Stephen J Payne
University of Oxford
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Library of Congress Cataloging-in-Publication Data
Names: Payne, Stephen (Of University of Oxford. Department of Engineering Science), author.
Title: Cerebral blood flow and metabolism : a quantitative approach / Stephen J. Payne.
Description: New Jersey : World Scientific, 2017. | Includes bibliographical references.
Identifiers: LCCN 2017026746 | ISBN 9789813220560 (hardcover : alk. paper)
Subjects: | MESH: Cerebrum--blood supply | Cerebrum--metabolism | Blood Flow Velocity--physiology | Cerebral Blood Volume--physiology | Cerebrovascular Circulation--physiology
Classification: LCC QP385.5 | NLM WL 307 | DDC 612.8/25--dc23
LC record available at https://lccn.loc.gov/2017026746
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Preface
Healthycerebralbloodflowandmetabolismarevitalforhumanwellbeing. Withanincreasinglyelderlypopulationworldwide,cerebrovasculardiseasessuchasstrokeanddementiapresentaverysubstantial,andgrowing, clinicalchallenge.Asjustoneexample,inEnglandandWalesdementia andAlzheimer’sdiseaseovertookcardiacdiseaseastheleadingcauseof deathin2015.Likewise,theimportanceofahealthycerebralvasculature andadequateperfusionisnowappreciatedacrossanincreasingrangeof cerebraldiseases,highlightinghowmaintaininghealthycerebralbloodflow andmetabolismarecriticalinpreventingoratleastdelayingmanycerebral diseases.
Thisbookaimstoprovideabroadintroductiontoallaspectsofcerebral bloodflowandmetabolism,fromthebasicphysiologytomathematical models,andfromthedetailsofmeasurementtechniquestotheirrole inclinicalpractice.Cerebralbloodflowhastendedtobeapproachedin asomewhatqualitativemanner,butthereisnowanincreasedclinical emphasisonquantitativemetricsthatcanbeusedbothinclinicalprotocols andguidelines,andinpersonalisedapproaches,suchasclinicaldecision supportandothermachinelearningtools.Thisbookthushasaparticular focuson quantitative cerebralbloodflowandmetabolism,sothatsuch measurementscanbeutilisedtotheirgreatestextent.
Asecondkeyfeatureofthisbookisthedrawingtogetherofawiderange ofknowledgeacrossavarietyofbothclinicalandtechnicalareas.Thebook issquarelyaimedatboth,helpingthetechnicalcommunitytoappreciate theuseofquantitativecerebralbloodflowandmetabolismmeasurements inclinicalpractice,andtheclinicalcommunitytoappreciatehowcerebral bloodflowandmetabolismcanbemeasuredandquantifiedinorderto helptoprovidepersonalisedinformationforuseinadecision-making
context.Thebookcomprisesfourpairsofchapters:Chapters1–2examine thephysiologyandmodelsofbloodflowandmetabolisminthebrain; Chapters3–4examinethecontrol,bothglobalandlocal,ofbloodflow andperfusion;Chapters5–6examinethewaysinwhichbloodflowand metabolismaremeasured;andChapters7–8examinehowcerebralblood flowandmetabolismareaffectedinphysiologicalandpathophysiological conditions.
Evenacursoryglancewillshowthatthereisanenormousliteratureon thistopic.However,despite(orpossiblybecauseof)this,therehasbeen littlepublishedinthelast10–15yearsthatprovidesabroadsummaryof thecurrentstate-of-the-artandhenceastartingpointforthosenewtothe fieldoraguideforthosewantingtobroadentheirunderstandingofavery diversefield.ReadingthenowclassictextsofEdvinsson etal.(1992)and EdvinssonandKrause(2002)onCerebralBloodFlowandMetabolism veryclearlypointsouttheenormousprogressthathasbeenmadeinthis fieldacrossmanyareasoverthistime.Thesevolumesremainenormously informative(ifnowincreasinglydifficultandexpensivetoobtain),butitis nowtimeforanewbookthatemphasisesthe quantitative approachesto thissubjectactingasacomplementarytexttotheseother,predominantly qualitative,volumes.
