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Assessment of predicting blood flow and atherosclerosis in the aorta and renal arteries
by
Alexander Fuchs
August 2020 Technical Reports
KTH Royal Institute of Technology Department of Engineering Mechanics
SE-100 44 Stockholm, Sweden
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Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 28:e augusti 2020 klockan 14:00 i Sal F3, Lindstedtsvägen 26, Stockholm
ISBN: 978-91-7873-585-3 TRITA-SCI-FOU 2020:23
Cover: Time-averaged Wall Shear-Stress (TAWSS) distribution over a human aorta and in the main arteries branching from the thoracic and abdominal aorta. Heart-rate 60 BPM (beats per minute) and cardiac output of 5 LPM (liters per minute).
© Fuchs Alexander
Tryck: Universitetsservice US AB, 2020
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To Louise, Gunnar and Bernard
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Assessment of predicting blood flow and atherosclerosis in the aorta and renal arteries
Alexander Fuchs
KTH, Dept. Engineering Mechanics
Abstract
Cardiovascular diseases (CVD) are the most common cause of death in large parts of the world. Atherosclerosis (AS) has a major part in most CVDs. AS is a slowly developing disease which is dependent on multiple factors such as genetics and life style (food, smoking, and physical activities). AS is primarily a disease of the arterial wall and develops
preferentially at certain locations (such as arterial branches and in certain vessels like the coronary arteries). The close relation between AS sites and blood flow has been well established over the years. However, due to multi-factorial causes, there exist no early
prognostic tools for identifying individuals that should be treated prophylactically or followed up. The underlying hypothesis of this thesis was to determine if it is possible to use blood flow simulations of patient-specific cases in order to identify individuals with risk for developing AS.
CT scans from patients with renal artery stenosis (RAS) were used to get the affected vessels geometry. Blood flow in original and “reconstructed” arteries were simulated. Commonly used wall shear stress (WSS) related indicators of AS were studied to assess their use as risk indicators for developing AS. Divergent results indicated urgent need to assess the impact of simulation related factors on results. Altogether, blood flow in the following vessels was studied: The whole aorta with branches from the aortic arch and the abdominal aorta, abdominal aorta as well as the renal arteries, and separately the thoracic aorta with the three main branching arteries from the aortic arch. The impact of geometrical reconstruction, employed boundary conditions (BCs), effects of flow-rate, heart-rate and models of blood viscosity as function of local hematocrit (red blood cell, RBC, concentration) and shear-rate were studied in some detail. In addition to common WSS-related indicators, we suggested the use of endothelial activation models as a further risk indicator. The simulations data was used to extract not only the WSS-related data but also the impact of flow-rate on the extent of retrograde flow in the aorta and close to its walls. The formation of helical motion and flow instabilities (which at high flow- and heart-rate lead to turbulence) was also considered.
Results
A large number of simulations (more than 100) were carried out. These simulations assessed the use of flow-rate specified BCs, pressure based BCs or so called windkessel (WK) outlet BCs that simulate effects of peripheral arterial compliance. The results showed high
sensitivity of the flow to BCs. For example, the deceleration phase of the flow-rate is more prone to flow instabilities (as also expressed in terms of multiple inflection points in the streamwise velocity profile) as well as leading to retrograde flow. In contrast, the acceleration phase leads to uni-directional and more stable flow. As WSS unsteadiness was found to be pro-AS, it was important to assess the effect flow-rate deceleration, under physiological and pathological conditions. Peaks of retrograde flow occur at local temporal minima in flow-rate.
WK BCs require ad-hoc adjusted parameters and are therefore useful only when fully patient
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specific (i.e. all information is valid for a particular patient at a particular point of time) data is available. Helical flows which are considered as atheroprotective, are formed naturally,
depending primarily on the geometry (due to the bends in the thoracic aorta). Helical flow was also observed in the major aortic branches. The helical motion is weaker during flow deceleration and diastole when it may locally also change direction.
Most common existing blood viscosity models are based on hematocrit and shear-rate. These models show strong variation of blood (mixture) viscosity. With strong shear-rate blood viscosity is lowest and is almost constant. The impact of blood viscosity in terms of dissipation is counter balanced by the shear-rate; At low shear-rate the blood has larger viscosity and at high shear-rate it is the opposite. This effect and due to the temporal variations in the local flow conditions the effect of blood rheology on the WSS indicators is weak.
Tracking of blood components and clot-models shows that the retrograde motion and the flow near branches may have so strong curvature that centrifugal force can become important. This effect may lead to the transport of a thrombus from the descending aorta back to the branches of the aortic arch and could cause embolic stroke. The latter results confirm clinical
observation of the risk of stroke due to transport of emboli from the proximal part of the descending aorta upstream to the vessels branching from the aortic arch and which lead blood to the brain.
Conclusions
The main reasons for not being able to propose an early predictive tool for future development of AS are four-folded:
i. At present, the mechanisms behind AS are not adequately understood to enable to define a set of parameters that are sensitive and specific enough to be predictive of its development.
ii. The lack of accurate patient-specific data (BCs) over the whole physiological “envelop”
allows only limited number of flow simulations which may not be adequate for patient- specific predictive purposes.
iii. The shortcomings of current models with respect to material properties of blood and arterial walls (for patient-specific space- and time-variations) are lacking.
iv. There is a need for better simulation data processing, i.e. tools that enable deducing general predictive atherosclerotic parameters from a limited number of simulations, through e.g. extending reduced modeling and/or deep learning.
The results do show, however, that blood flow simulations may produce very useful data that enhances understanding of clinically observed processes such as explaining helical- and retrograde flows and the transport of blood components and emboli in larger arteries.
Key words: Blood flow simulations, Atherosclerosis, Wall shear stress (WSS), blood rheology models
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Sammanfattning
Hjärt- och kärlsjukdomar är den vanligaste dödsorsaken i stora delar av världen.
Åderförkalkning (atheroscleros) spelar betydande roll för denna grupp av sjukdomar.
Åderförkalkning utvecklas under lång tid och beror på många olika faktorer såsom genetiska och livsstilsrelaterade (exempelvis kost, rökning och fysisk aktivitet). Åderförkalkning drabbar blodkärlens, artärernas, väggar och formas oftare på vissa lokaler än andra (t ex vid kärlförgreningar och i särsklida kärl som exempelvis hjärtats kranskärl). Det nära sambandet mellan blodflöde och åderförkalkning är väl etablerat sedan många år. P.g.a. den
multifaktoriella genesen existerar inget tillförlitligt test för att tidigt upptäcka individer i behov av förebyggande behandling eller uppföljning vid atherosclerotisk hjärt- och kärlsjukdom. Den bakomliggande hypotesen för denna avhandling var att bestämma om blodflödessimuleringar i patient-specifika fall kan identifiera risk för atherosclerosutveckling.
Datortomografiundersökningar från patienter med njurartärstenos användes för att framställa blodkärlens utseende (geometri). Blodflödet simulerades i de drabbade kärlen samt efter att de
”rekonstruerats till originalskick”. Vanligt använda indikatorer baserade på
väggskjuvspänningen (VSS) studerades för att bedöma risk för atherosclerosutveckling. Bitvis spretiga resultat visade på stort behov att bedöma känsligheten för simuleringsberoende faktorer. Blodflödet har huvudsakligen studerats i hela stora kroppsålderna (aorta) inklusive dess stora grenar i bröstkorgen och buken, bröstkorgens aorta med tre stora tillhörande grenar samt bukaorta inklusive njurartärerna. Inverkan av kärlgeometrin, dess rekontruktion,
randvillkor, hjärt-minut-volym, puls och blodets viskositet (den sistnämnda beroende på röda blodkropparnas volymfraktion (hematokrit) och den lokala skjuvhastigheten) studerades.
