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TRANSDERMAL DELIVERY OF THERAPEUTIC COMPOUNDS BY IONTOPHORESIS

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TRANSDERMAL DELIVERY OF THERAPEUTIC COMPOUNDS BY IONTOPHORESIS
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2008

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Critical frequencies ( jstor )
Electric current ( jstor )
Electrolytes ( jstor )
Epidermis ( jstor )
Lipids ( jstor )
Signals ( jstor )
Skin ( jstor )
Spectroscopy ( jstor )
Statistical discrepancies ( jstor )
Transdermal application ( jstor )

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TRANSDERMALDELIVERYOFTHERAPEUTICCOMPOUNDSBYIONTOPHORESISByMICHAELA.MEMBRINOADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA 2002

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ACKNOWLEDGMENTSIwouldliketoexpressmysinceregratitudetothenumerousindividualswhocontributedtothiswork.Sincerethanksandappreciationgotomyadvisor,Dr.MarkE.Orazem,forhistechnicalguidance,patienceandunwaveringcommit-menttoresearchexcellence.Hisinsightfulcommentsandsuggestionsplayedanintegralroleinthesuccessofthisproject.Iamgratefulthathegavemetheoppor-tunitytoexploremyscienticcuriosity.IalsothankthemembersofmyresearchcommitteeDr.OscarCrisalle,Dr.RajRajagopalan,Dr.FanRenandDr.KennethSloan.SpecialthanksgotoDr.KennethSloanforsharinghisexpertiseofthephysicalandbiochemicalpropertiesoftheskin.IextendgratitudetomycolleaguesSteveCarsonandPaulWojcikfortheiras-sistanceinthedevelopmentofthesoftwaretocontroltheelectrochemicalequip-ment.GenuineappreciationgoestoDougRiemerformaintainingourresearchgroup'scomputernetworkandforhishelpindesigningthedualbeamspectrom-etercell.IthankMadhavDurbhaandKerryAllaharfortheirdiscussionsandadvicerelatedtothemodelingwork.IexpressmygratitudetoPavanShuklaforhisassistanceinthestatisticalanalysisoftheimpedancedataandNellianPerez-GarciaforherhelpwiththeUV-visabsorptionspectroscopyexperiments.Ithankthelegionoflabassistantswhoservedasmyhandsfortheexperi-ments.IextendspecialrecognitiontoMariaCorena,SteveAchinger,JunGao,ScottBuntin,GlendonParker,JuanVarela,NathanAldous,IanJohns,ErikaVarela,DougHoffman,CraigVitan,WhitneyKurzandAnnFarrellfortheirdedicatedservice. ii

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IacknowledgetheNationalScienceFoundation,ALZACorporationandtheDepartmentofChemicalEngineeringattheUniversityofFloridafortheirnan-cialsupportofthisproject.IextendspecialrecognitiontoDr.GeraldWestermann-ClarkforhiseffortsinhelpingmetosecuretheNationalScienceFoundationMEDIfellowshipandobtainfundsformylabassistants.IwanttothankDeanWarren”Bud”Viessmanforhispersonalsupportandinvolvementinmygraduatecareer.SpecialthanksgoestoMarlaKendigofALZAforpreparingtheskinspecimensusedinthiswork.Igraciouslyacknowledgetheeffortsofmyfriendsandfamilywhoattendedtomymedicalneedsanddailylivingactivities.Thesuccessofthisprojectwouldhavebeenimpossiblewithouttheirhardworkanddedication.Iextendspecialthankstomybrother,Matt,forlivingwithmeandmaintainingmyhome.HebailedmeoutofmoreemergenciesthanIcaretomention.Hiseffortspermittedmetofocusmyattentionontheresearchpresentedhere.Finally,andmostimportantlyIextendadeepexpressionofgratitudetomyparents,RobertandDenise.Myparentsmadenumerouspersonalandprofes-sionalsacricesovertheyearstogivemeopportunitiesthattheyneverhad.Theirgenerousandunwaveringsupportallowedmetopursuemydreams.TheyaretremendouspeopleandIamtrulyblessedtohavesuchwonderfulparents.ThesenseofrespectandadmirationthatIhaveforthemisunbounded.Wordscan-notadequatelyexpressthetruefeelingsofgratitudeandappreciationthatIwillalwayshaveformyparents. iii

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TABLEOFCONTENTSpage ACKNOWLEDGMENTS ::::::::::::::::::::::::::::ii LISTOFTABLES ::::::::::::::::::::::::::::::::viii LISTOFFIGURES :::::::::::::::::::::::::::::::x KEYTOSYMBOLS :::::::::::::::::::::::::::::::xv ABSTRACT :::::::::::::::::::::::::::::::::::xviCHAPTERS 1INTRODUCTION :::::::::::::::::::::::::::::1 2PHYSICOCHEMICALPROPERTIESOFSKIN ::::::::::::::5 2.1StructureandFunctionofSkin ..................... 5 2.2Dermis ................................... 7 2.3Epidermis ................................. 7 2.3.1StratumBasale .......................... 9 2.3.2StratumSpinosum ........................ 9 2.3.3StratumGranulosum ....................... 10 2.4StratumCorneum ............................. 10 2.4.1Corneocytes ............................ 12 2.4.2StratumCorneumLipids .................... 12 2.4.3ModelMembraneSystems ................... 17 2.4.4IntercellularLamellarLipidOrganization ........... 18 2.4.5DomainMosaicModel ...................... 23 2.5IntercellularAppendages ........................ 25 2.5.1HairFollicles ........................... 26 2.5.2SweatGlands ........................... 27 2.6InuenceofElectricFieldsonSkinProperties ............. 28 2.6.1ElectricalPropertiesoftheStratumCorneum ......... 28 2.6.2IontophoreticTransportPathways ............... 33 2.7SummaryofSkinPropertiesAffectingIontophoreticTransport ... 34 iv

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3MODELSFORTRANSDERMALIONTOPHORESIS ::::::::::36 3.1Nernst-PlanckContinuumModels ................... 36 3.2HinderedTransportModels ....................... 38 3.3RenedHinderedTransportModels .................. 40 3.4NonequilibriumThermodynamicModels ............... 44 3.5KineticRateTheoryBasedModels ................... 47 3.6ElectrochemicalImpedanceSpectroscopy ............... 50 3.6.1ElectricalCircuitModelsofSkinImpedanceResponse ... 51 3.6.2RenedCircuitModels ..................... 53 3.6.3LimitationsofIdealCircuitModels .............. 56 3.7Summary .................................. 58 4EXPERIMENTALMETHODOLOGY :::::::::::::::::::60 4.1ElectrochemicalImpedanceSpectroscopy ............... 61 4.1.1PrinciplesofElectrochemicalImpedanceSpectroscopy ... 61 4.1.2ModulationProcedureforEISExperiments .......... 66 4.1.3Methodology ........................... 67 4.1.4StatisticalAnalysisofImpedanceSpectra ........... 70 4.2PotentialandCurrentStep-ChangeStudies .............. 74 4.3Materials .................................. 75 4.4UV-visAbsorptionSpectroscopy .................... 77 4.4.1InstrumentationandDataCollection .............. 78 4.4.2SoftwareControl ......................... 82 4.4.3CalibrationStudies ........................ 82 4.5InvestigationofTransdermalIontophoresis .............. 83 5DEVELOPMENTOFVAGMODULATION :::::::::::::::85 5.1PreliminaryInvestigationofSkinImpedance ............. 85 5.1.1Kramers-KronigConsistencyCheck .............. 88 5.1.2ProposedDrivingForceforSkinPropertyChanges ..... 91 5.1.3DeviationinPotentialResponsefromLinearity ....... 93 5.2DevelopmentofVAGModulationTechnique ............. 96 5.2.1Kramers-KronigConsistencyCheckofImpedanceSpectra . 100 5.2.2ComparisonofModulationMethods ............. 109 5.3ComparisonofExperimentswithLiteratureResults ......... 111 6RESULTSANDDISCUSSIONOFSKINIMPEDANCESTUDIES ::::114 6.1InuenceofReferenceElectrode .................... 116 6.1.1Results ............................... 118 6.1.2K-KConsistencyCheckforCalomelElectrodeData ..... 118 6.1.3K-KConsistencyCheckforMicro-ReferenceElectrodeData 123 6.1.4ComparisonofCalomelandMicro-ReferenceElectrodes .. 124 6.2InuenceofHydrationonSkinImpedance .............. 127 v