Inevitably,thebookremainsonlyapartialcoverageofanenormously broad(andfascinating)subject;itissimplynotpossibletocoverevery aspectinfulldetailwithoutcompilinganencyclopaediaandsoitishoped thatnoreaderwillfeeltoodisappointedifaparticulartopicisskipped overorcoveredonlysuperficially.Evenonthetopicscoveredhere,itis notpossibletociteeveryrelevantstudythathasbeencarriedout;themore than900referencesthatareincludedinthisbookshould,however,provide agoodstartingpointforfurtherreading.Attimes,ithasindeedfeltlike ‘tacklingthejungle’soaptlydescribedinEdvinssonandKrause(2002), soitishopedthatthisvolumedoesatleastprovidesomepathswithinthe forest.
Therehavealsobeenmanychangestoourunderstandingofcerebral bloodflowandmetabolisminthelast10–15years.Tocitejusttwo examples,theroleofthecerebralvasculatureindementia,particularly inAlzheimer’sdisease,whichwastraditionallythoughttobesecondary toamyloidplaques,isnowmoregreatlyappreciated,andthechangesin venouscerebralbloodvolumethatwerethoughttodrivethefunctional
BOLDresponsetoactivationhavebeenfoundtobenegligible.Bothof theseexamplesservetohighlighttheenormousadvancesthathavebeen madeinbrainimagingthathaveopenedupnewavenuesforexploration. Thisnewbookthusaimstoprovideastagingpostinourcontinuingjourney towardsafullunderstandingofcerebralbloodflowandmetabolism,one thatcanhopefullybewidelyusedtohelptodrawtogetheraverydisparate fieldinawaythatwillhelpbothresearchersandclinicianstounderstand thefieldmoreclearly.
Itshouldbenotedthatthefocusofthisbook,whichwillalsosetitapart fromothersources,isprimarilyandintentionallyonhumanstudies.There havebeenverymanyexcellentstudiesinawiderangeofanimalmodels, butthereisnowaverysubstantialliteratureoncerebralbloodflowand metabolisminhumans.Ofcourse,thereremainmanyareasinwhichanimal modelshaveyieldedvaluableinsights,particularlywhendataarenoteasily obtainableinhumansubjects.However,thepoortranslationratebetween animalmodelsandhumansubjectshasbeenacknowledgedformanyyears, seeforexampleAaslid etal.(1991),andmanytherapiesthathavebeen foundtobeverypromisinginanimalmodelshavecompletelyfailedto translateintoclinicalbenefit(Kidwell etal.,2001).1 Ifwearetoimprove thecurrentlyverylimitedrangeoftherapiesavailableforcerebrovascular disease,thenwewillneedtomakeuseofhumanstudiesasmuchaspossible, withanimalmodelshelpingtoinformsuchstudies,butperhapswithamore realisticviewofwhatcanbedirectlytranslatedfromthemintoclinical practice.
Thecentralimportanceofbloodflowandmetabolisminthehealthy functioningofthehumanbrainandtheincreasingclinicalimportanceof cerebrovasculardiseasethusprovideourdualmotivationforunderstanding betterhowcerebralbloodflowandmetabolismbehaveandhowtheyare affectedinmanyphysiologicalandpathophysiologicalconditions.Only bydoingsocanwehelptoimproveclinicaloutcomesandcontributeto improvedpublichealth,amelioratingwhatcanoftenbethedevastating effectsofcerebrovasculardisease.Thatmustremainourprimarygoal.
