Citation
Verification and Validation of the Hybrid Pulmonary Gas Exchange Model of the Human Patient Simulator

Material Information

Title:
Verification and Validation of the Hybrid Pulmonary Gas Exchange Model of the Human Patient Simulator
Creator:
Wehry, Hillary A
Publisher:
University of Florida
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
VAN OOSTROM,JOHANNES H
Committee Co-Chair:
O'DELL,WALTER G
Committee Members:
WHEELER,BRUCE
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Alveolar consonants ( jstor )
Carbon dioxide ( jstor )
Hantavirus pulmonary syndrome ( jstor )
Lungs ( jstor )
Mathematical variables ( jstor )
Modeling ( jstor )
Oxygen ( jstor )
Simulations ( jstor )
Software ( jstor )
Ventilation systems ( jstor )
hps
simulation

Notes

General Note:
The Human Patient Simulator (HPS), developed at the University of Florida and manufactured by CAE Healthcare Inc., Montreal, Canada, provides a platform for immersive medical training. Patient responses to typical clinical scenarios are simulated by physiologic models, and trainees interact with the simulator to evaluate clinical signs and monitored signals and provide therapeutic interventions. Such physiology based simulators are complex, dynamical systems and are challenging to evaluate. The HPS contains two models of pulmonary gas exchange (PGE) based on the same underlying conceptual model: a mathematical model implemented in software only, and a hybrid model implemented with hardware and software components. A reference software implementation based on the same conceptual model and acting as a 'gold standard' was developed as part of a previous project and used to evaluate the software implementation of the HPS lung. This thesis project expands the method for verification and validation of simulation models and applies it to the hybrid HPS PGE model. We designed and implemented the control software for a hybrid 'benchtop' implementation consisting of HPS PGE model hardware. Simulation of the physiological operating point demonstrated a moderate discrepancy in simulated partial pressures of oxygen and carbon dioxide in the alveolar space between the hybrid model and the reference standard. We formulated hypotheses for the origin of these discrepancies. Simulation of dynamic experiments reflecting extreme physiological situations, such as apnea, demonstrate the physical limitations of the hybrid lung model, which can be attributed to a specific gas flow rate in the lung model. Both observations are expected to lead to optimizations and improvements of the hybrid lung model. The overall verification and validation method was presented in an invited lecture at an international conference.

Record Information

Source Institution:
UFRGP
Rights Management:
All applicable rights reserved by the source institution and holding location.
Embargo Date:
8/31/2016

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VERIFICATIONANDVALIDATIONOFTHEHYBRIDPULMONARYGAS EXCHANGEMODELOFTHEHUMANPATIENTSIMULATOR By HILLARYA.WEHRY ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2014

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c 2014HillaryA.Wehry

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Tomyparents,MarkandLauraWehry

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ACKNOWLEDGMENTS Firstandforemost,IsincerelywanttothankDr.JohannesHansvanOostromfor hisunwaveringguidanceandsupport.Withouthistechnicalassistanceanddedicated involvement,thisthesiswouldhaveneverbeenpossible.Inadditiontosponsoringmy researchassistantship,hegenerouslysupportedmyinvitationtospeakatthe20th AnniversaryMeetingofSESAMSocietyinEuropeforSimulationAppliedtoMedicine inPoznan,PolandinJune2014.Iamsofortunateforandappreciativeofhisexemplary mentorshipduringthisperiodofintensepersonalandprofessionalgrowth.Throughhis guidance,Ifeelpreparedtopursuealifelongcareerinscienceandengineering. IespeciallywanttothankDr.WillemvanMeursforhismodelingconsultationsand support.Hisfeedbackanddiscussionswereinstrumentalinthedevelopmentofthiswork. IalsowishtothankDr.WalterO'DellandDr.BruceWheelerforhavinggraciously agreedtoserveonmysupervisorycommittee. IwouldliketothanktheacademicstaintheUFDepartmentofBiomedical Engineering,includingTinyMcDonald,AndreaFabic,RuthMcFetridge,DiDampier, andDawnSmith,fororchestratingmycombineddegreeandtimelygraduationinthewake ofceaselessadministrativehurdles. Noneofthisworkwouldhavebeenpossiblewithoutthegenerousnancialsupport fromDr.vanOostrom,theUFOceofResearch,theUFDepartmentofBiomedical Engineering,andCAEHealthcare,Inc.Thankyouforallofyourcontributions. Lastly,Iamsothankfulforthepersonalsupportofmyfriendsandfamilyoverthe pastveyearsattheUniversityofFlorida.Thisdegreehasrequiredmorethanacademic support,andIhavemanypeopletothankforlisteningtoand,attimes,toleratingmeand myordeals.Icannotbegintoexpressmygratitudeandappreciationfortheirfriendship. Thisthesisisatestamenttotheirunconditionalloveandencouragement. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS.................................4 LISTOFTABLES.....................................6 LISTOFFIGURES....................................7 ABSTRACT........................................8 CHAPTER 1INTRODUCTION..................................10 1.1TheHumanPatientSimulatorHPS.....................10 1.2IntroductiontoVericationandValidationofSimulationModels.....11 1.3UseofaReferenceImplementation......................12 1.4ProjectAim...................................13 2METHODOFCOMPARISON...........................14 2.1OverviewofHPSandReferenceImplementations..............14 2.2DesignofReferenceImplementation......................15 2.2.1ModelRequirements..........................17 2.2.1.1SimpliedlungmechanicsLM...............18 2.2.1.2PulmonarygasexchangePGE...............19 2.2.2PGEConceptualModel.........................21 2.2.3MathematicalModels..........................22 2.2.3.1DerivationofLMmodelequations.............22 2.2.3.2DerivationofPGEmodelequations.............25 2.2.4SoftwareImplementation........................27 2.3VericationProcessoftheReferenceSoftwareImplementation.......31 2.3.1SpecicationVerication........................31 2.3.2CodeVerication............................32 2.3.3CrossVericationwithAnalyticalSolutions..............32 3HYBRIDBENCHTOPMODEL..........................34 3.1ModelRequirements..............................34 3.2ConceptualModel................................35 3.3ImplementationoftheHybridModel.....................37 3.4DesignoftheBenchtopControlSystem....................41 3.4.1Andros4700GasAnalyzerCommunication..............41 3.4.1.1Communicationhardware..................41 3.4.1.2Softwarecommunicationprotocol..............43 3.4.2MassFlowControllersMFCs.....................47 3.5DierencesbetweentheHPSHybridandtheHybridBenchtop.......49 5

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4EXPERIMENTDESIGNANDRESULTS.....................51 4.1ConstantExperimentalConditions......................51 4.1.1LungMechanics.............................51 4.1.1.1Minuteventilation......................51 4.1.1.2Respiratorywaveform....................52 4.1.2PulmonaryGasExchange.......................52 4.2DescriptionoftheScenariosforComparison.................53 4.2.1Scenario1:NormalVentilationandNormalCirculation.......54 4.2.2Scenario2:VentilatoryArrestandNormalCirculation.......54 4.2.3Scenario3:NormalVentilationandCirculatoryArrest.......55 4.2.4Scenario4:SimultaneousVentilatoryandCirculatoryArrest....56 4.3SimulationResults...............................57 4.3.1Scenario1:NormalVentilationandNormalCirculation.......57 4.3.2Scenario2:VentilatoryArrestandNormalCirculation.......59 4.3.3Scenario3:NormalVentilationandCirculatoryArrest.......61 4.3.4Scenario4:SimultaneousVentilatoryandCirculatoryArrest....62 4.4DiscussionofSimulationResults........................64 4.4.1DiscrepanciesandSystemLimitations.................64 4.4.2CriticalModelingAssumptionsandGeneralConsiderations.....67 5CONCLUSIONSANDFUTUREDIRECTIONS..................70 5.1Conclusions...................................70 5.2RecommendationsforFutureWork......................70 APPENDIX:ANDROS4700COMMANDANDRESPONSEFORMATS.......72 REFERENCES.......................................73 BIOGRAPHICALSKETCH................................74 6

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LISTOFTABLES Table page 2-1InputandoutputvariablesoftheLungMechanicsmodel.............19 2-2PGEmodelrequirements...............................20 2-3CharacteristicparametersoftheLungMechanicsmodelusedinthereference MATLABimplementation[5]............................23 2-4StatevariablesofthePGEmodelusedinthereferenceMATLABimplementation25 2-5SummaryofequationsusedtoimplementLMmodelinMATLABreference...28 2-6SummaryofequationsusedtoimplementPGEmodelinMATLABreference..28 2-7ProcessofVerication,adaptedfrom[5]......................31 3-1InputandOutputVariablesoftheHardwareComponentsoftheHybridBenchtop PGEModel......................................35 3-2InputandOutputVariablesoftheSoftwareComponentsoftheHybridBenchtop PGEModel......................................35 3-3CommunicationDB9ConnectionsoftheAndros4700GasAnalyzer.......42 3-4Andros4700GasAnalyzerInitializationProtocol.................44 3-5DataReportingRangeandResolutionoftheAndros4700GasAnalyzer....47 4-1CharacteristicLungMechanicsParametersAcrossPlatforms...........52 4-2CharacteristicPGEParametersAcrossPlatforms.................53 4-3ModelParametersforScenario1:NormalVentilationandNormalCirculation.54 4-4ModelParametersforScenario2:VentilatoryArrestandNormalCirculation..55 4-5ModelParametersforScenario3:NormalVentilationandCirculatoryArrest..56 4-6ModelParametersforScenario4:SimultaneousVentilatoryandCirculatory Arrest.........................................57 4-7Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario1:NormalVentilationandNormalCirculation..............58 4-8Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario2:VentilatoryArrestandNormalCirculation..............61 4-9Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario3:NormalVentilationandCirculatoryArrest..............61 7

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4-10Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario4:SimultaneousVentilatoryandCirculatoryArrest...........63 A-1HostCommandFormatoftheAndros4700GasAnalyzer[9]...........72 A-2ACK/AcknowledgeResponseFormatoftheAndros4700GasAnalyzer[9]...72 A-3NAK/NegativeAcknowledgmentResponseFormatoftheAndros4700GasAnalyzer [9]...........................................72 8

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LISTOFFIGURES Figure page 1-1HPSfull-bodymannequinandstand-alonecontrolsoftware,Muse........10 2-1HPSandreferenceimplementationsofthehumanpulmonarysystem......15 2-2RelationshipbetweenMuseandMATLABsoftwareimplementations......16 2-3Overviewofrespiration................................17 2-4BlockdiagramofLungMechanicsmodel......................18 2-5BlockdiagramofPGEmodel............................20 2-6ComponentdiagramofPGEmodel.........................21 2-7FlowdiagramrepresentingthealgorithmfortheMATLABreferenceimplementation30 3-1Blockdiagramrepresentingtherelationshipbetweenthehardwareandsoftware componentsofthehybridbenchtop.........................34 3-2Blockdiagramofthehybridbenchtopmodel....................36 3-3Componentdiagramofthehybridbenchtopmodel................37 3-4HybridbenchtopPGEhardwareairwayandlungbox...............38 3-5HybridbenchtopPGEhardware,CAEHealthcareInc.hybridrack.......39 3-6Hybridbenchtopsoftwareowdiagram.......................46 4-1PAO 2 andPACO 2 undernormalventilationandnormalcirculation.......58 4-2PAO 2 andPACO 2 underventilatoryarrestandnormalcirculation,fulltime course.........................................59 4-3PAO 2 andPACO 2 underventilatoryarrestandnormalcirculation,reducedtimescale60 4-4PAO 2 andPACO 2 undernormalventilationandcirculatoryarrest........62 4-5PAO 2 andPACO 2 undersimultaneousventilatoryandcirculatoryarrest....63 9

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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience VERIFICATIONANDVALIDATIONOFTHEHYBRIDPULMONARYGAS EXCHANGEMODELOFTHEHUMANPATIENTSIMULATOR By HillaryA.Wehry August2014 Chair:JohannesvanOostrom Major:BiomedicalEngineering TheHumanPatientSimulatorHPS,developedattheUniversityofFlorida andmanufacturedbyCAEHealthcare,Montreal,Canada,providesaplatformfor immersivemedicaltraining.Patientresponsestotypicalclinicalscenariosaresimulated byphysiologicmodels,andtraineesinteractwiththesimulatortoevaluateclinicalsigns andmonitoredsignalsandprovidetherapeuticinterventions.Suchphysiology-based simulatorsarecomplex,dynamicalsystemsandarechallengingtoevaluate.TheHPS containstwomodelsofpulmonarygasexchangePGEbasedonthesameunderlying conceptualmodel:amathematicalmodelimplementedinsoftwareonly,andahybrid modelimplementedwithhardwareandsoftwarecomponents.Areferencesoftware implementationbasedonthesameconceptualmodelandactingasagoldstandard"was developedaspartofapreviousprojectandusedtoevaluatethesoftwareimplementation oftheHPSlung[1].Thisthesisprojectexpandsthemethodforvericationandvalidation ofsimulationmodelsandappliesittothehybridHPSPGEmodel.Wedesignedand implementedthecontrolsoftwareforahybridbenchtop"implementationconsistingof HPSPGEmodelhardware.Simulationofthephysiologicaloperatingpointdemonstrated amoderatediscrepancyinsimulatedpartialpressuresofoxygenandcarbondioxidein thealveolarspacebetweenthehybridmodelandthereferencestandard.Weformulated hypothesesfortheoriginofthesediscrepancies.Simulationofdynamicexperiments reectingextremephysiologicalsituations,suchasapnea,demonstratethephysical 10

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limitationsofthehybridlungmodel,whichcanbeattributedtoaspecicgasow rateinthelungmodel.Bothobservationsareexpectedtoleadtooptimizationsand improvementsofthehybridlungmodel.Theoverallvericationandvalidationmethod waspresentedinaninvitedlectureataninternationalconference. 11

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CHAPTER1 INTRODUCTION 1.1TheHumanPatientSimulatorHPS TheHumanPatientSimulatorHPS,developedattheUniversityofFloridaand manufacturedbyCAEHealthcare,Montreal,Canada,isaneducationaltoolthatprovides aplatformforrealisticmedicaltrainingprograms.Patientresponsestotypicalclinical scenariosaresimulatedbyintegratedphysiologicmodels.Traineesmustinteractwith thesimulatortoevaluateclinicalsignsandmonitoredsignalsandprovidetherapeutic interventions.Dierentpatientsandscenariosmaybeexecutedinterchangeablydepending ontheeducationalobjectives.Theappearanceandbehaviorofthesimulatormustclosely matchthatofthehumanbodyinordertomaximizerealismandbestpreparepersonnel forhigh-performanceclinicalenvironments. Figure1-1illustratesthefull-bodymannequinandstand-alonecontrolsoftwareof theHPS.TheHPSistheonlyfull-bodysimulatorthatoershigh-delitysimulation Figure1-1.TheHumanPatientSimulatorHPSfull-bodymannequinandstand-alone controlsoftware,Muse.ReprintedwithpermissionfromCAEHealthcare, http://caehealthcare.com/images/uploads/documents/ HPS-with-Muse-User-Guide.pdf May10,2014[8]. ofpulmonaryfunctionthroughtheexchangeofrealgases.IntheHPSsystem,the oxygen,carbondioxide,andevenanestheticgascontentofexpiredgasescanbedetected withconventionalmonitoringsystems.Thehighrealismanddelityofthissystemis particularlyadvantageousforuseinanesthesia.Thesubtletiesofreal-liferespiratory diseasestatesandmanagementofanestheticagentscanbemodeledusingahigh-delity 12

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simulator,andrarebutcriticalclinicalscenarioscanbepracticedwithoutendangeringreal patients. Small et.al rstdemonstratedimprovedemergencymedicineclinicianperformance incrisisresourcemanagementusinghigh-delitysimulationofemergencyscenarios inanesthesia[2].Since1999,numerousotherstudieshaveshownsimilartrendsin performanceimprovements[3].ThepopularityoftheHPSmotivatesfurthereortsto improvethehardwareandsoftwaredelitytorealpatientdata. 1.2IntroductiontoVericationandValidationofSimulationModels Themainpurposeofthesimulationengineofmedicaltrainingsimulatorsisto produceevolvingclinicalsignsandmonitoredsignalsandmakethemrespondto therapeuticinterventions.Physiologysimulatorsarecomplex,dynamicalsystemsthat arechallengingtoevaluate,sinceerrorsmayoccuratanypointinthemodelingprocess. Forexample,thephysiologicmodelsintheseenginesmaybeinvalidfortheconditionsin whichtheyareused,ortheircodeimplementationmaycontainerrors. Toevaluatethequalityofthemodelsunderstudy,wemustdistinguishbetweentwo terms:modelvericationandmodelvalidation,rstdenedbymodelersSargent et.al [4].Thesetermsweredevelopedinthecontextofcardiorespiratorysystemmodelsbyvan Meursin2011[5]andsummarizedbelow. ModelVerication Targetsthecorrectsoftwareimplementationofmodelequations ModelValidation Targetsthelegitimacyofthemodel 1.Conceptualvalidity{Thetheoreticalbasisandassumptionsarereasonablefor theintendedapplication 2.Operationalvalidity{Thebehaviorofthemodelisaccuratewithinarange consistentwiththeintendedapplication Thuscodevericationtargetsrelativelysimpleraspectsofmodelquality,suchas checkingthederivation,discretization,andcodeimplementationofmodelequations 13

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bycomparingsimulationresultsagainstknownanalyticalsolutions.Modelvalidation requiresanunderstandingoftheintendedapplicationortargetsystem.Themodelmust answertwokeyquestions:Arethetheoriesandsimplifyingassumptionsforthemodel appropriate;Dosimulationresultsmatchtargetdata?Theseconceptsofverication andvalidationaresimilarbutrepresentfundamentallydierentstepsinthemodeling process.TheyareexploredmoredeeplyinSection2.2.4,butforadditionalinformationon vericationandvalidationofsimulationmodels,wedefertoSargent[6]andvanMeurs[5]. Sargentfurtherclariedhistermsandoutlinedageneralapproachtomodel vericationandvalidationin2013[6].Thoughbroadlyapplicable,hisworkwaslimitedin itstranslationtotheindustrialsphere,theprimarysponsorsofphysiologicmodel-driven simulators. 1.3UseofaReferenceImplementation Wedevelopedamethodforvericationandvalidationofsimulationmodelsthat isbothrigorousandpracticalforindustry.ThisworkwasrstproposedinMunje2013 buthassincebeenexpandedandreformulatedforclarity[1].Ourmethodassumes theconceptualmodelofthesystemunderstudyasastartingpoint,butmakescertain simplicationstofocusoncriticalaspectsofmodelbehavior.Amathematicalmodelis derivedfromthisconceptualmodelandimplementedintestcode,whichisveriedby comparingselectedsimulatedresponsestoanalyticalsolutionsofmodelequationswhere available.Thetestcodeislesscomplex,andthereforeeasiertoverifyandmanipulatethan theproductcodeandsimulatorhardware.Theveriedtestcodeisthenusedtovalidate selectedmodelresponsesbycomparingthemtotargetdataorsubmittingthemtoexperts. Finally,responsesoftheveriedandvalidatedsimulationmodelareusedtoverifythe productcodeimplementationofthemodel. Thedesignofavalidatedreferenceortestcodetoanalyzeacommercialproduct implementationisfullydevelopedinChapter2.Werstappliedthismethodtothemodel forpulmonarygasexchangePGEincludedintheMusesoftwareCAEHealthcare,Inc. 14

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inMunje2013[1].WethenusedthissamemethodtoevaluatethePGEmodeloftheHPS hybridbenchtop,whichconsistsofbothhardwareandsoftwarecomponents,inChapter4 ofthiswork. 1.4ProjectAim TheHPScontainsahybridsoftwareandhardwareimplementationofmodelsof humanphysiology.Areferencesoftwareimplementationofthemathematicalmodels underlyingthesimulatedHPSpulmonarysystemwasindependentlydevelopedin MATLAB,veried,andvalidatedasagoldstandard"inpreviouswork.Thisreference standardwasthenusedasacomparisontoolbywhichtoevaluatethesoftware-only implementationoftheHPSlungMuse[1].Theobjectiveofthisprojectistodesign asystemconsistingofbothhardwareandcontrolsoftwareforahybridbenchtop" implementationcontainingHPSPGEmodelhardwareandthenusethevalidatedtest implementationasagoldstandard"toassesstheperformanceoftheHPShybridlung model. ThisworkwillbepresentedtoCAEHealthcareInc.inordertoaddresskeyconcerns intheredesignoftheHPShybridproduct. 15

