Inspecting endovascular aneurysm treatments with porous medium flow simulations and the use of ...

73 Pages·2012·3.77 MB·English

Universit¨at Stuttgart - Institut fu¨r Wasser und
Umweltsystemmodellierung
Lehrstuhl fu¨r Hydromechanik und
Hydrosystemmodellierung
Prof. Dr.-Ing. Rainer Helmig
Diplomarbeit
Inspecting endovascular aneurysm
treatments with porous medium flow
simulations and the use of a statistical
framework
Submitted by
Sebastian Warmbrunn
Matrikelnummer 2425845
Stuttgart, October 31th, 2012
Examiner: Prof. Dr.-Ing. R. Helmig Tutors: Dipl.-Ing. K. Baber
Dr. Kent-Andre Mardal
Øyvind Evju, M.Sc.

Preface
This thesis was written during the period of May 2012 - November 1st 2012.
It is the final project for the degree program “Umweltschutztechnik” at the
University of Stuttgart.
Most parts of this thesis were written at the Simula Research Laboratory,
Oslo. I am very grateful for the possibility that was given to me, to work
abroad in such a great working environment, with so many open-minded
people.
First of all I want to thank Prof. Rainer Helmig, who gave me this op-
portunity. I want to thank Kent-Andre Mardal, who was my supervisor in
Oslo. He was always very helpful and supportive during my stay at Simula.
Thanks to Øyvind Evju, who was my second supervisor in Oslo helped me
when needed.
Another thanks goes to Katherina Baber. She was my supervisor in Ger-
many and helped me, especially during the last month of finalizing my work.
A five year long study now comes to an end and I would like to thank my
friends and the people who were surrounding me during this period of my
life.
Last, but not the least, I want to thank my parents and my sisters for their
love and support.

