# Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***

Vuk Milišić; Amélie Rambaud; Kirill Pichon Gostaf

ESAIM: Proceedings (2010)

- Volume: 30, page 70-89
- ISSN: 1270-900X

## Access Full Article

top## Abstract

top## How to cite

topMilišić, Vuk, Rambaud, Amélie, and Pichon Gostaf, Kirill. Bresch, D., et al, eds. "Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***." ESAIM: Proceedings 30 (2010): 70-89. <http://eudml.org/doc/251230>.

@article{Milišić2010,

abstract = {This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time
dependent case. Whereas in the second part some preliminary numerical simulations aim to
give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat
equation in a straight channel that mimics the axial velocity under an oscillating
pressure gradient. We derive first order approximations with respect to
ϵ, the size of the roughness. In order to understand the problem and set
up correct boundary layer approximations, we perform a time periodic fourier analysis and
check that no frequency can interact with the roughness. We show rigorously on this toy
problem that the boundary layers remain stationary in time (independent on the frequency
number). Finally we perform numerical tests validating our theoretical approach. In the second part, we determine actual limits, when running three-dimensional blood flow
simulations of the non-homogenized stented arteries. We solve the stationary Stokes
equations for an artery containing a saccular aneurysm. Consecutive levels of uniform mesh
refinement, serve to relate spatial resolution, problem scale, and required computation
time. Test computations are presented for femoral side aneurysm, where a simplified
ten-wire stent model was placed across the aneurysm throat. We advocate the proposed stent
homogenization model, by concluding that an actual computation power is not sufficient to
run accurate, direct simulations of a pulsatile flow in stented vessels.},

author = {Milišić, Vuk, Rambaud, Amélie, Pichon Gostaf, Kirill},

editor = {Bresch, D., Calvez, V., Grenier, E., Vigneaux, P., Gerbeau, J-F.},

journal = {ESAIM: Proceedings},

language = {eng},

month = {12},

pages = {70-89},

publisher = {EDP Sciences},

title = {Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***},

url = {http://eudml.org/doc/251230},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Milišić, Vuk

AU - Rambaud, Amélie

AU - Pichon Gostaf, Kirill

AU - Bresch, D.

AU - Calvez, V.

AU - Grenier, E.

AU - Vigneaux, P.

AU - Gerbeau, J-F.

TI - Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***

JO - ESAIM: Proceedings

DA - 2010/12//

PB - EDP Sciences

VL - 30

SP - 70

EP - 89

AB - This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time
dependent case. Whereas in the second part some preliminary numerical simulations aim to
give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat
equation in a straight channel that mimics the axial velocity under an oscillating
pressure gradient. We derive first order approximations with respect to
ϵ, the size of the roughness. In order to understand the problem and set
up correct boundary layer approximations, we perform a time periodic fourier analysis and
check that no frequency can interact with the roughness. We show rigorously on this toy
problem that the boundary layers remain stationary in time (independent on the frequency
number). Finally we perform numerical tests validating our theoretical approach. In the second part, we determine actual limits, when running three-dimensional blood flow
simulations of the non-homogenized stented arteries. We solve the stationary Stokes
equations for an artery containing a saccular aneurysm. Consecutive levels of uniform mesh
refinement, serve to relate spatial resolution, problem scale, and required computation
time. Test computations are presented for femoral side aneurysm, where a simplified
ten-wire stent model was placed across the aneurysm throat. We advocate the proposed stent
homogenization model, by concluding that an actual computation power is not sufficient to
run accurate, direct simulations of a pulsatile flow in stented vessels.

LA - eng

UR - http://eudml.org/doc/251230

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.