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CHAPTER2 METHODOFCOMPARISON 2.1OverviewofHPSandReferenceImplementations TheHPSproductcontainsahybridsoftwareandhardwareimplementationofthe humanpulmonarysystemthatsimulatespatientresponsestotypicalclinicalscenarios. TheHPSsoftwareMuse"servesastheuserinterfaceandexecutesdierentscenariosby establishingtheconditionsforthehardwaresystem,whichmanipulatesphysicalgasesto simulatethehumanlung.TheresponsesgeneratedbytheHPShybridmodelarecaptured usingagasanalyzeranddatacollectionsoftware.Musemayalsofunctionindependently ofthehybridimplementationtogeneratesimulatedpatientresponses. Fourdistinctplatformsforthesimulatedpulmonarysystemarediscussedthroughout: 1.HPShybridproduct 2.HPSsoftware-onlyMuse 3.IndependentreferencestandardimplementedinMATLAB 4.Hybridbenchtop" Thersttwoplatforms,theHPShybridandtheHPSsoftware-onlyMuse,havebeen commercializedbyCAEHealthcareInc.andareincurrentuseworldwide.Inconsistencies inperformancenecessitateathoroughproductevaluationtoaddresssystemlimitations. Thisledtotheindependentdevelopment,verication,andvalidationofasimplied referencesoftwareinMATLAB,whichwasthenusedtoassesstheperformanceofthe Musesoftware-onlysimulationsinpreviouswork[1].Themodelingprocessanddesignof thereferenceimplementationarefurtherdevelopedinSection2.2. Thebenchtop"isalsoahybridimplementation,whichconsistsofbothhardware andsoftwarecomponents,thatwasdevelopedfortheexpresspurposesofthisthesis project.TheHPShardwarelungusedintheHPShybridproductservesasthebasisfor thebenchtop"model,butanindependentlydevelopedhardwareandsoftwarecontrol systemisusedasasubstitutefortheMuseinterface.Thecontrollerforthepulmonary systemrequiresfewercomponentsthantheMuseinterface,whichhandlesintegrated 16

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modelresponses,butthePGEhardwareremainsthesameinbothimplementations.The designofthecontrollerisdiscussedinChapter3.Figure2-1illustratestherelationships betweenthevariousimplementations. Figure2-1.HPSinredandreferenceinblueimplementationsofthehumanpulmonary system 2.2DesignofReferenceImplementation WeusethesamemodelingapproachastheinitialdesignoftheHPS.Thepulmonary systemcanbedividedintotwomodelsbasedonphysiology:theLungMechanicsmodel LMandthePulmonaryGasExchangemodelPGE.Thesephysiologicalsystemsare functionallydependentandexhibitadynamicrelationshipthatmustbecapturedtobuild acompletemodel.Bothmodelsaredescribedinthreeparts:requirementsforthemodel, theconceptualmodel,andthemathematicalrepresentation. Themodelrequirementsidentifyinputandoutputvariablesandtheirunits.A conceptualmodelisthenconstructedwithintheseconstraintsandspeciescertain 17

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simplicationsnecessarytodevelopanecient,realisticmodel.Itisvisualizedthrough blockorcomponentdiagramsandcharacterizesthecriticalfeaturesofthephysiological system. Thefollowingdiagram,Figure2-2,illustratestherelationshipbetweentheHPS softwareimplementationMuse"andtheMATLABreferencestandard.Bothimplementations arederivedfromahighlysimilarconceptualmodel.TheconceptualmodelforMuseisa bilateralrepresentationoflungmechanicsandpulmonarygasexchange,whichmeans theleftandrightlungsareconsideredseparateentitieshavingdistinctsetsofinputand outputvariables.Incontrast,theconceptualmodelfortheMATLABimplementationisa unilateralmodelhavingamergedrepresentationofleftandrightlungs. Figure2-2.RelationshipbetweenMuseandMATLABsoftwareimplementations.Steps A-Eareincludedforlaterreference. 18

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Theseconceptualmodelsformthebasisofboththebilateralandunilateral mathematicalrepresentations,whichconsistofasetofequationsrepresentingthelung mechanicsandgasexchangethroughalveoli.Theseequationsarefunctionoftime, variables,andparametersofthesystem.Theunilateralmathematicalmodeldeveloped onlyforPGEisusedtoimplementtheindependentsoftwaremodelinMATLAB.This MATLABmodelwillhaveitsownlungmechanicsthatwilldrivethePGE. TheMATLABimplementationwillserveasareferenceimplementationtocompare allfutureimplementations.RigorouscodevericationoftheMATLABstandardwas performedtoensureproperimplementationofthemathematicalmodelandisdiscussedin 2.2.4. 2.2.1ModelRequirements Figure2-3illustratestheveprocessesinvolvedinrespiration.Theprimaryfocusof thisprojectisthesecondstep,pulmonarygasexchangePGE.Theremainingprocesses arerepresentedbyothermodels.Thissectiondescribesthequalitativeandquantitative Figure2-3.Overviewofrespiration.Source:E.P.Widmaier,H.Ra,andK.Strang, Vander'sHumanPhysiology.McGraw-Hill,2007[7]. 19

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aspectsofthemodeldesign.Itincludesidentifyinginputandoutputvariablesand determiningtheirunitsandranges. 2.2.1.1SimpliedlungmechanicsLM TheLungMechanicsmodelsimulatespulmonaryventilation:thebulkowofair intoandoutofthelungscausedbythepressureandvolumechangesofthelung.Inthe humanbody,thededicatedpairofmusclesattachedtotheribcagesurroundingthelungs aswellasthediaphragmmusclecauseperiodicexpansionandcontractionofthethoracic cavity.Thisleadstoachangeintheintrapleuralpressureandthesubsequentchangein thevolumeofthelungs.Underconstanttemperatureconditions,thechangeinvolumeof lungsisinverselyproportionaltochangeinpressureinsidethelungsaccordingtoBoyle's law. Therefore,thepurposeofthesimpliedLungMechanicsmodelistogeneratealveolar owratesandtotalvolumeinsidethelung.Forthecurrentproject,weassumethemodel issuppliedwithmechanicalventilationsincetheHPSbenchtopimplementationdoesnot havemusclesimulationandrequiresanexternalventilatorformechanicalrespiration.All implementationsmustoperateundersimilarconditionsforavalidcomparison.Hence,the musclepressureappliedisconsideredzero.Aparameterizedwaveformgeneratorprovides theowofairrequiredforpulmonaryventilation, fi A t ,andbehaveslikeacontrolled volumeventilator. Figure2-4.BlockdiagramofLungMechanicsmodel. p referstoabsolutepressure. fi A t isonlyaninputduringinspirationandfollowspassiveexhalationduring expiration.Table2-1deneseachofthevariables. Tidalvolume V t ,inspiratorytoexpiratorytimeratio I : E ,andrespiratoryrate rr parameterizethewaveformgeneratoranddeterminetheprimaryinputow, fi A t . 20

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Theseparametersareconsideredconstantforonecompleterespiratorycycleinthismodel butmaybevariedfromcycletocycle,ifrequired.Thetimerequiredforonerespiratory cycleisfurthersplitintoinspiratorytimeandexpiratorytimeaspertheparameter I : E ratio.Theseparametersdetermineowduringinspiration,butthewaveformgenerator doesnotcontrolowduringpassiveexpiration.Musclepressureisassumedzerosince mechanicalventilationisprovided. Certainassumptionsarenecessarytosimplifytheconceptualmodel.Theeectof gaswarmingandhumidicationonalveolarvolumeuponinspirationisignored.Thegases consideredinthismodelareoxygenO 2 andcarbondioxideCO 2 ,andtherestofthe gasesareclassiedasother".Thesesystemparametersareassumedtobeconstantfora system.However,thesevaluescanbechangedifdemandedbytherepresentationofthe clinicalscenario.Table2-1indicatestheinputandoutputvariablerequirementsforthe LungMechanicsmodel. Table2-1.InputandoutputvariablesoftheLungMechanicsmodel VariablesNameUnit/value Inputvariables fi A t InspiredgasowratemL/s Outputvariables f A t GasowrateintoalveolarspacemL/s v A t AlveolarvolumemL 2.2.1.2PulmonarygasexchangePGE LungMechanicsdistributetheinspiredairoverthealveoli,andgasexchangetakes placeatthelevelofthealveoli.ThePulmonaryGasExchangePGEmodelisprimarily basedontheprocessofdiusionofgasesfromonecompartmenttotheother.Theratesof diusiondependonthedierenceinpartialpressuresofgasesbetweentwocompartments: gaseousalveolianduidbloodcompartments. ThePGEmodelmustgeneratethepartialpressuresofalveolargases,whichis aectedbythedeadspace".Anatomicaldeadspacereferstotheairwaysthatdonot 21

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participateinthegasexchangewiththeblood.Thepartialpressuresofgasesinthe conductingzonesoftherespiratorysystemsuchasthenose,pharynxandtracheadier fromthoseinthealveolarspacesincethereisnogasexchange.Alveolardeadspacerefers toairwithinthealveolithatcannotcontributetogasexchangeduetopoorbloodsupply tothealveoliandisnegligibleinanormalhealthyhuman.Physiologicdeadspace,or thesumtotaloftheanatomicaldeadspaceandthealveolardeadspace,isconsidered forsimulationinthismodel.Thefollowingtablestatestheinputandoutputvariable requirementsforthePulmonaryGasExchangemodel. Table2-2.PGEmodelrequirements VariablesNameUnit/value InputVariables p i X t PartialpressureofinspiredgasXmmHg f A t GasowrateintoalveolarspacemL/s v A t LungvolumemL exchX t ExchangeofgasXmL/s OutputVariables p A X t PartialpressureofgasXinalveolarspacemmHg p e X t PartialpressureofgasXexhaledatthemouthmmHg Figure2-5.BlockdiagramofPGEmodel ThePGEmodelmustgeneratepartialpressuresofgasesindeadspaceandinalveolar space.AsperTable2-2andFigure2-5,theinputtothismodelispartlytheoutputof lungmechanicsmodel.Theprimaryinputsarealveolarow,alveolarvolume,inspiredgas 22

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partialpressures,andexchangerateofgases.Thecompositionofalveolargasesremains theprimaryoutput. Thesystemisdesignedtobeseparatefromamodelofthecardiovascularsystem, yetthesesystemsarefunctionallylinkedinthehumanbody.Thisrequiresanadditional inputvariable exchX t tothemodelsofthepulmonarysystemtorepresenttherateof exchangeofgasesbetweenalveoliandblood.ThisenablestheisolationofthePulmonary GasExchangemodelfromthemodelforthedistributionofgasesbetweenthecirculatory systemandlungs. 2.2.2PGEConceptualModel Acommonconceptualmodelunderlieseachmathematicalimplementation.The PGEmodelisconceptualizedintheformofacomponentdiagram.Itconsistsoftwo homogenouscompartments,onefordeadspaceandoneforalveolarspace.Thedeadspace isassumedtobeaventilatedcompartmentwithaconstantvolume V D .Theonlycarrier forthiscompartmentisair. Figure2-6.ComponentdiagramofPGEmodeladaptedfromvanMeurs[5].Table2-2 deneseachofthevariables. TheinowandoutowratesofthiscompartmentareobtainedfromtheLung Mechanicsmodel.Theowintothealveolarspaceistheoutowofthedeadspaceduring inspiration.Duringexpiration,gasowsfromalveolarspaceintodeadspace.Thealveolar spaceisaventilatedandperfusedcompartment.Itisasinglehomogenouscompartment representingthevolumeofallthealveoliinthelung.Thecarriersforthiscompartment 23

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arebothairandblood.Thiscompartmenthasnotissuesastheamountofgasdissolved inlungtissueandpulmonarybloodvolumeareignoredascomparedtotheamountof gasinalveolargasmixture.Theexchangerateisdenedforeachgasanditcontributes tothechangesinthealveolarcompartmentduetothediusionintooroutoftheblood. Directionisdenedasup-takefromthelungsintotheblood:generallypositiveforO 2 , negativeforCO 2 .Thus,PulmonaryGasExchangeisaadynamicalsystemthatcanbe representedbyamodelcharacterizedbystatevariablesandasetofordinarydierential equations. 2.2.3MathematicalModels 2.2.3.1DerivationofLMmodelequations Themathematicalmodelisderivedassumingtheconceptualmodeloutlinedabove. Theinputowisconsideredconstantinordertomaintainthesimplicityofthemodel. ThisinputtothePGEmodeliscreatedusingawaveformgeneratorasdescribedinthe derivationbelow,asadaptedfrompg.145-158ofvanMeurs[5]. Table2-3describesthecharacteristicparametersusedinthereferenceMATLAB implementation.Lungcompliance,orthestretchabilityofthelung,referstothe magnitudeofthechangeinlungvolumeproducedbyagivenchangeintranspulmonary pressure.Thegreaterthelungcompliance,theeasieritistoexpandthelungs.Here, thetotalcompliance C parameterrepresentstheseriescombinationoftheaveragelung andchestwallcompliances.Airwayresistance R ,sometimesreferredtoasbronchial resistance,determinesthevolumeofairthatowsintooroutofthealveoliforagiven pressuredierencebetweenthealveoliandtheatmosphere.Thefactorsthatdetermine airwayresistanceincludethelengthoftheairways,theairwayradii,andinteractions betweenmovinggasmolecules,butonlytheaveragephysiologicalvalueisconsideredin thereferenceimplementation.Innormalhumanphysiology,thelungsstillcontainavery largevolumeofairafterexpirationofarestingtidalvolume.Thisvolumeistermedthe 24

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functionalresidualcapacity FRC andtheaveragephysiologicalvalueisusedinthe referenceimplementation[7]. Table2-3.CharacteristicparametersoftheLungMechanicsmodelusedinthereference MATLABimplementation[5] SymbolNameUnit/value Parameters C Totalcompliance149.84mL/mmHg R Airwayresistance2.7*10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(3 mmHgmL )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 s FRC Functionalresidualcapacity2300mL DerivedVariables t i Timeofinspirations t e Timeofexpirations Componentdescriptions. Theparameterrespiratoryrate rr determinesthe timespanorrespiratoryperiodofonerespiratorycycle =rr .Therespiratoryperiodis dividedintoinspiratoryandexpiratorytimeasperthe I : E timeratio,resultinginxed fractions. t i = IE 60 =rr {1 t e = )]TJ/F22 11.9552 Tf 11.955 0 Td [(IE 60 =rr {2 Thedierenceinpressuresacrosstwopointscausesowandisusuallyrepresented aschangeinpressuredividedbythepathresistance.Hence,theowthroughanairway resistanceisthedierenceinpressureatthemouthandattheendofairway,e.g.lung. Duringpassiveexpiration,noexternalpressureisexercised,sothepressureatthemouth, p t ,iszero. f A t = p t )]TJ/F22 11.9552 Tf 11.955 0 Td [(p A t R = )]TJ/F22 11.9552 Tf 9.299 0 Td [(p A t R {3 Flowcanalsobedenedastherateofchangeofalveolarvolume: f A t = dv A t dt {4 25

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Thealveolarcompliancecanberepresentedastheratioofchangeinalveolarvolume tochangeinalveolarpressure.Hence,thealveolarpressurewillbeapressureacross complianceduetochangeinvolume: p A t = v A t )]TJ/F22 11.9552 Tf 11.956 0 Td [(FRC C 0
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Thiscanbesplitbetweeninspirationandexpirationusingtheequationforowasfollows: p A t = v A t )]TJ/F22 11.9552 Tf 11.956 0 Td [(FRC C + V t =t i R 0
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Massbalanceofgasesreectssupplyofagasduetoalveolarow.Undertheassumption thatinowandoutowpressuresequal,thisquantitydependsonlyonthedierencein partialpressureofagasintheinspiredgaseousmixtureandthedeadspace.Referringto Figure2-6,themassbalanceforthetotalamountofgasXinthedeadspace a D t canbe writtenasfollows: da D t dt = u [ f A t ] f A t p in t P T )]TJ/F22 11.9552 Tf 13.151 8.087 Td [(p D t P T )]TJ/F22 11.9552 Tf 11.955 0 Td [(u [ )]TJ/F22 11.9552 Tf 9.298 0 Td [(f A t ] f A t p A t P T )]TJ/F22 11.9552 Tf 13.151 8.087 Td [(p D t P T {14 wherethersttermontherightsiderepresentsgasowratesduringinspiration,with positive f A t ,andthesecondtermrepresentsgasowratesduringexpiration,with negative f A t . u [ : ]istheunitstepfunction. Substituting2{13,isolatingthederivativeofthestatevariable p D t ,andeliminatingthe parameter P T fromtheequationyields: dp D t dt = u [ f A t ] f A t [ p in t )]TJ/F22 11.9552 Tf 11.955 0 Td [(p D t ] )]TJ/F22 11.9552 Tf 11.956 0 Td [(u [ )]TJ/F22 11.9552 Tf 9.299 0 Td [(f A t ] f A t [ p A t )]TJ/F22 11.9552 Tf 11.955 0 Td [(p D t ] v D {15 Massbalanceofgasinalveolarspace. Thealveolarspaceisahomogenous compartmentwithavariablevolume.Theamountofgasinthealveolarspacedependson thevolumeofthealveolarspaceandthepartialpressureofthegasinthatvolume.The changeintheamountofgascanbeobtainedbydierentiatingitwithrespecttotime: da A t dt = d dt v A t p A t P T = v A t P T dp A t dt + p A t P T dv A t dt {16 = v A t P T dp A t dt + p A t P T f A t {17 Consideringthebidirectionalowrateduetorespiratorycyclevariations,therstterm representsgasowratesduringinspiration,withpositive f A t ,andthesecondtermgas owratesduringexpiration,withnegative f A t . u [ : ]istheunitstepfunction. da A t dt = v A t P T dp A t dt + p A t P T f u [ f A t ]+ u [ )]TJ/F22 11.9552 Tf 9.299 0 Td [(f A t ] g f A t {18 28

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Themassesofcarbondioxideandoxygengaschangeduetoventilationandgasexchange withthebloodinthealveoli.Duringinspiration,theowofairfromdeadspacetoalveoli causesthepartialpressureofoxygeninthealveolitoincreaseandthepartialpressure ofcarbondioxidetodecrease.Theairowrateandpartialpressuresinthedeadspace determinetheseuiddynamics. Gasexchangebetweenthealveoliandbloodvesselscausesthepartialpressureof oxygeninthealveolitodecreaseandthepartialpressureofcarbondioxidetoincrease. Regardlessofventilationphase,theexchangeofoxygenisconsideredpositive,andthe exchangeofcarbondioxideisconsiderednegative.Exchangemayberepresentedasanet subtractionforsimplicitysinceweareconsideringthestateofgasesinthealveoli.During expiration,thenetchangeinthemassofeachgasinthealveolidependsonexchangerate andcurrentalveolarpartialpressures.ReferringtoFigure2-6,themassbalanceforthe totalamountofgasXinthealveoli a A t canbewrittenasfollows: da A t dt = u [ f A t ] f A t p D t P T )]TJ/F22 11.9552 Tf 11.955 0 Td [(u [ )]TJ/F22 11.9552 Tf 9.298 0 Td [(f A t ] )]TJ/F22 11.9552 Tf 9.298 0 Td [(f A t p A t P T )]TJ/F22 11.9552 Tf 11.955 0 Td [(exch t {19 wherethersttermontherightsiderepresentsgasowratesduringinspiration,with positive f A t ,andthesecondtermgasowratesduringexpiration,withnegative f A t . u [ : ]istheunitstepfunction.Substituting2{17andisolatingthederivativeofthestate variable p A t yields: dp A t dt = u [ f A t ] f A t f p D t )]TJ/F22 11.9552 Tf 11.955 0 Td [(p A t g)]TJ/F22 11.9552 Tf 20.59 0 Td [(exch t P T v A {20 2.2.4SoftwareImplementation ThissectionexplainsthemethodusedtoimplementtheLungMechanicsandPGE modelequationsinMATLAB.Table2.2.4liststheequationsusedtoimplementthe referencemodelinMATLAB,andFigure2-7describestheiterativecalculationsofoutput variablesusingthesemodelequations. 29

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Table2-5.SummaryofequationsusedtoimplementLMmodelinMATLABreference LungMechanicsLM: Calculationofinspiratoryandexpiratoryperiods t i = IE 60 =rr t e = )]TJ/F22 11.9552 Tf 11.955 0 Td [(IE 60 =rr Stateequations dv A t dt = f A t 0
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ThemathematicalmodelforLungMechanicsandPGEconsistsofasetofordinary dierentialequations.Numericalmethodsareusedtosimulatetheseequations.Figure2-7 depictsthealgorithmusedtocalculatetheoutputvariables. Thetotalexecutiontimeisdividedintorespiratorycyclesdeterminedbytheperiod foreachrespiratorycycle.Therespiratorycycleisdividedintoinspirationandexpiration, andeachphasehasaspecicsetofequations.Bothphasesrstexecuteequationsrelated toLungMechanicsandthencalculatetheoutputvariablesforPGEmodel.Thechange ofphasefrominspirationtoexpirationandsimultaneousswitchingofthesetofequations ismonitoredthroughatimevariable tb .Variablesareintroducedtorepresentdierent timeslotsrequiredtosuccessfullysimulatethebreathingcyclesforthedesiredperiodof time.Thedescriptionofthesevariablesandtheprocessofexecutionaregivenbelow. Theinspiredgases,initialconcentrationsofdeadspacepartialpressures,andalveolar spacepartialpressuresandexchangeratesaresettoastandardvalue.Thetimevariable t isinitializedtozero.Thevariable t final representstotalsimulationtimeandisaninput givenbytheuser. Thetimevariable t b isusedtorepresenttimesincethebeginningofthecurrent breathcycleanditsmaximumvalueisequaltotherespiratoryperiod.Itisinitializedto zero,incrementedby T untilitisequaltotherespiratoryperiod,andsubsequentlyreset tozero.Thevariables t i and t e representconstantinspirationtimeandconstantexpiration time,respectively,dividedbytheinspirationtoexpirationtimeratio I : E setbythe user.Afterinitializingallmodelvariables,thetime t isincrementedby T torepresent thesimulationtime.Thevariable t b isalsoincrementedwiththesamestepsize T andis repeatedlycomparedtothetotalinspirationtime t i .Themodelvariablesarecalculated accordingtotheinspiratoryphaseequations.Thisiscontinueduntil t b isequaltothe inspirationtime t i .Once t b isbeyondtheinspirationtime,theequationsinexpiration phaseareusedtocalculatetheoutputvariables.When t b isequaltoonerespiratorycycle time ti + te ,itisresettozero.Thismarksthecompletionofonerespiratorycycle.The 31

