inertia
Elasticity

8. Modeling the wall as a mass-spring system
The wall is covered with pointmasses (markers)
The markers are connected with springs
For each marker a momentum equation is applied
x: the vector of marker positions

9. The mass-spring system compared to the (simplified) Navier equations
Material points move in radial and longitudinal direction only
Generalized string model
Material points move in radial direction only
Mass-spring system
Material points (markers) are completely free: Conservation of momentum in all directions:
Inertia
Shear
Pressure
Elasticity
Damping

10. Coupling the submodels
Carotid bifurcation
Weak coupling between
fluid equations (PDE)
and wall equations (ODE)
local and global
hemodynamic submodels
Future work: Numerical stability
Fluid dynamics
PDE
wall motion
pressure
Wall dynamics
ODE
Boundary conditions
Global
Cardiovascular
Circulation
ODE

11. Results: clinical data and CFD
Example: Doppler flow wave form. Model variations: Rigid wall / elastic wall, Traction-free outflow / peripheral resistance A B C D
Elastic wall No
Yes
Peripheral resistance

12. Results (2): Conclusion
Both elasticity and peripheral resistance must be taken into account to obtain a close resemblance between measured and calculated flow wave forms
Future work:
Clinical follow-up data
3D ultrasound
Patient specific modeling