Utöver vanligen använda VSS-baserade parameter har även modeller för aktivering av endotelceller prövats som riskindikator för åderförkalkning. Därtill användes resultaten från simuleringarna till att kvantifiera backflöde (både inne i aorta och vid dess vägg). Förekomst av helikalt (spiralformat) flöde och instabiliteter (vilka leder till turbulens vid hög puls och hjärt-minut-volym) betraktades också.
Resultat:
Ett stort antal simuleringar (över 100) har utförts. Utvärdering har gjorts av flödesspecifika randvillkor, blodtryckbaserade randvillkor och s.k. ”windkessel (WK)”-randvillkor på kärlens utlopp för att simulera effekterna av kärlträdets perifera eftergivlighet. Resultaten visar
betyande känslighet för randvillkoren. Decelerationsfasen i hjärtcykeln ger förutsättningar för flödesinstabiliteter och bakåtflöde. Motsvarande accelerationsfasen ses istället mer stabilt flöde huvudsakligen utmed kärlriktningen. Ostadigheter i VSS verkar driva
atherosclerosutveckling och är därför viktiga för att bedöma decelerationsfasens effekter under både normala och sjukliga flödesförhållanden. Backflödet är som störst under den tidpunkt då inflödet från hjärtat är som minst. WK-randvillkor kräver ”ad hoc”-justeringar (anpassade till tillgänglig information vid varje tidpunkt) för att bli patientspecifika. Heliska flöden är ansedda att skydda mot åderförkalkning och formas som en naturlig följd av kärlens geometri (p.g.a. krökarna i aortabågen). Heliska flöden förekommer i alla större artärgrenar och försvagas under deceleration samt diastole då helixen kan byta riktning.
De vanligaste modellerna för blodets viskositet baseras på hematokrit och skjuvhastighet.
Modellerna visar stora inbördes variationer. Vid höga skjuvhastigheter är viskositeten låg och nästan konstant. Viskositetens effekter på energiförluster agerar motvikt till variationer i
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skjuvhastighet. Vid låg skjuvhastighet är viskositeten hög och tvärtom. Detta fenomen ger dock liten effekt på de VSS-relaterade indikatorerna.
”Spårning” av partiklar (t ex celler, proteiner och blodproppar) i det strömmande blodet visar att backflödet i aorta och nära dess förgreningar kan ge upphov till stark krökning och därmed betydande centrifugalkrafter på partiklarna. Dessa kan då slungas från nedåtstigande aorta in i dess större grenar från aortabågen vilket i fallet med blodpropp kan ge upphov till stroke. Det sistnänmnda fenomenet har observerats kliniskt.
Slutsatser:
Det som ommöjliggör tidig upptäckt och prgonos av åderförkalkning vid blodflödessimuleringar i stora kärl kan tillskrivas 4 huvudorsaker:
i. I nuläget är mekanismerna bakom åderförkalkning inte tillräckligt bra kvantitativt beskrivna för att definiera parametrar vilka både är tillräckligt känsliga och specifika att beskriva
processens utveckling.
ii. Bristen på tillräckligt noggranna patientspecifika mätningar av hjärtats, blodets och kärlens fysiologi räcker inte som underlag till de randvillkor som erfodras för simuleringar som skall ge förutsägelser i individuella fall.
iii. Nuvarande modeller för kärlväggens och blodets materialegenskaper (samt deras interaktion och variationer över rum och tid) har flera tillkortakommanden.
iv. Med hänsyn till i-iii erfodras bättre verktyg för databearbetning i form av verktyg som från ett begränsat antal simuleringar härleder mer generella parmetrar beskrivande atheroscleros genom s.k. modellreducering eller djup maskininlärning (s.k. ”deep learning”).
Blodflödessimuleringar kan dock med fördel användas för att dra mer generella slutsatser om flödets effekter på kliniskt observerbara fenomen som exempelvis bakåtflöden vid t ex hjärt- och klaffsjukdom samt transport av blodprodukter och -proppar i stora kärl.
Nyckelord: Blodflödessimulering, Åderförkalkning, Väggskjuvspänning, Blodreologiska modeller.
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Summary of the papers and contributions
The thesis deals with blood flow simulation in the human aorta and renal arteries. The overall aim of the work was to assess the possibility to use wall shear stress (WSS) based indicators with the ability to predict risk for future development of atherosclerosis. Sclerotic renal arteries were “reconstructed to original shape” and used as test bed for studying three
commonly used WSS indicators. The results were summarized in Paper 1. Strong dependence, of the results, on geometrical and modeling related parameters was observed and hence the following studies focused on clarifying the impact of boundary conditions (BCs, Paper 2);
The impact of heart-rate and flow-rate and its temporal variation (Paper 4) and the impact of blood rheological modeling (Paper 5). Paper 3 deals with the mechanisms that lead to formation of large scale structures (retrograde and helical flow) and their dependence of the temporal variation of flow-rate as well as the formation of small scale instabilities that my lead to transitional flow. Finally, the transport of blood components (cells, certain proteins and emboli) from the aorta is discussed in the thesis and Paper 6.
Division of work between authors:
The main advisor for the research is Lisa Prahl Wittberg (LPW). The research was done in close collaboration with a former fellow PhD student (Niclas Berg, NB). The contribution of Alexander Fuchs (AF) and co-authors to the publications is given below.
1. Paper 1:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. Stenosis Indicators Applied to Patient-Specific Renal Arteries without and with Stenosis. Fluids. 4.26. 2019. DOI:10.3390/fluids4010026.
AF wrote the ethical approval applications (for using patient CTA data). The CTA data was segmented by AF who also generated the different grids. The simulations were done using a version of OpenFoam which was modified and compiled by NB. The initial set-up was done by AF with the help of NB. Post-processing was done by AF using paraview and python scripts written by AF and/or NB. The initial version of the paper was written by AF and reviewed by NB and LPW. AF was the corresponding author and coordinated the response to reviewers and revision of the paper.
2. Paper 2:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). Pulsatile aortic blood flow – A critical assessment of boundary conditions. Accepted for publication in ASME Journal of Engineering and Science in Medical Diagnostics and Therapy.
AF set up the problem (segmentation of the thoracic aorta, generating five different grids) with nine inlet-flow profiles and different outlet BCs. The windkessel BC was implemented by NB. The simulations and post-processing was done by AF. Post-processing was done by python scripts written by either NB or by AF. The initial version of the paper was written by AF. The paper was reviewed before submission by LPW and NB. AF was the corresponding author, coordinating paper revision and response to reviewers.
3. Paper 3:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020) - Fluid mechanical aspects of blood flow in the thoracic aorta. Submitted for journal publication.
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AF set-up the problem of the flow in the thoracic aorta. The simulations and post- processing was done by AF. Post-processing was done by python scripts written by either AF or NB. The initial version of the paper was written by AF. The paper was reviewed before submission by LPW and NB. AF was the corresponding author coordinating paper revision.
