Simulating Blood Flow in an Anatomical Arterial Network

187 Pages·2015·9.66 MB·English

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Simulating Blood Flow in an
Anatomical Arterial Network
Soroush Safaei
Supervised by:
Dr Vinod Suresh
Dr Chris Bradley
A thesis submitted in fulfilment of the requirements for
the degree of Doctor of Philosophy in Bioengineering
Auckland Bioengineering Institute
University of Auckland
May 2015

Abstract
The overall aim of this thesis is to develop a computational model of the human arte-
rial system to predict blood pressure and flow rates throughout the body. The model
used an anatomical vascular network derived from the Visible Human Project and im-
plemented in OpenCMISS, an open-source mathematical modelling environment that
enables the application of finite-element analysis and other techniques to a variety of
complex bioengineering problems.
This arterial model coupled a one-dimensional arterial tree model with a lumped pa-
rameter description of the peripheral circulation is capable of simulating global hemody-
namics and arterial wave propagation simultaneously and can provide the downstream
boundaryconditionsforthree-dimensionalsimulationsattheparticulararteriallocation
using one-dimensional models of the entire arterial system and zero-dimensional models
at the distal ends. The model provided better predictions of published experimental
measurements compared to existing one-dimensional models.
The model was used to simulate pressure and flow waveforms in pathological conditions
toinvestigatepotentialusesinsurgicalplanningandtheuseofinexpensiveflowandpres-
suremeasurementsfordiagnosis. Thisincludestheuseofthemodeltoexplorethepossi-
bility of non-invasive disease diagnosis and comparison of different surgical options.
The flow model was then coupled with an advection-diffusion equation to simulate the
transport of solutes (drugs, hormones) through the vasculature. For the first time, by
coupling with lumped parameter descriptions of metabolism and excretion in target
organs, the extended model provides a physiologically based pharmacokinetic model
that will be useful in drug development and regulatory toxicology to predict the kinetics
and metabolism of substances in the body. The coupled framework has the ability to
modelpharmacokineticresponsetotheadministrationofdrugsinamorephysiologically
realistic manner compared to the traditionally used compartmental models.
iii
An important contribution to the state of knowledge is the free availability of the code-
base. Source code and anatomical data are not available for any of the existing models
which makes it impossible to independently validate published results and to modify
or extend the model for different applications. By providing this capability the thesis
provides a useful computational resource to the bioengineering community.
Acknowledgements
I am incredibly grateful for the guidance, support, and encouragement that I have re-
ceived throughout the course of my doctoral research.
I am indebted to my two supervisors Dr Vinod Suresh and Dr Chris Bradley for their
guidance,encouragementandchallenge. Chrishasbeenaconstantsourceofenthusiasm,
energy and advice. He has been a great help, particularly in the completion of this work
reading drafts in great detail, quickly and efficiently. Vinod has constantly supported,
guided and helped me from my day one in Auckland. He has been a great help with
his attention to detail, his oversight, his diligence, and his thoughtful insights at critical
moments. Thank you Vinod for your sage advice, despite the many demands on your
time and for cheerfully keeping an eye on my progress.
Prof Peter Hunter, I consider a role model and an inspiration. His patience, human
values, technical brilliance, and visionary ideas have made the Auckland Bioengineering
Instituteacooperativeanddynamicplacetowork. ThankyouPeterfortheopportunity
to work with you and complete this project.
As a part of the Auckland Bioengineering Institute and OpenCMISS group, I have
enjoyed and appreciated working with many colleagues through the course of this work.
I would like to thank the Maurice Wilkins Centre for providing funding for the project,
to enable this research to take place.
Finally, my family have unconditionally loved me, encouraged me, and taken an enor-
mous interest in both the pain and triumphs of this work. I would like to express my
deep gratitude to my family and friends for their support, which constantly reminded
me of the high aspiration of the pursuit of knowledge.
v

Contents
Abstract iii
Acknowledgements v
List of Figures xiii
List of Tables xv
List of Abbreviations xvii
List of Symbols xvii
1 Motivation and Objectives 1
1.1 Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Introduction 7
2.1 Blood flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Historical overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 0D lumped parameter models . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 1D distributed models . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 3D distributed models . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4 Multi-scale models . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Review of recent 1D circulation models. . . . . . . . . . . . . . . . . . . . 21
2.3.1 Tube law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Solution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 1D modelling of specific vascular beds . . . . . . . . . . . . . . . . . . . . 23
2.4.1 Cerebral circulation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
vii
viii Contents
2.4.2 Stenoses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.3 Aneurysms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.4 Veins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Validation of 1D models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 Clinical applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6.1 Parameter studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6.2 Surgical planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6.3 PBPK modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7 OpenCMISS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7.1 Data structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7.2 Multi-physics modelling . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7.3 Integration with CellML . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7.4 Open-source libraries . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7.5 Parallel processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Model Development and Implementation 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 General equations for blood flow . . . . . . . . . . . . . . . . . . . 40
3.2.2 1D system formulation . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Wall equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.5 Non-dimensionalisation . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.6 Characteristic system . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.7 Steady state solution . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.8 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.9 Branching conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.10 Peripheral circulation . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.11 0D-1D coupling method . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.12 Numerical scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.1 Network geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.2 Platform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.3 OpenCMISS implementation . . . . . . . . . . . . . . . . . . . . . 61
3.3.4 Solvers and solver equations . . . . . . . . . . . . . . . . . . . . . . 64
3.3.5 CellML implementation . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.6 CellML and OpenCMISS coupling . . . . . . . . . . . . . . . . . . 66
Contents ix
3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2 Single vessel results . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.3 Simple bifurcation results . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Model Validation and Applications 79
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Case 1: Physiological conditions. . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.2 Comparison between rest and exercise conditions . . . . . . . . . . 86
4.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3 Case 2: Abdominal aortic aneurysm . . . . . . . . . . . . . . . . . . . . . 91
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.2 Comparison between normal and diseased conditions . . . . . . . . 92
4.3.3 Parameter study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.4 Case 3: Aortic coarctation . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.2 Comparison between rest and exercise conditions . . . . . . . . . . 99
4.4.3 Comparison between pre-surgical and post-surgical conditions . . . 99
4.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.5 Case 4: Renovascular hypertension . . . . . . . . . . . . . . . . . . . . . . 102
4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.5.2 Comparison between rest and exercise conditions . . . . . . . . . . 103
4.5.3 Stenoses in both renal arteries . . . . . . . . . . . . . . . . . . . . 103
4.5.4 Peripheral vasoconstriction . . . . . . . . . . . . . . . . . . . . . . 109
4.5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 Pharmacokinetic Modelling 113
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.1 PBPK modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2.1 Advection-diffusion equation . . . . . . . . . . . . . . . . . . . . . 114