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Figure2-7.FlowdiagramrepresentingthealgorithmfortheMATLABreference implementation 32

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iterationcounterisincreasedbyonewitheachstep,andtheprocesscontinuesuntilthe timevariable t reachesthedesiredtotaltimeperiod t final . 2.3VericationProcessoftheReferenceSoftwareImplementation SincetheMATLABreferencewillserveasagoldstandard"bywhichtocompareall futuresoftware,rigorouscodevericationisrequiredtoensureproperimplementationof themathematicalmodel.Theprocessofvericationinvolvescrosscheckingthestep-to-step transitionofthemodelillustratedinFigure2-2,aserrorsmayoccuratanypointin theprocess.Thestrategyusedforvericationofthemodelisbasedontheprocessof vericationdevelopedinvanMeurs2011[5]andpresentedinMunje2013[1]andis summarizedbyTable2-7. Table2-7.ProcessofVerication,adaptedfrom[5] Process CompleteuseofthelistedinputandoutputvariablesSpecication AppropriateunitsandrangesofthevariablesVerication Inclusionofrequiredanatomicalstructuresandphysiologicalprocesses CorrectderivationandimplementationofmodelequationsCodeVerication Appropriatechoiceofintegrationmethodandstepsize ComparisonbetweensimulationresultsandanalyticalsolutionCrossVerication SpeedofcodeexecutionwithAnalytical Solution AdequacyofvericationprocessOverallConrmation ThisprocesswasperformedontheMATLABreferenceimplementation.Wehighlight criticalpointsinthevericationprocessdevelopedinMunje2013[1]. 2.3.1SpecicationVerication Transition A inFigure2-2representstheconversionofthesimpliedconceptual modelintoasimpliedmathematicalmodel.Vericationofthisstageinthemodeling processisreferredtoasspecicationverication"[5],whichconsiderstherstthree checkpointsmentionedinTable2-7. ThesummaryofequationsinTable2.2.4describesthemanipulationofevery parameterandinputvariableintheevolutionoftheoutputvariable.Thephysical principlesformingthebasisoflungmechanicsandpulmonarygasexchangeconceptual 33

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modelsdescribedinSection2.2.2shouldbereectedinthesetofmathematicalequations. Inaddition,thelogicalassumptionsmadeinformulatingamathematicalmodelmustbe coherentwiththeassumptionsoftheconceptualmodel.Thereferenceconceptualmodel forlungmechanicsandpulmonarygasexchangeisaunilateralmodelthatassumesa single,homogenouslungcompartment.Thusthismathematicalmodelcannotsimulate scenariossuchaspneumothorax,astherearenotseparatevariablesfortheleftandright lungs. 2.3.2CodeVerication Transition B inFigure2-2depictstheconversionofmathematicalequationsinto programmedcodeinMATLAB.Thisinvolvescodevericationbasedonthefourthand fthcheckpointsgiveninTable2-7. Thevariablesusedtodenethegivenmodelareallcontinuousvariablesthatmust bediscretizedintimetoconstructasoftwaremodel.Thisisachievedbyusingnumerical methodstosolvethedierentialequationsanditerativelycalculatetheoutputvaluesfor smalltimeincrements,orstepsizes.Euler'sforwardmethodandtheRunge-Kuttamethod RK4wereusedtodiscretizethemodelequationsandcomparedinMunje2013fora rangeofstepsizes[1].Thetwomethodsperformquitesimilarlyforsmallerstepsizes,and thusEuler'smethodwaschosenforitsreducedcomputationaldemand. SincetheMusesoftwaresamplesthedataevery12ms,thenumericalanddynamic stabilityofEuler'smethodwasassessedusingthisstepsizeinMATLAB.Dynamicstep analysisrevealedaclinicallyinsignicantartifactbutotherwisesupportedtheuseof thisnumericalmethodandstepsize.Thusthemodelequationswereimplementedin MATLABusingEuler'smethodwithastepsizeof12msforconsistencywiththeMuse software. 2.3.3CrossVericationwithAnalyticalSolutions Theintermediatestep D inFigure2-2veriesthattheMATLABsimulation resultsfoundthroughStep C accuratelyreectthemathematicalmodelbyconsidering 34

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thesixthandseventhcheckpointsgiveninTable2-7.Thesecomparisonsconrmthe correctimplementationofthemodelequations,revealthesettlingtimerequiredtoreach steadystate,andsupportthatthespeedofcodeexecutionisreasonableforreal-time applications.Thenumericalsolution,orsimulation,canbecomparedtoasetofstandard analyticalsolutionsobtainedundervarioussetsofconditions.Theanalyticalsolution foreachoutputvariableisobtainedbysolvingthesetofdierentialequationsofthe mathematicalmodelsimultaneouslyandmustbedeterminedthroughmanualderivation. Specicsetsofconditionsorscenarioswereselectedsinceitisnotpossibletoformulate theequationsforallthevariablesandallscenarios.Extremescenariosweredesignedto testtheboundaryconditionsoftheimplementation. Thescenariosdesignedfortheanalyticalderivationsaregivenbelow: NormalventilationandNormalcirculationwithconstantowinput NormalventilationandNormalcirculationwithrampowinput NoventilationandNormalcirculation Thefollowingoutputvariableswereusedforcomparison: Flow Lungvolume Totalalveolarpressure Deadspacepartialpressureforoxygenandcarbondioxide Alveolarspacepartialpressureforoxygenanddioxide Highcoherencebetweentheanalyticalsolutionandthenumericalsolutionofthe softwareimplementationisshownineachsetofconditionsinMunje2013[1].This conrmsthatthemodelequationswerecorrectlyimplementedinMATLAB.Thusthe referenceLMandPGEmodelhasbeenfullyveriedandmaybeusedasabenchmarkfor comparisonwithothermodels.Themodelresponseshavebeenvalidatedusingproduct codebutremaintobecomparedwithindependentlycollectedclinicaldata. 35

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CHAPTER3 HYBRIDBENCHTOPMODEL TheHPShybridmodelincorporatesbothhardwareandsoftwarecomponentsto simulatepulmonaryfunctionthroughtheexchangeofrealgases.TheHPSsystem generatestheO 2 andCO 2 contentofthelung,whichcanbedetectedwithconventional monitoringsystems.Inadditiontoitssoftware-onlysimulations,theMusesoftware operatesastheuser-interfaceandcontrolsoftwareforthehardwarecomponentsofthe HPShybridproduct.Thecardiovascularandrespiratorysystemmodelsareintegrated intheHPShybridproduct,butinconsistenciesinperformanceprompteddevelopersto evaluatethesemodelsseparatelyandindependentlyoftheMuseinterface.Thisrequired thedesignandindependentimplementationofhardwareandcontrolsoftwareforahybrid benchtop"implementationcontainingonlytheHPSPGEmodelhardware.Thusthe benchtoponlysimulatesPGEbutishighlysimilartotheHPShybridproduct. 3.1ModelRequirements Thebasicfunctionalrequirementofthehybridmodelistogeneratealveolar andexpiredgascompositionsintheclinicalrangeforahealthyadultduringnormal ventilation.Figure3-1illustratestheprimaryinputsandoutputsofthehybridbenchtop modelandrepresentstherelationshipbetweenthehardwareandsoftwarecomponents. Figure3-1.Blockdiagramrepresentingtherelationshipbetweenthehardwareand softwarecomponentsofthehybridbenchtop TheinputandoutputvariablesofthehybridbenchtopmodelarelistedinTable3-1. 36

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Table3-1.InputandOutputVariablesoftheHardwareComponentsoftheHybrid BenchtopPGEModel HardwareVariableNameUnitSource Input f A t GasowrateintoalveolarspacemL/sVentilator p in t InspiredgascompositionmmHgVentilator mfc t MassFlowControllergasowratemL/sControlSW Output p A t AlveolarpartialpressuresofgasesmmHg| p t PartialpressuresatthemouthmmHg| Table3-2.InputandOutputVariablesoftheSoftwareComponentsoftheHybrid BenchtopPGEModel SoftwareVariableNameUnitSource Input exch t ExchangerateofgasesmL/sFixedinControlSW p A t AlveolarpartialpressuresmmHgGasAnalyzer Output mfc t MassFlowControllergasowratemL/sModeled 3.2ConceptualModel Thehybridbenchtopimplementationdoesnothavemusclesimulationandrequiresan externalventilatorformechanicalrespiration.ThusonlythePGEmodelissimulatedby thehybridbenchtop. Thebenchtopsimulatestheexchange"ofgasesinsidethealveolarcompartments usinggassubstitution.Abulkquantityofmixedgasisremovedfromthealveolar compartmentsbyavanepumpataxedrate.Agasanalyzerreportsthecompositionof thisgasintermsoftheirpartialpressures.Thesepartialpressuresareusedtocalculate thegasowratesattheoutputoftheMassFlowControllersMFCsforeachgas.The MFCsaddnewgastothealveolarcompartmentsintheproportionnecessarytoobtain theirrespectivesetexchangerates.Thecompletehybridbenchtopmodelisrepresentedin Figure3-2. 37

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Figure3-2.Blockdiagramofthehybridbenchtopmodel ThehybridPGEmodelisconceptualizedinFigure3-3,whichillustratestheinow andoutowofthehomogenousalveolarcompartments.Thehybridmodelhastwo physicallungcompartments,butdoesnototherwiseseparatetherepresentationof therightandleftlung.Thereisonlyonesetofvariablesusedtorepresentthegas compositioninthelungs,andtheyreceivethesameinputfromtheventilatorandthe MFCs.Thusthetwolungscanbesafelyassumedtohavethesamemixtureofgases andcanberepresentedbyasinglecompartment.Thedeadspaceisassumedtobethe ventilatedairwaytubingwithaconstantvolume. 38

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Figure3-3.Componentdiagramofthehybridbenchtopmodel 3.3ImplementationoftheHybridModel Conventionalventilatorequipmentisusedtomechanicallyventilatethehybrid benchtop.Thexed-volume"modeisnecessarytobeconsistentwiththelungmechanics modelsontheotherplatforms. TheHPSfull-bodymannequinhasamouth,pharynx,larynx,bronchialtubes,and esophagusthatareanatomicallyrepresentativeofahumanpatient.Thishardwareis usedinthehybridbenchtopandcontributestothedeadspace.Thepatient"mustbe intubatedtoconnecttheventilatortotherestofthehardware.Thebronchialtubesofthe mannequin,onceintubatedandsupportedbytheventilator,areconnectedtothelungor alveolarcompartments,referredtoasthelungbox,"asshowninFigure3-4. Thelungsareelasticballoonswithinseparatexedvolumecontainersthatare connectedtotheleftandrightbellowsfoundinthehybridrackshowninFigure3-5 providedbyCAEHealthcare,Inc[8].Theowofairintotheballoonscausesachange ofpressureinthecontainers,whichthenrelatestoachangeofpressureatthebellows duetotheirconnectionviagastubing.Thebellowsarefreelymoving,andtheirintrinsic compliancecausesthemtoriseinresponsetothisincreaseinpressure.Thustheowof airintothelungboxduringinspirationindirectlyraisesthebellowsinordertomaintain thesamepressureintheelasticballoons,lungcontainers,andthehybridracktubing. 39

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Figure3-4.HillaryA.Wehry. HybridbenchtopPGEhardwareairwayandlungbox .May 10,2014.Gainesville,FL. Duringexpiration,theweightofthebellowsissucienttocausetheinversechangein pressurerequiredduringpassiveexhalation. TheremainingPGEhardwareisassembledinthehybridrack.Asindicatedin Figure3-5,theprimarycomponentsintherackarethebellows,gasanalyzer,vanepump, andmassowcontrollersMFCs.Thepowersupplyandgastubingarealsoshownbut areunlabeled.TheN 2 ,O 2 ,andCO 2 MFCsareconnectedtotherespectivegascylinders, andtheventilatorisconnectedtoboththeO 2 cylinderandthecompressedairline.The additionalcomponentsarenotnecessarytothediscussionofthebenchtopmodelsinceit doesnotrespondtoanestheticagents. 40

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Figure3-5.HybridbenchtopPGEhardwarerackobtainedfromCAEHealthcareInc. Frontofrackwithoverremoved .ReprintedwithpermissionfromCAE Healthcare, http://caehealthcare.com/images/uploads/documents/ HPS-with-Muse-User-Guide.pdf May10,2014.[8] Atmosphericair%O 2 isprovidedastheinputtothehomogenouslung compartmentsthroughxedvolumeventilationduringinspiration.Thevanepump removesgasfromdirectlyfromthelungcompartmentsataconstantowratecontinuously throughtherespiratorycycle.Thevariable F vane representsthevolumeofgasremoved perminute.Theproportionsofthesegases,whichareassumedequaltothealveolar partialpressures,arereportedbyagasanalyzer.Real-timeconcentrationsof O 2 , CO 2 , 41

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andavarietyofanestheticagentsarereportedevery40milliseconds.Controlsoftware isrequiredtocommunicatewiththegasanalyzerandacquirethesealveolarpartial pressures. ThesealveolarpartialpressuresareusedtocalculatetheN 2 ,O 2 ,andCO 2 mass owcontrolratesusingthemodelequationsimplementedintheHPShybridproduct. Asdiscussedpreviously,theexchangeratesareconstant.Thegasanalyzeronlyreports thepartialpressuresofO 2 andCO 2 ,sothepartialpressureofN 2 isassumedtobethe remainingproportionofgas.Themassowcontrollersoperateonastrictlylinearrange. Thevariables F mfc X representthemaximumowratesoftheMFCforagivengasX andareincludedhereasaconstantfactortoprovideavalueforthemassowratesasa percentofthetotalrange. p A N 2 = P T )]TJ/F22 11.9552 Tf 11.955 0 Td [(p A O 2 )]TJ/F22 11.9552 Tf 11.955 0 Td [(p A CO 2 {1 mfcN 2 = F vane p A N 2 P T 1 F mfc N 2 {2 mfcO 2 = F vane p A O 2 P T )]TJ/F22 11.9552 Tf 11.955 0 Td [(exchO 2 1 F mfc O 2 {3 mfcCO 2 = F vane p A CO 2 P T + exchCO 2 1 F mfc CO 2 {4 Since F vane , P T , exchX ,and F mfc X areallxedvalues,themasscontrolratesare onlyafunctionofthealveolarpartialpressuresandcanbecalculatedasthedatais sampled.Herethe mfcX variablesareexpressedasapercentofthetotalrangeofoutput owforeachMFC.TheMFCsareanalogdevices,whichrequiresthatthesemassow ratesaresentthroughadigitaltoanalogconverterDAC.Additionalhardwareisthus requiredtocommunicatewiththeMFCs.TheseMFCsthenfeednewgasbacktothe compartmentstoreplacewhatwastakenoutbythevanepumpintheproportionthat maintainsthexedexchangerates. Theacquisitionofdata,calculationofmassowcontrolrates,andcontrolofmass owcontrollersisperformedbythecontrolsoftwareinreal-time.Thedesignofthe 42

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hardwareandcontrolsoftwarerequiredforthebenchtopimplementationisgivenin Section3.4.AbriefcomparisontotheHPSHybridproductisprovidedinSection3.5. 3.4DesignoftheBenchtopControlSystem AnATmega328-basedmicrocontrollerwasusedtoacquirethedata,calculatethe massowcontrolrates,andcontroltheMFCs.Acomplexcommunicationprotocol isrequiredtoinitializeandreceivedatafromthegasanalyzerandisdescribedin Section3.4.1.Thereportedpartialpressureswereusedtocalculatethemassowcontrol ratesusingthehybridmodelequationsshownin3{2.Theserateswerethenconvertedto analogvoltagestocontroltheMFCsusinglteredpulse-widthmodicationPWM,the designofwhichisdescribedinSection3.4.2. 3.4.1Andros4700GasAnalyzerCommunication ThegasanalyzerusedinboththeHPShybridproductandthehybridbenchtopis theAndros4700,manufacturedbyAndrosInc.ofBerkeley,CA.AServomexO 2 sensor wasincorporatedintheproducttoimprovetheaccuracyoftheoxygenmeasurements. ComprehensiveproductinformationmaybefoundintheModel4700AnesthesiaGas Subsystemmanual,butthedetailsrelevanttothecontrollerdesignaresummarizedbelow [9]. 3.4.1.1Communicationhardware TheAndros4700receivesandtransmitsusingasynchronousserialcommunications conformingtotheEIA-RS232Celectricalandtimingspecications.Thefollowing communicationsfeatureswereusedtoconnecttheserialportoftheATmega328to theAndros4700: Interfaceconnector:DB9 Serialdataformat:1startbit,8databits,0paritybit,1stopbit,19200bps Typicaldrivelevel:ON=+8V;OFF=-8V Hardwarehandshaking:CTShostsystemto4700handshakingenabled.The4700 transmitsdataonlywhenthehostsystemsetstheCTSlineON > +3VDC 43

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HostSystemCommandInter-characterTiming:250millisecondsmaximum. Isolation:Logicsignalsareopto-isolatedfromthe4700electronics. Table3-3liststheDB9connectionsrequiredtoconnecttheAtmega328totheAndros 4700.SincetheATmega328hardwareserialportusesTTLlogicON=+5V;OFF= 0V,anadditionalcommunicationsmodulewasusedtotoconverttheRS232andTTL voltagesSMAKNMAX232CSE".ADB9M/FNullModemAdapterwasrequired toconnecttothelogicconvertermodule,switchingtheserialRX/TXlines.Thusthe ATmega328serialpins0RXand1TXareconnectedtotheRS232RX/TXlines onthelogicconverter,respectively.TheATmega328functionsasthehostsystemin communicatingwiththeAndros4700. Table3-3.CommunicationDB9ConnectionsoftheAndros4700GasAnalyzer Pin#SignalNameSourceSignalDescriptionandUse 2TXD4700 TRANSMITDATA .Datatransmittedby the4700tothehostsystem 3RXDHOST RECEIVEDATA .Datatransmittedby thehostsystemtothe4700. 5GNDHOST SIGNALGROUND . 7CTSHOST CLEARTOSEND .Hostsystemto4700 handshaking.The4700transmitsdataonly whenthehostsystemsetstheCTSlineis ON > +3VDC. Inordertocollecttheoutputdatainrealtime,anadditionalSoftwareSerial"port isusedtosendthedataoveraserialCOMportandeasilyrecordedinaserialterminal .csv"log.AnFTDIdriverisusedtoconvertthedigitalportsoftheAtmega328toa COMUSBport.Theuseoftheserialportallowsforreal-timedataacquisitioneven thoughtheAtmega328memoryisgreatlylimited.ThedatacannotbestoredinFLASH evenovershortperiodsoftimeandcannotbesavedtoEEPROMwithoutcausing performancedelays.Theuseoftheserialterminalhasoneminordrawback.Whilethe hexadecimalcharacterarraysareformattedtoallowtheusertointerprettheresponseof theAndrosduringtheinitializationperiod e.g. viewerrorcodes,thequantitativedata 44