Contents
1 Introduction 10
2 Medical Background 12
2.1 The clinical picture . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 The treatment methods . . . . . . . . . . . . . . . . . . . . . 13
3 Physical Model 16
3.1 Simplifying the fluid . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Simplifying the structure and boundaries . . . . . . . . . . . . 18
3.3 Generation of the aneurysm model . . . . . . . . . . . . . . . 22
4 Mathematical Model 29
4.1 Mathematical approach for the free flow . . . . . . . . . . . . 29
4.2 Mathematical approach for the porous medium flow . . . . . . 31
4.3 Coupling of the approaches . . . . . . . . . . . . . . . . . . . . 32
4.4 The surrogate management framework . . . . . . . . . . . . . 33
5 Numerical Model 39
5.1 The finite element method . . . . . . . . . . . . . . . . . . . . 39
5.2 The incremental pressure correction scheme . . . . . . . . . . 45
5.3 Implementation in FEniCS . . . . . . . . . . . . . . . . . . . . 46
5.4 Verification of the implementation . . . . . . . . . . . . . . . . 49
6 Results 51
6.1 Two dimensional flow field . . . . . . . . . . . . . . . . . . . . 51
6.2 Aneurysm geometry - three design variables . . . . . . . . . . 53
6.3 Aneurysm geometry - stent . . . . . . . . . . . . . . . . . . . . 62
6.4 Mesh convergence . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5
List of abbreviations
CT computed tomography
FEM finite element method
FSI fluid structure interaction
GDC Guglielmi detachable coil
IPCS incremental pressure correction scheme
LHS latin hypercube sampling
PDE partial differential equation
REA represatentive elementary area
SMF surrogate management framework
vmtk vascular modeling toolkit
WSS wall shear stress
6
List of Figures
1 Different treatment methods for the endovascular treatment
of an aneurysm. Top left: many coils, lower left: less coils,
top right: stent, lower right: flow diverter . . . . . . . . . . . . 10
2 The two considered types of a cerebral aneurysm. A sidewall
aneurysm on the left side and a bifurcation aneurysm on the
right side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 A very simplified scheme of the Circle of Willis. The arrows
represent the blood flow from the heart. . . . . . . . . . . . . 14
4 Illustration of the procedure to define the representative ele-
mentary area . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 The porosity of the coil configuration with a shrinking area. . 20
6 The user can drag the three planes along their normals to
investigate the cerebral vessel system. The structures with a
higher contrast are bones, the ones with a lower contrast are
vessels. The red encircled part is an aneurysm. . . . . . . . . . 23
7 The fast marching method with the start point on the left
image, the end point on the center image and the result on
the right image. . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8 Thetwopointsforthecollidingfrontmethodonthetopimage,
the resulting vessel structure on the bottom image. . . . . . . 25
9 A smoothed aneurysm geometry with added flow extensions. . 26
10 The aneurysm geometry with the size information for the gen-
eration of the mesh cells. Red is a small mesh size and dark
blue a coarse mesh size. Those parameters can be scaled. . . . 27
11 The aneurysm geometry with a small sphere, representing a
flow diverter and a bigger sphere representing a coiling. The
white line marks the degree of freedom. . . . . . . . . . . . . . 28
12 Illustrations of the surrogate management framework. On the
top, the initial points for the calculation of the first Kriging
surrogate are shown. The picture in the middle shows a first
mesh, with new chosen points. On the bottom, the mesh was
refined and the poll step is initiated. . . . . . . . . . . . . . . 37
13 The surrogate management framework as a flow chart . . . . . 38
14 The domain on which the Poisson equation is solved. The
Dirichlet condition continues on the green axes. . . . . . . . . 41
15 The results for the pressure drop of the Poisson equation . . . 44
7
16 Illustration of the example problem . . . . . . . . . . . . . . . 50
17 Pressure distributions for the two different models . . . . . . . 50
18 The velocity distribution for the third surrogate management
framework (SMF) run . . . . . . . . . . . . . . . . . . . . . . 53
19 Different placement possibilities for the spheres and the cor-
responding porous medium areas (red) . . . . . . . . . . . . . 54
20 The geometry of the sidewall aneurysm . . . . . . . . . . . . . 55
21 Streamlines for the three results of the SMF runs and without
coil placement . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
22 Velocity inside the aneurysm for the three results of the SMF
runs and without coil placement . . . . . . . . . . . . . . . . . 58
23 The geometry of the bifurcation aneurysm . . . . . . . . . . . 59
24 Streamlines for the three results of the SMF runs and without
coil placement . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
25 Velocity inside the aneurysm. No coiling on the very left,
following run01 - run03 from the left to the right . . . . . . . . 61
26 The sidewall aneurysm geometry with a spherical shaped disk,
representing the aneurysm. . . . . . . . . . . . . . . . . . . . . 62
27 The change of the volume V , used for the calculation of
kinen
the kinetic energy measure E . . . . . . . . . . . . . . . . . 64
kin
28 The aneurysm with the coiled area (red) and the point of the
velocity measurement (white dot) . . . . . . . . . . . . . . . . 66
29 The pressure drop from inlet to outlet with increasing mesh
resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
30 The kinetic energy inside the aneurysm with increasing mesh
resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
31 The velocity at a measurement point with increasing mesh
resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8
List of Tables
1 The thresholds for the design variables. First row: lower
threshold. Second row: upper threshold . . . . . . . . . . . . . 52
2 The results for the SMF runs of the example problem . . . . . 52
3 The results for the design variables and cost functions for the
sidewall geometry . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 The results for the SMF runs on the bifurcation geometry . . 60
5 The thresholds of the design variables for the SMF . . . . . . 63
6 The comparision between stent and coils on the sidewall ge-
ometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7 The components of the goal function for a stent and a coil
situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
8 The components of the goal function with another V . . . 65
kinen
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1 Introduction
In fact, the interrelation between medical science and engeneering already
exists quite a long time. The design of surgical instruments, the building of
medical devices like an ultrasound device or the inspection of material prop-
ertiesoftissuesareallexampleswhereengeneeringexperienceandknowledge
from clinicians fuse together. With the constant development of new tech-
nologies, especially in the field of computer science, this interrelation grew
stronger during the past decades.
Therefore, itisnotsurprisingthatalsocomputersimulationscontributemore
and more to the understanding of medical processes.
In the context of this work, a computer simulation begins with setting up
a simplified physical model for a certain phenomenon or process in nature.
The physical model is then described by mathematical equations. Most of
the time those mathematical equations are too complex to be solved without
the help of numerical tools and fast computers.
Figure 1: Different treatment methods for the endovascular treatment of an
aneurysm. Top left: many coils, lower left: less coils, top right: stent,
lower right: flow diverter
In this case, we are interested in the blood flow through an aneurysm. Dif-
ferent variants of treatment are considered and compared with respect to the
developing flow. Figure 1 gives an idea of how an aneurysm and the different
treatments look like. Chapter 2 describes the clinical picture of an aneurysm
and the relevant treatment methods more detailed. The physical model is
10