Hemodynamics of Cerebral Aneurysms: Physiology and Numerical

111 Pages·2011·16.99 MB·English

Hemodynamics of Cerebral Aneurysms:
Physiology and Numerical Simulations
Susana Cruz Coelho de Mira Ramalho
Dissertation submitted to obtain the Master’s Degree in
Biomedical Engineering
Jury
President: Prof. Doutor Paulo Jorge Peixeiro de Freitas
Supervisor: Prof. Doutora Ad´elia da Costa Sequeira dos Ramos Silva
Supervisor: Prof. Doutor Jorge Rodolfo Gil Guedes Cabral de Campos
Supervisor: Doutora Alexandra Bugalho de Moura
External: Prof. Doutor Jo˜ao Paulo Vicente Janela
February 2011
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Acknowledgements
I would like to start by expressing my sincere gratitude to Prof. Ad´elia Sequeira, for giving me
the opportunity to work with her, not only in this thesis, but also over the past three years. Both
her kindness and wisdom are remarkable, and I will always be thankful for believing in my work
and proposing me new challenges.
To Prof. Jorge Campos, for providing me the anatomical geometries, which were a crucial
aspect of this work, and for the medical feedback.
A special thanks to Doutora Alexandra Moura. For her knowledge and almost daily support,
that guided me throughout this work. I am profoundly grateful for her words of encouragement in
the most frustrating moments and for her tremendous patience and dedication. Obviously, none
of this could have happened without her.
I also like to thank Alberto Gambaruto for the time he spent processing the geometries used in
this work, and also for the insightful comments, that improved the quality of this thesis.
A big thanks to all my friends and colleagues for all the funny times throughout these years.
To my parents, sister and grandmother, for the unconditional support and for always being
there when I needed the most. There is nothing more important to me than my family.
To Madalena, the most wonderful and precious gift I received last year.
At last, I would like to thank Miguel, especially for his (almost) never ending patience and
constant care. You are my rock!
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Resumo
Oobjectivodesteestudofoideterminaroimpactodaescolhadomodelomatem´atico,edevariac¸˜oes
geom´etricas, na hemodinˆamica no interior de um aneurisma. Efectuou-se uma comparac¸˜ao exaus-
tiva, sistem´atica, quantitativa e qualitativa, usando geometrias 3D idealizadas e reais de aneuris-
mas saculares cerebrais. Foram avaliadas as diferen¸cas resultantes do uso de dois tipos de mode-
los fluidos, Newtoniano e n˜ao-Newtoniano inel´astico (Carreau), regime estacion´ario ou puls´atil, e
condi¸c˜oesdefronteiradistintasnassecc¸˜oescomputacionaisdesa´ıda. Asu´ltimasincluemcondi¸c˜oes
standard sobre a tenso normal, bem como o acoplamento com modelos reduzidos 1D ou 0D, sim-
ulando o sistema cardiovascular, no sentido da modelac¸˜ao geom´etrica de multi-escala. Os efeitos
hemodinˆamicos da presen¸ca de vasos laterais tamb´em foi analisada, com base na inclus˜ao ou ex-
clus˜ao, quer atrav´es de modelos 3D ou de modelos reduzidos.
De um modo geral, as simulac¸˜oes num´ericas mostraram ser bastante sens´ıveis ´as alterac¸˜oes
analisadas neste trabalho, tanto para os modelos, como para a geometria. Foram observadas
varia¸c˜oes substanciais nas diferentes geometrias. Para al´em disso, na maior parte dos casos, as
diferen¸cas entre as solu¸c˜oes estacion´arias e puls´ateis foram mais significativas do que as diferen¸cas
entre as duas leis da viscosidade do fluido, mostrando a importˆancia das simulac¸˜oes puls´ateis.
Os resultados demonstram uma semelhan¸ca consider´avel ao considerar a geometria com os vasos
laterais ou a geometria truncada acoplada com modelos reduzidos nas secc¸˜oes de sa´ıda. Apesar
de o modelo 0D aqui considerado se ter mostrado insuficiente para simular a circulac¸˜ao sist´emica,
´e poss´ıvel concluir que em alguns casos os modelos reduzidos podem ser usados para simular os
efeitos dos vasos laterais em geometrias reais.