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cannotbevisualizeduntilitisprocessedandimportedintosoftwaresuchasMicrosoft OceExcelandMathworksMATLAB.ThisiscontrasttosoftwaresuchasLabVIEW, whichallowstheintegrationofdataacquisitionandvisualization. 3.4.1.2Softwarecommunicationprotocol Thesensorsusedtomeasurethegasconcentrationsareverysensitivetotemperature. Thethermalstabilityoftheinstrumentationisrequiredtoensureaccuracyofthe measurement.ThustheAndros4700requiresacomplicatedinitializationprotocolto calibratetheinstrumentsandcompensateformeasurementerrorslistedinTable3-4.This processrequiresbetween5-20minutes.Threeoperatingmodesmanagethe4700andhost systemactivities:StartupMode,WarmupMode,andNormalMode. DuringStartupMode,therangeofcommandsarequitelimitedsincesucient thermalstabilityhasnotbeenachieved.Thepumpandsolenoidcontrolcommandsare notallowedsincetheyareusedbythe4700tocalculateambientpressureandServomex O 2 sensorowrateoset.Warmupmodeallowsforadditionalcommands,butthe fullcalibrationoftheinstrumentationspancalibration"isnotyetallowed.Datais availableaftertheNormalmodeisreachedandthefullcalibrationsofthegasanalyzer, includingtheServomexO 2 sensor,areperformed.Thesummaryofthecommandsand correspondingoperatingmodesaregivenbelow.TheAndrosmanualmaybeconsultedfor moredetailedinformation[9]. EachhostcommandconsistsofastringofcharacterssenttotheAndros.Theseare expressedinhexadecimalcharacterarraysthroughoutforclarity.TheAndrosresponds toeachcommandinoneofthreeways:anacknowledgmentthatthecommandhasbeen receivedandwillbeperformedACK,$06,anegativeacknowledgmentthatthecommand hasbeenreceivedbutcannotbeexecutedNAK,$15ornoresponse.TheNAKresponse alsoincludesanerrorcodeECthatmaybereferencedinthemanual.Thehostsystem mustwaitforaACK/NAKresponsebeforetransmittingthenextcommand.Most ACK/NAKresponsesaretransmittedbythe4700within0.5secondsfromreceivingthe 45

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Table3-4.Andros4700GasAnalyzerInitializationProtocol CommandCodeCommandInstructions StartupMode $34Wakeupfromwatchdog $E5Disablewatchdog $E3Selecttheactivecommandset $D7Dataoutputformat $D8Setlterstooutput $30Requestsinglestatusupdateevery30suntilmodechanges $31Requestsingleerrorreportevery30suntilmodechanges WarmupMode $62Setpumptohighowrate $E2Setsolenoidcontroltopatientsample $30Requestsinglestatusupdateevery30suntilmodechanges $31Requestsingleerrorreportevery30suntilmodechanges NormalMode $E2Setsolenoidcontroltoroomair $1FPerformzerocalibration $E2Setsolenoidcontroltopatientsample $30Requestsinglestatusupdate $31Requestsingleerrorreport $42Requestcontinuousdataupdates hostsystemcommand,buttimeoutexceptionsarecommonandvarybycommand.A noresponse"fromthe4700maybeduetoreceivingrandomgarbage"data, aninvalidcommandcode,theprevioushostcommandhadnotbeenrespondedto witheitherACKorNAK,theintercharacterdelayexceeded250milliseconds,an incorrectlengthbyteLB,oranincorrectchecksumCSbyte.Appendix5.2provides additionaldetailsonthehostcommandandresponseformatting,includingadescription ofthelengthbyteLBandchecksumCSbyte. Theserestrictionsmustbecarefullyaddressedwhenprogrammingthecommunication protocol,whichincludesthesendingofhost"commandsandhandlingtheAndros4700 responses,intheAtmega328.Eachcommandmustbeacknowledgedbeforesendingthe next,whichrequiresthateachresponsecanbeparsedappropriatelyandinatimely manner.Duringtheinitializationperiod,errorhandlingisnecessarytocheckthe 46

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operatingmodeandquicklyrespondtoanyproblemswiththeinstrumentation.Once theAndrosisoperatingnormallyandcanprovidecontinuousstatusupdatesevery40ms, thesoftwaremustbeabletoparsethedata,calculatethemassowrates,andcontrolthe MFC'sinreal-time. Thusastatemachineimplementationwaschosentoallowthesoftwaretobehave dierentlyinthevariousoperatingmodes.ThethreeinitializationperiodsStartup Mode,WarmupMode,andNormalModecorrespondedtothreedistinctstatesusing thecommandcodeslistedinTable3-4.Alloftheabovecommandstringsmustbe acknowledgedbeforecollectingdata.TheoperatingmodeoftheAndrosisreectedin the4700responsetothestatusupdatecommand$30andmustreectthenextmodeto safelytransitiontothenextstate.AnalstateReceivingData"wasusedtodelineate thereal-timeparsingofcontinuousdataupdatesandcontroloftheMFC's. Thecharactersreceivedbythehostsystemserialportsmustbetemporarilystoredin aserialbuertoretainallincomingcharacters.Thismustbeaccomplishedbycontinually pollingtheserialport.Sinceeachincomingresponseorpacket"beginswiththeACK orNAKbytesbutvariesinlength,thebueredarrayofcharactersmustbescannedto considereachpacketseparately.Ifacompletepacketisavailable,i.e.thenumberofbytes isequaltothelengthbyteLBandthechecksumiscorrect,thenthedataeldsofthis packetcanbeprocessed. Duringtheinitializationperiod,theACKcodeandreceiptofthefullpacketare sucientconditionstoproceedtothenextcommand.IfaNAKisreceived,thepacket mustberesentafteradelayperiod.Thecommandmustalsoberesentifnoresponseis receivedpastthegiventimeoutperiodstoconsiderallexceptions.Quiteoften,the NAKistheresultofaninternalsynchronizationerrororaBusy"response,andboth canberesolvedbyincorporatingadelaybeforeresendingthecommand.Iftheerrorcode correspondstoproblemswiththeinstruments,itisisrecordedontheserialterminalfor immediate. 47

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Whenthecompletestatusupdateordataupdatepacketisreceived,thedataeldof theresponsepacketmustbeparsed.The4700responsetothestatusupdatecommand $30includesabyterepresentingtheoperatingmode,whichrequiresbit-wiseparsingto updatethestatemachine.Thebytesrepresentingthegasdatamustalsobeconvertedto theirdecimalrepresentationbeforetheycanbeusedinthecalculationofthemassow rates,describedin3.4.2.ThesoftwareowdiagramshowninFigure3-6describesthe dataprocessingimplementedinCusingtheAtmega328microcontroller. Figure3-6.HybridbenchtopsoftwareowdiagramimplementedusingtheAtmega328 microcontroller Theresultingcodeimplementationwasoptimizedforeciencytoensurethatthe calculationofthemodelequationsandprintingofdatathroughtheserialCOMportof 48

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alaptopcouldbeperformedevery40msasthecontinuousdataupdatesarereceived. Thecommunicationprotocolmustincorporaterobustdatahandlingtechniquesduetothe memoryconstraintsoftheAtmega328.Run-timeerrorsassociatedwithdynamicmemory allocationwereaddressedandresolvedtoallowcontinuousoperationofthesoftware. Table3-5liststhedatareportingrangeandresolutionoftheAndros4700.The physicallimitationsofthegassensorsmustbeconsideredwhenevaluatingtheresponsesof thehybridbenchtoptothescenariosoutlinedinChapter4. Table3-5.DataReportingRangeandResolutionoftheAndros4700GasAnalyzer Gas/DataReportingRangeResolution O 2 -5.0to105.0%0.1% -40.0to840.0Torr0.1Torr CO 2 -0.7to13.2%0.1% -5.3to105.3Torr0.1Torr 3.4.2MassFlowControllersMFCs Aftertheincomingdatapacketisparsed,thestoredO 2 andCO 2 partialpressures mustbeusedtocalculatethemodelequationsgivenin3{1and3{2.Asdiscussedin Section3.3,the mfcX variablesareexpressedasapercentofthemaximumoutputow foreachMassFlowControllerMFC.TheseMFCsarehigh-precisioninstrumentsand aremanufacturedbyPneucleus,Inc.EachMFCrequiresacontrolvoltageintherangeof 0-5V.Theyarestrictlylineardevices,where0Vcorrespondsto0%ofthemaximumow rate,2.5Vcorrespondsto50%ofthemaximumowrate,and5Vcorrespondsto100%of themaximumowrate.TheMFCshavebeencalibratedbythemanufacturer,butsome deviationinoutputowisexpectedattheextremaofthisvoltagerange. SinceMFCsareanalogdevices,thesemassowratesmustbeconvertedtoanalog voltagesviaaDACDigitaltoAnalogConverter.TheAtmega328-basedmicrocontroller usedtodevelopthecommunicationprotocoloutlinedabovedoesnotincludeDAC hardware.Ratherthanusingadditionalhardware,however,theoutputofapulse-width modulatedPWMsignalcanbelteredtoproduceastableDCvoltage.The mfcX 49

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variables,whichareeachrepresentedasapercentmaximumow,canbedirectly discretizedandmappedtotherangeforthePWMoutputsto255bits ! 0to5 V. ForthehighestprecisionPWMwaveforms+/-0.1%,thetimerscontrolling thePWMoutputsmustbeinitializedtothehighest-frequencysettings ~ 977Hz.A straightforwardlow-passRC"ltermaybeusedtoimplementthisprocesssincethe MFCsuseaseparatevoltagesupplyonthehybridrack,andthecurrentconsumptionof thecontrolsignallinesislimitedtotherangeofmicroamps.Theresistorandcapacitor valuesforthiscircuitwerechosentominimizeripplevoltageandsetalowfrequency cut-o.Ideally,thiswouldbeaperfectDCvoltage,whichischaracterizedbyafrequency of0Hz.However,thereisatrade-obetweenripplevoltageandresponsetime,which directlycorrespondtotheresistorandcapacitorvalueschosentocompletethecircuit. Settlingtimewasconsideredasecondarylimitation,asthechangestotheowaresmall. Inotherwords,thealveolarpartialpressureswillnotchangerapidly.Inaddition,the responsetimeoftheMFCsislimitedto100ms,whichthusdoesnotrequirefastsettling times. ThuswechosetheresistorandcapacitorvaluesforthethreeMFCcontrolsignalsto improvetheaccuracyoftheDCvoltage.Theresultingcutofrequencywas3.75Hz,the peak-to-peakvoltageripplewas0.060Vor1.2%ofthevoltagerange,andthesettling timewaschosentobe97.7ms.Thusthecircuitwasdesignedtoliewithinthetime responselimitationsetbytheMFCs,butstillretainedhighaccuracy. ThecurrentconsumptionoftheMFCs,thoughsmall,requiredcalibrationofthe PWMtothedesiredoutputvoltageandoutputow.Theduty-cycleofthePWM waveformwasgraduallychangedwhiletheoutputvoltagewasmeasuredusinga voltmeter.Linearregressionwasusedtondtheidealcalibrationsettingtomaximize thecorrespondencebetweenthedesiredvoltageandtheresultingoutputvoltage. ThecurrentconsumptionoftheMFCsisdependentontheowrate,butingenerala 50

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veryhighcorrespondencebetweenthedesiredandoutputvoltageswererecordedover theentireoperatingrange R 2 =0 : 999post-calibration.Thecodeshownin3{5 describetheoatingpointcalculationsimplementedinCthatarenecessarytomapthe mfcX variablestothePWMfrequencyrangeto255bits ! 0to5Vafterthelinear calibration. int N 2 =int mfcN 2 1 : 0235+0 : 5;{5 int O 2 =int mfcO 2 1 : 0158+0 : 5;{6 int CO 2 =int mfcCO 2 1 : 0089+0 : 5;{7 3.5DierencesbetweentheHPSHybridandtheHybridBenchtop WesummarizethemostsignicantdierencesbetweentheHPShybridproductand thehybridbenchtopheretomaintainconsistentterminologyandprovideclarityonthe designofthebenchtopcontroller. IntheHPShybridproduct,theacquisitionofdata,calculationofmassowcontrol rates,andcontrolofmassowcontrollersisperformedbytheMusesoftware.The supportinghardwareisindicatedinFigure3-5.Thebenchtop,incontrast,doesnotuse theMusesoftwareandinsteadrequiredthedesignofthehardwareandcontrolsoftwareas describedinSection3.4. IntegratedmodelresponsesareusedintheHPShybridproduct.Inotherwords,the modelofthecirculatorysystemaectstheexchangeratesofgases.Inthehybridbenchtop model,thegasexchangeratesareconstanttosimplifythemodel.Forthisreason,the responsesofthetwoimplementationsdiersignicantly,butthePGEhardwareis expectedtobehaveverysimilarlyunderidenticalconditions. TheHPShybridproductdoessimulateapatient'sresponsetoanestheticgases,which requiresconsiderablehardwareinadditiontotheimplementationdescribedinSection3.3. Althoughtherightandleftalveolarcompartmentsarephysicallyseparate,theyare treatedasasinglehomogenouscompartmentinbothimplementations.Thereisonlyone 51

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setofvariablesusedtorepresentthegascompositioninthelungs,andtheyreceivethe sameinputfromtheventilatorandtheMFCs.Thusneitherhybridimplementationcan simulateclinicalscenariossuchaspneumothorax,eventhoughthisfeatureisintrinsicto thedesignoftheMusesoftware-onlyimplementation. 52

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CHAPTER4 EXPERIMENTDESIGNANDRESULTS ThehybridbenchtopandreferenceimplementedinMATLABsimulatedynamic experimentsreectingextremephysiologicalsituations.Theresponsesarequantitatively comparedunderequivalentsetsofconditionstoassessproductperformance.Dierent conditionsareapplicableunderdierenttestscenarios.Thiscomparisonmethodologywas appliedtoevaluatetheHPSsoftware-onlyimplementationMuseinMunje2013[1]. 4.1ConstantExperimentalConditions 4.1.1LungMechanics Theparametersgoverningthelungmechanicsmodelsinbothimplementationswere carefullycontrolledtoachieveequivalentventilationconditions.Thehybridbenchtop requiresacommercialventilatorformechanicalrespiration,whichpresentslimitationsthat mustbeaddressedindividually.AsdiscussedinChapter2,thereferenceimplementedin MATLABcontainsamodeloflungmechanicsthatisseparatefromthePGEmodeland mimicsthebehaviorofamechanicalventilator.Allparametersmaybeadjustedbythe userinsoftware. 4.1.1.1Minuteventilation Minuteventilation,whichisequivalenttotidalvolumemultipliedbytherespiratory rate,isacriticalcomponentofthepulmonarygasexchangemodel.Precisionventilation controlisthereforemandatoryacrossplatforms.Withrespecttothereferenceimplementation, minuteventilationiscontrolledbyxingthetidalvolume V T andrespiratoryrate rr parametersinMATLAB.Theseparametersareequivalenttotheventilatorsettingsfor thehybridbenchtopunderxed-volumeventilation"4-1.Bothrespiratoryrateand tidalvolumeareadjustablesettingsontheventilator,butaprecisionow-meterprovides areal-timeestimateofthetruetidalvolume.Thedesiredtidalvolumewasmanually adjustedsothatthemeasuredtidalvolumewasequaltothe V T parameterinMATLAB. Theventilatorrequiresapproximately1minutetoreachstabilitynecessaryforaccurate 53

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testing,whichwascontainedwithinthe6minutesrequiredforthehybridbenchtopto reachsteady-state. 4.1.1.2Respiratorywaveform Controllingtherespiratoryrateandtheinspiratorytoexpiratorytimeratio I : E ensuresaconstantrespiratoryperiodicitysuchthatthetimecoursesofbothplatforms maybedirectlycompared.The I : E ratioisanadjustableparameterontheMATLAB platformbutisnotdirectlyavailabletotheuserontheventilatorusedwiththeHybrid Benchtop.ThepeakowvaluewasadjustedmanuallytoachievethedesiredI:Eratio afterequatingthemeasuredtidalvolume,asmeasuredbytheventilator. Underidenticalminuteventilation,cross-platformdierencesincomplianceand bronchialresistancearenotrelevanttothemodelsunderstudy.Theseparametersare providedforreference4-1. ThefunctionalresidualcapacityFRCanddeadspacevolumeofthephysicalsystem cannotbemeasuredaccurately;thus,cross-platformdierencesarecurrentlyassumed insignicantbutmayrequirefurtherinvestigation. Table4-1.CharacteristicLungMechanicsParametersAcrossPlatforms SymbolNameUnitsReferenceBenchtop rr RespiratoryRatebreaths/min,bpm1212 V T TidalVolumemL500500 IE InspiratorytoExpiratoryRatio|1:31:3 C TotalCompliancemL/mmHg149.84| R AirwayResistancemmHg/mL2.7 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(3 | FRC FunctionalResidualCapacitymL2300| V D DeadSpaceVolumemL150| Thesesettingsremainxedduringallperiodsofventilation. 4.1.2PulmonaryGasExchange Thetotalatmosphericpressurewasassumedconstant.Minordeviationsassociated withelevationandhydrostaticpressureapplytoallgasesinthePGEmodelandare negligibleinthenalproduct.Theinspiredpartialpressuresofoxygenandcarbon dioxideareconstantintheMATLABreferenceandaresubjecttominoructuationsof 54

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theventilatorinthehybridbenchtopmodel.Thevolumepercentofoxygenistheonly parameteraccessibletotheuserandissetto21%,or159.6mmHg. TheexchangeratesforoxygenandcarbondioxidegivenbelowinTable4-2are validduringallperiodsofcirculationornormalperfusion.Thechangesappliedtothese conditionswillbeexplicitlydeclaredinSection4.2. Theinitialconditionsforthestatevariablesusedinthereferenceimplemented inMATLABwerechosentohelpthesystemreachsteady-statemorerapidlyandare includedbelowthePGEsystemparameters. Table4-2.CharacteristicPGEParametersAcrossPlatforms SymbolNameUnitsReferenceBenchtop P T TotalatmosphericpressuremmHg760760 P in O 2 InspiredpartialpressureofoxygenmmHg159159.6 P in CO 2 InspiredpartialpressureofcarbondioxidemmHg0.30 eO 2 ExchangerateofoxygenmL/min250250 eCO 2 ExchangerateofcarbondioxidemL/min-200-200 P D O 2 InitialdeadspacepartialpressureofO 2 mmHg130| P D CO 2 InitialdeadspacepartialpressureofCO 2 mmHg0| P A O 2 InitialalveolarpartialpressureofO 2 mmHg108.5| P A CO 2 InitialalveolarpartialpressureofCO 2 mmHg44| 4.2DescriptionoftheScenariosforComparison Thetwoimplementationswerecomparedunderphysiologicallynormalandextreme conditions.ThesetestconditionsaresummarizedbelowasdenedperMunje2013[1]: 1.NormalVentilationandNormalCirculation 2.VentilatoryArrestandNormalCirculation 3.NormalVentilationandCirculatoryArrest 4.SimultaneousVentilatoryandCirculatoryArrest ThecirculationconditionscorrespondtoxedexchangeratesforO 2 andCO 2 betweenthebloodandalveoliintheabsenceofamodelofthecardiovascularsystem,as discussedin2.2.1.2.Innormalhumanphysiology,therateofgasexchangeisdependent onthepartialpressuredierenceofeachgasbetweenthealveoliandvenousblood.Fixed 55

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exchangeratesremovethedependenceofthepulmonarygasexchangemodelonthe cardiovascularsystemmodelintheHPSplatforms,andthissimplicationallowsfora straightforwardanalysisofthepulmonarysystembehavior.Moreover,thismodeling choiceisidenticalacrossplatforms,andsotheHybridBenchtopmaybedirectlycompared tothegoldstandard"referenceimplementedinMATLAB. 4.2.1Scenario1:NormalVentilationandNormalCirculation Thisscenarioisdesignedtosimulatenormalrespiratoryfunction.Normalventilation referstoaxedtidalvolume,respiratoryrate,andinspiratorytoexpiratoryratiowithin thephysiologicallytypicalrangeforahealthyadult.Normalcirculationreferstothe averageratesofgasexchangeinthehealthyadultlungunderrestingconditions, setconstantintheabsenceofacirculatorysystemmodel.Alltheparametersand initializationsgiveninTable4-1andTable4-2remainunchanged,butthosethatvary acrossscenariosarerepeatedhereinTable4-3forconsistency. Table4-3.ModelParametersforScenario1:NormalVentilationandNormalCirculation SymbolNameUnitsReferenceHybridBenchtop V T TidalVolumemL500500 eO 2 ExchangeRateofOxygenmL/min250250 eCO 2 ExchangeRateofCarbonDioxidemL/min-200-200 Undernormalconditions,thealveolarpartialpressuresofoxygenandcarbondioxide shouldvaryrhythmicallywiththesetrespiratoryrateand I : E ratioafterreaching steady-stateequilibrium.PAO 2 islowestatthebeginningofeachbreathandreaches itspeakvalueattheendoftheinspiratoryperiod.Similarly,PACO 2 ishighestatthe beginningofeachbreathandreachesaminimumattheendofinspiration.Thesimulation ofnormalrespirationbybothplatformscanbefoundinSection4.3.1. 4.2.2Scenario2:VentilatoryArrestandNormalCirculation Thisscenarioisphysiologicallysimilartosustainedapnea,inwhichtheowofairto thelungsisblocked.Withrespecttothereference,ventilationmaybeimmediatelyhalted 56

