Multi-scale modeling of the

skillfulbuyerUrban and Civil

Nov 16, 2013 (3 years and 6 months ago)

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Computational Mechanics & Numerical Mathematics

University of Groningen

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

Computational Mechanics & Numerical Mathematics

University of Groningen

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!

Computational Mechanics & Numerical Mathematics

University of Groningen


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

Global

Cardiovascular

Circulation


Computational Mechanics & Numerical Mathematics

University of Groningen

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:

Computational Mechanics & Numerical Mathematics

University of Groningen

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

Computational Mechanics & Numerical Mathematics

University of Groningen

The wall dynamics (1)


Simple algebraic law:




Independent rings model:

w
r
(z,t) and w
z
(z,t):
displacement of vessel
wall in radial and
longitudinal direction

Elasticity

Pressure

Pressure

Elasticity

Inertia

Computational Mechanics & Numerical Mathematics

University of Groningen


Generalized string model:





Navier equations:








Wall dynamics (2)

Elasticity

Pressure

Inertia

Damping

Shear

Elasticity

Pressure

Shear

Inertia

Computational Mechanics & Numerical Mathematics

University of Groningen

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

Computational Mechanics & Numerical Mathematics

University of Groningen

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

Computational Mechanics & Numerical Mathematics

University of Groningen

Weak coupling between

fluid equations (PDE)

and wall equations (ODE)



Weak coupling between

local and global

hemodynamic submodels



Future work: Numerical stability

Coupling the submodels

Carotid bifurcation

Fluid dynamics

PDE

Wall dynamics

ODE

Global

Cardiovascular

Circulation


ODE


pressure

wall motion

Boundary conditions

Computational Mechanics & Numerical Mathematics

University of Groningen

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

Computational Mechanics & Numerical Mathematics

University of Groningen

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