1 Thisisdescribedasa“generallydismalrecord”andisnotfoundinmostotherareasof medicine.
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Introduction
Thebrainisahighlycomplexdynamicsystemthatreliesonasufficient andcontinuoussupplyofoxygenandglucosetomaintainhealthyfunction underawiderangeofdifferentconditionsandinresponsetomanydifferent internalandexternalstimuli.Astoppageinthissupplywillleadtocelldeath withinafewminutes.However,theprocessesthatgoverncerebralblood flowandmetabolismareconceptuallyrelativelystraightforward.Theheart pumpsoutoxygenatedblood,whichenterstheneckandthenthehead. Throughanetworkofbloodvesselsthatreacheswithintensofmicrometres ofeverycellinthebrain,everypartofthebrainiscontinuouslysupplied withnutrients,whilstthemetabolicwasteproductsaretransportedbackout forreprocessing.Thereisaverytightmatchbetweenthesupplyofblood andthedemandsofmetabolism,withflowcontinuallyadjustedinorderto respondtobothshorttermandlongtermchangesinlocalmetabolism.
Ahighlysimplifiedhigh-levelschematicoftheinteractionbetween thekeyvariablesisshowninFigure1.Thedifferencebetweenarterial bloodpressure(ABP)andintracranialpressure(ICP)istermedcerebral perfusionpressure(CPP):itisthisthatisthedrivingforcethatprovides cerebralbloodflow(CBF),sincevenousbloodpressureisnormallyclose toICP.Theamountofperfusionthatreachesthevascularbediscontrolled bytheresistanceofthecerebralvasculature.Thisisadjustedbyanumber ofmechanismsthatcanberoughlydividedintothemyogenicresponse,the metabolicresponseandthesympatheticresponse.Themyogenicresponse isgovernedbybothCPPandlevelsofcarbondioxideinthebloodstream: asaresult,thevasculatureadjustsperfusioninresponsetoboth,givingrise tobothautoregulationandcerebrovascularreactivityrespectively.CBF iscloselyrelatedtocerebralbloodvolume(CBV),which,inconjunction withchangesincerebrospinalfluid(CSF),controlthepressurewithinbrain
Figure1. Schematicofinteractionsbetweenmaincerebralvariables. tissue(thisiswhatistermedICP)duetotheincompressibilityofwaterand therigidconfinesoftheskull.
Theproductofcerebralbloodflowandarterialoxygenconcentration givesthesupplyofoxygentothebrain;thedifferencebetweenthissupply andthemetabolicdemandsofthebrainalsocontrolsCBFthroughchanges invascularresistanceaspartofthemetabolicresponse.Themyogenicand metabolicresponsesare,ofcourse,notindependent,andchangesinany onevariablewillaffectallaspectsofthecerebralvasculature’sbehaviour. Finally,thesympatheticresponseactsthroughthecentralnervoussystem withatwincoordinationandover-riderole.Itshouldbenotedthatevery componentofthishighlysimplifieddiagramcomprisesacomplexsystem initself,withmultiplepathwaysandmanyinteractionsexistingbetween thesedifferentcomponents.Itdoesthusservetohighlightthecomplexity ofthesystemandwewillexploreallofthecomponentsindetailaswe progressthroughthisbook.
Thetightcouplingbetweenstructureandfunctionfoundinthebrain ispartlytheresultofthefactthatthebraincanstoreverylittleoxygen andglucoseandisthusheavilydependentuponnutrientsupplyviathe bloodstreamatallpointsinspaceatalltimes.Despitethisseeminglack ofreserve,thebrainisinfactremarkablyrobustinresponsetochanges, mirroringthefactthatitissowellprotectedphysicallybytheskull. Thepresenceofcollateralflowvesselsandthehighdegreeofcontrol ofbloodflowatbothlocalandglobalscalesmeanthatbloodflowis maintainedatnearconstantlevelsdespiteavarietyofchanges.Theclassical pictureofthisistheLassencurvethatshowshowcerebralbloodflowis
maintainedatnearconstantlevelsdespitelargechangesinABPthroughthe mechanismscollectivelyknownascerebralautoregulation.Evenlargelocal interruptionstobloodflowthatcauseneuronaldeathinspecificregionsof thebraincanstillhavetissuesalvagedaftermorethan4hours(the‘window ofopportunity’afterischaemicstroke).
