Ghassan S. Kassab Coronary Circulation Anatomy, Mechanical Properties, and Biomechanics Coronary Circulation Ghassan S. Kassab Coronary Circulation Anatomy, Mechanical Properties, and Biomechanics GhassanS.Kassab CaliforniaMedicalInnovationsInstitute SanDiego,CA,USA ISBN978-3-030-14817-1 ISBN978-3-030-14819-5 (eBook) https://doi.org/10.1007/978-3-030-14819-5 LibraryofCongressControlNumber:2019936004 ©SpringerScience+BusinessMedia,LLC,partofSpringerNature2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Coronaryarterydisease(CAD)cancauseinadequatemyocardialperfusionandpoor contractility,resultingindeficientcardiacoutputandpotentialheartfailure.CADis theleadingcauseofdeathworldwide,andby2020,itisestimatedthatCADwillbe theleadingcauseofdiseaseburden(e.g.,directandindirectfinancialcost,disability, mortality,morbidity)worldwide.IntheUnitedStates,specifically,CADplacesthe most severe clinical and financial burden of the healthcare system than any other disease conditions. Currently, over 16 million Americans have CAD, which is the leading cause of cardiovascular death in the United States (one out of every six deaths is caused by CAD). CAD is closely related to other conditions such as obesity, diabetes mellitus, hypertension, and heart failure. As a result, treatment for CAD in the United States leads to the highest cost of any disease condition (~ $100B per year). Between 2010 and 2030, the total direct medical cost of cardio- vasculardiseasesisprojectedtotriple,from$270billionin2010to$800Bin2030. The coronary circulation consists of an integrated system of complex anatomy, mechanical properties, boundary conditions representing the hemodynamics, and myocardial-vesselinteraction,whichleadstophasicpatternsofcoronarybloodflow into, within, and out of the myocardium. Coronary blood flow is substantially heterogeneous spatially (throughout the myocardium) and temporally (within car- diaccycle).Thesetemporalandspatialheterogeneitiesareimportantphysiologically andclinicallybutaredifficulttostudyattheinnerlayersofthemyocardium,where susceptibility to ischemia is an important clinical phenomenon. Hence, rigorous validated models of the coronary vasculature, mechanical properties, boundary conditions, and myocardial-vessel interaction are critical to produce realistic pre- dictionsofbloodflowthroughoutthewalloftheheart. Thebiomechanicsofcoronarycirculationisintimatelyrelatedtothebloodsupply oftheheart(globally)aswellastotheinitiationofandprogressionofCAD(locally). Hence, there is a significant need for understanding coronary blood flow in both healthanddiseaseattheglobalandlocallevel.Thisbookisintendedtoaddressthis need by providing a comprehensive compendium on coronary circulation both globally, as it relates to blood perfusion of the heart muscle, and locally at the site v vi Preface of CAD initiation and progression. Furthermore, this is the first text to provide a distributiveanalysisofcoronarycirculationbasedondetailedmeasuredvasculature and mechanical properties. This book provides quantitative physiology of the coronary circulation, using biomechanics to couple structure with function. It pro- videsadetailedbiomechanicalsynthesisofcoronarycirculationbasedonadistrib- utiveanalysisofmeasuredpropertiesofthesystem(anatomy,mechanicalproperties, andboundaryconditions)thataddressesboththeglobalandlocalcirculations. This book, Coronary Circulation: Anatomy, Mechanical Properties, and Bio- mechanics, provides a quantitative description of the coronary vasculature and mechanicalproperties.Anumberofboundaryvalueproblemsaresolvedtoprovide analysesofcoronarybloodflowandstressdistributionthroughthecoronaryvascu- lature, e.g., longitudinal pressure and flow distribution, local bifurcation flow and stressanalysis,etc.Thebookconsistsofthefollowingchapters:(1)Biomechanics, (2) Morphometry of Coronary Vasculature, (3) Mechanical Properties and Micro- structure of Coronary Arteries, (4) Constitutive Models of Coronary Arteries, (5) Network Analysis of Coronary Circulation: Steady-State Flow, (6) Network Analysis of Coronary Circulation: Pulsatile Flow, (7) Scaling Laws of Coronary Vasculature,and(8)LocalCoronaryFlowandStressDistribution. Chapter1providesanoverviewofthebasicprinciplesofbiomechanicsincluding terminology, approach, conservation laws, and some numerical methods of solu- tions. It sets the framework for the biomechanical approach to understand the function of an organ (specifically the heart) in a quantitative manner. Chapter 2 focuses on the anatomy and morphometry of the coronary vasculature. It provides both the reductionist (reducing the system into its individual components) and integrationist (rebuilding the system from the individual components) approaches tounderstandthecoronaryvasculature.Chapter3usesthereductionistapproachto