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byinitializingthetidalvolumeto0directlyinMATLABsincetheinitializationsofthe statevariableswerechosenasthesteady-statevaluesundernormalrespiration. Thehybridbenchtopmustrstreachthesteady-statealveolarpartialpressuresof oxygenandcarbondioxide.6minutesofnormaloperationScenario1,4.2.1arerequired toreachsteady-state,whicheectivelyfunctionsastheinitializationsofthestatevariables inMATLAB.Afterthese6minutes,theventilatoristurnedo,buttheendotrachaeltube remainsinplace.ThechangetotidalvolumeonbothplatformsisgiveninTable4-3.The remainingparametersandinitializationsgiveninTable4-1andTable4-2areunchanged. Table4-4.ModelParametersforScenario2:VentilatoryArrestandNormalCirculation SymbolNameUnitsReferenceHybridBenchtop V T TidalVolumemL00 eO 2 ExchangeRateofOxygenmL/min250250 eCO 2 ExchangeRateofCarbonDioxidemL/min-200-200 Duringventilatoryarrest,noadditionaloxygenisinhaled,andexcesscarbondioxide isnotexhaled.Sincetheexchangeofoxygenandcarbondioxideismaintainedunder normalcirculation,theamountofoxygeninthelungswillbedepletedovertimewhile carbondioxideaccumulates.Physiologically,theexchangeratesofbothgasesshould decaytozeroduetoreducingpartialpressuredierencesbetweenthebloodandalveoli, whichlimitsthedepletionofoxygenandaccumulationofcarbondioxide.However,these exchangeratesareconstantinourmodels,andthereforewedoexpectthealveolarpartial pressureofoxygentodecreaselinearlytozeroandthealveolarpartialpressureofcarbon dioxidetoincreaselinearlyindenitely. 4.2.3Scenario3:NormalVentilationandCirculatoryArrest Thisscenarioisphysiologicallysimilartocardiacarrest.Thelungsareconstantly ventilatedbytheowofair,butgasexchangecannolongeroccur. Inthereferenceimplementation,theinitializationsofthestatevariablesarethe steady-statevaluesundernormalconditionsasperTable4-2.Similartothediscussion 57

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forScenario4.2.2,theseinitializationsallowcirculationtobestoppedimmediatelyby initializingthegasexchangeratesto0directlyinMATLAB. Thehybridbenchtoprequires6minutesofnormaloperationScenario1,4.2.1to reachsteady-statevalues.Sincetheexchangerateofgasesisstoredonthemicrocontroller, asperChapter3,thesoftwareowmustbeadjustedtoautomaticallysetbothexchange ratesto0after6minutes. Table4-5.ModelParametersforScenario3:NormalVentilationandCirculatoryArrest SymbolNameUnitsReferenceHybridBenchtop V T TidalVolumemL500500 eO 2 ExchangeRateofOxygenmL/min00 eCO 2 ExchangeRateofCarbonDioxidemL/min00 Sincethepartialpressureofinhaledoxygenishigherthanthatinalveolarspace, thealveolarpartialpressureofoxygenwillrisetoatmosphericlevelswitheachbreath. Similarly,theconstantexhalationofcarbondioxidewilldepleteallthatremainsinthe alveolarspace.Thealveolarpartialpressuresofbothgaseswillcontinuetochangeuntil theyareequaltotheinspiredpartialpressures. 4.2.4Scenario4:SimultaneousVentilatoryandCirculatoryArrest Thisscenarioisrepresentsthemostextremesystembehaviorinwhichthereisno owofairtothelungsandthereisnogasexchangeinthealveoli.Thisisphysiologically similartosimultaneousapneaandcardiacarrest. Inthereference,theinitializationsofthestatevariablesarethesteady-statevalues undernormalconditionsasperTable4-2.Theseinitializationsallowtheimmediatearrest ofbothventilationandcirculationbyinitializingthetidalvolumeandgasexchangerates to0directlyinMATLAB. Thehybridbenchtoprequires6minutesofnormaloperationScenario1,4.2.1to reachsteady-statevalues.Sincetheexchangerateofgasesisstoredonthemicrocontroller, asperChapter3,thesoftwareowmustbeadjustedtoautomaticallysetbothexchange 58

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ratesto0after6minutes.Thesoftware-controlledchangeinexchangeratessimultaneously signalsforthemanualshutdownoftheventilator. Table4-6.ModelParametersforScenario4:SimultaneousVentilatoryandCirculatory Arrest SymbolNameUnitsReferenceHybridBenchtop V T TidalVolumemL00 eO 2 ExchangeRateofOxygenmL/min00 eCO 2 ExchangeRateofCarbonDioxidemL/min00 Inthisscenario,thealveolarpartialpressuresofbothoxygenandcarbondioxideare expectedtoremainattheirinitialvaluesduetothelackofventilationandperfusion. 4.3SimulationResults TheresponseoftheHybridBenchtopisdirectlycomparedtotheMATLABreference underthesimulationconditionsdescribedin4.2.Foreachscenario,thetimecourseofthe partialpressuresofbothoxygenandcarbondioxideinalveolarspaceareshownfromboth implementationsinthesamegure. 4.3.1Scenario1:NormalVentilationandNormalCirculation Asdescribedin4.2.1,thisscenarioisdesignedtosimulatenormalrespiratory function.Thisexperimentwasperformedinthehybridbenchtoppriortoeachsubsequent scenariotoallowthehybridbenchtoptoreachsteady-statealveolarpartialpressures. Figure4-1illustratesthattheHybridBenchtopsimulationofO 2 andCO 2 alveolar partialpressuresreachesphysiologicallystereotypic,steady-statebehaviorfollowinga 6-minutetransientphase.ThevalueofPAO 2 variesintherangeof103.6-107.6mmHgand PACO 2 variesintherangeof46.4-49.7mmHg.Theperiodofthiswaveformisconsistent withtheventilationparameterof12breaths/min.Visualinspectionalonerevealsthat thebehaviorofthetwoimplementationsishighlysimilarunderthisrstcondition,and quantitativecomparisonsareprovidedinTable4-7.Themostmeaningfuldierence betweenthetwosetsofwaveformsistheendexpiratoryosetofbothO 2 andCO 2 .On 59

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Figure4-1.PAO 2 andPACO 2 generatedbytheHybridBenchtopandMATLABreference undernormalventilationandnormalcirculation average,thehybridbenchtopsimulatesameasurablylowerPAO 2 andhigherPACO 2 than thereference. Table4-7.Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario1:NormalVentilationandNormalCirculation AverageValueReferenceHybridBenchtop PAO 2 Range109.7-114.2mmHg103.6-107.6mmHg EndExpiratoryOset5.9mmHg EndInspiratoryOset6.8mmHg ExpiratoryGradient-1.21mmHg/s-0.96mmHg/s PACO 2 Range36.1-39.8mmHg46.4-49.7mmHg EndExpiratoryOset9.8mmHg PeakInspiratoryOset10.5mmHg ExpiratoryGradient0.97mmHg/s0.81mmHg/s 60

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4.3.2Scenario2:VentilatoryArrestandNormalCirculation Thisscenarioisdescribedin4.2.2. Figure4-2.PAO 2 andPACO 2 underventilatoryarrestandnormalcirculation UponvisualinspectionofthePACO 2 timecourseinFigure4-2,notethatthe Androsgasanalyzerisnotequippedtoreportpartialpressuresofcarbondioxidehigher than100.5mmHg,asdiscussedinChapter3.TheMATLABreferencedoesnotlimit thegeneratedpartialpressureofCO 2 andthusincreasesindenitely.Quantitative comparisonsareonlyappropriatepriortoreachingthismaximumvalueat68.4seconds, sincethetruepartialpressureofCO 2 shouldbesignicantlyhigher,andtheCO 2 ow ratenolongerincreaselinearly.ThedecayrateofthereportedPAO 2 isalsomisleading, sincethepartialpressureofoxygeninthisscenarioisdependentontheexpectedPACO 2 61

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inow.IfthePACO 2 curvewerenotcappedbythephysicallimitationsoftheAndrosgas analyzer,thereportedPAO 2 curvewoulddecaymoresharplyandexhibitmorelinearity overalongerperiodoftime. Theshortenedtimescale,whichexcludesthedatacollectedafterthemaximumpartial pressureofCO 2 isreportedbytheAndros,isincludedbelowinFigure4-3. Figure4-3.PAO 2 andPACO 2 underventilatoryarrestandnormalcirculationwitha reducedtimescale Visualinspectionrevealsthatthebehaviorofthetwoimplementationsdiverges signicantly,andquantitativecomparisonsareprovidedinTable4-8. Mostsignicantly,thePAO 2 andPACO 2 gradientsgeneratedbythehybridbenchtop aremoregradualthandemandedbythevalidatedreference.Anonlineardecayofthe hybridbenchtopisalsoevidentthroughvisualinspectionofthesecondhalfofthetime scale. 62

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Table4-8.Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario2:VentilatoryArrestandNormalCirculation AverageValueReferenceHybridBenchtop PAO 2 mmHg Steady-StateRange109.7-114.2103.6-107.6 InitialValue108.5107.4 FinalValue14.351.0 Gradient-1.38/s-0.82/s PACO 2 mmHg Steady-StateRange36.1-39.846.4-49.7 InitialValue4447.2 FinalValue100.2100.2 Gradient1.12/s0.77/s MaxValTimeOset18.4s 4.3.3Scenario3:NormalVentilationandCirculatoryArrest Thisscenarioisdescribedin4.2.3. Visualinspectionrevealsthatthebehaviorofthehybridbenchtopimmediately divergesfromthereference.QuantitativecomparisonsareprovidedinTable4-9.The initiallinearascentanddescentaredenedastheapproximatelineargradientbetween 0sand60s.Thiscomparisonwasincludedtohighlightthesharpdierencebetweenthe initialbehaviorofthehybridbenchtopascomparedtothereference. Table4-9.Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario3:NormalVentilationandCirculatoryArrest AverageValueReferenceStandardHybridBenchtop PAO 2 mmHg Steady-StateRange109.7-114.2103.6-107.6 InitialValue108.5106.0 InitialLinearAscent0.75/s0.44/s PACO 2 mmHg Steady-StateRange36.1-39.846.4-49.7 InitialValue4448.5 InitialLinearDescent-0.66/s-0.35/s 63

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Figure4-4.PAO 2 andPACO 2 undernormalventilationandcirculatoryarrest SimilartothediscussionoftheScenario2resultsin4.3.2,thereisconsiderabledelay betweentheresponseofthehybridbenchtopandthereference. 4.3.4Scenario4:SimultaneousVentilatoryandCirculatoryArrest Asdescribedin4.2.4,thearrestofbothventilationandcirculationshouldmaintain theinitialvaluesforPAO 2 andPACO 2 . Figure4-5illustratesthattheinitialvaluesforPAO 2 andPACO 2 arenotmaintained overtimeinthehybridbenchtop.Overaperiodof5minutes,PAO 2 graduallydecreases whilePACO 2 increases.ThisimbalancerevealsthattheoutputoftheMFCsdoesnot matchthevolumeofgasremovedbythevanepump. 64

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Figure4-5.PAO 2 andPACO 2 undersimultaneousventilatoryandcirculatoryarrest Table4-10.Quantitativecomparisonsbetweenthereferenceandhybridbenchtopduring Scenario4:SimultaneousVentilatoryandCirculatoryArrest AverageValueReferenceHybridBenchtop PAO 2 mmHg InitialValue108.5105 FinalValue108.595.7 Gradient-1.9/min MinuteVolumeOset7.3mL PACO 2 mmHg InitialValue4449 FinalValue4468.9 Gradient4/min MinuteVolumeOset15.7mL/min 65

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Thedierenceinpressureisillustratedbytheaveragevalueshownforthegradientin thelistofquantitativecomparisonsareprovidedinTable4-10.Onaverage,thePACO 2 rises4mmHghigherthantheexpectedvalueperminute.Similarly,PAO 2 decreases 1.9mmHglowerthanthantheexpectedvalueperminute.Althoughthesearesmall dierencesinpressure,thismismatchisquitesignicantoveraperiodof5minutes.Note alsothatPACO 2 increasestwiceasfastasPAO 2 decreases. TheMinuteVolumeOset"iscalculatedasfollows: MinuteVolumeOset= FinalValue )]TJ/F15 11.9552 Tf 11.955 0 Td [(InitialValue P T 60 s 300 s F vane where F vane =3000 mL and P T =760mmHg.Evidently,asmalldierenceinow correspondstoalargeosetinthepartialpressuresandthusexpectedvolumesofgasover time.SincePACO 2 isrisingandPAO 2 isdecreasing,theoutputoftheMFCsmustbe higher thanthevolumeofgasremovedbythevanepump. 4.4DiscussionofSimulationResults ThediscrepanciesreportedinSection4.3areclinicallyrelevantanddemandfurther investigationbeforeproposingstrategiesforoptimizationandredesign. 4.4.1DiscrepanciesandSystemLimitations Therstscenario,thesimulationofnormalrespiratoryfunctionanalyzedin Section4.3.1,revealsasignicantosetbetweenthepartialpressuresgeneratedby thehybridbenchtopandthereferencestandard.Straightforwardphysiologicarguments maybepresentedtoaddresstheseobserveddierences.Inthehumanbody,hypernea orbreathingthatisfasterordeeperthannormalcausesthealveolarpartialpressureof oxygentoincreaseandthealveolarpartialpressureofcarbondioxidetodecreasethrough increasedminuteventilation.Physiologically,thiscompensatesforexcessproductionof carbondioxideproducedduringexercise,forexample.AsshowninTable4-7,thehybrid benchtopsimulateslowerPAO 2 andhigherPACO 2 thanthereference.Sinceahigher 66

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minuteventilationwouldincreasePAO 2 anddecreasePACO 2 ,thereporteddierences maybepartiallyattributedtoareductionintheapparentminuteventilation. Similarly,alowerexchangeofO 2 wouldalsoincreasePAO 2 anddecreasePACO 2 sincethebalanceofgaseswouldbemoresimilartoatmosphericlevels.Bytheprevious argument,thereporteddierencesbetweenthehybridbenchtopandreferencemaybe partiallyattributedtoanincreaseintheapparentexchangeofgases. Thereporteddierencesmaybepartiallyattributedtoeitherorbothareductionin theapparentminuteventilationandanincreaseintheapparentexchangeofgases.Two simpleexperimentsmaybeperformedtofurtherhighlightthesediscrepancies.Byholding therespiratoryrateconstantbutincreasingtheminuteventilation,weexpecttoincrease PAO 2 anddecreasePACO 2 andthusreducethereportedoset.Asimilarresponseis expectedbyholdingtheminuteventilationconstantandreducingtheexchangeofO 2 andCO 2 .Theconrmationoftheseexpectedoutcomes,whichweredevelopedthrough basicphysiologicreasoning,wouldsuggestthatourproposedexplanationsforthereported osetsarecorrect. Areductionintheapparentminuteventilationmaybeduetoaleakorduetopoor calibrationoftheventilatorowmeterresponsibleforreportingthemeasuredtidal volume.Therstexperimentdescribedabovewouldprovideaquantitativeperspectiveon thedierenceinapparentminuteventilationandthereforeanexpectationforthevolume ofleakedgas.If,forexample,atidalvolumeof600mLwererequiredtomatchthe steady-statepartialpressuresofthereferencestandard,then100mLofleakedgascould bethesourceoftheproblem.However,onlymuchsmallerleakswouldpassunnoticed, andsoitwouldthenbesafetoassumethattheproblemcannotbecompletelyattributed toleaks.Sincethemeasuredtidalvolumeisusedtoensurethatminuteventilationis equalacrossplatforms,andanexternalowmeterisnotavailabletoconrm,itisvery reasonablethattheventilatoristhesourceofthisosetandmustbecloselyinspected. 67

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Anincreaseintheapparentexchangeofgasesisasecondexplanationforthe reportedosetinpartialpressures.Thisismorediculttounderstandduetothe physicalimplementationofgasexchangeviathexed-volumevanepump.Sincethe massowcontrollersMFCsarehigh-precisioninstrumentsandwerecalibratedbythe manufacturer,itisquiteunlikelythattheiroutputishigherthanexpected.However,a precisionow-metermaybeusedtoverifytheseows.Alessobviousexplanationisthat thepartialpressuresoftheindividualgasesremovedbythevanepumparenotequalto thoseoftheentirelung.Inotherwords,thegasesarenotfullymixedinthelungbefore reachingthevanepump.Inthisinstance,oxygencouldbepreferentiallyremovedby thevanepump,whichwouldinturnsimulateahigherexchangeratethancontrolledin software. ThesecondscenarioofVentilatoryArrestandNormalCirculation,presentedin Section4.3.2,revealsmajordiscrepanciesinthedynamicbehaviorofthehybridbenchtop ascomparedtothereference.Inadditiontotheosetobservedundernormalventilation andnormalcirculation,thehybridbenchtopcannotgeneratetheexpectedchanges inpartialpressuresasrapidlyasthereference.Asimilarbehaviorisobservedinthe simulationofthethirdscenarioofNormalVentilationandCirculatoryArrest.Alinear approximationofthechangeinsimulatedpartialpressuresduringtherstminuteofthe experimenthighlightstheextremediscrepancy. Thesecondscenarioalsopromptsadiscussionofafundamentallimitationofthe vanepumpdesign.VisualinspectionFigure4-3revealsthatthePAO 2 simulatedbythe hybridbenchtopdecaysnonlinearlyinthesecondhalfoftheexperiment.Asdiscussedin Chapter3,thevanepumpremoves3000mL/minofbulkgasN 2 ,O 2 ,CO 2 tosimulate oxygenuptakebyremovingoxygen.SincetheexchangerateofO 2 issetataconstant250 mL/min,theremustbeatleast250mLofO 2 presentinthebulkgasremovedbythevane pump: 250 = 3000=8 : 333% O 2 68

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8 : 333% O 2 760 mmHg =63 : 33 mmHg Oncethepartialpressureofoxygendropsbelow63.33mmHg,thevanepumpcanno longerremoveenoughgastorepresentaxedexchange250mL/min. Onesolutiontothisproblemwouldbetoincorporateavariablevanepumpintothe hybridbenchtopmodel.Asthepartialpressureofoxygendecreases,thevolumeofgas removedbythevanepumpcouldbeincreasedtoremoveagreaterquantityofoxygen andtherebyallowsimulationoflowerpartialpressures.Regardless,theconsiderabledelay betweentheresponseofthehybridbenchtopandthereferencecannotbesolelyattributed tothedesignchoiceofthevanepump. ThefourthscenariopresentedinSection4.3.4revealsanimbalancebetweenthe outputoftheMFCsandthevolumeofgasremovedbythevanepump.Slightdierences inowyieldlargedierencesinpartialpressuresonascaleof5minutes.Asdiscussed above,aprecisionow-metermaybeusedtoverifytheoutputoftheMFC's,butitis unlikelythattheydeviatefromtheexpectedowratessincetheywerepreciselycalibrated bythemanufacturer.Morelikely,thevanepumpwithdrawslessthan3000mLofgasper minute.Sincethemodelequationsaredependentonanaccuratevalueforthevolumeof gasremovedbythevanepump,itiscrucialthatthevanepumpisrecalibratedpriorto performingsubsequentexperiments. Allfourscenariosrevealasignicantdelayintheresponseofthehybridbenchtop ascomparedtothereferencestandard.Acarefulanalysisofthehardwarecontroller presentedinChapter3supportsthattheresponsetimeofthehigh-precisionMFCs remainsalimitingfactorintheresponseofthesystem. 4.4.2CriticalModelingAssumptionsandGeneralConsiderations SeveralassumptionsimplicitintheimplementationdescribedinSection3.3mustbe addressedwhenconsideringthebehaviorofrealgases.Theseassumptionsmaycontribute tothereporteddiscrepancies. 69

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First,theinspiredgasisassumedtobedry,orfreeofwatervapor,andthe temperatureinsidetheairwaytubingandlungcompartmentsisassumedtobeequalto theroomtemperature.Theseassumptionsarecriticaltothepressure-volumerelationships governingthebehavioroftheHPSPGEmodelhardware. ThemostcriticalassumptionmadeinthedevelopmentoftheHPSPGEhardware isthattheelasticlungsarehomogenouscompartments.Inotherwords,weassume thatthegasesareperfectlymixedinthelungsandareextractedbythevanepumpin concentrationsequaltothoseinthelungs.Moreover,thefunctionalresidualcapacity FRCofthelungscannotbemeasuredaccuratelyandisassumedtobesimilartothe clinicalaverage.Thisaectsthegasmixinginthecompartmentandmayrequirefurther investigationtopreventselectivesamplingofanyparticulargas. SimilarlytotheFRC,thedeadspacevolumeofthephysicalsystemisalsoignored, buttheHPSmannequinhardwarethemouth,pharynx,larynx,bronchialtubes,and esophagusareanatomicallyrepresentativeofahumanpatient,andtheowlinesleading tothevanepumpandthegasanalyzerwereminimizedtoreducethevolumeofgas trappedintheairwaytubing.Wealsoassumethatthevanepumpowrateisconstant andindependentoftotalgaspressureandcomposition.Thisallowsustocalculatethe volumesofeachofthegasesremovedbythevanepumpthroughouttherespiratorycycle andisimplicitinthemodelequationsdescribedin3{2. Thereporteddiscrepanciesmaybeattributabletotheseimplicitmodelingassumptions. Forexample,poormixingofgasesmayleadtoanimbalanceinthephysicalexchangeof gases,resultinginundesirabledynamicbehaviors. Inaddition,itisimportanttoaddressthemodelingchoiceofxedgasexchangerst describedinChapter2.Althoughxedgasexchangesimulatesunphysiologicalbehaviors, thisallowsaquantitative,dynamicanalysisofthehybridbenchtoppulmonarysystem independentofamodelforthecardiovascularsystem.TheHPSproductultimatelyuses integratedmodelresponses,butindependentconsiderationofthepulmonarysystemis 70