Palavras chave: Aneurismas cerebrais, dinˆamica computacional de fluidos, metodologia de
multi-escala geom´etrica, geometrias idealizadas, geometrias espec´ıficas de pacientes.
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Abstract
Thepurposeofthisstudywastoassesstheimpactofthemathematicalmodelchoice,andgeomet-
ricalvariations,inthehemodynamicsinsideananeurysm. Exhaustiveandsystematicquantitative
and qualitative comparisons were carried out, using both idealized and patient-specific 3D ge-
ometries of saccular aneurysms. The differences between using two fluid models, Newtonian and
inelastic non-Newtonian (Carreau), steady or pulsatile flow regimes, and distinct boundary con-
ditions at the downstream computational sections, were evaluated. The latter include standard
normal stress boundary conditions, as well as the coupling with 1D or 0D reduced models for the
cardiovascular system, in the framework of the so-called ’ geometrical multiscale approach’. Fur-
thermore, the influence of the presence of side branches was analyzed, by neglecting or including
them, either through 3D or reduced models.
Overall,thenumericalsimulationswereverysensitivetothemodelingandgeometricalchanges
analyzedinthiswork. Substantialvariationsinusingdifferentgeometrieswereobserved. Moreover,
in most cases, the differences between the steady and unsteady solutions were more significant
than the differences between the two fluid viscosity laws, showing the importance of unsteady
simulations. Results demonstrate a remarkable resemblance between considering a wide geometry,
with side branches, or a clipped geometry coupled to reduced models at the downstream sections.
Even though the 0D model here considered has shown to be not sufficient in accounting for the
systemic circulation, it is possible to conclude in some cases of realistic geometries the reduced
models can be used to simulate the effects of the side branches.
Keywords: Cerebral aneurysms, computational fluid dynamics, geometrical multiscale ap-
proach, idealized geometries, patient-specific geometries.
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Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 About Intracranial Aneurysms 5
2.1 Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Structural and etiological classification . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Anatomy and histology of cerebral arteries. . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Aneurysm treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Medical image acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5.1 Digital Subtraction Angiography (DSA) . . . . . . . . . . . . . . . . . . . . 11
2.5.2 Three-Dimensional Rotational Angiography (3DRA) . . . . . . . . . . . . . 11
2.5.3 Computed Tomography Angiography (CTA) . . . . . . . . . . . . . . . . . 11
2.5.4 Magnetic Resonance Angiography (MRA) . . . . . . . . . . . . . . . . . . . 12
2.6 Dynamic properties of blood flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6.1 Steady versus pulsatile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6.2 Newtonian versus non-Newtonian . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6.3 Laminar versus turbulent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 Inherited and acquired factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.8 Hemodynamic factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.9 Pathogenesis of aneurysm formation, growth and rupture . . . . . . . . . . . . . . 18
3 The 1D mathematical model 23
3.1 The equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Numerical discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Time discretization: The Lax-Wendroff scheme . . . . . . . . . . . . . . . . 26
3.2.2 Space discretization: the finite element method . . . . . . . . . . . . . . . . 27
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3.3 Initial, boundary, and compatibility conditions . . . . . . . . . . . . . . . . . . . . 28
3.4 Coupling 1D models together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 The 3D mathematical model 33
4.1 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Image segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 Surface extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.3 Surface smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 The fluid equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 Newtonian fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.2 Generalized Newtonian fluids . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.4 Similarity parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.4.1 Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4.2 Womersley number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5 Hemodynamic indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6.1 The artery wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6.2 The artificial sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6.2.1 3D-1D coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6.2.2 3D-0D coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.7 Numerical approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.7.1 Time discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.7.2 Space discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Computational simulations and discussion 53
5.1 Inflow conditions and parameter definition . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Idealized geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Straight tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.2 Straight tube with a side branch . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.2.1 Comparing the 1D coupling with standard boundary conditions . 58
5.2.3 Curved tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.4 Curved tube with a side branch . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.4.1 Comparative study of the different boundary treatments . . . . . 65
5.3 Pacient-specific geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.1 Saccular aneurysm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3.2 Analyzing the presence of side branches . . . . . . . . . . . . . . . . . . . . 72
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