understand the material properties of the coronary vasculature; i.e., it provides the mechanicalresponse(orstress-strainrelation)ofindividualsegmentsofthecoronary vasculature. It also provides the microstructural vessel wall data that dictates the macrostructuralresponseofthevesselstoloading.Chapter4usestheintegrationist approach to synthesize the constitutive relation of the vessel wall. Both phenome- nological and microstructural constitutive laws are discussed. These mechanical measurements and mathematical formulations connect microstructure (e.g., elastin, collagen,groundsubstance,cells)tomacro-mechanics(e.g.,responsetomechanical load such as pressure, axial load, torsion). Chapters 5 (steady-state flow) and 6 (pulsatile flow) present network analysis of global circulation (pressure-flow rela- tion, perfusion, etc.) including models of coronary flow regulation. Analysis of coronary circulation is presented that includes the interaction between myocardial contractionandcoronarybloodflow.Chapter7presentsscalinglawsthatexplainthe design of the coronary vasculature. The principles of biomechanics are used to connectform(e.g.,geometryofvasculatureincludingdiameters,lengths,numbers) withfunction(e.g.,bloodvolume,flow).Finally,Chapter8presentslocalbloodflow mechanics and the resulting vessel wall stresses (e.g., shear stresses, intramural stresses). These analyses provide the mechanical culprits for the spatial propensity ofCADinitiationandprogression. Preface vii Biomechanics-based modelling, which couples form (i.e., the structure of coro- nary vessels) with function (i.e., coronary perfusion), is the major theme of this book. The mathematical models of coronary circulation are both informed and calibrated by experimental data to minimize ad hoc assumptions. The predictions of pressure, flow, shear stresses, and intramural stresses, among others, are also validatedagainst experimental data to provide confidence in the models for under- standing coronary physiology and pathology. In order to understand local flow patterns, the key equations representing conservation of mass, momentum, and energy are described and applied in the context of the coronary circulatory system asawhole,aswellasregionally.Thetechnicaldetails(includingmorphometricand mechanicaldataaswellasmathematicalanalysis)aresummarizedinappendicesfor the interested reader to avoid technical detraction from the main discussions. The distributive models of the coronary vasculature presented are based on actual measured anatomy and mechanical properties of the system as opposed to the “black box” approach of lumped models. These idealized lumped models lack the realanatomyormechanicalpropertiesofthesystem(i.e.,analogcircuitsthatdonot reflecttheactualdistributedvasculatureoritsmaterialproperties). This book is intended for bioengineers, physiologists, cardiologists, surgeons, andindustryengineerswhodesireaclearunderstandingofcoronarybloodflowfor furtherresearch,diagnostics,andtherapeutics.Althoughabalancedtreatmentofthe topicisattemptedwithnumerousreferencestootherworks,thereisanemphasison theworkconductedbymyresearchteamoverthepast25years.Myhopeisthatthis work can embrace and stimulate the next generation of scientists, bioengineers, researchers,andclinicianstocontinuetocontributetothisveryvitalareaofresearch to understand the coronary circulation and heart function. Moreover, a similar biomechanicalapproachmaybeusedbyresearcherstoformulateasimilarlydetailed systematicunderstandingofotherorgansandbodysystems. This work would not have been possible without the dedications and tireless efforts of numerous talented students, fellows, and collaborators over the past 25years. Thecoauthors,listed onmypublicationsinthereferencesection, aremy collaborators to whom I am greatly indebted. The knowledge presented in this book would not have been possible without their tireless efforts. I would also like to acknowledge my current team for their dedication and contributions (inalphabeticalorder):HenryChen,HuanChen,SusyChoy,BillCombs,AliDabiri, YaghoubDabiri,GregDick,FredField,LijuanFu,XiaomeiGuo,LingHan,Terry Hubbard, Carlos Labarrere, Xiao Lu, Bhavesh Patel, Mengjun Wang, and Yanmin Wang.AspecialthankstoProf.DhanjooGhistaandDr.AmySpilkinforthereview and critique of thechaptersand Martha Sanchez for technical assistance.Finally,I would like to thank Merry Stuber of Springer for her constant encouragement and commitment to this project and Maria David for shepherding this book to publication. viii Preface Thisbookisdedicatedtothememoriesofmyfather(SleewaKassab,1934–1967) whopassedawayyoungwhenIwasatoddler.Ihopetoinspiremychildren(Gabriel andGianno)asmyfather’smemoriesandcouragehaveinspiredme. SanDiego,CA,USA GhassanS.Kassab Contents 1 Biomechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 BasicTerminologyinBiomechanics. . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.3 Compliance,Stiffness,Distensibility, andYoung’sModulus. . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.4 Viscoelasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 StructureandGeometry. . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . 11 1.5 MaterialProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 LawsofMechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 BoundaryConditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.8 BoundaryValueProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.9 SolutionsofBoundaryValueProblems. . . . . . . . . . . . . . . . . . . 16 1.9.1 ComputationalFluidDynamics. . . . . . . . . . . . . . . . . . . 16 1.9.2 FiniteElementMethod. . . . . . . . . . . . . . . . . . . . . . . . . 18 1.9.3 Fluid–StructureInteraction. . . . . . . . . . . . . . . . . . . . . . 19 1.9.4 ALEFormulationforFluid–StructureInteraction. . . . . . 19 1.9.5 ImmersedBoundary(IB)Method. . . . . . . . . . . . . . . . . 20 Appendix1:DerivationofCircumferentialStress (Laplace’sLaw)andLongitudinalStressinaVessel. . . . . . . . . . . . . . . 21 Appendix2:ConstitutiveEquationofaHomogeneous, Isotropic,andLinearElasticSolid(Hooke’sLaw). . . . . . . . . . . . . . . . . 22 Appendix3:EquationsforFluidsandSolids. . . . . . . . . . . . . . . . . . . . 24 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 MorphometryofCoronaryVasculature. . . . . . . . . . . . . . . . . . . . . . 29 2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 CoronaryVasculature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 ix x Contents 2.3 ReductionofCoronaryVasculature. . . . . . . . . . . . . . . . . . . . . . 31 2.3.1 CastingMaterial. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. 32 2.3.2 AnimalandIsolatedHeartPreparation. . . . . . . . . . . . . . 32 2.3.3 PolymerCastofCoronaryVasculature. . . . . . . . . . . . . 32 2.3.4 HistologicalandCastSpecimens. . . . . . . . . . . . . . . . . . 33 2.3.5 MorphometricMeasurements. . . . . . . . . . . . . . . . . . . . 34 2.3.6 MathematicalDescriptionofBranchingPattern. . . . . . . 36 2.3.7 Diameter-DefinedStrahlerSystem. . . . . . . . . . . . . . . . . 38 2.3.8 MeshingofHistologicalandCastData. . . . . . . . . . . . . 39 2.3.9 SegmentsandElements. . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.10 ConnectivityMatrix. . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.3.11 LongitudinalPositionMatrix. . . . . . . . . . . . . . . . . . . . 42 2.3.12 AsymmetryRatios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.13 CountingTotalNumberofElements. . . . . . . . . . . . . . . 44 2.3.14 Arcade-LikeVessels:EpicardialVeins. . . . . . . . . . . . . 46 2.3.15 Network-LikeVessels:Capillaries. . . . . . . . . . . . . . . . . 47 2.3.16 DiametersandLengthsofCapillarySegments. . . . . . . . 47 2.3.17 TopologyofArteriolarandVenularZones andMeanFunctionalCapillaryLength. . . . . . . . . . . . . 48 2.4 Integrationof3DCoronaryVasculature. . . . . . . . . . . . . . . . . . . 50 2.4.1 Node-to-NodeComputerReconstruction ofCoronaryNetwork. . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.2 AnatomicalInputFiles. . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4.3 Statistical3DReconstructionofCoronary Vasculature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.4 ExistingDatabaseandAdditionalAssumptions. . . . . . . 52 2.4.5 ReconstructionApproach. . . . . . . . . . . . . . . . . . . . . . . 55 2.4.6 GeometricOptimization. . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.7 VerificationofCoronaryNetwork. . . . . . . . . . . . . . . . . 56 2.5 Non-treeStructures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.6 LaborSavingsinMorphologicalReconstruction. . . . . . . . . . . . . 58 2.7 Automation:SegmentationandCenterlineDetection. . . . . . . . . . 60 2.7.1 ImageProcessing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.7.2 SegmentationofVesselBoundary. . . . . . . . . . . . . . . . . 60 2.7.3 SegmentationUnderTopologicalControl. . . . . . . . . . . 60 2.7.4 CenterlineDetection. . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.7.5 VectorField.. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. 62 2.7.6 DeterminationofCenterlines. . .. . . . .. . . .. . . .. . . .. 62 2.7.7 GeometricReconstruction. . . . . . . . . . . . . . . . . . . . . . . 63 2.8 GridGeneration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.8.1 ElementQuality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.9 VisualizationofReconstructedNetwork. . . . . . . . . . . . . . . . . . . 67 2.10 Patient-SpecificCoronaryMorphometry. . . . . . . . . . . . . . . . . . . 68