Itisworthnotingtwopointsaboutbloodflow,however,rightat thestart.First,althoughcerebralbloodflowisakeyparameterinthe behaviourofthebrain,itdoesremainfundamentallyonlyasurrogate measureforthedeliveryofnutrientstocerebraltissue.Asinmanyother physiologicalcontexts,whatwecanmeasureisnotexactlywhatismost important.Second,althoughwehaveusedtheterms bloodflow and perfusion somewhatinterchangeablythusfar,wewillinfactmakeaclear distinctionbetweenthetwo.Theformerisused(havingunitsofvolumeper unittime,typicallyml/s)fortheflowpassingthroughparticularvessels, whereasthelatterisused(havingunitsofvolumeofbloodpervolumeof tissueperunittime,typicallyml/100g/min)fortheflowpassingthrough avascularnetworkwithinadefinedvolumeoftissue.Crudely,theformer deliversbloodoverlargedistancestoprovidetissuewiththelatter.Itis largelyperfusionthatisconsideredtocontrolthesupplyofnutrientsto andtheremovalofmetabolicwasteproductsfrombraincells,withblood flowinlargevesselsdeterminingthesupplytoparticularregions.We willre-examinethisdistinction,however,inthecontextofmodelsand measurementsofbothlater.
Theeightchaptersofthisbookarepresentedinfourpairs.InChapters1 and2wewillexaminetheanatomyofthecerebralvasculatureandmodelsof bloodflowandmetabolismrespectively,asthesesetthefoundationsforthe laterchapters.InChapters3and4wewillexaminefirsttheglobalcontrolof bloodflow(i.e.bloodflowtothewholebraininresponsetoexternalstimuli) beforeconsideringthelocalcontrolofperfusion(i.e.bloodflowwithina particularregioninresponsetointernalstimuli).InChapters5and6we thenturnourattentiontomeasurementsofbloodflowandperfusionaswell asmetabolism.InChapters7and8wefinallyexaminehowcerebralblood flowandmetabolismbehavein‘normal’physiology(i.e.theeffectsof,for example,ageing,fitnessandtemperature)andin‘abnormal’physiology(i.e. diseasestatessuchasstrokeanddementia).Thereareover900references citedoverthecourseofthebook,whichprovideastartingpointforfurther reading:itisworthnotingthattherehavealsobeenmanyexcellentreview
paperspublishedwithinthelastfewyears,whicharehighlightedwhere appropriate.
Anotherconsiderationwhenexaminingcerebralbloodflowand metabolismisthatthereareverynoticeablesimilaritiesbetweenthebrain andotherbodyorgans,intermsofthevascularstructureandtheresponseto stimuli.Possiblythemostobviousparalleliswiththecoronarycirculation, i.e.thosevesselsthatperfusethecardiacmusclethatdrivestheheart. Thisisofparticularinterestasthemodellingofcoronarybloodflow andmetabolismismoreadvancedthanthatofcerebralbloodflowand metabolism;manymathematicaltoolscanbeappliedinbothcontextsand therehavebeensomeelegantexamplesoftechniquestranslatingfromone contexttotheother.
Therearehoweverobviousdifferences,withtheskullimposinga limitationonbothbloodflowmechanicsandwhatcanbemeasuredin waysthatarenotthecaseinotherorgans.However,modellingoftheheart hasledthewayintheuseofmodelswithinaregulatoryframework,as wewillexaminebelow.Thispioneeringworkhasclearlydemonstratedthe valueofpatient-specificmodelsandthisisanareainwhichmodelsofthe cerebralvasculaturehavemuchtoofferinthefutureinunderstandinghow individualpatientsrespondtotreatmentandhencehelpingtooptimiseboth thediagnosisandtreatmentofindividualsubjects.