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requiredtofacilitateoptimizationandredesign.However,itisreasonabletoconsiderthat theextremebehaviorsdemandedbytheconditionofxedexchangemaynotbereplicable intheHPSPGEhardware. 71

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CHAPTER5 CONCLUSIONSANDFUTUREDIRECTIONS 5.1Conclusions Wedesignedandimplementedthecontrolsoftwareforahybridbenchtop" implementationconsistingofHPSPGEmodelhardware.Theresultingcodeimplementation wasoptimizedforeciency,andtheadditionaldelaysassociatedwiththehardware interfacetotheMFCswereensuredtobelessthantheMFCresponsetimes.Thus thereportedsystembehaviorsareduetointrinsicpropertiesoftheHPSPGEmodel hardware. Simulationofnormalphysiologicaloperatingconditionsdemonstratedamoderate discrepancyinthehybridbenchtopsimulatedpartialpressuresofoxygenandcarbon dioxideinthealveolarspaceascomparedtothereference.Weformulatedhypothesesfor theoriginofthesediscrepanciesandproposedfutureexperimentsforfurtherinvestigation. Thedynamicexperimentsreectingextremephysiologicalsituations,suchasapnea, demonstratethephysicallimitationsofthehybridlungmodel,whichcanbeattributedto aspecicgasowrateinthelungmodel. 5.2RecommendationsforFutureWork Theexperimentsoutlinedabovemaybeperformedtofurtherhighlightandquantify thelimitationsofthepresentsystemdesign.However,itmaybenecessarytomove towardsmoredynamicaltesting.Themodelingchoiceofxedgasexchangeenabled theanalysisofthehybridbenchtoppulmonarysystemindependentlyofamodelforthe cardiovascularsystem.However,thisdecisionrequiresextremesystembehaviors,which arephysicallylimitedbytheresponsetimeofthehigh-precisionmassowcontrollers.In otherwords,thehybridbenchtopcannotreactrapidlyenoughtomeetthedemandsof xedexchangerates.Sinceitisnotpossibletoreplicatetheseextremebehaviorsinthe physicalsystem,itmaybenecessarytodesignadditionalscenariosthataremoresimilar tophysiologicalconditions. 72

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Thedesignofadditionalscenariosmayreducethediscrepanciesindynamicbehaviors reportedfortheextremescenarios.However,itmaybenecessarytoincorporatethe variableexchangeratesimplementedintheHPSsoftware-onlyMuseintothesoftware portionofthehybridbenchtopimplementation. 73

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APPENDIX ANDROS4700COMMANDANDRESPONSEFORMATS TableA-1.HostCommandFormatoftheAndros4700GasAnalyzer[9] DID-LB-CMD-[DF]-CS DID DeviceIdenticationNumber.The4700DIDis$20. LB LengthByte.Statesthenumberofbytesfollowing,excludingthechecksum. CMD CommandCode.EachcommandhasauniqueCMD. [DF] DataField.Variesinlengthbycommand. CS Checksum.CS=notDID+LB+CMD+[DF]+1.Thisisequivalent toamodulo256,2'scomplimentofthesumofthespeciedbytes. TableA-2.ACK/AcknowledgeResponseFormatoftheAndros4700GasAnalyzer[9] ACK-CMD-LB-[DF]-CS ACK ACK=$06.Theacknowledgmentthatthecommandwillbeperformed. CMD Thecommandcodebeingrespondedto. LB LengthByte.Statesthenumberofbytesfollowing,excludingthechecksum. [DF] DataField.Variesinlengthbyresponse. CS Checksum.CS=notDID+LB+CMD+[DF]+1.Thisisequivalent toamodulo256,2'scomplimentofthesumofthespeciedbytes. TableA-3.NAK/NegativeAcknowledgmentResponseFormatoftheAndros4700Gas Analyzer[9] NAK-CMD-LB-EC-CS NAK NAK=$15.Thenegativeacknowledgmentthatthecommandhasbeen receivedbutcannotbeexecuted. CMD Thecommandcodebeingrespondedto. LB LengthByte.Statesthenumberofbytesfollowing,excludingthechecksum. EC ErrorCode.Indicateswhyacommandcannotbeexecuted. CS Checksum.CS=notDID+LB+CMD+[DF]+1.Thisisequivalent toamodulo256,2'scomplimentofthesumofthespeciedbytes. 74

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REFERENCES [1]R.Munje,Criticalanalysisofhybridandmathematicalmodelsforeducational simulationofpulmonarygasexchange,"Master'sthesis,UniversityofFlorida,August 2013. [2]Hpswithmuseuserguide,"CAEHealthcare,Inc.,Tech.Rep.,2006. [3]S.D.Small,R.C.Wuerz,R.Simon,N.Shapiro,A.Conn,andG.Setnik, Demonstrationofhigh-delitysimulationteamtrainingforemergencymedicine," AcademicEmergencyMedicine ,vol.6,no.4,pp.312{323,1999.[Online].Available: http://dx.doi.org/10.1111/j.1553-2712.1999.tb00395.x [4]P.Z.Fritz,T.Gray,andB.Flanagan,Reviewofmannequin-basedhigh-delity simulationinemergencymedicine," EmergencyMedicineAustralasia ,vol.20,no.1,pp. 1{9,2008.[Online].Available:http://dx.doi.org/10.1111/j.1742-6723.2007.01022.x [5]R.G.Sargent, SimulationandModel-basedMethodologies:AnIntegrativeView. Springer-Verlag,1984,no.537-555,ch.Simulationmodelvalidation,Chapter19. [6]W.vanMeurs, ModelingandSimulationinBiomedicalEngineering:Applicationsin cardiorespiratoryphysiology ,M.Penn,Ed.McGraw-Hill,2011. [7]R.G.Sargent,Vericationandvalidationofsimulationmodels," Journal ofSimulation ,vol.7,no.1,pp.12{24,022013.[Online].Available: http://dx.doi.org/10.1057/jos.2012.20 [8]E.P.Widmaier,H.Ra,andK.Strang, Vander'sHumanPhysiology .McGraw-Hill, 2007. [9]Model4700anesthesiagassubsystem,"AndrosInc.,2332FourthStreet,Berekeley, CA94710,Tech.Rep.,May1997. 75

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BIOGRAPHICALSKETCH HillaryA.WehrywasraisedinPensacola,Floridaandhasbeenworkingtowardsa combineddegreeB.S./M.S.inelectricalengineeringandbiomedicalengineeringfrom theUniversityofFloridainGainesvillesinceAugust2009.Herundergraduatedegree wasawardedinDecember2013,andhermaster'sthesisworkwascompletedunderthe supervisionofDr.JohannesHansvanOostrominAugust2014.Hillarywillbeworking withDr.IlkaDiesterattheUniversityofFreiburginGermanyonoptogeneticsand neuralsignalprocessingasa2014-2015WhitakerFellow.ShewillthenjointheUniversity ofPittsburghtopursueherPh.D.inbioengineeringinAugust2015throughtheNSF GraduateResearchFellowship. 76



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2112 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 LearningFromData:RecognizingGlaucomatous DefectPatternsandDetectingProgressionFrom VisualFieldMeasurements SiamakYouseÞ ,Member,IEEE ,MichaelH.Goldbaum,MadhusudhananBalasubramanian,FelipeA.Medeiros, LindaM.Zangwill,JeffreyM.Liebmann,ChristopherA.Girkin,RobertN.Weinreb,andChristopherBowd Abstract —Ahierarchicalapproachtolearnfromvisualeld datawasadoptedtoidentifyglaucomatousvisualelddefectpatternsandtodetectglaucomatousprogression.Theanalysispipeline includedthreestages,namely,clustering,glaucomaboundarylimit detection,andglaucomaprogressiondetectiontesting.First,crosssectionalvisualeldtestscollectedfromeachsubjectwereclusteredusingamixtureofGaussiansandmodelparameterswere estimatedusingexpectationmaximization.Thevisualeldclusterswerefurtherestimatedtorecognizeglaucomatousvisualeld defectpatternsbydecomposingeachclusterintoseveralaxes.The glaucomavisualelddefectpatternsalongeachaxisthenwere identied.Toderiveadenitionofprogression,thelongitudinal visualeldsofstableglaucomaeyesontheabnormalclusteraxes wereprojectedandtheslopewasapproximatedusinglinearregression(LR)todeterminethecondencelimitofeachaxis.For glaucomaprogressiondetection,thelongitudinalvisualeldsof eacheyeontheabnormalclusteraxeswereprojectedandtheslope wasapproximatedbyLR.Progressionwasassignediftheprogressionratewasgreaterthantheboundarylimitofthestableeyes; otherwise,stabilitywasassumed.Theproposedmethodwascomparedtoarecentlydevelopedprogressiondetectionmethodandto clinicallyavailableglaucomaprogressiondetectionsoftware.The clinicalaccuracyoftheproposedpipelinewasasgoodasorbetter thanthecurrentlyavailablemethods. ManuscriptreceivedJanuary24,2014;revisedMarch21,2014;accepted March22,2014.DateofpublicationApril1,2014;dateofcurrentversionJune 14,2014.ThisworkwassupportedbyNIHR01EY022039,NIHR00EY020518, NIHR01EY008208,NIHR01EY011008,NIHR01EY019869,P30EY022589, anunrestrictedgrantfromResearchtoPreventBlindness(NewYork,NY,USA), EyesightFoundationofAlabama,CorinneGraberResearchFundoftheNew YorkGlaucomaResearchInstitute,DavidandMarilynDunnFund,andparticipantincentivegrantsintheformofglaucomamedicationatnocostfromAlcon Laboratories,Allergan,andPÞzer. Asteriskindicatescorrespondingauthor . S.YouseÞ,M.H.Goldbaum,F.A.Medeiros,L.M.Zangwill,andR.N. WeinrebarewiththeHamiltonGlaucomaCenterandtheDepartmentofOphthalmology,UniversityofCaliforniaSanDiego,CA92093USA(e-mail: syouseÞ@ucsd.edu;mgoldbaum@ucsd.edu;fmedeiros@ucsd.edu;lzangwill@ ucsd.edu;rweinreb@ucsd.edu). M.BalasubramanianiswiththeHamiltonGlaucomaCenterandtheDepartmentofOphthalmology,UniversityofCaliforniaSanDiego,CA92093USA, andalsowiththeDepartmentofElectricalandComputerEngineeringandthe DepartmentofBiomedicalEngineering,UniversityofMemphis,Memphis,TN 38111USA(e-mail:madhu@glaucoma.ucsd.edu). J.M.LiebmanniswiththeDepartmentofOphthalmology,NewYorkUniversity,NewYork,NY10012,USA(e-mail:jml18@earthlink.net). C.A.GirkiniswiththeDepartmentofOphthalmology,Universityof Alabama,Birmingham,AL35487USA(e-mail:cgirkin@uab.edu). C.BowdiswiththeHamiltonGlaucomaCenterandtheDepartmentof Ophthalmology,UniversityofCaliforniaSanDiego,CA92093USA(e-mail: cbowd@ucsd.edu). ColorversionsofoneormoreoftheÞguresinthispaperareavailableonline athttp://ieeexplore.ieee.org. DigitalObjectIdentiÞer10.1109/TBME.2014.2314714 IndexTerms —Dataanalysis,glaucoma,machinelearning,progressiondetection,visualeld. I.I NTRODUCTION M ACHINElearningtechniqueshavebeenwidelyused inbiomedicalapplications[1]Ð[14].Recentadvances indataanalysisandasigniÞcantgrowthinavailabledatabase sizehavepromotedclassiÞcationmethodsthatarecapableof identifyingpreviouslyhiddenclustersandpatternsinavailabledatasets.Inparticular,unsupervisedmachinelearningtechniquescanmathematicallydescribepatternsindatawithoutthe useofpriorclassknowledgeorheuristics[15]Ð[17].Revealingthesepatternscanserveasafundamentalsteptowardmore speciÞcminingandlearningtasks[18].Suchlearningtasks recentlyhavebeenappliedtothedetectionandmonitoringof glaucoma[9],[19]Ð[21]. Glaucomaisanopticneuropathythatisthesecondleading causeofblindnessintheworld[22]Ð[24].Glaucomamanagementisdependentonidentifyingdisease-relatedfunctionalor structuraldefectsandmonitoringtheirprogressionovertime. Recognitionofglaucoma-relatedvisualÞelddefects(i.e.,functionaldefects)isanaspectonwhichclinicianshavereliedsince themid-1800s[25]Ð[28].Foroveracentury,glaucomaspecialistshaveaccumulatedknowledgetodescribepatternsof glaucoma-relatedvisualÞelddefects[29],[30].IncreasedacceptanceofStandardAutomatedPerimetry(SAP)testingabout 25yearsagostandardizedvisualÞeldtestingforglaucoma. CurrentSAPsoftwareincludesastatisticalanalysispackage andprovidestheclinicianwithinformationaboutvisualfunctionintheformofmeasurementsofretinalsensitivitytolightat 52differenttestpoints(for24-2stimuli)acrossthecentral24 ofthevisualÞeld[25],[31].Individualpatientresultsalsoare comparedtoanormativedatabasethatprovidestheclinicianan age-adjustedprobabilityofabnormalityforeachtestpoint. AnumberofcommerciallyavailableprogressiondetectionalgorithmsareincludedintheSAPsoftware,suchasprogression byvisualÞeldindex(VFI)[32]andguidedprogressionanalysis(GPA)[33].Thesearestatisticalmethodsthatuselinear classiÞcationmethodstorepresenttherateandmagnitudeof change(forVFI)orusevarianceanalysistoidentifychange outsidenormallimits(forGPA),toclassifyeyesasprogressing orstable.RecentadvancesinunsupervisedclassiÞcationtechniquesprovideanalternativeapproachforglaucoma-related 0018-9294©2014IEEE.Personaluseispermitted,butrepublication/redistributionrequiresIEEEpermission. Seehttp://www.ieee.org/publications standards/publications/rights/index.htmlformoreinformation.

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2113 progressiondetectionfromSAP.Forinstance,machinelearninganddataminingtechniqueshavebeenusedtorecognize glaucoma-relatedSAPvisualÞelddefectpatternsanddetect progressionofglaucoma-relatedvisualÞelddefects[9],[19], [20],[34]. Inthecurrentstudy,wedescribetheperformanceofa Gaussianmixturemodel[35],[36]andexpectationmaximization(GEM)methodsfor1)clusteringeyesasglaucomatous orhealthyand2)discriminatingbetweeneyeswithknown glaucomatousprogressionandstableeyes.Wecomparethe progression-detectionperformanceofGEMtothatofseveral otheralgorithms,includingSAPsoftware-basedcommercially availabletechniques(e.g.,VFIandGPA).Resultsalsoare comparedtothosefromapreviouslydescribedunsupervised learning-basedprogressiondetectionalgorithm,progressionof patterns(POP),whichisbasedonchangeovertimeofpatterns revealedusingthevariationalBayesianindependentcomponentanalysismixturemodel(VIM)[34],[37],[38].WehypothesizethatchangeinGEM-deÞnedpatternsofdefectwould performaswellasorbetteratdetectingknownglaucomatous changethanothertechniques.IfourhypothesisisconÞrmed, changeinGEM-deÞnedpatternsmightbeabettercandidatefor glaucomaprogressiondetectionfromSAPdatathanchangein VIM-deÞnedpatterns,becausecomputationalrequirementsto identifypatternsaresigniÞcantlylessusingGEMthanVIM,and trackingchangeinVIM-deÞnedpatterns(i.e.,POP)alreadyhas beenshowntooutperformsomecommerciallyavailableprogressionalgorithms[19]. II.M ETHODS Inthissection,weÞrstdescribetheinstrumentsusedtocollect data,dataacquisition,andtheassessmentofstudyparticipants. Wethenexplainthemathematicalderivationsformodelingthe datausingGEM.Weelaborateontheframeworkandimplementationoftheglaucomaprogression-detectionpipelineandthe performancemetricsemployed.Next,wedescribetheclustering,boundarylimitdetection,andprogression-detectiontesting steps.Finally,wereportanddiscussourresults. A.Instruments Colorphotographpairsweresimultaneouslyobtained throughmaximallydilatedpupilsusingastereoscopiccamera(KowanonmydWX 3D ,softwareversionVK27E,Kowa OptimedEuropeLtd.).SAP-measuredvisualÞeldsensitivity wastestedat52points[54points,with2blind-spotpoints excluded;seeFig.1(b)]usingthe24-2SITAteststrategy (HumphreyFieldAnalyzerII,CarlZeissMeditecInc.,Dublin, CA,USA).Fig.1(left)showstheopticdiskregionandperipapillaryretinaofaglaucomatouseye.Fig.1(right)displaysthe 24-2SAPvisualÞeldmeasurementsasabsolutesensitivitiesin decibelsattheavailable52testpointsthatareuniquelyspeciÞed bytheirangularlocationfromÞxationinthesuperior,inferior, nasal,ortemporalzones. Fig.1.(Left)sampleopticdiskphotographimage,(right)absolutesensitivities (indB)ofSAPvisualpointstestedusingthe24-2system. B.DataAcquisitionandAssessment AllparticipanteyeswererecruitedfromtheUniversityof CaliforniaSanDiego(UCSD)-basedDiagnosticInnovationsin GlaucomaStudy(DIGS)andtheAfricanDescentandGlaucomaEvaluationStudy(ADAGES)[39].ADAGESisamulticenterstudythatincludesUCSD,UniversityofAlabamaat Birmingham,andNewYorkEyeandEarInÞrmary.BothstudiesfollowthetenetsoftheDeclarationofHelsinki,HealthInsurancePortabilityandAccountabilityActguidelinesandthe studysiteHumanResearchProtectionProgramshaveapproved allmethodology.Writteninformedconsentwasobtainedfrom allstudyparticipants. Eachstudyparticipantunderwentacomprehensiveophthalmicevaluation,includingreviewofmedicalhistory,best correctedvisualacuity,slit-lampbiomicroscopy,intraocular pressuremeasurementwithGoldmannapplanationtonometry, gonioscopy,dilatedslit-lampfundusexamination,simultaneous stereoscopicopticdiskphotography,andSAPvisualÞeldexam ateachvisit. Thecurrentoverallgoalsaretoclusterglaucomatousvisual Þeldsintorecognizabledefectpatterns,toestablishamethod ofdatarepresentation,andtodetectglaucomatousprogression. Here,weexplainhowwecreatedthereferencestandardsfor theclusteringassessmentandprogression-detectionsteps.To createagoldstandardforclusteringassessment,alleyeswere classiÞedasabnormal(glaucomatous)orhealthybasedonthe SAPsoftware-providedglaucomahemiÞeldtest(GHT)andpatternstandarddeviation(PSD).Eyeswereconsideredabnormal iftheinstrumentsoftwaredeÞnedGHTwasoutsideofnormal limitsorifPSD 5%ofnormal,ontwoconsecutivetests[40]. HealthyeyeshadbothGHTandPSDwithinnormallimits.939 eyesfrom677subjectswereclassiÞedasabnormaland1146 eyesfrom721subjectswereclassiÞedashealthy. Tocreateareferencestandardforprogressionassessment, alleyeswereclassiÞedasprogressedorstablebyevaluationof imagesoftheopticdisk.Opticdiskimageswerechosenbecause theydifferedfromthevisualmeasurementsbeinganalyzedfor progression.Hence,glaucomatousprogressionwasbasedon structuralevidencesoasnottobiasthedetectionofSAP-related visualÞeldprogression.Eyesshowedprogressionorstability basedonserialanalysisofopticdiskstereoscopicphotographs. Thebaselineandeachfollow-upphotographwereassessedfor progressiveglaucomatousopticneuropathy(PGON)bytwo expert-trainedobserversviewingdigitizedimagepairona21-in orlargercomputermonitor.PGONwasdeÞnedasadecrease

