Table Of ContentBiological and Medical Physics, Biomedical
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Jiyuan Tu • Kiao Inthavong
Kelvin Kian Loong Wong
Computational
Hemodynamics—Theory,
Modelling and Applications
1 3
Jiyuan Tu Kelvin Kian Loong Wong
School of Aerospace Mechanical and School of Aerospace Mechanical and
Manufacturing Engineering Manufacturing Engineering
RMIT University RMIT University
Bundoora Bundoora
Victoria Victoria
Australia Australia
Kiao Inthavong
School of Aerospace Mechanical and
Manufacturing Engineering
RMIT University
Bundoora
Victoria
Australia
ISSN 1618-7210 ISSN 2197-5647 (electronic)
Biological and Medical Physics, Biomedical Engineering
ISBN 978-94-017-9593-7 ISBN 978-94-017-9594-4 (eBook)
DOI 10.1007/978-94-017-9594-4
Library of Congress Control Number: 2014954751
Springer Dordrecht Heidelberg New York London
© Springer Science+Business Media Dordrecht 2015
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Preface
Traditionally, cardiovascular studies have been limited to medical textbooks and
courses, taught by medical experts. Now, computational modeling and simulation
has infiltrated the medical field which has advanced to a point where it can be cat-
egorized into its own sub fields. The use of Computational Fluid Dynamics (CFD)
for modeling cardiovascular flow leads to a new field of study known as computa-
tional biomedical engineering. In particular when we model blood as a biofluid and
compute its flow, we establish a branch termed as Computational Haemodynamics
(CHD). This new field of engineering constitutes important knowledge in the study
of blood flow mechanics, surgical and medical treatment, and design of biomedical
devices. This has only been possible through the emergence of advanced technolo-
gies in medical imaging, and computers. Since the fundamental principles of CHD
are based on CFD, these two terms are quite similar and used interchangeably in
this book.
This book is designed to convey information pitched at an appropriate level of
knowledge to new students with a diverse background of medicine, physiology,
pharmaceutical science, mechanical engineering, and mathematics. This book can-
not deliver the entire scope of knowledge that is related to cardiovascular modeling.
Rather, it provides an important link between traditional engineering and computa-
tional fields with the medical field. For example, an undergraduate who is trained in
engineering can selectively read the relevant chapters of the book that provides new
knowledge on the computational simulation or medical aspects.
There is a diverse range of CFD books in the market are written with different
levels of complexity. To ensure the reader is not overwhelmed by overly advanced
mathematical notation and theory, this book describes fundamental mathematical
ideas, coupled with sufficient description and backed up with examples. It is intui-
tive and systematically structured for enhancing the learning process and allowing
students to be able to quickly use CFD practically. Nevertheless, a fundamental
knowledge of calculus such as basic anti- and differentiation is still required prior to
reading the book. With the hands on practice and reading, this book can enable CFD
beginners to efficiently perform reliable CFD simulations for the CHD applications.
The book begins with Chap. 1, which prepares the reader for an overview of
CHD, its advantages and disadvantages, a preliminary understanding of CHD, and
v
vi Preface
its numerous applications in the cardiovascular system. It aims to initiate curiosity
and stimulate creativity for the reader to think of possible solutions to engineering
problems related to cardiovascular flow.
In Chap. 2, the human cardiovascular system is presented concisely. By provid-
ing the description of the cardiovascular anatomy and physiology at an elementary
level, this chapter is useful for readers that have previously not received any form of
medical training. An understanding of the cardiovascular anatomy provides a basis
for an accurate computational fluid flow setup for geometrical reconstruction based
on medical imaging, definition of the relevant anatomical structures, and determin-
ing cardiovascular flow boundary conditions.
Medical image reconstruction of the cardiovascular anatomy is covered in
Chap. 3, which introduces the reader to medical imaging, geometrical reconstruc-
tion, manufacturing or reverse engineering, and Computer-Aided Design (CAD).