Clinicalpracticeandtrends
Theclassicclinicalcontextofcerebralbloodflowandmetabolismisstroke, bothischaemic(‘block’)andhaemorrhagic(‘bleed’).Althoughdependent upontheexactpopulationbeingconsidered,therelativeincidenceis approximately85:15,withthesubstantialmajorityofstrokesbeingcaused bytheblockageofamajorbloodvesselresultinginhypoperfusiontoa regionofbraintissue;withoutrapidreperfusionsignificantcelldeathcan occur,withasubstantialimpactonsubsequentqualityoflife.Conversely, thelattertypeiscausedbythereleaseofbloodfromabloodvesselinto theinterstitialspace.WithintheUK,approximately100,000peoplehave astrokeeachyear.
Therelativerateofstrokehasinfactfallenoverthelastfewdecades, withbothreducedstrokeincidenceandlowerfatalityrates.Thisappears tobeprimarilyduetotheloweringofbloodpressureinthegeneral
populationduetoeffortstocontrolhypertensionthathavebeenon-going sincethe1970s,althoughthecontrolofdiabetesandattemptstotacklehigh cholesterollevelsandtoreducesmokingratesalsoseemtohaveplayeda part(Mozaffarian etal.,2016).By2013strokehadfallentothefifthleading causeofdeathintheUSA,withthenumberofdeathsfromstrokefalling by18.2%injust10yearsfrom2003–2013;thiseffectismostnotablein theelderly.
However,whathasbecomeamuchmorecommoncerebraldiseaseis dementia,ofwhichthemostcommonformisAlzheimer’sdisease(AD). Itwasreportedrecentlythatdementiahadovertakencardiacdiseaseas theleadingcauseofdeathinEnglandandWales,partlyduetoreductions incardiacdiseaseandpartlyduetoimproveddiagnosisofdementia,as wellastheincreasedlongevityofthepopulation.WithintheUKalone, approximately850,000peoplehavedementia,withover60,000deathsdue todementiainEnglandandWalesin2015,comparedtoaround35,000 deathsduetocerebrovasculardisease(OfficeofNationalStatistics,2016). Thechangesincausesofdeathforbothmenandwomenareshownin Figure2overtheperiod2001–2015;theimprovementsinischaemicheart diseaseandstrokeratesareveryclearlyseen,asaretherisesinratesof deathduetodementiaandAlzheimer’sdisease.Althoughthetrendsarethe sameformenandforwomen,itisalsoworthnotingthattherearevery notabledifferencesintheabsoluteratesbetweenmenandwomen,partly duetothedifferencesinthepopulationdemographics.
Inthecontextofcerebralbloodflowandmetabolism,theclassical understandingofAlzheimer’sdiseaseasbeingessentiallyanon-vascular diseasedrivenbytheformationofamyloidplaqueshasbeenwidely challengedrecentlyanditisnowmoregenerallyacceptedthatvascular factorsplayasignificantroleinbothAlzheimer’sdiseaseandvascular cognitiveimpairment.Theevidencebaseforthiswillbeexaminedin moredetailinChapter8,buttheimportanceofthecerebralvasculature indementiaisnowmorefullyappreciated,witharesultingincreased clinicalinterestincerebralbloodflowinthiscontext.Howquantitative measurementsandmodelsofcerebralbloodflowandmetabolismcanassist indiagnosisandinthedevelopmentoftherapiesthataimtoamelioratethe effectsofdementiaremaintobeseen,butthisisanareaofgreatpotential forthefuture.
Death rate (men) in England and Wales
Death rate (women) in England and Wales
Ischaemic heart diseases
Cerebrovascular diseases
Chronic lower respiratory diseases
Lung cancer
Ischaemic heart diseases
Cerebrovascular diseases
Chronic lower respiratory diseases
Lung cancer
Figure2. Ratesofdeathfortheperiod2001–2015inEnglandandWales,figurestaken fromtheOfficeofNationalStatistics(2016).