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2114 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 TABLEI D EMOGRAPHIC I NFORMATIONOF S UBJECTS U SEDFOR C LUSTERING TABLEII D EMOGRAPHIC I NFORMATIONOF S UBJECTSAND F OLLOW UP V ISITS U SEDFOR P ROGRESSION D ETECTION intheneuroretinalrimwidth,ortheappearanceofanewor enlargedretinalnerveÞberlayerdefectinpairedstereoscopic images.ObserversweremaskedtothepatientidentiÞcationand diagnosis.Athirdobserveradjudicatedanydisagreementin assessmentbetweentheÞrsttwoobservers[41].76eyesfrom 70subjectswereidentiÞedasprogressedbyPGON(24eyes alsowerelabeled"likelyprogression"bySAPGPA).Atotal of414SAPvisualÞeldmeasurementswerecollectedfromthis group.Themeannumberoffollow-upvisitswas5.5,andthe meanfollow-uptimewas3years. StableeyesweretestedusingSAPoverashortperiodoftime withtheassumptionthatanychangeinmeasurementswasdue tovariabilityinfunctionofdiseasedganglioncellsorinattentivenessofthepatientandnotduetodisease-relatedprogression (thisisbecausedisease-relatedprogressioninadequatelytreated glaucomaeyesgenerallyoccursoveryears,notweeks). Stableglaucomawassimulatedinasetof91eyesfrom48 subjectsthathadbeenidentiÞedasglaucomatousatbaseline withrepeatableSAPdefects,asdeÞnedearlier.Stableeyeswere testedonceaweek,providinganaverageof4.5consecutive testsforeacheyeoveranaverageof4.3weeks.Atotalof428 SAPvisualÞeldmeasurementswerecollectedfromeyesinthis group. TableIshowsthedemographicinformationofthesubjectsin theabnormalandhealthyvisualÞeldgroups.TableIIshowsthe demographicinformationofthesubjectsintheprogressedand stablegroups.Themeandeviation(MD)andPSDofeachgroup, globalindicesthatindicatethedeviationofavisualÞeldfrom ameanofnormalvisualÞeld,alsoarelistedinbothTables. C.DataModelingUsingGaussianMixture Model-ExpectationMaximization Assumewehave n samplesofdataandthateachsample has d dimensions.Thegoalistomodelthegivendatawitha c -componentGaussianmixturemodel.Let Y =[ Y 1 ,...,Y d ] T representthe d -dimensionalGaussianrandomvariableandlet y =[ y 1 ,...,y d ] T representaparticularoutcomeof Y .Then, theprobabilitydistributionfunctionofa c -componentÞnite Gaussianmixturemodelcanbewrittenas[35],[36] p ( y | )= c m =1 m p ( y | m ) (1) where 1 ,..., c areweightsofeachmixingdistribution,and each m isthesetofparametersdeÞningthe m thmixingdistributioncomponent.Therefore,thecompletesetofmodelparameterscanbewrittenas { 1 ,..., c , 1 ,..., c } . Assumethedatasamples, Y = y (1) ,..., y ( n ) areindependentandidenticallydistributed.Then,wecanwritetheloglikelihoodofthe c -componentGaussianmixturemodelas log p ( Y | ) =log n i =1 p y ( i ) | m = n i =1 log c m =1 m p y ( i ) | m (2) withconstraintsontheweightingcoefÞcientsas m 0 ,m = 1 ,...,c and c m =1 m =1 . ThemainapproachesbelowcanbefollowedtoÞndtheparametersofthismodel.Themaximumlikelihood(ML)estimate canbewrittenas ML =argmaxlog p ( Y | ) (3) Themaximum aPosteriori (MAP)criterioncanbewrittenas MAP =arg max { log p ( Y | )+log p ( ) } (4) where p ( ) isthepriorontheparameters. ItiswellknownthatneitherMLnorMAPestimatescan befoundanalytically.Theexpectationmaximization(EM)is theproperchoiceforcomputingtheparametersinMLorMAP.

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2115 Fig.2.Glaucomaprogressiondetectionpipeline. UsingEMinaniterativeprocedure,thelocalmaximumofMLor MAPcanbefound.Assumethat Z = z (1) ,...,z ( n ) indicate whichGaussianmixturecomponentproducedeachdatasample. Therefore,eachlabelisabinaryvector z ( i ) = z ( i ) 1 ,...,z ( i ) c , where z ( i ) m =1 and z ( i ) q =0 for q = m ,meansthatthesample y ( i ) wasgeneratedbythe m th Gaussianmixturecomponent. Addingmembershipdatatothemodel,wecanwrite log p ( Y , Z | )= n i =1 c m =1 z ( i ) m log[ m p ( y ( i ) | m )] . (5) Then,theExpectationstepcanbewrittenas[42] Q , ( t ) E [log p ( Y , Z | ) | Y , ( t )]= log p ( Y , W| ) (6) where W = E [ Z | Y , ( t )] and { t =0 , 1 , 2 ,... } representsa timesequence. Becausetheelementsof Z arebinary,wecanwrite w ( m i ) E [ z ( i ) m | Y , ( t )]=Pr[ z ( i ) m =1 | Y ( i ) , ( t )] = m ( t ) p ( y ( i ) | m ( t )) c j =1 j ( t ) p ( y ( i ) | j ( t )) . (7) InthecaseofMAP,themaximizationstepcanbewrittenas ( t +1)=argmax Q , ( t ) +log p ( ) . (8) TheEMalgorithmisiterateduntilreachingaconvergence criterion. III.G LAUCOMA P ROGRESSION D ETECTION P IPELINE Thepipelineusedforglaucomaprogressiondetectioniscomposedofthreestages:clustering,glaucomaboundarylimitdetection,andglaucomaprogressiondetectiontesting(seeFig.2). InFig.2,theclusteringstageisshownatthetop,theboundary limitdetectioninthemiddle,andtheprogressiondetectiontestingatthebottom.Theaxes,whichmakeuptheoutputofthe topstage,aretheinputtothesecondstage.Adifferentdataset wasusedtocompleteeachstage.Weusedadatasetofabnormal andwithinnormallimits(i.e.,healthy)SAPvisualÞelds(refer toTableI)fortheclusteringstage,adatasetofstableglaucoma visualÞelds(refertoTableII,column2)fortheboundarylimit detectionstage,andweusedadatasetcontainingtimesequences ofSAPvisualÞeldsofPGONeyes(i.e.,thosedesignatedasprogressingbyopticdiscassessment)intheprogression-detection testingstage(refertoTableII,column3).Wewillexplaineach stageinmoredetailinthesubsequentsections. A.ImplementationandPerformanceMetrics TheGEMdatamodelingintroducedintheprevioussectionessentiallycombinedmultivariateGaussiancomponents tomodelthevisualÞelddatapoints.Numberofsamples, n , was2085andthenumberofdimensions, d ,was53(52SAP absolutesensitivityvaluesandage).Clusterswereassignedby selectingthecomponentthatmaximizedtheMAPbasedonthe EM-estimatedparameters.Principalcomponentanalysis(PCA) wasutilizedtodecomposeeachclusterintoseveralaxes.To identifyagloballyoptimalGEMmodelthatrepresentsglaucomacategoryandvisualÞelddefectpatterns,wegenerated severalGEMmodelsandselectedamodelthatprovidedthe bestsensitivityatnear95%speciÞcity.Wechosethenumber ofclustersinourGEMmodels, c ,asthreetoreßectthethree broadcategoriesofvisualÞeldnamely,normal,early,andadvancedglaucoma.Allstagesofthemodelwereimplemented inMATLAB(Mathworks,Natick,MA,USA).Thefollowing performancemetricswereutilizedtoassesstheaccuracyofthe clusteringstage. 1)TruePositives(TP),whicharepositiveinstancescorrectly classiÞedaspositive,2)FalsePositives(FP),whicharenegative instancesincorrectlyclassiÞedaspositive,3)TrueNegatives (TN),whicharenegativeinstancescorrectlyclassiÞedasnegatives,and4)FalseNegatives(FN),whicharepositiveinstances incorrectlyclassiÞedasnegatives. SpeciÞcity isdeÞnedastheproportionofallthosewithout diseasecorrectlyidentiÞedasnegative. Speci“city= TN TN+FP . Sensitivity isdeÞnedastheproportionofallthosewithdiseasescorrectlyidentiÞedaspositive. Sensitivity= TP TP+FN . Weassessedtheperformanceoftheclusteringstageusing thereferencestandarddataset(abnormalandnormalSAPvisualÞelds)andthesensitivity/speciÞcityperformancemetrics deÞnedpreviously.Toassesstherelativeperformanceofthe entirepipeline,wecomparedtheoutcomeofourmethodto GPA[33],linearregression(LR)oftheVFI,andLRoftheMD. GPAindicatesvisualÞeldchangefrombaselinebyevaluating alltestpointsandindicates"likelyprogression"forthefullÞeld ifvisualÞeldchange(greaterthanthevariabilityobservedin twobaselinemeasurements)inthreeormoreofthesamepoints isrepeatableinthreeconsecutiveexams[33].TheVFIandMD areglobalindicesprovidedforeachindividualtest.Wealso comparedtheperformanceofGEMwiththatofthepreviously

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2116 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 Fig.3.PerformanceofalltrainedGEMmodels. describedVIM-basedmethod[19].Wewillprovidethedetails oftheassessmentsinthesubsequentsections. B.ClusteringStage TheabsolutevisualÞeldsensitivityvaluesfromthe52perimetriclocations(54,excluding2blindspotlocations)andage wereusedasinputtoGEMfordatamodeling.Agewasincluded becausebothglaucomatousandnormalvisualÞeldsexpressed asabsolutesensitivityareaffectedbyage,andagewasusedin thepreviousunsupervisedlearningstudies[10],[34],[43].The unsupervisedclusteringwasperformedusingtheGEMmodel todetectglaucomatousvisualÞelddefects.Usingthe2085 SAPvisualÞelds(crosssectional)asinput,GEMmodeled c categoriesofglaucomastages(i.e., c clusters)fromthedataand assignedeachofthesevisualÞeldstothebestÞttingcluster. Theinitiatingvariableforthelearningprocesswasthenumber ofmixingGaussians,theirmeanandvariance,andthenumber ofclusters, c ,whichrangedfrom c = 2Ð5.Validationwasdone afterlearningtheclustersbyobservingthedistributionofabnormalandnormalÞeldsineachclusterandtheGEMmodelwith nearly95%speciÞcityandthehighestsensitivitywasselected from600trainedGEMmodels.Fig.3showsthespeciÞcity versussensitivityfor600trainedGEMmodels. Fromourassessmentofsensitivity-speciÞcitytradeoffamong the600trainingGEMmodels,wefoundthatthreeclustersprovidedabetterseparationofglaucomaandhealthyÞelds.These threeclusterswerecategorizedintonormalclusterN,moderateglaucomaclusterG1,andadvancedglaucomaclusterG2 dependingonthecentroidoftherawthresholdsensitivitiesof theseclusters(normalÞeldshavehigherthresholdvaluesthan glaucomatousÞelds).InFig.4,weshow2-Dscatterplotsof these53-Dclustersforvisualization.Fig.4(top)showsthe scatterplotofthesuperiorhemiÞeld(i.e.,allvisualÞeldlocationsabovethemiddlehorizontalmeridianshowninFig.1) averagethresholdversustheinferiorhemiÞeld(allvisualÞeld locationsbelowthemiddlehorizontallineasinFig.1)average thresholdforalleyes. AscanbeseenfromthisÞgure,theeyesindifferentclusters areorganizedfromtoprighttothebottomleft.Theclinical Fig.4.2-DScatterplotoffeatures.(Top)averageofsuperiorhemiÞeldversus averageofinferiorhemiÞeld.(Bottom)MDversusPSD. interpretationofthisorganizationisdiscussedinResultsand Discussionsection.Fig.4(bottom)showsthescatterplotof MDversusPSD(twoglobalclinicalindicesofvisualfunction) foralleyes.AscanbeseenfromthisÞgure,threeclustershave beenorganizedfromhightolowMDandPSDvalues. WedecomposedallofthevisualÞeldscomprisingeachclusterintodifferentaxesusingPCA.ThevisualÞeldsassociated witheachaxisdeÞnethepatternsofvisualdefectthatweare seeking.Withineachcluster,therelativecontributionofeach axiswasassessedbasedonitsrespectiveeigenvalue.Onlyaxes withsigniÞcantcontributions(higheigenvalues)wereretained inacluster.ThenumberofaxesinclustersNandG 1 was2 each,andthenumberofaxesinclusterG 2 was5. ToorganizethevisualÞeldlosspatternsfrommildtoadvanced,thevisualÞeldpatternsarerepresentedasaxesthrough eachclustercentroid.Clinicianstypicallyrelyonthetotaldeviation(TD)orpatterndeviation(PD)plotssuppliedbytheHFA Statpacanalysis(CarlZeissMeditec,Inc.,Dublin,CA,USA). WeusedsimulatedTDplotsinouranalysistodisplaythepatternsofvisualdefectsinrelationtonormaleyes.Thesimulated TDplotisa52-DvectorobtainedbysubtractingabsolutesensitivitiesatthecentroidofthenormalclusterNfromtheabsolute sensitivitiesatthecentroidoftheglaucomatousclusters,and then,representingÞelddefectsasplotsatÐ2,0(clustercentroid),and + 2standarddeviation(SD)alongeachoftheaxes. ThenumericalTD-likeplotswerefurtherconvertedintocolor

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2117 Fig.5.VFpatternsrepresentedbythecentroidofeachGEMcluster.IncreasedredsaturationindicatesincreaseddeteriorationofthevisualÞeld.T hetopleft patternrepresentsthevisualÞeldstheclusterN,thetopmiddleshowingearlyvisualÞelddeteriorationrepresentsclusterG 1 ,andthetoprightshowingmildto advancedvisualÞelddeteriorationrepresentsclusterG 2 .ThebottomÞgureisthecolor-codinglegend. representationstoaidinvisualization.The Š 26to + 26values weredisplayedinequalstepsofcolorfromredtogreen,with Š 26aspureredand + 26aspuregreen. Fig.5(Þrstrow)showsthegeneratedmeanpatternsofeach clusterafterTDsimulation. ThecentroidoftheÞrstcluster(seeFig.5left)haszero dBMDatallpointsandiscomposedmostlyofnormalvisual Þelds(clusterN),thecentroidofthesecondcluster(seeFig.5 middle)deviates Š 2.6dBonaveragefromthenormalmean andiscomposedmostlyofabnormalvisualÞelds(clusterG 1 ), andthecentroidofthethirdclusterdeviates Š 9dBonaverage fromthenormalmean(seeFig.5right)andiscomposedonly ofabnormalvisualÞelds(clusterG 2 ).Thecolorcodedlegend usedtodisplaytheTDsimulatedplotpatternsisshowninFig.5 (secondrow). Wecreatedthepatternsalongeachaxisbyaddingtoorsubtractingfromtheclustercentroid,2standarddeviationsalong thataxisdirection(i.e., ± 2SD).Fig.6showsthevisualÞeld patternsat + /Ð2SDalongeachclusteraxiswithineachcluster.Usingthedistancebetweeneach52-DvisualÞeldandeach oftheaxeswithineachofthethreeclusters,weassignedeach visualÞeldtoitsclosestaxiswithintheclosestcluster. Forfurtherexamination,thevisualÞeldswereprojectedon totheirrespectiveassignedaxesandthevisualÞeldsassignedto eachaxisweresorteddependingontheirprojectionmagnitudes fromtheclustercentroid. SortingthevisualÞeldsfromnegativetopositivedepictsthe earliestvisualÞelddefectstothemostadvancedones.Thevisual ÞeldswerenotedfortheirresemblancetothegeneratedÞelds ontheaxis,tothesimilarityofothervisualÞeldsassignedtothe sameaxis,andfortheconsistencyinincreasingseverityasthe visualÞeldswerelocatedfurtherinthepositivedirectionalong theaxis.ThisprocedurewillbediscussedinSectionIV. C.GlaucomaBoundaryLimitDetectionStage WeperformedglaucomaboundarylimitdetectionbyprojectingthelongitudinalsequenceofvisualÞeldsofeachstable eyeinthe53-DspaceontoeachofthesevenpredeÞnedGEM glaucomaaxesasidentiÞedbytheclusteringstage(referto SectionII-BandTableIItorecallstablegroupdeÞnitionand demographicinformation).WethenpermutedthevisualÞeld sequenceofeachstableeyetomaximizethenumberofslopes usedtodeterminethepercentilelimit(PL)forstableeyeson eachaxis.ForaneyewithÞveconsecutivevisits,wegenerated 5!(=120 )longitudinalsequencesofVFs,andthen,we projectedeachsequenceontheaxis.Thetemporalintervalbetweenvisitsforeachstableeyewasaboutoneweek;however, weresetthisintervaltooneyeartoapproximatethelimitsof stabilityofeyesandtobeinagreementwiththeconventionthat glaucomapatientsarecommonlyfollowedatintervalsbetween sixmonthstooneyear.Next,weapproximatedtheslopeof eachlongitudinalseriesofprojectedvisualÞeldsbyaLR.Due totheintervisitvariabilityofthevisualÞelds,thelongitudinal sequenceofvisualÞeldsfromsomestableeyeshaveapositive slope,indicatingimprovement,whileothershaveanegative slope,suggestingdeterioration. The95thsingletailpercentilestowardthedirectionofdeteriorationforallsevenaxesfordetectingglaucomaprogression werethencalculated.Singletailwasused,becausewewereinterestedonlyinsigniÞcantdeteriorationandwerenotinterested insigniÞcantimprovement.Becauseeyesinthestablegroup presumablyshowednodiseaserelatedprogression,thevariabilityinthisgroupwasusedtodeÞnethemaximumvariability thatindicatednochange.Fig.7demonstratesthehistograms ofalltheapproximatedslopesafterprojectingthelongitudinal visualÞeldsofthestableeyesoneachaxisofclustersG 1 and G 2 .

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2118 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 Fig.6.VFpatterns(axesand + /Ð2SD)inthreeclustersN,G1,andG2generatedbyGEM.Therepresentationsimulatestotaldeviationplotsgeneratedat Š 2/ + 2 standarddeviationunitsoneachaxis.IncreasedredsaturationindicatesincreaseddeteriorationofthevisualÞeld. TableIIIliststhe95thPLforglaucomaprogressiondetection afterprojectingthelongitudinalvisualÞeldofstableeyeson axesofclustersG 1 andG 2 (identiÞedattheclusteringstage), andthen,approximatingtheslopesbyanLRmodel.The95th PLoftheempiricalhistogramoftheslopesforeachaxisalone indicatesthatifweprojectthevisualÞeldofaneyeanditfalls abovethislimit,theeyeisstable,otherwise,theeyeisclassiÞed asprogressedat5%levelofsigniÞcance. D.GlaucomaProgressionDetectionTestingStage Forprogressiondetection,weprojectedthelongitudinalseriesofvisualÞeldsontoeachglaucomaaxis(axesdetermined attheclusteringstage),andthen,weapproximatedtheaverage progressionrate(slope)ofeachsequencealongtheglaucoma axesusinganLRmodel.Foreacheye,iftheapproximatedslope passesthe95%PLofthataxis(thelinefallsbelowthestable cutofflimit),theeyewasclassiÞedasprogressed;otherwise, theeyewasclassiÞedasstable.Theprogressiondetectionstage essentiallyusesGEMtodetectPOPduringglaucomaprogression,therefore,wecalltheentirepipelineGEM-POP.Wehave showntheoutcomeoftheproposedGEM-POPforfourexample eyesinFig.8.TheeyeinFig.8(topleft)providedtenvisual Þeldtestscollectedfrom2000to2006,theeyeinFig.8(top right)providedsevenvisualÞeldtestscollectedfrom2003to 2007,theeyeinFig.8(bottomleft)provided11visualÞeldtests collectedfrom2000to2007,andtheeyeinFig.8(bottomright) providedtenvisualÞeldtestscollectedfrom2001to2007.The orangecirclesindicatetheseverityafterprojectingthe53-D dataontotheÞrstaxisofclusterG 2 .Thebluescirclesindicate

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2119 Fig.7.Histogramoftheprojectedslopes.Toprowshowsthehistogramoftheslopesafterprojectingthestablegroup'slongitudinalvisualÞeldsona xis1and2 oftheclusterG 1 ,middlerowrepresentsthehistogramoftheslopesafterprojectingthestablegroup'slongitudinalvisualÞeldsonaxis1,2,and3ofclusterG 2 , andbottomrowshowsthehistogramoftheslopesafterprojectingthestablegroup'slongitudinalvisualÞeldsonaxis4and5ofclusterG 2 . TABLEIII 95%P ERCENTILE L IMITOF S TABLE E YESFOR E ACH A XIS theestimatedmeanslopeofprojectedvaluesbyLR(through theorangecircles).Notethatthe y -interceptofallseveritylines iszeroforthesecomparisons.Wealsoadjustedthecurveof actualprojectedvaluesaccordingly,tostartfromzeroseverity atbaseline.Thegraylineindicatesthe95%PLfortheslopes oftheÞrstaxisofclusterG 2 .Thiscutofflimitwasdetermined usingthepercentileboundarylimitdetectionstageutilizingthe stableeyesdescribedinthepreviousstep.Ifthelinearmodel approximatingtheslopefellbelowthegrayline(progression zone),thentheeyewasclassiÞedasprogressed,otherwise,the eyewasclassiÞedasstable.Therefore,theeyesinFig.8(top row)areclassiÞedasprogressed,becausethebluelineforboth fallsintheprogressionzoneandtheeyesinFig.8(bottomrow) areclassiÞedasstable,becausethebluelineforbothfallsinthe stablezone. Eventhoughtheslopeofthebluelinethatindicatesthechange inseverityofglaucomaisnegative(suggestsdeterioration)in thetwoeyesdisplayedatthebottomFig.8,thechangeisnot signiÞcantlynegative;hence,theeyesareclassiÞedasstable. Thisindicatesthattherateofdeteriorationisthefactorindicativeofprogression.ForassessingtheGEM-POPperformance, weusedlongitudinalSAPvisualÞeldsfromeyeswithknown progressingglaucoma,whichwillbediscussedinmoredetail inthenextsection. IV.R ESULTSAND D ISCUSSION Weselectedthebestmodeloutof600models,generated bytheclusteringstage,whichcontainedthreeclusters.TheMD value(globalindexofdeviationfromnormalvisualÞeld)ofeach clusterapproximatestheclinicalassessmentofdiseaseseverity. ClusterNwasmostlycomposedofnormalvisualÞeldswith anaveragemeandefect(MD)of Š 0.53 ± 1.3SD,ClusterG 1