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6.2.1DirectAnalysisofHydrationData ............... 128 6.2.2InuenceofCationChargeonSkinHydration ........ 133 6.3InuenceofElectrolyteCationChargeonSkinImpedance ..... 133 6.3.1ImpedanceofSkinImmersedinMonovalentElectrolyte .. 135 6.3.2ImpedanceofSkinImmersedinDivalentElectrolyte .... 137 6.3.3Kramers-KronigConsistencyAssessment ........... 139 6.4InuenceofLarge-AmplitudeACPotentialSwingsonSkin ..... 140 6.5InuenceofDCCurrentBiasonSkinImpedance ........... 145 6.5.1ComparisonofSkinImpedanceSpectra ............ 146 6.5.2IdenticationofCorruptedData ................ 148 6.5.3PolarizationResistanceandOpen-circuitPotentialData .. 149 6.6VariationofPropertieswithLocation .................. 153 6.7ComparisonofImpedanceDatawithLiteratureResults ....... 154 7STATISTICALANALYSISOFVARIATIONINSKINIMPEDANCE ::160 7.1StatisticalModelforSkinImpedanceData ............... 162 7.2AnalysisofSkinImpedanceDataforNormalDistributionCharac-teristics ................................... 164 7.3VarianceComponentsofPolarizationResistance ........... 168 7.4VarianceComponentsofCriticalFrequency .............. 170 7.5EffectofElectrolyteonSkinProperties ................. 173 7.6CorrelationBetweenCriticalFrequencyandPolarizationResistance 175 7.7ComparisonofVariationinSkinImpedancewithLiteratureResults 178 8POTENTIALANDCURRENTSTEP-CHANGESTUDIES :::::::180 8.1PotentialStep-ChangeResults ...................... 181 8.1.1ModelPredictionsofSkinPolarizationResistance ...... 181 8.1.2CalculatedDeviationFromConstantProperties ....... 182 8.2CurrentStep-ChangeResults ...................... 185 8.2.1MeasuredPotentialDifferenceAcrosstheSkin ........ 186 8.2.2CalculatedPolarizationResistance ............... 188 8.2.3ComparisonofResponsesforSkinSamples1and2. ..... 191 9TRANSDERMALLIDOCAINEFLUXMEASUREMENTS :::::::197 9.1SpectroscopySystemStability ...................... 197 9.2LidocaineCalibrationStudy. ....................... 201 9.2.1ComparisonofAbsorbanceSpectra. .............. 202 9.2.2DeterminationofLidocaineExtinctionCoefcients. ..... 204 9.3AbsorbanceChangesfromSkinSpecies ................ 209 9.4TransdermalDeliveryofLidocainebyIontophoresis ......... 211 10MATHEMATICALMODELOFTRANSDERMALIONTOPHORESIS :220 10.1SystemDescription ............................ 220 10.2BoundaryConditions ........................... 222 10.3BulkSolutionCompositions ....................... 223 vi

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10.4GoverningEquations ........................... 224 10.4.1MolarFlux ............................. 224 10.4.2MaterialBalanceExpressions .................. 225 10.4.3HomogeneousReactions ..................... 227 10.4.4Electroneutrality ......................... 230 10.4.5NumericalMethod ........................ 230 11MODELSIMULATIONRESULTS ::::::::::::::::::::232 11.1CalculatedFluxProles ......................... 233 11.2InuenceofBufferonpHWithinStratumCorneum ......... 235 12CONCLUSIONS ::::::::::::::::::::::::::::::237 13SUGGESTEDRESEARCH :::::::::::::::::::::::::242APPENDICES APREPARATIONOFEPIDERMIS :::::::::::::::::::::245 BVAGMODULATIONFORIMPEDANCESPECTROSCOPY ::::::247 B.1DesignEquations ............................. 247 B.2ErrorAnalysisofVAGModulationScheme .............. 248 CSTATISTICALOUTPUT ::::::::::::::::::::::::::252 C.1DistributionStatisticsfromEISMeasurementsofSkinHydration . 252 C.2AnalysisofVarianceforEISMeasurementsofSkinHydration ... 253 C.2.1RegressiontoPolarizationResistance ............. 254 C.2.2RegressiontoCriticalFrequency ................ 255 C.3HistogramsofSelectedSkinPropertiesDuringHydration ..... 257 REFERENCES ::::::::::::::::::::::::::::::::::262 BIOGRAPHICALSKETCH ::::::::::::::::::::::::::283 vii

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LISTOFTABLESTable page 5-1Minimumfrequenciesandassociatedmembranepotentialdiffer-encesforKramers-Kronigconsistentportionsofskinimpedancespectra. ................................... 91 5-2Errorstructureparametersofskinimpedancespectra. ........ 101 7-1Proposedhypothesesformodeleffectsonpolarizationresistance . 164 7-2Distributionstatisticsforcriticalfrequencyasafunctionofelec-trolytetype ................................. 168 7-3Distributionstatisticsforlog10ofcriticalfrequencyasafunctionofelectrolytetype .............................. 169 7-4Calculatedcontributionstotheoverallvarianceinthelog10ofskinpolarizationresistance .......................... 169 7-5Calculatedcontributionstothetotalvarianceinthelog10ofskinpolarizationresistance. .......................... 170 7-6Calculatedcontributionstothetotalvarianceofthelog10ofskinpolarizationresistanceforpiecesimmersedindivalentelectrolyte . 170 7-7Calculatedcontributionstotheoverallvarianceinthelog10ofskincriticalfrequency ............................. 171 7-8Calculatedcontributionstothetotalvarianceofthelog10ofskincriticalfrequencyforpiecesimmersedinmonovalentelectrolyte .. 171 7-9Calculatedcontributionstothetotalvarianceofthelog10ofskincriticalfrequencyforpiecesimmersedindivalentelectrolyte .... 172 7-10Proposedhypothesesforcomparisonofmeans ............ 173 7-11Proposedhypothesesforcomparisonofvariance ........... 174 viii