The book steps through all of the processes from medical image scanning (MRI or
CT scans) through to segmentation, and leading to model reconstruction. Important
features of each process with informative description of the approach used or avail-
able software are given in detail.
Chap. 4 presents the fundamentals of haemodynamics, firstly introducing the
properties of blood and then its flow properties. Since blood flow is enclosed by
the arterial walls, it is an example of the well-established internal pipe flow theory.
This incorporates the laws of fluid dynamics and its interaction with solid surfaces.
Characteristic flow features of blood flow in different regions of the circulatory
system are presented to exemplify its behaviour.
In Chap. 5, the governing equations of fluid flow, i.e. the Navier-Stokes equa-
tions are introduced. Each term in the equations is described in such a way that the
reader can appreciate its physical interpretation and impact on the flow. A brief
introduction to turbulence and its modelling is also given, which is quite unusual
for this type of book. However we feel that since cardiovascular flows through
stenosed arteries and some medical devices will exhibit some form of turbulence,
it is worth mentioning here. A summary of the different turbulence models is given
with guidelines on setting up the different models. A derivation of the equations for
solid dynamics is given with an emphasis on the elastic properties of arteries. The
discretisation of the continuum equations for the fluid and solid dynamics onto dis-
crete points in a computational domain are shown using the more well-known meth-
ods that include the Finite Difference, Finite Volume, and Finite Element Methods.
These methods are solved algebraically using both direct and iterative methods.
The coupling of the fluid and solid domains produce the Fluid-Structure-Interaction
(FSI). This takes place at a shared interface where the fluid and solid meet. Force
loadings and structural deformation results are passed from one analysis to the other
and the coupling approaches are described. A major difficulty with FSI is the stabil-
ity and convergence and these issues are discussed.
Description of mesh development for different anatomies are described in
Chap. 6. The discretised equations from Chap. 5 are transferred to a correspond-
ing discrete set of points in flow field where solutions of the flow variables such
as the velocity, pressure, temperature, and deformation are performed. Both static
Preface vii
and fluid-structure-interaction meshing are presented. Generation of a quality mesh
requires both a good sense of creativity and technical knowledge. Therefore, this
chapter provides guidelines to the reader prior to delving into the interesting ex-
periments of meshing different anatomical models. Different types of mesh and its
setup for simplified and more advanced geometries are illustrated without present-
ing overly complicated mathematical algorithms. Furthermore guidelines and best
practices are given for developing quality meshes and material presented will give
the reader an introduction into mesh creation.
Having laid the groundwork to establish a strong theoretical base, Chap. 7 ap-
plies the foundational knowledge and putting them into practice through selected
demonstrative applications. The entire process from scans to the final data analy-
sis is shown. The examples include models of a stenosed carotid artery, patient
specific carotid bifurcations, stented artery, and cardiac chamber. Post-processing
techniques are presented which involves converting the raw data into graphical rep-
resentations.
Computational simulations increase in complexity when it considers blood flow
within elastic wall structures of the cardiovascular system. Chap. 8 presents some
FSI cardiovascular applications to provide the reader with an overview of some
developments in this emerging field. FSI is being used as a demonstration of practi-
cality of achieving a higher physiological realism in haemodynamics analysis over
simple rigid wall assumptions. Applications include atherosclerosis in carotid bifur-
cation, calcified plaque rupture, aortic aneurysm, as well as coronary artery bypass
graft.
The book culminates with Chap. 9 that explores the future trends and more ad-
vanced modelling techniques. While the detailed treatment of these advanced tech-
niques are beyond the scope of this book, it is hoped that the chapter will stimulate
further enthusiasm in the advancing capability and innovative use of CFD and FEM
for studies related to computational haemodynamics.