Roleofmodelsandtheregulatoryprocess
Akeypartofthisbookistoexaminecriticallyandtosetoutthestatus ofmodelsofcerebralbloodflowandmetabolism.Thishasbeenlargely
overlookedinprevioussummariesofthefield:forexampleEdvinsson andKrause(2002)makealmostnomentionofmodelsofbloodflow. Althoughthishasbeenpartlyduetotherelativelyelementarystate oftheartinthisareaandthelimitationsthatareimposedbythe difficultiesinobtainingaccuratevaluesofmodelparameters,therehas infactbeenagreatdealofworkperformedindevelopingmodelsof cerebralbloodflowandmetabolismoverawiderangeoflengthandtime scales.
Itisthusnowpossibletoconsiderafull3-Dmodelofcerebralflow, basedonaccurateanatomicalinformationonapatient-specificbasis.As clinicianscontinuetofocusonpatient-specifictherapies,suchpersonalised modelshavepotentiallyaverysignificantroletoplay,astheyhaveinother clinicalscenarios.Substantialchallengesremaintobeovercome,butsuch modelsarenowwithintheboundsofthepossible.Oneofthedifficulties, ofcourse,isthesheercomplexityofthesemodelsandthevarietyof differentapproachesthatcanbeadopted;thisdoesmakethefieldsomewhat inaccessibletothenon-specialist.Therehasalsobeenagreatdealofwork performedinseparatecommunitiesonsimilarmodels,withoutmuchcrossoverbetween,forexample,modelsofautoregulation,reactivityandneural activity,despiteobviouscommonalities.
However,theworkthathasbeenperformedincardiacmodellingand itsusewithinaregulatorycontextdoesprovideanincentiveforfuture workinthisarea.Therehasbeenagreatdealofworkperformedinthe lastfewyearsandbothintheUSAandintheEU,modellingisnow appreciatedasanintegralpartofthisevidencebase.IntheUSA,theFDA nowregardsmodellingandsimulationasapotentialadditionalcomponent to‘validscientificevidence’andhaspublishedguidelinesforthereporting ofcomputationalmodellingstudiesinthesubmissionofmedicaldevices. IntheEU,theVirtualPhysiologicalHuman(VPH)project,buildingupon thePhysiomeproject,wasfirstformulatedinaroadmapin2007andnow hasasubstantialcommunityofresearchers.Thisputsthefieldofmodelling squarelywithinthemorewell-establishedproceduresthatplayapartinthe regulatoryprocess.Modellinghasmuchtoaddtothisfieldinwaysthat havenotbeenfullyappreciatedinthepast.
ThekeyconceptinthisisVVUQ(verification,validationanduncertaintyquantification).Althoughtherearewell-establishedtoolsforallthree ofthesecomponents,theirapplicationtophysiologicalmodelscanbe
extremelydifficult,becausethemodelsareintrinsicallyhighlycomplex withlargenumbersofmodelparametersandfewexperimentaldatafor validation.Greatcarehastobetakentodeveloptoolsthatareoptimal forsuchapplications,particularlygiventheneedforthepredictionof uncertaintyintheoutputs.Thisisanactiveareaofresearchincardiac modellinganditwouldbehopedthatcerebralmodellingwouldbeableto learnfromthesemethodsandtechniques.Therearenowproceduresthat havebeenpublishedbytheAmericanSocietyofMechanicalEngineers (ASME)viatheirV&V40verificationandvalidationincomputational modellingofmedicaldevicescommittee,withtheaimbeingtostandardise bothverificationandvalidationprocedures.Thesewillhelptoguide researchersbyprovidinginformationonhowmuchVVUQisrequiredto supportusingamodel.Wewillnotexaminethesetoolshereinanyfurther detail,asthisisahighlytechnicalsubject:however,itremainsanimportant issuetobearinmindintheapplicationofmodels.
Inthiscontext,theuseofpopulation-averagedparametervaluesasthe defaultsettingforamodelthatisthenappliedtothewholepopulation isnowunderstoodtobeover-simplistic.Therehasthusbeenincreased focusontheuseof‘virtualpopulations’wherethevariabilityinmodel parametervaluesisquantifiedanda‘virtualpopulation’iscreatedbased onsamplingfromtheseparametervaluedistributions.Eachresultistermed a‘virtualpatient’2 Thiskeyideaisbasedontheincreasedunderstandingof variabilitywithinaveryheterogeneouspopulation.Thefactthatnearlyall modelsarestronglynon-linearrelativetotheirparametervaluesmeansthat theresultscanbeverysubstantiallydifferentfromwhatmightbeexpected. Thereare,ofcourse,difficultieshereintheestimationofparametervalue distributions,butthisisaroutethatwillneedtobeexploredincreasingly inthefuture.