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7-12F-teststatisticsforcomparisonofvariancesinthelog10ofpolariza-tionresistanceforeachelectrolytetype ................. 175 7-13F-testparametersforcomparisonofvariancesinthelog10ofcriticalfrequencyforeachelectrolytetype ................... 175 7-14Student'st-testoutputstatisticsforcomparisonofmeansinthelog10ofpolarizationresistanceforeachelectrolytetype ....... 176 7-15Student'st-testoutputstatisticsforcomparisonofmeansinthelog10ofcriticalfrequencyforeachelectrolytetype .......... 176 8-1Regressionparametersforestimationofskinproperties ....... 182 9-1Regressionparametersforcalculationofextinctioncoefcientsfromabsorbancedataoflidocainesolutionswithconcentrationsgreaterthan200M ................................ 206 9-2Extinctioncoefcientsandregressionparameterscalculatedfromabsorbancedataoflidocainesolutionswithconcentrationslessthan175M ................................... 207 9-3Opticallycoupledspectroscopyexperimentsettings ......... 212 10-1Diffusioncoefcientsandbulksolutionconcentrationsforthespeciespresentinthetransdermaliontophoreticsimulation ......... 224 C-1Distributionstatisticsforskinpolarizationresistanceandcriticalfrequencyasafunctionelectrolytetype ................ 253 C-2Distributionstatisticsforlog10ofskinpolarizationresistanceandcriticalfrequencyasafunctionelectrolyte ............... 254 C-3Distributionstatisticsforsquarerootofskinpolarizationresistanceandcriticalfrequencyasafunctionelectrolyte ............ 255 C-4Calculatedcontributionstovariance .................. 255 C-5CalculatedcontributionstovariancefromregressionofGLMmodeltoskinpolarizationresistancedata ................... 255 C-6CalculatedcontributionstothetotalvariancefromregressionofGLMmodeltothecriticalfrequencyofskin .............. 256 C-7CalculatedcontributionstothetotalvariancefromregressionofGLMmodeltothecriticalfrequency .................. 256 ix

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LISTOFFIGURESFigure page 2-1Relativethicknessandstructureofthedermisandepidermis. ... 6 2-2Relativethicknessandstructureofcorneocytesinthevariouslayersoftheepidermis. ............................. 8 2-3Classicationschemeofstratumcorneumceramidesbasedonchem-icalstructureandcomposition. ..................... 16 2-4Alternating-widthlayeredstructureofstratumcorneumlamellarlipids. .................................... 19 2-5Structuralorganizationofstratumcorneumlipidphases. ...... 21 2-6Structureofskinappendagesthatpenetratethestratumcorneum. . 26 2-7Potentialroutesfortransportoftherapeuticcompoundsduringtrans-dermaliontophoresis. ........................... 33 3-1Schematicrepresentationofuidowthroughconstrainedpores. . 41 3-2Proposedschemeforstep-wisetransportofdissolvedspeciesthroughthestratumcorneum. ........................... 50 3-3Equivalentcircuitmodelforstratumcorneumimpedance. ..... 52 3-4Impedance-planeplotofskinimmersedin50mMCaCl2. ...... 54 3-5Equivalentcircuitmodelsoftransmissionlines. ............ 55 3-6Constantphaseelementnetworkrepresentationofstratumcorneumimpedance. ................................. 56 4-1Polarizationplotforatypicalelectrochemicalsystem. ........ 62 4-2Impedance-planeplotofskinimmersedin100mMNaCl. ...... 65 4-3Bodemagnitudeplotofatypicalimpedanceresponseofskin. ... 66 x

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4-4Micrographofheat-separatedcadaverskin.Picturetakenatamag-nicationof92x. .............................. 76 4-5Dualspectrometersystemconguration. ............... 79 4-6Dualspectrometerdiffusioncellconguration. ............ 81 4-7Dualspectrometerdiffusioncellphotograph. ............. 81 5-1Impedanceresponseofskinwhensubjectedtoaseriesofconstant-amplitudemodulatedexperiments. ................... 87 5-2NormalizedrealresidualerrorsfromanimaginarytoftheMea-surementModeltothe50Aspectrum. ................ 90 5-3Potentialdifferenceacrosstheskinasafunctionoffrequency. ... 93 5-4CalculatedDClimitofpotentialdifferenceacrossskininresponsetoaseriesofconstant-amplitudegalvanostaticimpedancescans. . 94 5-5ImpedanceresponseofskinasmeasuredbyVAGandconstant-amplitudegalvanostaticmodulation. .................. 98 5-6NormalizedresidualerrorsfromrealtoftheMeasurementModeltoa10mVVAGscanofskininCaCl2electrolyte. ........... 103 5-7NormalizedresidualerrorsfromanimaginarytoftheMeasure-mentModeltoa10mVVAGscanofskininCaCl2electrolyte. ... 105 5-8NormalizedresidualerrorsfromatoftheMeasurementModeltotherealpartofa10Aconstant-amplitudegalvanostaticscanofskininCaCl2electrolyte. ......................... 107 5-9NormalizedresidualerrorsfromatoftheMeasurementModeltotheimaginarypartofaselected10Aconstant-amplitudegalvano-staticscanofskininCaCl2electrolyte. ................. 108 5-10SkinimpedanceasafunctionoffrequencycollectedbybothVAGandconstant-amplitudemodulation. .................. 109 6-1Impedance-planeplotsofsuccessive100Aimpedancescansoffullyhydratedskin. ............................ 119 6-2NormalizedresidualerrorsfromatoftheMeasurementModeltotherealpartofskinimpedance. ..................... 120 xi

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6-3NormalizedresidualerrorsfromanimaginarytoftheMeasure-mentModeltoaselectedimpedancespectrumofhydratedskinmeasuredwithcalomelreferenceelectrodes. ............. 122 6-4NormalizedresidualerrorsfromarealtoftheMeasurementModeltoaselectedimpedancespectrumofhydratedskinmeasuredwithAg/AgClmicro-referenceelectrodes. .................. 125 6-5Normalizedresidualerrorsfromanimaginaryttoaselectedimped-ancespectrumofhydratedskinmeasuredwithAg/AgClmicro-referenceelectrodes. ........................... 126 6-6SelectedsequentialimpedancescansofskinhydrationinbufferedCaCl2electrolyte. ............................. 130 6-7Open-circuitpotentialacrossskinduringthehydrationstudy. ... 130 6-8Normalizedpolarizationresistanceplotsofskin. ........... 132 6-9Impedance-planeplotofskinimmersedin150mMNaClbufferedelectrolyte. ................................. 135 6-10Polarizationimpedanceandpotentialdifferenceacrossskinimmersedinbuffered150mMNaClelectrolyte. .................. 136 6-11Impedance-planeplotofskinimmersedin50mMCaCl2bufferedelectrolyte. ................................. 138 6-12Polarizationimpedanceandpotentialdifferenceacrossskinimmersedinbuffered50mMCaCl2electrolyte. .................. 139 6-13Impedance-planeplotofskinwherethetargetpotentialdropacrosstheskinwasincreasedperiodically. ................... 142 6-14Skinpolarizationresistanceuponcompletionoftheelevatedtargetpotentialimpedancescans. ........................ 143 6-15Polarizationresistancesolidbluediamondsandvoltagedropacrosstheskinsolidyellowcirclesfortheelevatedtargetpotentialimped-ancescans. ................................. 144 6-16ImpedancespectracollectedtodeterminetheinuenceofDCcur-rentonskinproperties. .......................... 147 6-17Skinpolarizationresistanceinresponseto6amplitudesofappliedcurrent. ................................... 149 xii