4. Paper 4:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020) - The impact of heart-rate and cardiac output on the flow in the human thoracic aorta. Submitted for journal publication.
AF used published data to define the different cases of physiological and pathological heart-rate and flow rates. AF carried out the simulation using the OpenFoam modules by NB. AF wrote the draft of the paper, which was revised by LPW. AF submitted the paper for journal publication as corresponding author.
5. Paper 5:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020) - Blood rheology modeling effects in aortic flow simulations. Submitted for journal publication.
AF set up the different cases with the aim of understanding the impact of the
rheological model on the WSS indicators. AF carried out the simulation and the post processing. The different mixture and transport models were implemented in
OpenFoam by NB. AF wrote the draft of the paper. The paper was reviewed by LPW and was submitted for journal publication with AF as corresponding author.
6. Paper 6:
Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020) - On the modelling of cell and lipoprotein transport in the thoracic aorta. To be submitted.
AF set up the problem with the aim of understanding the transport of cells and lipoproteins in the thoracic aorta. A possible clinical application was to explore potential risk for stroke due to embolism from thrombi in the descending aorta. AF carried out the simulations using OpenFoam modules written by NB. The draft of the paper was written by AF. The internal review process is on-going. Some of the results are included in Chapter 5 of the thesis.
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List of Abbreviations
0D/1D/2D/3D/4D Zero-, one-, two-, three-, four-dimensional ARAS Atherosclerotic Renal Artery Stenosis BC/BCs Boundary condition/Boundary conditions
BCA Brachiocephalic artery
CO Cardiac output (LPM)
CT/CTA Computed tomography/CT-angiography
CVD Cardiovascular disease
DNS Direct Numerical Simulation
EAI-N Endothelial Activation Index-Nobili EAI-S Endothelial Activation Index-Soares
ECMO Extra Corporal Membrane Oxygenation
FKE Fluctuating Kinetic Energy
HDL High Density Lipoprotein
HF Heart failure
HR Heart rate (beats/minutes, BPM, 1/60 s-1)
HU Hounsfield unit
LCCA Left Common Carotid artery
LDL Low Density Lipoprotein
LPM Litres per minute (10-3/60 m3/s)
LPT Lagrangian Particle Tracking
LRA Left renal artery
LSCA Left subclavian artery
MKE Mechanical kinetic energy
MRI Magnetic Resonance Imaging
NCD Non-Communicable Diseases
OSI Oscillatory Shear Index (eq. 4.8)
PAS Platelet Activation State (eq. 4.10--4.12) PDEs Partial Differential Equations
RAS Renal Artery Stenosis
RBC Red Blood Cell(s)
RNWSS Relative negative WSS (eq. 4.6b)
ROS Reactive oxygen species
RRA Right renal artery
RRT Relative Residence Time (eq. 4.9)
RVRF Relative volumetric retrograde flow (eq. 4.6a)
STL Stereo lithography
TAWSS Timer-Averaged WSS (eq. 4.7)
TKE Turbulent kinetic energy
US Ultrasound
VLDL Very Low Density Lipoprotein
VWF/vWF von Willebrand Factor
WBC White Blood Cell(s)
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WK Windkessel
WSS Wall shear-stress
WSS Wall shear-stress tensor
List of Symbols:
D Diameter
De Dean number
Db Diffusion coefficient (eq. 3.10)
j Mass flux (Zydney & Colton, eq. 3.11)
J Mass flux
ji Mass flux (Leighton & Acrivos, eq. 3.12)
L Characteristic length
p pressure
Q Flow rate (3.14-3.20)
Re, Rep Reynolds number, particle Reynolds number Rp, Rc, C Parameters of WK-3 (3.14-3.20)
ui velocity component in the i-th direction
Greek
Hematocrit, Womesley number
shear-rate (norm)
dynamic viscosity
kinematic viscosity (=)
density
ij shear-stress tensor (ij component), also magnitude ||
vorticity
Dimensionless numbers:
Dean number De = Re(D/Dc)0.5; D,Dc pipe and bend diameters, respectively Kundsen number Kn = /L; mean free path/mean distance between particles Péclet number (mass) Pe = L U /m ; m mass diffusivity
Reynolds number Re = U L /), U, L are characteristic velocity and length scale.
Schmidt number Sc=/m
Stokes number St=p/F ; particle and fluid times, respectively. p=1/(3 d U ).
f – frequency ( f) Strouhal number
Weissenberg number, Wi Shear-rate * Relaxation time
Womersley number
2 D
U f D S /
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Acknowledgments
First I like to thank my main supervisor associate professor Lisa Prahl Wittberg for bringing me back in to KTH and for all your support and never failing optimism.
I also thank my co-supervisors: Professor Örjan Smedby for all valuable advice in research as well as bringing me into the world of medical imaging; Associate Professor Chunliang Wang for all your help with and teaching about blood vessel segmentation and providing the software Mialab to perform the segmentations; Professor Anders Persson for all your support, particularly with the renal artery project.
I would like to give a special thanks to Dr. Niclas Berg whose earlier work and our joint work on blood flow simulations was invaluable for making this thesis come true. Thank you also for everything you thought me about, programing, numerical analysis, art and music and more.
The computations have largely been carried out with resources from the Swedish National
Infrastructure for Computing (SNIC) at the National Supercomputer Centre at Linköping University and at High Performance Computing Center North (HPC2N) at Umeå University.
I would like to acknowledge all support from the Department of Radiology in Linköping University Hospital: Head of department Mathias Axelsson for giving me the opportunity to combine research and clinical work and Johan Blomma for all practical support and adapting a proper schedule.
My colleagues in the MSK-section (Maria Lindblom, Layth George, Marcus Casselgren, Lena Törnqvist, Bengt-Åke Hedén, Jafar Yakob, Aleksandar Komnenov and Per Widholm).
My clinical advisor during residency Anders Knutsson, Linköping University Hospital.
All other colleagues (residents and senior), technicians, nurses and administrative staff in the radiology departments in Linköping and Norrköping that I got the wonderful opportunity to work with for a total of 6 years.
I also thank all my clinical/radiological colleagues in Karolinska University Hospital, in particular Dr Amar Karalli for recruiting me and giving support to perform researchas well as Natalia Luotsinen for invaluable last minute support with time for finalizing the thesis.
I also like to thank all the many people I worked with (former colleagues, nurses, heads of
department and other staff) in the hospitals I served at in Värmland, Örebro and Kalmar county for giving me an irreplaceable experience.
Many big thanks to all other people with whom I’ve had the wonderful opportunity to share office in the Mechanics Department: Dr. Lukas Shickhofer, Asuka Gabriele Pietroniro, Dr. Valeriu Dragan, Dr. Elias Sundström, Dr. Shyang Maw Lim, Emilie Trigell, Francesco Fiusco, Roberto Mosca and Frida Nilsson.
I also thank the other people in our group in the Mechanics Department: Associate Professors Anders Dahlkild and Mihai Mihaescu, as well as, Dr. Song Chen, Dr. Julien Lemétayer, Federico Rorro, Gustavo Mori Romero, Ghulam Majal, and Gaia Cairelli.
I thank everybody who I ever had the opportunity to play music with, in particular:
All musicians (past, present and provisional members) in the Royal Institute of Technology’s, KTH, Academic Chapel Orchestra (KTHAK) and the Nordic Youth Orchestra (NUO).