In2010,theFDAreleasedguidanceabouttheuseofpriorinformation inclinicaltrialdesign,basedonBayesiantechniques.Bydoingthis,itis possibletodecreasetherequiredsamplesizeandtriallengthforthesame outcomes:suchpriorknowledgecanbeeitherhistoricaldataorvalidated
2 http://mdic.org/computer-modeling/virtual-patients.
models.Anymodelsusedaspartofthisprocess,however,mustpredictnot justsafetyand/oreffectivenessbutalsotheuncertaintyintheprediction. Itisimportanttorealisethereforethatbothphysiologicalmodelsand probabilisticmodellingareneededtomakeaclinicallyrelevantprediction.
Scopeofthebook
Oneofthedifficultiesinvolvedinwritingadeliberatelybroadbooksuch asthisistheneedtochoosewhattoincludeandwhatnottoinclude,alsoto decideonwhatcanbeassumedasbackgroundknowledge.Althoughitis hopedthatthephysiologywillbeexplainedfromarelativelybasicstarting pointthatcanbeassumedformostreaders,itisnotpossibleinabook ofthissizetoexplainallofthefundamentaldetailsofthemathematical techniquesthatareused;ratheritisassumedthatthereaderhasabasic knowledgeofalgebraandcalculusinordertounderstandthemodelsthat arepresentedhere.Neitherisitpossibletocoverallofthephysicalconcepts thatunderpinmanyoftheapproachesadoptedwithoutmakingthebook over-lengthy.Thereareexcellentalternativesourcesforthisbackground detail,forexample‘TheMechanicsoftheCirculation’byCaro etal.(2012), whichprovidesaverysolidgroundinginsuchtechniques.
Itshouldalsobenotedthatwewillnotdescribeinanydetailthe numericaltechniquesthathavebeenusedtoimplementmodels;rather wepresentonlythegoverningequations,againforreasonsofspace andbecausethenumericalimplementationofphysiologicalmodelsisa substantialtopicinitsownright.Readerswishingtoimplementaparticular modelarereferredfirsttothepublicationinwhichthemodelisdescribed, wheredetailsarenormallygiven.Therearealsospecialisttextsthatprovide excellentcoverageofnumericaltechniques,seeforexampleLeVeque (2002,2007).
Sincethefocusofthebookisoncerebralbloodflowandmetabolism, wearealsoignoringmanyotheraspectsofbrainbehaviour.Wewill onlyexaminethetransportofwaterinthebrainverybrieflyandwillnot consideranymechanicalaspectsofbraintissueanditsmovement,seefor exampleCowinandDoty(2007).Wewillnotexaminethegeneticbasis ofanyaspectsofbrainbehaviour,norwillweconsidermanyaspectsof neuroscience.Allofthesetopicsarehighlyimportantandinterestingintheir
ownright,butintheinterestsoflengththeywillnotbeconsideredhere. Thereisanenormousliteratureonthebrainandthisbookwilldeliberately focusspecificallyonbloodflowandmetabolism.Thereaderisstrongly encouraged,however,tocontinuetheirreadingaroundthetopictogaina broaderappreciationofthebrain’sstructureandfunction.