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6-18Open-circuitpotentialdifferenceacrossthestratumcorneumbeforeandafterimpedancescans. ....................... 151 6-19Impedancespectraandtherelativelocationsforskinsampleextrac-tionoffourpiecesofskin. ........................ 155 7-1Proposedsourcesofvariationinskinproperties. ........... 161 7-2Histogramsofthecriticalfrequencyofheat-separatedepidermis. . 166 7-3Relationshipofcharacteristicskinimpedanceparameters,log10fcandlog10Rp. ............................... 177 8-1Sampleregressionoflinearmodeltopotentialstep-changedatatopredictskinproperties. .......................... 182 8-2Deviationinthemeasuredcurrentfromthecurrentassociatedwithpotentialindependentpolarizationresistanceskin. .......... 184 8-3Potentialdifferenceacrossepidermis. ................. 186 8-4Calculatedpolarizationresistanceofskin. ............... 189 8-5Responseofskinsamplesto14/cm2step-change. ......... 195 8-6Responseofskinsamplestoa140/cm2step-change. ........ 196 9-1Meanvaluesforthedark-correctedtransmissionintensityspectracollectedover2.4hours. ......................... 199 9-2Ratioofslaveandmasterspectrometertransmissionintensities. .. 201 9-3Normalizedabsorbancespectraforcalibrationoflidocaineconcen-tration. ................................... 203 9-4Absorbanceasafunctionoflidocaineconcentrationatselectedwave-lengths. ................................... 205 9-5Dependenceofcalculatedextinctioncoefcientonlightwavelength. 209 9-6AbsorbancespectraofskinimmersedinbufferedNaClsolution. .. 210 9-7Evolutionoftheabsorbanceresponseduringthetransdermalionto-phoresisexperiment. ........................... 212 xiii

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9-8Temporalevolutionofthecalculatedlidocaineconcentrationanduxinthereceptorcell. .......................... 214 9-9Temporalevolutionofskinpolarizationresistanceandtransdermallidocaineux. ............................... 216 10-1Dimensionsofthesimulatedsystemfortransdermaliontophoresis. 221 10-2Flowpatternofdissolvedspeciesthroughthesystemdomain. ... 226 11-1Potentialprolewithinthestratumcorneum. ............. 232 11-2Calculateduxprolesofthemajorionicspeciesthroughoutsys-temdomain. ................................ 233 11-3Calculateduxproleoflidocainethroughoutsystemdomain. .. 234 11-4CalculatedpHproleswithinstratumcorneum. ........... 236 B-1PercentrelativeerrorforpredictionofimpedancefromVAGalgo-rithm. .................................... 250 C-1Histogramsofthepolarizationresistanceofskinimmersedinmono-valentelectrolyte. ............................. 258 C-2Histogramsofpolarizationresistanceofskinimmersedindivalentelectrolyte. ................................. 259 C-3Histogramsofskincriticalfrequencyforpiecesimmersedinmono-valentelectrolyte. ............................. 260 C-4Histogramsofthecriticalfrequencyofskinimmersedindivalentelectrolyte. ................................. 261 xiv

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KEYTOSYMBOLSi=CurrentdensityF=Faraday'sconstantR=UniversalgasconstantT=Absolutetemperaturek=KineticrateconstantF=ElectrostaticpotentialVOC=Open-circuitpotential=Conductivityci=Concentrationofspeciesit=TimeNi=NetuxofspeciesiRi=RateofgenerationofspeciesiDi=Diffusioncoefcientforspeciesizi=Ionicchargeofspeciesiui=MobilityofspeciesiI=Ionicstrengthvx=Bulksolutionvelocityinthex-directionEIS=ElectrochemicalImpedanceSpectroscopyVAG=Variable-AmplitudeGalvanostaticmodulation xv

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyTRANSDERMALDELIVERYOFTHERAPEUTICCOMPOUNDSBYIONTOPHORESISByMichaelA.MembrinoMay2002 Chair:Dr.MarkE.OrazemMajorDepartment:ChemicalEngineeringTherapeuticadministrationofpharmaceuticalsrequiresthatsafeandcon-trolleddeliveryratesbeachieved.Iontophoresisisapromisingtechniquefordeliveringionicdrugsacrosstheskin.Topicaldeliveryoftherapeuticagentsbyiontophoresisisattractivebecausethelargesurfaceareaofskinprovidesforeasyaccess.Thetop-mostskinlayer,thestratumcorneum,doesnotfavorthetransportofmosttherapeuticallyactivecompoundsundernormalphysiologicalconditions.Iontophoresistakesadvantageofthenegativebackgroundchargeofskinwhichfavorsdeliveryofpositivelychargedspecies.Duringiontophoresisadrivingforceforenhancedtransportacrossskinisprovidedbyanappliedelectriceld.Alim-itationoftheapproachisthatskinmaybealteredduringtheprocess.Theobjectofthisworkwastoidentifytheinuenceofelectriceldsonthephysicochemicalpropertiesofskin.Theeffectofelectrolytesolutioncompositiononthesepropertieswasalsostudied.Electrochemicalimpedancespectroscopywasappliedtomonitorthepropertiesofskinbefore,duringandafteriontophorxvi

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esis.Statisticalmodelswereregressedtothedatatoidentifynonstationaryandnonlinearbehavior.Resultsindicatedthatskinpropertiesbegantochangeasthepotentialacrosstheskinexceededacriticalvalue.Anadaptivemodulationstrategywasdevelopedtopreventalterationstomembranepropertiesduringtheimpedanceexperiment.ThedeliveryrateoflidocaineacrosstheskinwasstudiedbyUV-visabsorp-tionspectroscopy.Acustomizeddual-beamdiffusioncellwasdevelopedtoac-countforthemildlynonstationarybehaviorofthespectroscopysystem.Theworkindicatedthatappliedcurrentenhancedthetransdermaluxoflidocaine.Anadditionalgoalofthisworkwastoidentifytheinuenceofcontrolledvariablesonconcentrationanduxproleswithintheskin.Aone-dimensionalsteady-statemathematicalmodelwasdevelopedtoprovideinsightintothecou-pledphenomenathatoccurinthestratumcorneum.Thegoverningequationsforthemodelaccountfordiffusionandmigration,homogeneousreactionsintheelectrolyteandthenegativebackgroundchargeofskin.Samplecalculationsareprovidedtodemonstratethecomplexnatureoftheinteractionsamongthespeciesinthesystemduringiontophoresis. xvii