Jiyuan Tu
Kiao Inthavong
Kelvin Kian Loong Wong
Acknowledgements
The authors are grateful to Springer, particularly Thijs van Vlijmen for reviewing,
endorsing, and supporting the idea of publishing this book, and to Sara Germans
for assisting in a smooth completion of our project. The authors like to thank re-
search students and colleagues working in the CFD Group at RMIT University for
their hard work and contribution. Special thanks are given to Pongpat Thavornpat-
tanapong and Jingliang Dong who have provided worked examples in geometric
modelling, meshing and simulations for this book. We would like to thank Dr Sher-
man Cheung, Prof David Reutens, Prof Thanh Phan, Dr Songlin Ding, Dr Huafeng
Li and Mr Nelson Choi for their early contribution of patient-specific geometric
reconstruction and CFD simulation, and are grateful to Dr William Yang for his
experimental validation of our simulations.
Prof Tu wants to dedicate this book to the memory of his former supervisors, Prof
Zhong-Yi Hua, former President of Fudan University, who died in a heart attack,
and Prof Shi-Jin Pang who died in a stroke. He would like to express his gratitude to
his wife, Xue, and his son, Tian for their understanding and support. Dr Inthavong
wishes to acknowledge the immense support, contributions, and fruitful discussions
from Laura Frances Portaro; and the constant challenges posed by Antonino Intha-
vong. He would like to dedicate this book to Samuel August Schmidt for the many
nights of online discussions on research, science, and all things academic—until
our next discussion. Dr Wong would like to thank his life mentors—Prof Dhanjoo
N. Ghista, Prof Jagannath Mazumdar and Prof Derek Abbott for their advice and
guidance in his research of computational hemodynamics. He expresses thanks to
his wife, Xindan for her understanding and support during the course of his career
when this book is being written.
Finally, to those that the authors have failed to mention but have been involved
in one way or another, the authors would like to take this opportunity of expressing
their deepest appreciation.
Jiyuan Tu
Kiao Inthavong
Kelvin Kian Loong Wong
ix
Contents
1 Computational Haemodynamics—An Introduction �������������������������������� 1
1.1 W hat is Computational Haemodynamics (CHD) ���������������������������������� 1
1.2 A dvantages of CHD ������������������������������������������������������������������������������ 3
1.3 A pplications in the Cardiovascular System ������������������������������������������� 4
1.3.1 CHD as a Research Tool ������������������������������������������������������������ 4
1.3.2 CHD as a Training Tool ������������������������������������������������������������� 5
1.3.3 Examination of Atherosclerosis ������������������������������������������������� 6
1.3.4 Plaque Rupture Risk Assessment ���������������������������������������������� 8
1.3.5 Preoperative Assessment of Atherosclerotic Arteries ���������������� 9
1.3.6 Surgical Treatment of Atherosclerotic Arteries ������������������������� 12
1.3.7 Preoperative Assessment of Aneurysm ������������������������������������� 16
1.3.8 Assessment of Medical Devices ������������������������������������������������ 17
1.4 Summary ����������������������������������������������������������������������������������������������� 18
1.5 Review Questions ���������������������������������������������������������������������������������� 19
2 The Human Cardiovascular System ���������������������������������������������������������� 21
2.1 Introduction ������������������������������������������������������������������������������������������� 21
2.1.1 Functions of the Circulatory System ����������������������������������������� 21
2.1.2 Organization of the Cardiovascular System ������������������������������ 23
2.2 Physiology of the Cardiovascular System ��������������������������������������������� 25
2.2.1 Anatomy of the Heart ���������������������������������������������������������������� 25
2.2.2 Cardiac Cycle ���������������������������������������������������������������������������� 26
2.2.3 Physiology of the Aorta ������������������������������������������������������������� 27
2.2.4 Physiology of the Carotid Bifurcation �������������������������������������� 28
2.2.5 Physiology of the Coronary Arteries ����������������������������������������� 31
2.2.6 Physiology of the Vascular Network ����������������������������������������� 32
2.2.7 Blood ����������������������������������������������������������������������������������������� 34
2.3 Disease of the Cardiovascular System �������������������������������������������������� 35
2.3.1 Atherosclerosis �������������������������������������������������������������������������� 35
2.3.2 Calcification of Lesions in Plaque �������������������������������������������� 36
xi