1.5.3Arachnoidbarrier
Chapter2.ModelsofBloodFlowandMetabolism43
2.1PoiseuilleEquation
2.2Viscosity ........................45
2.2.1Empiricalrelationshipsforviscosity .....45
2.2.2Model-basedpredictionsofviscosity
2.2.3Conclusions
2.3One-dimensionalBloodFlow
2.3.1Waveflow
2.3.2Linearised1Dmodels
2.3.3Womersleyflow ................61
2.3.4Non-axisymmetricflow
2.3.5Conclusions ..................68
2.4FlowinVascularNetworkModels ..........68
2.4.1Networkflowmodels
2.4.2Scalinglaws
2.4.3Conclusions
2.5ModelsoftheCerebralVasculature
2.5.1Modelsofthelargearterialvessels
2.5.2Modelsofthemicrovasculature
2.5.3Fullcerebralvasculaturemodels
2.5.4Conclusions ..................98
2.6TransportandMetabolism ...............99
2.6.1Governingequations
2.6.2Transportfrombloodtotissue
2.6.3Oxygenrelationships
2.6.4Conclusions
2.7ParameterFittingandSensitivityAnalysis
2.7.1Parameterfitting
2.7.2Sensitivityanalysis
2.7.3Modelsimplification
2.8Conclusions
Chapter3.GlobalControlofBloodFlow117
3.1Autoregulation
3.1.1Mechanismsofautoregulation
3.1.2Quantificationofautoregulation ........123
3.1.2.1Staticautoregulation
3.1.2.2Dynamicautoregulation .......125
3.2CerebrovascularReactivity ..............132
3.2.1MechanismsofCVR
3.2.2QuantificationofCVR ............134
3.2.3InteractionbetweenautoregulationandCVR.139
3.3ModelsofAutoregulationandCVR ..........140
3.3.1Lumpedcompartment + feedbackmodels..140
3.3.2Singlevesselmodels .............146
3.4Conclusions ......................155
Chapter4.LocalControlofPerfusion157
4.1NeurovascularCoupling ................157
4.1.1Physiologicalbasis
4.1.2Conductedresponse ..............167
4.1.3Brainmetabolism
4.2NeurogenicControl
4.2.1Physiologicalbasis
4.2.2Originsofcontrol
4.3ModelsofNeurovascularCoupling
4.3.1Lumpedcompartmentalmodels ........179
4.3.2Cerebralbloodvolume ............185
4.3.3Networkmodels ................188
4.3.4Nitricoxide ..................193
4.3.5Cellularmodels ................198
4.3.6Conclusions ..................201
4.4AngiogenesisandAdaptation
4.5Vasomotion
4.6Conclusions
Chapter5.Externally-basedMeasurements215
5.1Ultrasound
5.1.1Reproducibility ................219
5.1.2Insonationarea ................219
5.1.33DUltrasound .................222
5.2OpticalImaging
5.2.1Nearinfra-redspectroscopy(diffuseoptical spectroscopy)
5.2.2Diffusecorrelationspectroscopy .......233
5.2.3Otheropticalmethods
5.3Electroencephalography(EEG)
5.4Conclusion
Chapter6.Internally-basedMeasurements243
6.1DevelopmentofCBFMeasurements
6.2TracerKineticTheory
6.2.1Singlecompartmentmodel ..........249
6.2.2Twocompartmentexchangemodel ......251
6.2.3Spatiallydistributedcompartmentmodels..253
6.2.4Deconvolutionmethods ............253
6.2.5Conclusions ..................255
6.3ComputedTomography(CT)
6.4SinglePhotonEmissionCT(SPECT)
6.5PositronEmissionTomography(PET)
6.6MagneticResonanceImaging(MRI)
6.6.1DynamicSusceptibilityContrast(DSC)/ DynamicContrastEnhancement(DCE)MRI.265
6.6.2ArterialSpinLabelling(ASL) .........267
6.6.3Vessel-encodedASL ..............273
6.6.4Perfusionquantification
6.6.5 CMRO2 quantification .............279
6.6.6OtherusesofMRI
6.7Conclusions
Chapter7.GlobalChangesinCerebralBloodFlow
7.1Ageing
7.1.1Autoregulation
7.1.2Cerebrovascularreactivity
7.1.3Cerebralmetabolicrate
7.2Hypertension
7.6.1Autoregulation
7.6.2Cerebrovascularreactivity