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CHAPTER1INTRODUCTIONTheobjectofthisworkwastoprovideinsightintotheimportantfactorsthatin-uenceadministrationoftherapeuticagentsbytransdermaliontophoresis.Trans-dermaliontophoresisisatechniquefordeliveringioniccompoundsacrosstheskinwithanappliedelectriccurrent.Themotivationforusingtheappliedcur-rentistoprovideanadditionaldrivingforcefortransport,bywayoftheinducedelectriceld,toovercomethelowpermeabilityofskin.Anattractivefeatureoftransdermaliontophoresisisthatthedrugdeliveryrateisdirectlyproportionaltocurrent.Therapeuticlevelsofdrugconcentrationmaybeachievedbyadjustingthemagnitudeoftheappliedcurrent.Thisrelationship,inprinciple,makestheelectricalandmechanicaldesignofclinicaldevicesrelativelystraight-forward.Thedevelopmentofiontophoreticdevicesrequiresanunderstandingofskintransportpropertiesunderapplied-currentconditions.Amajorfocusofthisworkwastodeterminetheinuenceoftheappliedcurrentonskintransportproperties.Inaccordancewiththisgoal,avarietyofexperimentaltechniqueswereapplied.Aspartofthedesignprocess,experimentaltechniqueswererenedtominimizetheinuenceoftheexperimentonskinproperties.ThestructureandchemicalcompositionofskinundernormalphysiologicalconditionsaredescribedinChapter 2 .Anemphasiswasplacedonskinpropertieswhichaffectthedrugdeliveryprocess.Aliteraturereviewoftheinuenceofap-pliedelectriceldsonskinpropertiesispresentedinSection 2.6 .Theobjectofthereviewwastoestablishafoundationforthedevelopmentofexperimentaltech1

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2 niquestoinvestigatetransdermaliontophoresis.Theinformationwasalsousedtointerpretresultsandtodeveloptheoreticalmodelsfortransdermaliontophor-esis.Aliteraturereviewofmathematicalmodelsfortransdermaliontophoresiswasalsoperformed.TheimportantfeaturesofthetransportmodelsaresummarizedinChapter 3 .Thelimitationsandunderlyingassumptionsassociatedwiththevariousmodelsaredescribed.Theexperimentaleffortsweredirectedalongtwogeneralthemes.Therstwastoidentifytheinuenceofelectriceldsonthephysicochemicalpropertiesofskin.Thesecondwastoevaluatetheenhancementoftransdermaldeliveryratesofthemodeldruglidocainebyanappliedelectriceld.Theliteratureindicatesthatskinpropertiesmaybealteredbytheappliedelectricelds. 1 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(3 Thepotentialimpactofthisbehavioronthedesignofiontophoreticdevicesissignicantshouldthealter-ationsbeshowntobeirreversibleorassociatedwithadversereactions.Therefore,astrongemphasiswasplacedonidentifyingthemagnitudeofpotentialorcurrentwherethepropertiesofskinbegintochange.Thereversibilityofthechangesinskinpropertieswasalsoassessed.Heat-separatedhumancadaverskinwasse-lectedasthemodelforskin;therefore,alloftheexperimentswereconductedinvitro.ElectrochemicalImpedanceSpectroscopyandcurrentandpotentialstep-changeexperimentswereconductedtoachievethisgoal.TheimplementationofthesetechniquesisdiscussedinChapter 4 .Preliminarystudiesofskinbyimpedancespectroscopyindicatedthatthetraditionalmodulationmethodcanaltermem-braneproperties.Anadaptivemodulationstrategywasdevelopedtopreventchangesinskinproperties.Theresultsfromthepreliminarystudiesandtheim-plementationoftheadaptivemodulationmethodarediscussedinChapter 5 .

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3 Chapter 6 providesadiscussionoftheskinimpedancestudiesconductedun-derawiderangeofexperimentalconditions.Forexample,thedynamicsofskinhydrationwerestudiedperformingperiodicimpedanceexperimentsintheab-senceofanappliedcurrent.Thisinvestigationprovidedanestimateofthebase-linepropertiesofskin.Iontophoreticconditionsweresimulatedbyapplyingacurrentbiasacrosstheskin.Acomparisonoftheresultsprovidedanestimatefortheinuenceofcurrentonskinproperties.Alargedatabaseofskinimpedancespectrawascollectedinthiswork.Theskinsampleswereobtainedfromthedorsalandabdominalregionsof18humancadavers.Multiplepiecesofskinfromeachmacroscopicskinsamplewerestud-iedbyElectrochemicalImpedanceSpectroscopy.Visualinspectionofthespectrarevealedalargevariationintheimpedanceresponseofskin.Thestatisticalpro-cedureusedtoassesstherelativecontributionstotheoverallvariationinskinpropertiesisdescribedinChapter 7 .Forexample,thevariationwasassumedtobecausedbydifferencesamongthedonorsinter-individualdifferences,differ-enceswithinagivendonorintra-individualdifferencesorstochasticmeasure-menterrors.Estimatesforthecontributionstotheoverallvariationwereobtainedbyregressinganestedstatisticalmodeltotheimpedancedata.Thepolarizationresistanceandcriticalfrequencywereselectedastheindependentvariablesfortheregressionstoreducecomputationaleffort.Theresultsforthestep-changeexperimentsarepresentedinChapter 8 .Theobjectivewastoidentifytheresponseofskintoprolongedexposuretoelectricelds.Twostudieswereperformedwheretheappliedstep-changewaseithercurrentorpotential.Theworkwasdesignedtosupplementtheimpedancework.TheapplicationofUV-visabsorptionspectroscopyforinvitromonitoringoftransdermallidocaineuxesisdescribedinChapter 9 .Thetechniquewasused

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4 inconjunctionwithelectrochemicalimpedancespectroscopytosimultaneouslymeasuredrugdeliveryratesandmonitorskintransportpropertiesduringtrans-dermaliontophoresis.Thecombinedmethodologyprovidedforamoreaccurateassessmentoftheimportantfactorsaffectingtransdermaliontophoresis.Asteady-statemathematicalmodelwasdevelopedtoprovideinsightintotheexperimentalresults.Themodelwasderivedfrommacroscopictransporttheoryandwasdesignedtosimulatetheconditionsoftheexperimentalsystem.Contri-butionstothetotaluxfromdiffusion,migrationandconvectionwereincluded.Auniquefeatureofthemodelwasthatthemigrationcontributionwasevaluatedwithoutassumingaconstanteldwithintheskin.Furthermore,multiplehomo-geneousreactions,suchasthedissociationofwater,wereincluded.Thedevelop-mentofthemathematicalmodelisdiscussedinChapter 10 andtheresultsfromthesimulationsarepresentedinChapter 11 .ConclusionsfromtheworkpresentedinthisreportarediscussedinChapter 12 .SuggestionsforfutureresearchoftransdermaliontophoresisareprovidedinChap-ter 13 .Proposalsforsupplementalexperimentalstudiesaredescribedhere.Rec-ommendationsforrenementstothemathematicalmodelfortransdermalionto-phoresisarealsoincluded.