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Many unprecedented thanks to my in-laws Eva and Hans Olof Rixon for taking care of our children when dealing with the thesis work.
Thanks to my brothers-in-law Johan and Gustav for being good friends.
Thanks to my brother Gabriel for many stimulating discussions.
My most profound thanks goes to my parents Ilona and Laszlo for giving me more in life than I could ever repay.
Finally, I thank my wife Louise for all love and support in the ordeals of the last years and for giving birth to our wonderful boys (Gunnar and Bernard).
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Contents
i. Abstract i
ii. Summary of the papers and contribution v
iii. List of abbreviations and symbols vii
iv. Acknowledgements ix
1. Introduction-background 1
1. Epidemiology – medical challenges
2. Scientific/modeling/understanding challenges 3. Diagnostic/Radiological challenges
4. Computational challenges
5. Summary/disposition & achievements of the thesis
2. Physiology and pathology of arterial flows 10
1. The cardiovascular system 2. Cardiovascular diseases
3. Fluid mechanics of arterial flows
3. Blood flow in arteries and its modeling 28
1. Blood rheology-challenges
2. Mathematical modeling of blood flow 3. Blood as a transport medium
4. Boundary conditions
4. Simulation methods and data analysis 48
1. Segmentation and computational domain 2. Governing equations and BCs
3. Transport of blood components 4. Analysis of the results
5. Results 63
Introduction to the simulated results 1. Renal artery stenosis-background 2. Whole aorta simulations
3. Thoracic aorta simulation
6. Summary and conclusions 91
7. Future perspective 94
8. References 95
List of Papers:
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a. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2019). Stenosis Indicators Applied to Patient- Specific Renal Arteries without and with Stenosis. Fluids. 4.26.
DOI:10.3390/fluids4010026.
b. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). Pulsatile aortic blood flow – A critical assessment of boundary conditions. Accepted for publication.
c. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). - Fluid mechanical aspects of blood flow in the thoracic aorta. Submitted for journal publication.
d. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). - The impact of heart-rate and cardiac output on the flow in the human thoracic aorta. Submitted for journal publication.
e. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). - Blood rheology modeling effects in aortic flow simulations. Submitted for journal publication.
f. Fuchs, A. & Berg, N. & Prahl Wittberg, L. (2020). - On the modelling of cell and lipoprotein transport in the thoracic aorta. Paper draft, to be submitted.
Conference contributions and presentations:
a. Fuchs, A., Berg, N., & Prahl Wittberg, L. - Stenosis in renal arteries – a numerical study.
8th World Congress of Biomechanics, July, 2018, Dublin, Ireland.
b. Fuchs, A., Berg, N., Smedby Ö. & Prahl Wittberg, L. - Blodflödets inverkan på Arteriosclerosutveckling. Röntgenveckan (Radiology week by the Swedish Society of Radiology), September 2018, Örebro, Sweden.
c. Fuchs, A., Berg, N., & Prahl Wittberg, L. - Temporal and spatial wall shear stress characterization at the renal artery branching site. XXVII Congress of the International Society of Biomechanics (ISB2019), July 2019, Calgary, Canada.
Chapter 1: Background and introduction
Epidemiology – medical challenges
Cardiovascular diseases (CVDs) is an umbrella term for conditions that affects the circulatory system (heart and blood vessels). CVD encompasses several separate and at least partially independent types of pathology. Many of these different pathologies have in common that they reside or originate in a blood vessel. Most often, CVD refers to atherosclerotic disease of the blood vessel wall and related conditions such as ischemia. In general, CVDs also includes other pathologies including, arterial and heart valve stenosis, bleeding, thrombi, emboli, heart failure (HF), arrhythmias and congenital disorders. Indirect impact of such pathologies leads often to tissue and organ damages. In severe cases, the damages are irreversible and may lead to death.
The World Health Organization (WHO) estimates that in 2016 about 17.6 million people worldwide died from CVDs (31% of total death). Of these 85% due to heart attack and stroke. WHO also notes that this figure amounted to an increase of 14.5% from 2006. The age-adjusted death rate per 100 000 was 278, which represents a decrease of 14.5% from 2006. In Sweden, the estimate is that CVDs and other Non-Communicable Diseases (NCDs) are the primary cause of death with 35% and 22%, respectively (WHO, https://www.who.int/nmh/countries/swe_en.pdf).
WHO defines NCDs very vaguely: “No communicable diseases (NCDs), including heart disease, stroke, cancer, diabetes and chronic lung disease, are collectively responsible for almost 70% of all deaths worldwide. Almost three quarters of all NCD deaths, and 82% of the 16 million people who died prematurely, or before reaching 70 years of age, occur in low- and middle-income countries.
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The rise of NCDs has been driven by primarily four major risk factors: tobacco use, physical inactivity, the harmful use of alcohol and unhealthy diets. (https://www.who.int/ncds/en/). However, the major risk factors for NCDs are the same as for CVDs and therefore it is not always possible to distinguish between a pure CVD from an NCD. More commonly it is customary to attribute 50% or more of mortality in western countries to CVDs. As noted, stroke and atherosclerosis are the most common CVDs and pathological complications of atherosclerosis are important cause of mortality in the western world [cf Chatzizisis et al. (2007), Lozano et al. (2012)].
CVDs imply not only suffering for the individual patient and its kin but as lifesaving treatment is constantly improving and as curing treatment legs behind, the burden on society increases. Typical example of such tendencies are the treatment of heart attack, stroke and heart failure (HF). When patients with heart attack or stroke can get adequate (invasive) treatment within a short period of time (a few hours), life can be saved and secondary complications substantially reduced. Heart attack treatment may include coronary artery dilation and stenting or even Extracorporeal Membrane Oxygenation (ECMO) treatment during a shorter period of time. Advanced stroke treatment includes thrombectomy [Mokin et al. (2015)]. Treatment of HF was traditionally rather frustrating as it was mainly symptomatic (diuretics and inotropic drugs and/or Angiotensin-Converting-Enzyme Inhibitors or Angiotensin II Receptor Blockers) or ultimately palliative care (for detail see: American
Heart Association Therapy Guidelines; http://www.ksw-
gtg.com/hfguidelines/pdfs/HFGuidelinesAlgorithm.pdf). However, recent advances in mechanical assist device technology opens new options in addition to the commonly preferred heart transplantation [Seco et al. (2017)]. Using mechanical devices solves also a serious limiting factor for heart transplantation, namely the limited access to organs. The development of mechanical assist devices depends strongly on reducing the risks for thromboembolic events. In order to make advances in these areas better understanding of the processes involved and developing modeling tools are essential items.
In addition to the above mentioned organ pathologies, CVDs are strongly associated with pathological changes in the arteries and their walls. These changes initially manifest as buildup of lipid material and later inflammatory process, progressing into atheromatous and fibrous plaques and finally stenosis. The atherosclerotic artery tends to calcify at later stages and as its mechanical strength reduces, it may develop aneurysms which in turn may rupture. The different pathologies have predilection sites due to anatomical and hemodynamic reasons: Stenosis often forms at bifurcations and downstream of arterial branching sites in arteries of certain size (3-6 mm) and in those carrying relatively large amount of blood (around 1 LPM or more). Examples of such arteries are the larger arteries bifurcating from the aorta: Brachiocephalic artery (BCA), the left common carotid artery (LCCA) and the left subclavian (LSCA) and the (right and left) renal arteries (RRA and LRA) as depicted in Fig 2.5. Hemodynamic factors are believed to be the most important cause for arterial stenosis due to the focal nature of the disease, [Vanderlaan et al. (2004) and Berk (2008)]. Numerical simulation of the flow, as has been done in this thesis, are aimed at improving the understanding blood flow and relate the flow to some of the clinical observations of atherosclerosis.
