Computational Mechanics & Numerical Mathematics University of Groningen Multi-scale modeling of the carotid artery G. Rozema, A.E.P. Veldman, N.M. Maurits

Computational Mechanics & Numerical MathematicsUniversity of Groningen

Multi-scale modeling of the carotid artery

G. Rozema, A.E.P. Veldman, N.M. MauritsUniversity of Groningen, University Medical Center Groningen

The Netherlands


ACC: common carotid artery

ACE: external carotid artery

ACI: internal carotid artery

distal

proximal

Area of interest

Atherosclerosis in the carotid arteries is a major cause of ischemic strokes!


• 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)

A multi-scale computational model: Several submodels of different length- and timescales:

Carotid bifurcation

Fluid dynamics

Wall dynamics

GlobalCardiovascular

Circulation


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:


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)

Inflow

Outflow Outflow


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

Elasticity Pressure

PressureElasticityInertia


• Generalized string model:

• Navier equations:

Wall dynamics (2)

Elasticity PressureInertia DampingShear

Elasticity

PressureShear

Inertia


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


The mass-spring system compared to the (simplified) Navier equations

• 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 Elasticity Damping Pressure


Weak coupling betweenfluid equations (PDE)and wall equations (ODE)

Weak coupling betweenlocal and global hemodynamic submodels

Future work: Numerical stability

Coupling the submodels

Carotid bifurcation

Fluid dynamicsPDE

Wall dynamicsODE

GlobalCardiovascular

Circulation

ODE

pressurewall motion

Boundary conditions


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 No Yes Yes

Peripheral resistance No Yes No Yes


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

Documents

Computational Mechanics & Numerical Mathematics University of Groningen Multi-scale modeling of the carotid artery G. Rozema, A.E.P. Veldman, N.M. Maurits