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CHAPTER2PHYSICOCHEMICALPROPERTIESOFSKINAnextensivebodyofresearchrelatedtotransdermaliontophoresisisavailableintheliterature.Thischapterofthereportisadescriptionofthestructureandchemicalcompositionoftheskinundernormalphysiologicalconditions.Particu-larfocusisgiventothetop-mostlayeroftheskin,thestratumcorneum,sinceitisconsideredtobethedominantbarriertopercutaneousabsorption.ThephysicalbehaviorofthestratumcorneumduringiontophoresisisdescribedinSection 2.6 .2.1StructureandFunctionofSkinDevelopmentofefcientclinicaldevicesfortransdermaliontophoresisrequiresknowledgeofthechemicalcompositionandphysicalstructureoftheskin.Thecommonlyacceptedviewofthesepropertiesundernormalphysiologicalcondi-tionsissummarizedinthissection.Thephysicochemicalpropertiesthatinuencetransportofspeciesthroughtheskinareemphasized.Unlessotherwisenoted,thematerialpresentedhereislimitedtothepropertiesofskinundernormalphysio-logicalconditions.Moreextensivediscussionsdescribingtheanatomyandphys-iologyofskinareavailableelsewhere. 4 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(9 Theskin,alsoknownastheintegument,isthelargestorganofthehumanbody.Thetotalsurfaceareaofskinforanaverageadultisapproximately2m2. 10 Skinisaverydynamicorganthatfunctionstoaccommodatemechanicalstresses,preventexcessivewaterloss,facilitatetranspirationalcooling,protectagainsttheharmfulradiationofthesun,provideforskincellrenewalandpreventabsorptionofforeignbodies. 11 , 12 5

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6 Inordertoperformsuchawidevarietyoftasks,humanskinhasevolvedintoahighlyspecializedheterogeneousmembranepossessingacomplexmorpholog-icalstructureandchemicalcomposition.Physiologicalpropertiessuchasthick-ness,sweatproductionandbarrierfunctionexhibitconsiderablevariabilityfordifferentanatomicalsitesofthebody.Variationsinthesepropertiesaredirectlylinkedtodifferencesinthechemicalcompositionandstructuralorganizationoftheskin. 4 , 13 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(18 Theskiniscomposedoftwodistinctmacroscopicregionswhicharereferredtoastheepidermisandthedermis. 19 , 20 Thisanatomicaldivisionbecomesobviousuponcloserinspectionoftheuniquemorphologicalstructureandphysiologicalfunctionofeachoftheseregions.Forexample,thevasculardermisisaphysiolog-icallyactiveregionthatmakesupthemajorityofskin. 21 Thesecondmacroscopicregionoftheskin,theepidermis,islocateddirectlyontopofthedermisandcom-prisesonlyasmallfractionoftheoverallskinmass.AschematicofthethicknessandstructurescontainedwithineachskinregionispresentedinFigure 2-1 .Theimportantfeaturesofthedermisandepidermisarediscussedseparatelybelow. Figure2-1:Relativethicknessandstructureofthedermisandepidermis.FigurereproducedfromGoldsmith.7

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7 2.2DermisThedermisisacompositenetworkofbrousandelastictissuesparselypop-ulatedwithcells. 22 Fibrousproteinsofthedermisincludecollagen,elastinandreticulin. 23 Theorganizationofthesetissuesprovideskinwithitsabilitytowith-standavarietyofmechanicalstresses. 24 Thereisconsiderablevariationindermalthicknesswithlocationonthebody.Thetypicalthicknessofthedermisisontheorderof1-2mmwherethemaximumthicknessof4mmisfoundontheback. 25 Embeddedinthedermisisadensenetworkofbloodvessels,nerveendings,andlymphaticvessels.Thecapillarieslocatedinthedermisprovidefornutri-entandheatexchange. 4 Thecapillariesarealsobelievedtoactasasinkformoleculesdiffusingthroughtheskin. 26 , 27 Appendagessuchassebaceousglands,sweatglandsandhairfolliclesoriginateinthedermis.Thesestructureshavebeenimplicatedasroutesoftransportduringiontophoresis. 28 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(31 Discussionoftheim-portantcharacteristicsofskinappendagesisprovidedinSection 2.5 .2.3EpidermisTheepidermisisadynamicmulti-layeredstructurethatperformsabroadrangeofphysiologicalfunctions.Theepidermisisavascularincomparisontotheder-misandhasathicknessofapproximately100microns. 20 Theepidermisisnor-mallysubdividedintofouranatomicalregions.Theinnermostlayeristhestratumbasale,whichisalsoreferredtoasthestratumgerminativum.Thenextthreere-gionsaretheoverlyingstratumspinosum,theintermediatestratumgranulosum,andtheoutermostlayerknownasthestratumcorneum. 11 Theuniquefeaturesofeachoftheseregionsarediscussedinthesubsequentsectionsofthischapter.Corneocytes,alsoknownaskeratinocytes,composethemajorityofepidermalcells.Thereisaconstantturnoverofcorneocytesinallregionsoftheepidermis.Migrationofcellsoccursinanupwarddirectionfromtheinnermostlayersofthe

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8 epidermistothesurfaceoftheskin.Asthecorneocytestravelthroughtheepider-misavarietyofenzymaticprocesseschangethechemicalcompositionandstruc-turalorganizationofthecells. 32 Uponreachingthesurface,thecorneocytesareeventuallyshedfromthebody.Theturnoverratethroughthecompleteepidermisisapproximately28-42days. 21 Althoughbloodvesselsareabsentfromtheepidermis,nutrientexchangeoc-cursviapassivediffusionthroughtheinterstitialspace. 4 Thestructure,composi-tion,andorganizationofthecorneocytesandlipidsineachoftheregionsoftheepidermiscorrelatewiththestateofdifferentiationandphysiologicalfunction.ThecellularstructureandrelativethicknessineachoftherespectivelayersoftheepidermisareillustratedinFigure 2-2 . Figure2-2:Relativethicknessandstructureofcorneocytesinthevariouslayersoftheepidermis.FigurereproducedfromSchaeferandRedelmeier.4

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9 2.3.1StratumBasaleThestratumbasale,alsoknownasthebasallayer,consistsofabandofcolum-narcellslocateddirectlyabovethedermis.Thecellsinthisregionarephysiologi-callyactiveandpossessintactcellmembranes,functionalnucleiandtypicalcellu-larorganellessuchasmitochondriaandGolgiapparatus. 21 Thestratumbasaleisthesourceofallcorneocytesfoundintheepidermis.Uponmitosisthecorneocytesgraduallymigrateupward.Afterleavingthestratumbasale,thecorneocyteslosetheabilitytoperformcellulardivision.Thelipidspresentinthestratumbasaleprimarilyconsistofphospholipids.Thephospholipidsmakeupthecellmembranesofthecorneocytesinthisregionoftheepidermis. 4 Theinteriorofthecorneocytescontainbundlesofthebrousproteinkeratin.Keratinexhibitsahighafnityforwater, 24 althoughitisextremelyinsolubleinwater. 33 Anadditionalpropertyofkeratinisthatithasahighsulfurcontentduetothecysteineresiduesoftheprotein. 24 Connectionbetweenadjacentcorneocytesismadebybrousproteinaceousunitscalleddesmosomes.Thedesmosomesmaintainconnectionbetweenthecorneocytesastheymigratetowardthesurfaceoftheepidermis.Thedesmoso-malconnectionsarebelievedtodegradeintheuppermostlayersofthestratumcorneumtofacilitatecorneocyteexfoliation. 22 Thecorneocyteproductionrateinthestratumbasaleleadstotheformationofapproximatelyonenewcelllayerperday.Asthecellsmaturetheymigrateintothestratumspinosumatapproximatelythesameratetomaintainconstantbasallayerthickness. 34 2.3.2StratumSpinosumThestratumspinosumliesdirectlyontopofthebasallayer.Thecorneocytecellsofthisregionareshapedlikeovoids.Thesurfaceofthecorneocytespos-sessspinousextensionsthathelptomaintainadhesionbetweenadjacentcells.