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2120 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 Fig.8.graylineindicatesthe95thpercentilelimitforprogressionrate,theorangecirclesrepresenttheactualprojectedvisualÞeldvaluesonth eÞrstaxisof clusterG 2 ,andthebluecirclesarethelinearregressedlineapproximatingtheprojectedvisualÞeldvaluesontheÞrstaxisofclusterG 2 . wasmostlycomposedofearlyglaucomavisualÞeldswithan averageMDof Š 2.3 ± 1.6SDandClusterG 2 wascomposed ofmildtoadvancedglaucomavisualÞeldswithanaverageMD of Š 8.7 ± 6.4SD. ClusterNwascomposedof1237visualÞelds(1102normal and135abnormalÞelds),ClusterG 1 wascomposedof530 visualÞelds(44normaland486abnormal),andClusterG 2 was composedof318visualÞelds(0normaland318abnormal). ThespeciÞcitywas96%forplacingnormalÞeldsinClusterN, andthesensitivitywas87%forplacingabnormalvisualÞelds ineitherClusterG 1 orG 2 .BecausethestructuresofClusterN andClusterG 1 wererepresentedbytwoaxes,andthestructure ofClusterG 2 wasrepresentedbyÞveaxes,allvisualÞelds patternswerecharacterizedbyatotalofnineprincipalaxes. Wecharacterizedthepatternsatpointsonanaxisonthepositiveandnegativesides( ± 2SD)oftheclustermean,generating 18patterns. MostofthenormalÞeldswererepresentedbytwoaxesin ClusterN,andmostoftheglaucomatousÞeldswererepresented bysevenaxesinClustersG 1 andG 2 ;resultingin14patterns ofabnormalvisualÞelds.AscanbeseeninFig.5(left),the simulatedTDplotfortheÞrstcluster's(N)centroidresulted in0dBatalltestlocations,andthegeneratedÞeldsat Š 2 and + 2SDonaxis1(seeFig.6,Þrstandsecondrows)were uniformlymildlydepressed( Š 2dB)orabovenormal( + 2dB), respectively.ThegeneratedÞeldsat Š 2SDand + 2SDofaxis2 werewithin ± 1dBateachhemiÞeld.ThesimulatedTDplotfor thesecondcluster's(G 1 )centroid(FromFig.5middle)resulted inaverage Š 2.6dB,andthegeneratedÞeldsatalllocations onbothaxeswerebetween0and Š 7dB(seeFig.6,thirdand fourthrows).FromFig.5(right),thesimulatedTDplotforthe thirdcluster's(G 2 )centroidresultedinabout Š 9dB,andthe generatedÞeldsatalllocationsonallÞveaxeswerebetween Š 1and Š 22dB(seeFig.6,Þfthandsixthrows). Theclusteringstageassignedmostofthenormaleyestoaxes 1and2ofclusterNbasedontheminimumdistanceofthe visualÞeldfromeachaxis.Fromthetotaleyesinthenormal cluster,849eyeswereassignedtotheÞrstaxisand139eyes wereassignedtothesecondaxisofthenormalcluster.Fromthe totaleyesinclusterG 1 ,76eyeswereassignedtotheÞrstaxis and31eyeswereassignedtothesecondaxis.Fromthetotal eyesinclusterG 2 ,158eyeswereassignedtotheÞrstaxis,5 eyestothesecondaxis,44eyestothethirdaxis,41eyestothe fourthaxis,and40eyeswereassignedtotheÞfthaxis. InadditiontothefactthatageisasigniÞcantriskfactor forglaucoma,baselineageinthisstudywasalsosigniÞcantly

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2121 Fig.9.VFabsolutesensitivityvaluesandTDsimulatedpatternsforthreeeyesinabnormalclustersassignedtotheÞrstaxisofthatcluster.Project ingtheVF ofeacheyeontheÞrstaxis,andthen,sortingthevaluesfromthemostnegativetothemostpositive,calculatedtheseverity.TheVFthresholdsandTDs imulated valuesforeyescorrespondingtothemostnegative,mid,andmostpositiveprojectedseveritiesareplacedfromlefttoright,respectively. differentbetweennormalandabnormaleyes( p< 0 . 01 ; TableI).ThereisapossibilitythatagemightaffecttheclusteringoutcomesigniÞcantly.Toevaluatetheeffectsofageon theclusteringoutcome,wealsoassessedtheperformanceofthe clusteringstepexcludingage.Thebestclusteringmodelwithout agewas96%speciÞcand86.4%sensitive(versus96%and87% withage,respectively).Therefore,itisevidentthattheclusteringoutcomeisnotsigniÞcantlyaffectedbyage.Frommachine learningperspective,thisindicatesthatthespatialVFdatawithoutageinformationcontainssufÞcientdiagnosticinformation tomaintainahighdiscriminative/diagnosticpower. ToexaminetheindividualvisualÞeldsassociatedwitheach axis,weprojectedthevisualÞeldsassociatedwithanaxisand sortedthembytheirprojectionon(i.e.,distancealong)that axis.ThesortedvisualÞeldsfromnegativetopositiveindicated theearliestÞelddefectstomostadvancedÞelddefects.Fig.9 showsthevisualÞeldpatternsofsampleeyesalongtheÞrst axisofeachcluster.Fieldsareshownasabsolutesensitivities (top)andsimulatedTDplots(bottom)fromthreesampleeyes (fromlefttoright)fromtheÞrstaxisofeachcluster.Notethat theGEMclusteringstagegeneratessevenglaucomaaxes,as explainedearlier.IfwedeÞneprogressiondetectionbasedon

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2122 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 TABLEIV 95 TH P ERCENTILE L IMITOF S TABLE E YESTO R EACH O VERALL 95% S PECIFICITYONALL A XES anyoneaxisthatindicatesprogression,GEM-POPhasseven chancestodetectprogression;incontrast,GPA,MD,andVFI eachhaveonlyonechancetodetectprogression. TocompensateforthisadvantageforGEM-POP,weadjusted thespeciÞcityofeachaxisupwardstoachieveanoverallspeciÞcityof95%.Thiscompensationresultedinlargercutoffvalues forstabilityfortheindividualaxesthanthoselistedinTableIII. Weminimizedtheeffectofdifferencesamongthealgorithms byequatingforspeciÞcitypriortodeterminingprogression.TableIVliststheadjusted95thPLforeachaxistoreachoverall 95%speciÞcityonstableeyes. Totesttheperformanceofourproposedframework,weanalyzed76progressedeyes(refertotheprogressedcolumnof TableII).WeprojectedthelongitudinalSAPvisualÞeldsof alleyesonallsevenaxesofclustersG 1 andG 2 ,andwethen, computedtheapproximatedslopesbyLRforeachaxis.Then, foreacheye,wecomparedtheslopeofthelinearÞttothe95th percentilelimitforstableeyes(refertoTableIV)oneachaxis. Ifatleastoneoftheaxesshowedprogression,weclassiÞedthe eyeasprogressed;otherwise,weclassiÞedtheeyeasstable.To furtheranalyzetheeffectivenessofGEM-POP,wecompared itsperformanceforidentifyingknownprogressingeyestoLR ofthreeavailablevisualÞelddiagnosticindices,MD,andVFI. TableVliststheprogressiondetectionoutcomesofGEM-POP, GPA,MD,andPSD. SimilartoGEM-POP,wedeÞnedthe95thpercentilelimits ofstabilitybasedonthepermutationdistributionofthestable eyesanddeÞnedprogressionbyMDandVF. WealsocomparedtheGEM-POPoutcometotherecentlydevelopedVIMprogressionofpatterns(VIM-POP)method[19], forthesameeyesandforthesamefollow-upduration,andfound thatGEM-POPperformedslightlybutnotsigniÞcantlybetter thanVIM-POP(sensitivityforVIM-POPwas26.6%compared to28.9%forGEM-POP). ThepercentageofcorrectlyidentiÞedknownprogressing eyes(sensitivity)issomewhatlowforallmethods.Thereare severalexplanationsforthisÞnding.First,structuralchange (usedasthereferencestandardforprogressioninthisstudy) andfunctionalchange(basedonSAP)donotnecessarilyoccur atthesametime[44].Second,itisoftendifÞculttodetectactual changeinVFsfromnoiseduemeasurementerrorandrandom variation.ThiscanbealleviatedpartlybymodelingspatialcorrelationwithinvisualÞelds,whileconsideringtherelationship betweenthespatialarrangementsofthevisualÞeldsandthe anatomyoftheeye.Wehavenotconsideredspatialdependence inthispaper;however,itcouldbeinvestigatedinfuturework. Third,progressiondetectionmaybelessthanidealduetothe lackofagroundtruthreferencestandard. TABLEV P ROGRESSION D ETECTION P ERFORMANCE C OMPARISON InGEM-POP,theclusteringstageusesamixtureofGaussianstomodelthedata,toidentifytheclustersandtodecompose eachclustertoseveralaxesbasedonPCA.InVIM-POP,cluster identiÞcationandICAaxisdecompositionisperformedwithina singlestep,makingimplementationverycomplexandcreatinga computationallycomplexmodel.CreatingaprogressiondetectionenvironmentusingGEM-POPtakesminutesonastandard PC,whilecreatingsuchanenvironmentusingVIM-POPtakes severaldays.ItisworthmentioningthatGPAandLRofMDand VFIalluselinearstatisticalmethodstodetectprogressionthat lacktheinherentbeneÞtsofmachinelearning-basedmethods. Inaddition,wehaveshownthattheclusteringstagecapableof effectivelyextractingusefulfeaturesfromhigh-dimensiondata space(e.g.,pointwisevisualthresholds)canimprovethesensitivityofdetectingprogressioncomparedtoselective1-Dglobal indicessuchasMDandVFI.Incontrasttoglobalindices,GPA useshigh-dimensionaldataforanalysis.Therefore,thecomparisonofGEM-POPwithGPAfurtheremphasizesthestrengthsof GEM-POPincludingitsstrengthsofextractingusefulfeatures intheclusteringstage. Thefuturedirectionofthisstudycanbedevotedtoassessing theglaucomaprogressiondetectionrateusingotherophthalmic data. V.C ONCLUSION ApipelineforrecognizingglaucomatousvisualÞelddefect patternsandidentifyingglaucomatousprogressionwasdemonstrated.ThevisualÞelddataweremodeledusingamixture ofGaussiansandthemodelparameterswereestimatedusingexpectationmaximization.Then,thevisualÞelddatawere clusteredsuccessfullyintoonenormalandtwoglaucomaclusters(eachrepresentingdiseaseseverities).Therelativelygood performanceofourclusteringstageconÞrmsitsrelativeeffectivenessinstructuringdata.Eachclusterwasdecomposed toseveralaxesusingPCAtoidentifyglaucomatousprogression.GlaucomacutofflimitswerecalculatedonallidentiÞedglaucomaaxesandwereusedtodetectprogression.A datasetofprogressingglaucomatouseyeswasusedtoassess theperformanceoftheentireglaucomaprogressionpipeline andtheoutcomeofourmethodwascomparedtocommercially availableglaucomaprogressiondetectionsoftwarealgorithms andarecentlypublishedalgorithmforprogressiondetection. Overall,progressiondetectionbasedontheGaussianmixture modelusingexpectationmaximizationidentiÞedsigniÞcantly moreknownprogressingeyesthanallbutonecommercially availableSAPprogressiondetectionmethod.ProgressiondetectionbasedonchangeinGEM-POPdeÞnedaxesperformed

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YOUSEFI etal. :LEARNINGFROMDATA:RECOGNIZINGGLAUCOMATOUSDEFECTPATTERNSANDDETECTINGPROGRESSION2123 slightlybetterthanprogressiondetectionusingVIM-POP,while beingfarlesscomputationallycomplex.TheruntimeforclusteringandaxisidentiÞcationusingGEM-POPisasmallfraction oftheruntimerequiredtoperformthesametasksusingthe methodologyonwhichVIM-POPisbased. R EFERENCES [1]S.YouseÞ,N.Kehtarnavaz,M.Akins,K.Luby-Phelps,and M.Mahendroo,"Separationofpreterminfectionmodelfromnormal pregnancyinmiceusingtextureanalysisofsecondharmonicgenerationimages,"in Proc.IEEEEng.Med.Biol.Soc.Conf. ,2010,vol.2010, pp.5314Ð5317. [2]S.YouseÞ,N.Kehtarnavaz,M.Akins,K.Luby-Phelps,and M.Mahendroo,"Distinguishingdifferentstagesofmousepregnancyusing secondharmonicgenerationimages,"in Proc.42ndSoutheasternSymp. Syst.Theory ,2010,pp.44Ð46. [3]S.YouseÞ,B.Kim,andN.Kehtarnavaz,"Automatingporosityfeatures extractionfromsecondharmonicgenerationimagesofcervicaltissue,"in Proc.IASTEDInt.Conf.SignalImageProcess. ,2011,pp.129Ð132. 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Zangwill,R.N.Weinreb,J.G.Crowston,E.M.Hoffmann,F.A.Medeiros, T.Sejnowski,andM.H.Goldbaum,"Unsupervisedmachinelearningwith independentcomponentanalysistoidentifyareasofprogressioninglaucomatousvisualÞelds," InvestOphthalmol.Vis.Sci. ,vol.46,pp.3684Ð3692, Oct.2005. [39]P.A.Sample,C.A.Girkin,L.M.Zangwill,S.Jain,L.Racette,L.M. Becerra,R.N.Weinreb,F.A.Medeiros,M.R.Wilson,J.DeLe « onOrtega,C.Tello,C.Bowd,andJ.M.Liebmann,"Theafricandescentand glaucomaevaluationstudy(ADAGES):Designandbaselinedata," Arch. Ophthalmol. ,vol.127,pp.1136Ð1145,Sep.2009. [40]C.A.Johnson,P.A.Sample,G.A.CiofÞ,J.R.Liebmann,and R.N.Weinreb,"Structureandfunctionevaluation(SAFE):I.Criteriafor glaucomatousvisualÞeldlossusingstandardautomatedperimetry(SAP) andshortwavelengthautomatedperimetry(SWAP)," Amer.J.Ophthalmol. ,vol.134,pp.177Ð185,Aug.2002. [41]F.A.Medeiros,L.M.Zangwill,C.Bowd,P.A.Sample,and R.N.Weinreb,"Useofprogressiveglaucomatousopticdiskchangeas

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2124 IEEETRANSACTIONSONBIOMEDICALENGINEERING,VOL.61,NO.7,JULY2014 thereferencestandardforevaluationofdiagnostictestsinglaucoma," Amer.J.Ophthalmol. ,vol.139,pp.1010Ð1018,Jun.2005. [42]M.A.T.FigueiredoandA.K.Jain,"UnsupervisedlearningofÞnitemixturemodels," IEEETrans.PatternAnal.Mach.Intell. ,vol.24,no.3, pp.381Ð396,Mar.2002. [43]M.H.Goldbaum,"Unsupervisedlearningwithindependentcomponent analysiscanidentifypatternsofglaucomatousvisualÞelddefects," Trans. Amer.Ophthalmol.Soc. ,vol.103,pp.270Ð280,2005. [44]M.A.Kass,D.K.Heuer,E.J.Higginbotham,C.A.Johnson,J.L.Keltner, J.P.Miller,R.K.Parrish,M.R.Wilson,andM.O.Gordon,"Theocular hypertensiontreatmentstudy:Arandomizedtrialdeterminesthattopical ocularhypotensivemedicationdelaysorpreventstheonsetofprimary open-angleglaucoma," Arch.Ophthalmol. ,vol.120,pp.701Ð713,Jun. 2002. SiamakYouse (S'09ÐM'12)receivedthePh.D.degreefromtheUniversityofTexasatDallas,Richardson,TX,USA. HeiscurrentlyaPostdoctoralFellowattheHamiltonGlaucomaCenter,UniversityofCaliforniaatSan Diego,CA,USA,whereheisconductingresearch onophthalmicimageanddataanalysis.Hisresearch interestsincludebiomedicalimageanalysis,pattern recognition,andmachinelearning. Dr.YouseÞisamemberoftheARVO. MichaelH.Goldbaum receivedtheM.D.degree fromTulaneUniversity,NewOrleans,LA,USA (MD)andtheM.S.degreeinmedicalinformatics fromStanfordUniversityStanford,CA,USA. HeisanOphthalmicSurgeon,anEducator,and aScientistandisaProfessorofophthalmologyat theUniversityofCaliforniaatSanDiego,CA,USA. HeistheDirectorofGlaucomaInformaticsResearch, whereheappliesmedicalimageanalysisandmachine learningclassiÞerstoimprovecareofeyediseases. MadhusudhananBalasubramanian receivedthe Ph.D.degreefromLouisianaStateUniversity, BatonRouge,LA,USA. HeiscurrentlyanAssistantProfessorintheDepartmentofElectricalandComputerEngineeringat theUniversityofMemphis,Memphis,TN,USA.His researchinterestsincludetheintersectionofcomputationalscienceandengineering,biosolidmechanics andbioßuiddynamicswithemphasisinstudyingocularstructures,anddynamicsandthemechanismof visionlossinglaucoma. FelipeA.Medeiros receivedthegraduatedegreeand residencyfromtheUniversityofSaoPaulo. HeisaProfessorofophthalmologyandtheMedicalDirectoroftheHamiltonGlaucomaCenter,UniversityofCaliforniaSanDiego,CA,USA.Heisalso theDirectorofVisionFunctionResearchatthesame institution. LindaM.Zangwill receivedtheM.S.degreefrom theHarvardSchoolofPublicHealthandthePh.D. degreefromBen-GurionUniversityoftheNegev. SheisaProfessorofophthalmologyattheUniversityofCalifornia,SanDiego,CA,USA.Hisresearchinterestsincludeimprovingourunderstanding ofthecomplexrelationshipbetweenstructuraland functionalchangesintheagingandglaucomaeye, anddevelopingcomputationaltechniquestoimprove glaucomatouschangedetection. JeffreyM.Liebmann completedhisophthalmologyresidencyattheStateUniversityofNewYork/ DownstateMedicalCenterandhisfellowshipinglaucomaattheNewYorkEyeandEarInÞrmaryof MountSinai. HeispresentlyaClinicalProfessorofophthalmologyatNewYorkUniversitySchoolofMedicine, NewYork,NY,USAandtheDirectorofGlaucoma ServicesatManhattanEye,Ear,andThroatHospital, NewYorkandNewYorkUniversityLangoneMedicalCenter,NewYorkandanAdjunctProfessorof clinicalophthalmologyatNewYorkMedicalCollege,Valhalla,NY. ChristopherA.Girkin istheChairmanoftheDepartmentofOphthalmologyandaChiefMedicalOfÞcerfortheCallahanEyeHospital,theUniversity ofAlabamaatBirmingham(UAB),AL,USA.After residencyattheUAB,hecompletedafellowshipin neuro-ophthalmologyattheWilmerEyeInstituteat JohnsHopkins,Baltimore,MD,USAandinGlaucomaattheHamiltonGlaucomaCenter,theUniversityofCalifornia,SanDiego,CA,USA. RobertN.Weinreb receivedtheelectricalengineeringdegreefromtheMassachusettsInstituteofTechnology,Cambridge,MA,USAandtheM.D.degree fromHarvardMedicalSchool,Boston,MA. HeisaClinician,aSurgeon,anEducator,anda Scientist.HeistheDistinguishedProfessorofophthalmologyandtheChairmanoftheDepartmentof OphthalmologyattheUniversityofCalifornia,San Diego,CA,USA. ChristopherBowd receivedthePh.D.degreefrom WashingtonStateUniversity,Pullman,WA,USA. HeiscurrentlyaResearchScientistatthe HamiltonGlaucomaCenter,UniversityofCalifornia, SanDiego,CA,USA.Hiscurrentworkinvolvesearly detectionandmonitoringofglaucomawithstructural imagingoftheopticnerve,visualfunctionandelectrophysiologicaltestingusingstandardandmachine learningclassiÞer-basedanalyses.