Scientific challenges
Biological systems are complex by nature as they combine multiple physical and chemical phenomena and processes with strong influence from genetical factors and personal history effects.
Many of these entities are not commonly addressed by simplified models used in physics or engineering. The genetical set-up of a cell, or genotype, is not always translated into observable expressions (phenotypes). The genes may be activated or suppressed as a reaction to certain states or stimulus whereby the genetics are only one of the parameters controlling the biological processes. As a result of such multi-facetted set of coupled physical and biochemical conditions, it is impossible to define a pathological process like atherosclerosis in a simple unique and deterministic manner. It has
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so far not been possible to find a single test for determining the risk for developing atherosclerosis or monitoring treatment of the disease by following a marker. Traditional (measurable) markers that have been correlated with atherosclerotic CVD includes diabetes (elevated blood glucose levels), hypertension and body mass index (BMI). Nowadays, several more markers have been identified, such as family history and hs-CRP (an inflammatory reaction protein) [Yeboah et al. (2016)]. Most markers, not only in the case of atherosclerosis, may or may not directly have to do with the disease.
In general, markers should not be associated with the formation of the pathology, unless evidence exists for such a relation. Similar objection may be raised against using observation of pathologies (form, location and progress) and relate these to hemodynamical observations. Uncertainties are associated not only with observation and measuring concentration of markers but also in measuring for example size of anatomical structures (arteries) in vivo and not least determining the flow through the arteries.
Mathematical models are commonly used to extend understanding of phenomena which are only partially known and understood. Models are optimally knowledge based and reflect the understanding of the underlying processes. An example of such a model is the set of Partial Differential Equations (PDEs) that express conservation of mass and momentum in a continuous space-time domain.
However, when such understanding is too limited one has to rely on models with expressions that are more or less “curve fitting” to experimental data. In the field of blood flow simulations, there are several crucial models of the latter type rather than the former. Measured rheological properties of blood were used to calibrate models of different types (e.g. power law, gradient based, particle based).
Uncertainties in the empirical data used for calibration contribute to the shortcoming of models. Thus, a major scientific challenge is to extend the understanding which would lead to improved modeling that enables further improvement of the understanding and so on (that is what research is all about).
In over more than a decade there has been a large number of publications (google count is in the order of a million) and attempts to use flow simulations as a potentially clinical tool. Some typical attempts can be found in Capelli et al. (2018) on congenital heart disease; Zhong et al. (2018) on coronary and intra-cardiac flow simulation. The latter paper list a number of such patient-specific publications during the past 20 years.
The main challenges associated with blood flow simulation in arteries stem from the shortcomings of modeling the physical properties of the blood, the arterial wall properties and applying boundary conditions that can emulate the shifting character of the flow in arteries of a living individual. A less critical challenge, yet not negligible, is related of replicating a living artery into computational model and accounting for the uncertainties generated during the process.
Diagnostic challenges
The diagnosis of CVDs is based on clinical findings, laboratory test and medical imaging. In most cases, a combination of these is necessary to make a diagnosis. Imaging can be used both for initial detection of a certain diagnosis in the CVD group and as follow up for managing disease progression.
A common example is heart failure that is conveniently assessed with cardiac ultrasound. Laboratory markers include proteins found in the cardiac muscles (but released in the blood in case of muscle injury), e.g. troponin and creatine kinase (CK). These markers are relatively specific since they are found in muscular tissue. Other markers include concentration of lipids/lipoproteins and inflammatory markers as mentioned above. These markers are unfortunately very non-specific, the former are found also in “normal” blood and hence their presence is indicative at elevated concentrations. Inflammatory parameters could be elevated for different reasons (e.g. infection).
Imaging tools for CVD include ultrasound, conventional angiography, computed tomography (CT), magnetic resonance imaging (MRI) and nuclear medicine studies. The different imaging techniques
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(referred to as modalities in the radiologic community) can be used to visualize both the heart and blood vessels, each one with certain qualities and limitations.
Ultrasound in general has limited resolution in space but good time resolution compared to the other imaging modalities. Therefore, it is used to assess motion of the heart (muscles and valves). The theoretical maximal spatial resolution is about 0.1 mm (based on a frequency of 7 MHz and speed of sound of 1540 m/s) [Ashley et al. (2004)]. In practice, the maximal resolution is even more limited (in clinical practice an order of magnitude higher) due to noise (because of tissues attenuation of the sound waves), multiple sound pulses that has to be transmitted and wide beam of the sound wave (focused only in one depth) [Ng et. al. 2011].
With Doppler ultrasound it is possible to measure the speed of the flowing blood along the axis of examination, hence only 1D or actually 2D (1 spatial dimension over time). The flow could be shown qualitatively (color Doppler) or quantitatively (pulse wave or spectral Doppler) showing the variation in axial velocity over time (Figure 1.1).
Other limitations of ultrasound include the reflection and dispersion of sound waves by certain tissues making the deepest part of cardiovascular organs less suitable for examination. Ultrasound is however easily available and non-invasive making it suitable for many clinical purposes.
Figure 1.1: Ultrasound image with Doppler. A longitudinal view over the right radial artery. The gray scale image shows the blood vessel in the center of the upper image (arrow?) with surrounding soft tissues. Color Doppler shows the direction of the flowing blood (red corresponding to the arterial flow towards the transducer (upper part of the image) and blue the venous flow away from the transducer). Note the color bar in the upper right corner. The axial speed (the 60° angled component) of the arterial flow is shown in the bottom of the image with variations in time corresponding to the heart beats/cycle. (A. Fuchs).
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Conventional angiography (or angiogram) can be used to visualize a vessel stenosis (Fig 1.2).
Angiograms are performed invasively by inserting a catheter into the blood vessel of interest. Via this catheter, visualization is performed by injecting a contrast agent in the blood stream, thereby increasing the x-ray density. With the development of the other modalities mainly CT and MRI, angiograms are nowadays primarily used as guide for intravascular procedures (e.g. dilation, stenting, thrombectomy etc.) after a diagnosis has been made by other means.
Before treatment, it is possible to perform invasive measurement e.g. blood pressure (by inserting a pressure-guidewire via the catheter), a feature not available by other imaging tools.
The invasive character is both the main advantage and drawback of angiography.
Figure 1.2: Angiogram of the renal artery showing a narrow stenosis at the branching site (left image, A). The same artery is shown after treatment with dilation and placement of a metal stent.
Reproduced from [Arteriosclerotic renal artery stenosis: conservative versus interventional management, Haller, C.; 88(2), 193-197, Copyright 2002 by Heart] with permission from BMJ Publishing Group Ltd.