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10 Theinteriorofthecellscontainlargerbundlesofkeratinlaments.Theconcen-trationofkeratinbundlesinthestratumspinosumcorneocytesishigherthaninthebasallayercorneocytes.Thecorneocytesintheupperlayersofthestratumspinosumcontainnewlydevelopedorganellesknownaslamellargranules. 11 En-closedwithinthelamellargranulesisanabundanceofphospholipids,glycolipidsandcholesterolorganizedintolamellarsheets. 35 , 36 Thelamellargranulesalsocon-tainenzymesthatbegintosynthesizethelipidsthateventuallylltheintercellularspaceofthestratumcorneum. 37 2.3.3StratumGranulosumThecorneocytesofthestratumgranulosumexhibitagradualtransitioninchemicalcompositionandstructuralorganizationastheymigratetowardthesur-faceoftheskin.Asthecorneocytesmoveupwardthroughsuccessivelayersofthestratumgranulosumtheygraduallybegintolosetheirovoidshapeastheybecomemoreelongatedandattened.Theconcentrationofproteinscontinuestoincreaseandhighlycross-linkedproteinsbegintoaggregatearoundtheouterperipheryofthecorneocytes.Thenumberoflamellargranulesalsoincreasesinthestratumgranulosum.Thelamellargranulesbegintoorganizenearthecorneo-cyteborderstofacilitatetheextrusionoftheinternallipidsandenzymesintotheintercellularspace. 36 )]TJET1 0 0 1 6.447 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(38 Thelipidcompositionofthegranularlayersalsoexhibitsagradualincreaseintherelativeconcentrationofceramides,cholesterolandfattyacids. 4 , 6 , 39 2.4StratumCorneumTheoutermostlayeroftheskinisthestratumcorneum.Thestratumcorneumisdescribedindetailinthissectionofthereportbecauseitisgenerallyregardedasthedominantbarriertotransportintheepidermis. 20 , 23 , 24 , 40 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(42 Theexcellentbar-rierpropertiesofthestratumcorneumaremostlyprovidedbythechemicaland

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11 structuralchangesthatoccurinthecorneocytesintheunderlyinglayersoftheepidermis.Barrierfunctionsofthestratumcorneumincludetheretentionofwa-terwithinthebodyandprotectionfromtheinvasionofexternalspeciessuchastoxinsandmicroorganisms. 19 , 43 Thestratumcorneumisarelativelythintissuestructurethatrangesinthick-nessfrom10micronsontheundersideoftheforearm 20 toafewmillimetersonthesolesofthefeet. 44 Themacroscopicstructureofstratumcorneumconsistsofanetworkofanucleateproteinaceouscellsknownascorneocytesembeddedinalamellarlipidmatrix.Thestructureisoftenidealizedasatwo-compartmentbrick-and-mortarnetworkwherethecorneocytesarerepresentedbythebricksandtheintercellularlipidisrepresentedbythemortar. 45 , 46 Theassignmentoftheskintransportbarriertothestratumcorneumwasrstbasedontape-strippingexperiments. 47 Forexample,thestratumcorneumlay-erswereremovedbyrepeatedapplicationandremovalofadhesivetape.Adra-maticincreaseindruginuxandwaterefuxwasobserveduponremovalofthestratumcorneum. 48 , 49 Manystudieshavebeenconductedthatsupportthisas-signment. 35 , 50 )]TJET1 0 0 1 6.447 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(53 Anamazingpropertyofthestratumcorneumisthatthehighlyefcienttransportbarrierresideswithinsuchanarrowdomain. 54 Increasedwaterlossinseverelyburnedpatients,oftenleadingtodehydration,providesastrik-ingexampleoftheimportanceofthestratumcorneuminrestrictingtransdermaldiffusion.Untilrecently, 24 manyresearchersstudyingtransdermaldiffusionhavede-scribedthestratumcorneumasbeingadeadmembranewithrelativelyinvariantproperties.Thisconclusionwaspartlybasedonthefactthatthecorneocytesofthestratumcorneumlacktheorganellesrequiredforcellulardivision.Theconclusionwasalsosupportedbytheobservationthatthestratumcorneumhasamuchlower

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12 watercontentthanmostoftheothersofttissuesinthebody.Despitethisanecdo-talevidence,muchoftherecentliteraturesuggeststhatthestratumcorneumisahighlyfunctionalizedmembranewithconsiderableenzymaticactivity. 55 2.4.1CorneocytesAsmentionedearlier,thesourceofcorneocytesinthestratumcorneumistheunderlyinggranularlayer.Thecorneocytescomprise70-90%ofthetotalvol-umeofthestratumcorneum 17 withtheremainderconsistingprimarilyoflamellarsheetsoflipids. 56 Corneocytesareapproximatelydiskshapedwithanaveragediameterof30micronsandathicknessofapproximatelyonemicron. 11 , 57 , 58 Thereareapproximately15to20layersofcorneocytesstackedontopofeachotherinthestratumcorneum. 22 , 59 , 60 Thecorneocytesarelledwithkeratinlamentssurroundedbyadensebandofinterwovenbrousproteinslocatedattheouteredgesofthecell.Amonolayerofcovalentlyboundlipidsisattachedtotheproteinslocatedontheoutermostsur-faceofthecorneocytes. 61 Thelipidmonolayerconsistsofhydroxyceramideswithattached!-hydroxyacidspossessingchainlengthsof30-34carbons. 22 Theinte-gratedprotein-lipidmonolayerenvelopeenclosingthecorneocytesprovidesthecellswithexcellentstructuralintegrityandmayserveasascaffoldingfortheinter-cellularlipidbilayers. 35 Thestructureandcompositionoftheproteinaceousenve-lopeisdramaticallydifferentthanthetypicalphospholipidbilayermembraneofothercellsinthebody.2.4.2StratumCorneumLipidsThesourceofthestratumcorneum'spermeabilitybarriercharacteristicsaregenerallyattributedtotheuniquecompositionandstructuralorganizationoftheintercellularlipids. 29 , 41 , 62 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(64 Supportforthisassignmentwasprovidedbyexperi-mentswhereremovalofstratumcorneumlipidsbyorganicsolventextractionled

