Finite element analysis of blood flow
through a stenosed carotid bifurcation

The Navier-Stokes equations were solved using an open source code FreeFem++
Implicit method is used along with P2/P1 Taylor-Hood spatial discretization.
Geometry modeling Pro|E, discretization Catia, data visualization Mayavi2

This work made use of the facilities of HECToR, the UK's national high-performance computing service

Project report: Domain decomposition for problems of hemodynamics

Hosted by: Dr Peter Hoskins
Medical Physics and Medical Engineering
University of Edinburgh

Special thanks to: Prof. Ian Marshall

healthy carotid


h=2 mm

stenosis 30pc


h=2 mm

stenosis 64pc


h=2 mm

Pulsatile blood flow : reproducing the MRI data 3 - 20 mL/s

Inflow range: 3 - 20 mL/s (initial 4 mL/s flow)
h=0.08 mm, dt=0.01 sec
Iso-surface
h=0.08 mm, dt=0.01 sec
Iso-surface
h=0.08 mm, dt=0.01 sec
Iso-surface
Vectors frontal plane

Steady blood flow 10.5 mL/s benchmark

We compute an initial velocity - pressure guess by the Stokes equations,
This is a good strategy for low Reynolds number flow. However, for Re = 450, the non-linear, convective
term should not be neglected. The following simulations illustrate the influence of the convective term.
t = 0 - 1 sec: steady Navier-Stokes flow
h=1 mm, dt=0.005 sec

MRI style
Iso-surface

h=1 mm, dt=0.0025 sec

MRI style
Iso-surface

h=0.8 mm, dt=0.002 sec

MRI style
Iso-surface Iso-surface zoom
Vectors Vectors frontal plane

Pulsatile blood flow : sinusoidal benchmark

Inflow range: 7 - 14 mL/s (initial 10.5 mL/s flow)
t = 0 - 1 sec: steady Navier-Stokes flow
t = 1 - 7 sec: pulsatile Navier-Stokes flow
t = 7 - 8 sec: steady Navier-Stokes flow
h=1 mm, dt=0.002 sec
Iso-surface [116MB]
h=1 mm, dt=0.002 sec
Iso-surface [116MB]
Iso-surface [avi 6MB vlc player]
cad models

You are allowed to use these models for free.
Please contact the author before publishing any related work.

Healthy carotid model data, h=1 mm
===========================MESH===DATA==============================
 Nv, Ntet, Ndof: 13201  65984  303142

 Area1: 65.6909   Area2: 38.5022   Area3: 26.3877
 Diam1: 9.14551   Diam2: 7.00161   Diam3: 5.79636
===========================MESH===DATA==============================


===========================Global Matrix Method=====================
Pressure:  [min,max]  -0.00036     0.07805
      ux:  [min,max]  -5.89720     320.45148
      uy:  [min,max]  -231.77369   180.92578
      uz:  [min,max]  -82.96522    108.74870

 u1_mean:  159.89826    Q1[mL/s]:  10.50386
 u2_mean:  176.27867    Q2:        6.78711
 u3_mean:  140.85175    Q3:        3.71675

     Re1:  442.883     Re2:  373.797     Re3:  247.261
     
Solver (single time step):  99.491 [sec]
Total wall time:            30412.091 [sec]
===========================Global Matrix Method=====================

References
Ian Marshall, Computational simulations and experimental studies of 3D phase-contrast imaging of fluid flow in carotid bifurcation geometries, 2010,
Acknowledgments
The work was carried out under the HPC-EUROPA2 project (project number: 228398) with the support of the European Commission - Capacities Area - Research Infrastructures. This work made use of the facilities of HECToR, the UK's national high-performance computing service, which is provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc and NAG Ltd, and funded by the Office of Science and Technology through EPSRC's High End Computing Programme.

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