During the last decades, there has been a significant technological development in medical imaging particularly in CT and MRI making both significant improvements in both spatial and temporal resolution and discovering new means of visualization. This development has enabled much more detailed diagnostics of CVD with both qualitative and quantitative data. Moreover, it has made possible to replace angiography as the main diagnostic method since CT and MRI are only minimally invasive.
CT utilizes X-rays to create 2D and 3D images of the human body. The heart and blood vessels are well visualized by injecting a contrast agent in the blood stream. Most of these agents contain Iodine which is x-ray dense, has a suitable x-ray energy spectrum for imaging, and could be incorporated in molecules which are relatively well tolerated by the human body [Lee et al. (2015)]. The iodine contrast agent will “highlight” the inside of the heart chambers and the blood vessels lumen (Fig 1.3).
A CT scan using contrast agent to visualize blood vessels (most commonly arteries) is called CT Angiography (or CTA). The equivalent term when using MRI in a similar way is MRA.
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Figure 1.3: Two axial CT images of the upper abdomen before injection of a contrast agent (upper image) and after (lower image). Note how the abdominal aorta (AA) with surrounding arteries as well as right and left kidneys (LK and RK) gets brighter due to enhancement, that is obtaining a higher x-ray density because of the contrast agent in the blood. (A. Fuchs).
The maximum resolution of most clinical CT scanners used today is in the order of magnitude of 0.1 mm, with isotropic voxels from 0.1-0.3 mm. To reduce noise, the images are usually reconstructed about 0.75-5 mm thick. However, with the emerging technique of photon counting CT, the resolution could today be down to (0.07 x 0.07 mm2) in each cross sectional image [Willemink et al. (2018)].
Theoretically, this could be pushed at least one order of magnitude more if a suitable photon detector is available. Doing this would set the resolution in the order of magnitude of cells. CT is with current technology not able to perform hemodynamical measurements but the high resolution anatomical data would be well suited for deriving patient specific geometrical shapes needed for blood flow simulations [Doost et al. (2016)].
Recent development in dual-energy and multi-energy as well as phase contrast CT opens up the quantitative tool of spectroscopy. Because different tissues/substances show different energy spectrums (at different X-ray energies), it is possible to quantify tissue contents, e.g. fat, water, blood, iodine and by this differ atherosclerotic plaques with various compositions, e.g. lipid-rich plaques from fibrotic plaques [Wang et al. (2008)].
MRI utilizes the phenomenon nuclear magnetic resonance (NMR) to obtain images based on the spin of protons (or equivalently hydrogen atoms). Hydrogen atoms are present everywhere in the body in different concentration, hence very suitable for diagnostics. Just like CT, MRI is useful to provide 3D images of the cardiovascular system but can also measure blood flow in 4D (based on the movement of protons in the blood and phase shifts in the radio waves used to detect these). In cardiovascular MRI, the limits of the spatial and temporal resolution are dependent of each other and a trade-off has
21
to be made between them. In cardiac MRI, the resolution is down to about 1.5 x 1.8 mm2 with maximum temporal resolution of 50 ms [Saaed et al. (2015)]. For the aorta and carotid arteries, the corresponding figures are about 0.5-1 x 0.5-1m2 and 30-60 ms, respectively [Potters et al. (2015)8].
The difference is due to variation in size and the relative movement of the heart and arteries. Heart movement is relatively large and thereby giving more “noise”. Although the theoretical spatial resolution could be several orders of magnitude lower, it is limited by impractically long scanning times (several hours), a general problem in MRI imaging. So called 4D-MRI captures MRI images in sequence at a rate of up to about 40 images/second, whereby flow visualization up to 40Hz is possible.
Fig 1.4 depicts helical flow in the ascending aorta. There has been recent attempts to extract turbulence data from 4D-MRI sequences [cf Ha et al. (2018)].
Figure 1.4: Examples of helix grade levels. 4D flow MRI-generated streamlines showing (A) grade 2 helical flow, (B) grade 1 helical flow, and (C) grade 0 helical flow in the ascending aorta (AAo), left ventricle (LV).
Allen, Bradley D.; Choudhury, Lubna, Three-dimensional haemodynamics in patients with obstructive and non-obstructive hypertrophic cardiomyopathy assessed by cardiac magnetic resonance, Eu heart J cardiovasc Imag, 2014, 16(1), 29-36, by permission of Oxford University Press/European Society of Cardiology.
In summary, medical imaging, provides both qualitative and quantitative means for diagnosing CVD.
The various modalities have advantages and disadvantages relating mostly to limits in spatial and temporal resolution, cost and availability.
Summary of the scientific challenges
Understanding the fluid mechanical mechanisms behind the atherosclerotic process would not only explain the reasons for development of atherosclerotic pathology, but could also enable assessing the risk for developing the pathology and possibly to take measure to prevent or at least delay the manifestation of the pathology. Blood flow and formation of atherosclerotic pathologies in the aorta and the renal arteries are the topics of this thesis.
The scientific challenges are substantial as the results ultimately should boil down to deduce generally valid theories and models that enable the understanding of observation and measured data, with the goal that better understanding may lead improved clinical treatment.
22 Summary of the thesis
The thesis is structured with the aim to give more detailed background material to the publications related to the thesis and some further results not included in the publications. Chapter 2 gives a description of the physiology and pathology of the cardiovascular system (CVS). The emphasis is, however, more focused around the items that are treated in the papers enclosed to the thesis. This includes CVS pathologies with emphasis to atherosclerosis (AS), but also some accounts for related diseases, such as the impact on arterial aneurysms and myocardial infarction (MI). The impact of HF on the pumping properties of the heart and its relation to the CO is also discussed shortly.
Chapter 3 deals with modeling blood flow in large arteries. The chapter describes blood composition and challenges in modeling its rheology. The mathematical framework for modeling the flow of blood in the arteries is described, along with the advantages and limitation of different options. Different inlet and outlet conditions are stated shortly as these are studied in Paper 2. The rheology and its modeling are discussed along with potential limitations of different approaches. Different possible approaches are discussed in terms of advantages and disadvantages.
Chapter 4 shortly provides the numerical methods and post-processing tools that were used in the framework of this thesis.
Chapter 5 summarizes the results of the thesis complimentary to the results presented in Papers 1-5.
Further details and results are given in cases that did not fit into journal papers which commonly set limits the number of figures/tables that are allowed to be included. The additional data also reflects potential utilization of the computed data for deeper post-processing to allow further and better understanding the questions under consideration.
Chapters 6 and 7 give a short summary/conclusions of the results and propose a possible future path to further research.
The background to and the development of the thesis work can be summarized as follows: The thesis work started with the hypothesis that atherosclerosis develops as an outcome of unfavorable blood flow conditions leading to “activation” of endothelium, with associated response of the immune and coagulation systems. Renal artery stenosis is a “silent” disease, such that it is discovered often rather late and commonly as an outcome of hypertension inquiry. The basic approach was to evaluate the blood flow in the abdominal aorta and the proximal segments of the renal artery in patients with renal artery stenosis (RAS). Computed Tomography Angiography (CTA) data form these patients provided a starting geometry of the involved arteries. Blood flow was simulated using models and methods described in the thesis. In further simulations the stenosis was “removed” from the pathological renal arteries. The impact of stenosis on the Wall Shear Stress (WSS) and on parameters commonly used to identify regions with risk for developing stenosis were evaluated (Paper 1). The outcome of the work showed that the results can be sensitive to the models used for blood flow simulations.
Paper 2 considered the impact of choosing inflow- and outflow-boundary conditions applied to the thoracic aorta, using two different inlet geometries: one with aortic sinus and a second without aortic sinus but instead having a straight cylinder simulating the left ventricle without the effect of the aortic root. At the aortic and vessel outlets, specified flow rates, pressure, pressure gradient and a 3-element Windkessel model were evaluated. Any of these approaches require further knowledge and assumptions. The sensitivity of the results to boundary effects implies that such simulations can be very useful as foundation for understanding hemodynamically relevant phenomena but not directly for predicting blood flow under normal conditions which show large variability in terms of heart rate and cardiac output. The variations also make it difficult to use simulations predictive for development of pathologies in a deterministic sense. On the other hand, the simulations can be useful in statistical sense with determination of the uncertainty due to boundary effects.
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Paper 3 explores simulated data for exposing the underlying mechanism for the formation of larger scale flow structures in the thoracic aorta; namely, helical and retrograde flow structures in the aortic lumen along with formation of negative WSS at the wall. The relation between the driving flow-rate and retrograde flow was clearly shown (extended to more than two dozen cases in Paper 4). Helical motion is primarily the result of the geometry of the vessel (bend and torsion) and spatial distribution of the inlet velocity profile. Helical flow is common also in bifurcating branches of the aorta due to strong streamline curvature leading to secondary flow formation. Generation of vortical structures and the risk for formation of turbulence was further discussed in Paper 3. Paper 4 gives further details on the WSS and related potentially predictive parameters for different heart pumping variations;
Heart-rate (HR), flow-rate (Cardiac Output, CO) and cardiac contraction/relaxation rate variations.
The different cases emulate normal, healthy cases at rest and at exercise as well as cardiac pathological cases such as aortic stenosis and heart failure. Paper 5 discusses the impact of blood rheology on the simulations. The transport of cells (RBC, White Blood Cells (WBC), platelets), some lipoproteins (Chylomicrons, Very Low Density Lipoproteins (VLDL), High Density lipoproteins (HDL)) and von Willebrand Factor (VWF) as well as emboli in the thoracic aorta are discussed in the draft of Paper 6. The results show that the retrograde flow that is associated with the deceleration phase of the cardiac cycle may lead to upstream transport of small blood clots which, during systole will enter the arteries leading to the head which in turn may result in stroke.
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Chapter 2: Physiology and pathology of arterial flows
2.1 Cardiovascular System
The cardiovascular system has several important functions for maintain necessary conditions for life.
Blood has multiple essential functions: it carries oxygen, “fuel” and substances needed for converting our food into chemical compounds needed for building the body. Blood also transports hormones to cells throughout the body and removes metabolic wastes (carbon dioxide, nitrogenous wastes). Blood plays an important role in maintaining the right environment for life (pH and temperature) and generate compounds (e.g. ATP) that are used by different muscles in the body. Blood is also the carrier of major parts of the immune and inflammatory systems which are needed to defend the body against foreign microbes and toxins. Clotting mechanisms are also present, protecting the body from blood loss when injured. Blood flow is regulated, as described below, enabling the body to optimize the flowing blood for the needs; for example, during exercise more blood is needed for active muscles, the heart and the lungs. To maintain body temperature, capillary flow can be regulated to increase or decrease blood flow in the skin. After a meal, more blood is directed towards the intestine and liver.
In emergency, the most important measures to take are to maintain blood circulation, free airways and sustained breathing.
The cardiovascular system consists primarily of two coupled loops through which the blood flow is driven by the left and right parts of the heart, respectively. The systematic circulation includes the left heart ventricle, the aorta, with its branches to the head, neck, upper and lower limbs, as well as the thorax, abdomen and pelvis. The arterial blood, rich in oxygen, flows through the capillary system in the different tissues, whereby nutrition and oxygen is delivered. The de-oxygenated blood flows back through veins converging in the right atrium, the right ventricle, through the lungs and, after re- oxygenation, back to the left atrium and the left ventricle.
Figure 2.1: The main arteries of the systematics circulation loop. In this thesis we consider the thoracic aorta together with the three main branches of the neck/head/arm. Blood flow in the region of the bifurcation of the renal arteries from the abdominal aorta is also studied.
Original image title: Aorta branches.
Link to original image:
https://commons.wikimedia.org/wiki/File:Aorta_branches.j pg – 2020-07-13.
The author to whom credit is given for publishing the image under a creative commons license: Mikael
Häggström(https://commons.wikimedia.org/wiki/User:Mik ael_H%C3%A4ggstr%C3%B6m – 2020-07-13).
License: The image was reused in its original form under the Creative Commons Attribution-Share Alike 3.0 Unported license
(https://creativecommons.org/licenses/by-sa/3.0/deed.en).
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Figure 2.2: The pressure in the systematic and the pulmonary circulations. Note the increase in the pulse pressure in the large arteries due to the property of the arterial wall.
Original image title: Circulation pressures V1. Link to original image:
https://commons.wikimedia.org/wiki/File:Circulation_pressures_v1.tif – 2020-07-13.
The author to whom credit is given for publishing the image under a creative commons license: Adh30 (https://commons.wikimedia.org/w/index.php?title=User:Adh30&action=edit&redlink=1 - 2020-07-13).
License: The image was reused in its original form under the under the Creative Commons Attribution- Share Alike 4.0 International license (https://creativecommons.org/licenses/by-sa/4.0/deed.en)
The arterial part of the circulation system is characterized by higher pressure (about 120 mmHg, 16kPa) as compared to the vein side (about 20 mmHg, 2.7kPa) (Fig 2.2). The blood pressure in the systematic circulation loop reaches the same peak as the peak pressure in the heart in systole (about 100-120 mmHg at rest). During diastole, the pressure is lower (the change in pressure is the pulse pressure which is defined as the difference in pressure between systole and diastole) by about 40 mmHg, whereby the aorta maintains a mean pressure of about 100mmHg throughout the cardiac cycle. To understand the functionality of the major arteries, it is instructive to consider their histology.
A schematic summary of the sizes and the composition is depicted in Table 2.1. More detailed structure of the arterial wall and a histological picture are given Figs 2.3 and 2.4.
The arteries differ histologically from the veins as they are adjusted to handle the higher pressure.
The arteries as all vessels, have a single layer of cells (endothelium) placed upon a base membrane under which smooth muscle cells along with connective tissue cells (fibroblasts) are found. The latter generate fibers and interstitial material. The arterial wall can be divided into three layers.
Tunica Intima consists of a continuous single cell layer endothelium supported by an elastic and one collagenous layer (membrane).
Tunica Media consists of a layer composed of variable portions of muscular and elastic components
Tunica Adventitia has varying thickness composed of collagen with interspersed bundles of elastin. Blood supply to larger arteries are through vessels inside the vessel wall (vasa vasorum).
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A schematic picture of the arterial wall is depicted in Fig 2.3 and a corresponding histological picture in Fig 2.4. The histology of the artery reflects its function. The three layer allows the major arteries to respond to blood pressure and lead to minimal losses as blood flows thorough them.
Table 2.1: Typical characteristics of arteries, veins and capillaries (cf. Wnek & Bowlin (2008)).
Arteries Veins Capillaries
Function Oxygenated blood to body
Return blood to heart Solvent exchange Pressure 120 mmHg - aorta
> 60 mmHg - arteriole
20 mmHg 50-20
Lumen diameter 25-30 mm (aorta) 5-10 mm (medium) 20-50m (small arteriole, sphincter)
30 mm (v. cava) 5 mm
20-30 m (venule)
1-8 m
Wall thickness Thick Thin Extremely thin
Wall layers Tunica intima Tunica media - thick Tunica adventitia - thick
Tunica intima Tunica media - thin Tunica adventitia - thin
Tunica intima
Muscles and elastic fibers
Large amounts Small amount None
Valves No Yes No
Figure 2.3: The structure of the arterial wall.
Original image title: Artery.
Link to original image:
https://commons.wikimedia.org/wiki/File:Artery.
svg – 2020-07-13.
The author to whom credit is given for publishing the image under a creative commons license:
Kelvinsong
(https://commons.wikimedia.org/wiki/User:Kelvi n13 - 2020-07-13).
License: The image was reused in its original form under the Creative Commons Attribution- Share Alike 3.0 Unported license
(https://creativecommons.org/licenses/by- sa/3.0/deed.en).
27 The amount of elastin is largest in the
aorta whereas smooth muscles dominate medium sized arteries (such as the main branches from the aorta; e.g. Brachiocephalic, Common carotid, subclavian, and renal arteries). The elastin in the arterial walls gives the compliance needed to modulate the pulsatile heart pumping into a strong mean flow with pulsation of only about
10%. The smooth muscles have a regulatory function through which the body can increase or decrease the pressure in parts of the arterial system leading to improved perfusion in required organs. Such a regulation is carried out normally rather frequently during the day; more blood is supplied to the stomach after a meal, more to the skeletal muscle at work/exercise, etc.
Systematic regulation of the systematic circulation depends not only on the smooth muscles of the medium sized arteries, but also on major sensory organs. Systematic pressure is regulated by local, humoral, or neural reflex mechanisms. Baroreceptors are found in the carotid body (glomus cells are innervated both by sensory and autonomic fibers mostly from the carotid sinus nerve), the aortic arch, the right atrium and kidneys. The cardiovascular center also receives data from chemoreceptors, i.e.
sensory neurons that monitor levels of CO2 and O2. These neurons alert the cardiovascular center when levels of O2 drop or levels of CO2 rise (which result in a drop in pH). Chemoreceptors are found in carotid bodies located near the carotid sinus, aortic arch and in the kidney (juxtamedullary glomeruli cells). The cardiac center stimulates cardiac output by increasing heart rate and contractility. These nerve impulses are transmitted over sympathetic cardiac nerves. Additionally, the cardiac center inhibits cardiac output by decreasing heart rate mediated by the parasympathetic Vagus (X-th cranial) nerve branches. Local vasomotor regulation of artery diameter is exercised by sympathetic motor neurons (vasomotor) nerves that innervate smooth muscles in arterioles.
The hormonal regulation of blood pressure includes the kidney and the liver/lung through management of blood volume. Hypoxia-mediated renal and carotid body afferent signaling triggers activation of the renin‐angiotensin‐aldosterone system (RAAS). In response to rising blood pressure, the juxtaglomerular cells in the kidneys secrete renin into the blood. Renin converts the plasma protein angiotensinogen to angiotensin I, in turn converted to angiotensin II by enzymes from the lungs.
Angiotensin II acts throughout the body by constricting blood vessels and thereby raising blood pressure. Constricted blood vessels reduce the amount of blood delivered to the kidneys, which decreases the excretion of water through the kidneys and thereby raising blood pressure by increasing blood volume. Additionally, Angiotensin II stimulates the adrenal cortex to secrete aldosterone.
Aldosterone is a hormone that reduces urine volume by increasing retention of water and Na+ by the kidneys.
Figure 2.4: Histology of common carotid artery. The arrow pointing on the (tunica intima) which consist of the endothelium placed on an internal elastic lamina. The middle (tunica media) and the outer (tunica adventitia) layers are marked by the black and green brackets, respectively.
Original image title: Fig 1: Histology of common carotid artery. Link to original image:
https://www.nepjol.info/index.php/NHJ/article/view/197 05/16251 – 2020-07-13.
The author to whom credit is given for publishing the image under a creative commons license: Murari Prasad Barakoti
(https://www.nepjol.info/index.php/NHJ/article/view/197 05 - 2020-07-13).
License: The image was reused in its original form under the under the Creative Commons Attribution-Share Alike 4.0 International license
(https://creativecommons.org/licenses/by-sa/4.0/deed.en)
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Blood pressure may also be regulated by natural (body owned) substances and artificial analogs.
Epinephrine and norepinephrine, are body own hormones secreted by the adrenal medulla, can raise blood pressure by increasing heart rate and the contractility (inotrope effect) of the heart muscles and by causing vasoconstriction of arteries and veins. These two hormones, called sometimes as “stress”
hormones, are released as stress response. Antidiuretic hormone (ADH), is also a hormone (produced by the hypothalamus and released by the posterior pituitary gland) as the name says, acts on kidney to retain water. Water retention leads to increase in blood volume and thereby increasing also blood pressure. NO (nitric oxide) is a very small molecule acting as local hormone in several life maintaining circuits. NO is released among others by endothelial cells causing local vasodilatation.
Alcohol lowers blood pressure by inhibiting the vasomotor center leading directly to vasodilation and by inhibiting the release of ADH and increase diuresis. Nicotine raises blood pressure by stimulating sympathetic neurons to increase vasoconstriction and by stimulating the adrenal medulla to increase secretion of epinephrine and norepinephrine.
The inner walls of the (young) arteries is smooth, with small viscous losses. The dispensability (compliance) of the arterial wall allows the cross-sectional area and its length of the artery to adjust to the pressure in the artery. Through this functionality, the larger arteries expand in their volume and can maintain the relatively high pressure also during diastole. Thus, the larger arteries and in particular the aorta and its main branches act a flexible vessel that store parts of the energy supplied during systole by the heart and releases that energy during diastole. Unfortunately, the composition of the arterial wall changes with age. As the larger arteries becoming stiffer, the heart has to produce higher pressure to maintain the same functionality (i.e. flow) as the arteries had at younger age. Over time, partially as consequence of the elevated pressure, a sclerotic process takes place in the arteries which results in a more permanent hypertension.
2.2 Cardiovascular diseases Atherosclerosis
Normal aging of the body implies a general loss of elastic substances in various tissues, including the skin and blood vessels. Lower elasticity and reduced compliance of the larger arteries also leads to elevated systemic blood pressure. Yet, atherosclerosis is initiated in certain locations. The disease is an outcome of multiple factors. In spite of its multifactorial genesis, its location is usually distinct:
The process predominantly located to arterial branches and bifurcation of arteries of certain size and range regions (Fig 2.5 from (VanderLaan et al. 2004) and only those arteries which carry a certain volume of blood. Flow in a bifurcation region leads to streamline curvature having a radius of curvature of the same order or possibly even small than the diameter of the bifurcating vessel.
Therefore, it is not surprising that in addition to vessel bifurcation also vessel with stronger curvature may be sites for arterial pathologies (Gimbrone et al. 2000)). An example of such an “artery” is the Circle of Willis, which is prone to develop flow induced aneurysms.