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13 toadramaticincreaseinwaterlossfromtheskin. 65 , 66 Furthermore,thelipidcom-positionofskinfrompatientswithpathologicallycompromisedbarrierfunctionwasfoundtobedifferentthantheskinofhealthypatients. 63 Considerableefforthasbeendirectedtowardidentifyingtheexactcompositionandstructuralorganizationofthestratumcorneumlipids.Despitetheprogressmadeinthiswork,therelationshipbetweenlipidpropertiesandcorrespondinganatomicalfunctionisnotcompletelyunderstood.Anoverviewoftheimportantchemicalandphysicalcharacteristicsofstratumcorneumlipidsispresentedinthissection.Thecurrentlyacceptedviewsoftherelationshipbetweenlipidstruc-tureandanatomicalfunctionisalsodiscussed.Theintentwastodevelopaphys-icalbasisforinterpretationofthetransdermaliontophoreticstudiesconductedinthiswork.Manuscriptsprovidingdetaileddiscussionsofstratumcorneumlipidsareavailableelsewhere. 14 , 17 , 22 , 35 , 56 , 67 Lipidscomposeapproximately8to10%ofthedrystratumcorneumweight, 68 whichcorrespondsto5to30%ofthetotalstratumcorneumvolume. 17 Thetypesandrelativecompositionofstratumcorneumlipidsisuniquetothisregionoftheepidermis.Forexample,stratumcorneumlipidsprimarilyconsistofceramides,cholesterolandfattyacids. 69 , 70 Thefractionofthesetypesoflipidsismuchsmallerintheunderlyingstratumgranulosum.Anotherexampleofuniquecompositionofstratumcorneumlipidsisprovidedbytherelativelylowweightfractionofphospholipids.Inthestratumcorneum,phospholipidscompriselessthan5%ofthetotallipidweightfraction,ascom-paredto25%inthestratumgranulosum. 64 , 66 , 71 Furthermore,phospholipidsareusuallyfoundingreatabundanceaspartofthecellularmembranespresentinotherregionsofthebody. 72 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(74 Thedifferenceinlipidcompositionissignicantbe-causethebilayerphospholipidsofcellularmembranesaremuchmoreamenable

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14 toaqueoustransport.Thisprovidesapartialexplanationastowhytheuniquecompositionofstratumcorneumlipidsisconsideredastheprimarysourceofthemembrane'slowpermeabilitycharacteristics.Fattyacidsandcholesterol.Fattyacidsmakeupapproximately10to20weightpercentofstratumcorneumlipids. 12 , 35 , 75 Thefattyacidscontainlonghydrocarbonchainsthatarepredominantlysaturatedconsistingof20to28carbons, 22 withmostpossessing22or24carbons. 35 Thehydrocarbontailsofstratumcorneumfattyacidsarelongerthanfattyacidsfoundelsewhereinthebody.Thelongertaillengthsdecreasethestiffnessandrigidityofstratumcorneumintercellularbilay-ersascomparedtocellularmembranes. 76 Cholesterol,alongwithsmalleramountsofcholesterolsulfateandthefattyacidsofcholesterolesters,composeapproximately20to25weightpercentofthetotallipidsindrystratumcorneum. 12 , 35 , 75 Cholesterolisacommoncomponentofmostlipidbilayermembranes. 73 Cholesterolisarelativelyrigidmoleculethatinuencespackingofthelamellarbilayers.Dependingonthecompositionoftheothercomponentsinthelipidbilayers,cholesterolcaneithercondensethelipidsintomorestructuredstates 77 oruidizethemembraneasawhole. 4 , 71 , 78 Theinu-enceofcholesterolonthephasebehaviorofstratumcorneumlipidsisalsodepen-dentontemperature. 77 Ceramides.Ceramidescomposeapproximately35to50%ofstratumcorneumlipidsbyweight. 12 , 14 , 35 , 75 Ceramidesalsomakeupthemajorityofpolarlipidspresentinthestratumcorneum,althoughtheyaregenerallymuchlesspolarthanthephospholipidsfoundincellularmembranes. 12 Ceramidesareaheterogeneousfamilyoflipidsthatpossessacommonbackboneofsphingosinewithlesseramountsofsphinganineandphytosphingosine.Theheadgroupsarelinkedtolong-chainedfattyacids.Thesphingosinecomponentoftheceramidesprovidesthelipidswith

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15 apolarregion.Thefattyacidsattachedtotheceramidespossesscharacteristicallylonghydrocarbontails-34carbonsthatarepredominantlysaturatedormo-nounsaturated. 35 Ingeneral,lipidswithextraunsaturationdecreasethestiffnessandrigidityoftheintercellularbilayers. 76 Ceramidesaregenerallygroupedintosixorsevenclassesaccordingtoheadgroupcomposition,hydrocarbontaillengthanddegreeofunsaturation. 35 , 63 , 79 , 80 AschematicofthechemicalstructuresoftypicalstratumcorneumceramidesispresentedinFigure 2-3 .ThesphingosineandphytosphingosineheadgroupsareindicatedbytheboundingboxesinFigure 2-3 .Ceramides1,2,4,5and6apos-sesssphingosineheadgroupswhereasthefattyacidsofCeramides3and6bareattachedtophytosphingosine. 67 TheclassicationschemeshowninFigure 2-3 wasdevelopedtohelpidentifytheceramideorcombinationofceramidesthatprovidesthegreatestcontributiontothepermeabilitybarrierofthestratumcorneum.Partialvalidationofthisap-proachwasprovidedbylipidextractionstudieswherepatientswithpathologi-callycompromisedbarrierfunctionexhibitedlowerproportionsofCeramide1incomparisontohealthypatients. 63 Ceramide1isalsofoundinlowerconcentrationsinhealthy,nonkeratiniz-ingoralstratumcorneum,i.e.,theepithelialliningofthemouth,ascomparedtohealthyepidermalstratumcorneum. 35 Furthermore,thepermeabilityoforalstratumcorneumisgenerallyhigherthanforepidermalstratumcorneum. 48 , 81 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(83 ThesetwoobservationsstronglysuggestthatCeramide1isthedominantcontrib-utortothestratumcorneumtransportbarrier.ThechemicalstructureofCeramide1alsosuggeststhecompoundcanprovideexcellentdiffusionlimitingproperties. 84 Forexample,Ceramide1consistsofasphingosineheadgroupesterlinkedtoahydroxyacidwithahydrocarbontail

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16 Figure2-3:Classicationschemeofstratumcorneumceramidesbasedonchemi-calstructureandcomposition.FigureadaptedfromSchurer.17 ofmuchlongerlengththantailsoftheotherceramidespresentinthestratumcorneum. 22 Thelongerhydrocarbontailwasusedtodevelopastructuralmodelfortheorganizationoftheintercellularstratumcorneumlipids. 22 , 38 ThemodelisdiscussedfurtherinSection 2.4.4 Thelonghydrocarbontailalsoprovidestheintercellularbilayerwithamorerigidstructure.Therigidorganizationofthebilayersprovidesforanenhancedtransportresistancetodiffusingcompounds. 85

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17 2.4.3ModelMembraneSystemsThediversenumberoflipidspresentinthebilayersmakesitdifculttoisolatecontributionstooverallbarrierfunctionfromspeciccomponents.Determinationoftherelationshipbetweenlipidcompositionandbarrierfunctioninvivoisfur-thercomplicatedbythepresenceofsebaceouslipidsonthesurfaceoftheskin.Inordertostudytherelationshipbetweenrelativelipidcompositionandmem-branestructure/permeability,avarietyofmodelmembranesystemshavebeendeveloped. 64 , 69 , 71 , 84 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(89 Themodelmembraneapproachhasbeensuccessfulinrelatingstructureandcompositiontocellularfunctioninbilayermembranes. 90 Modelmembranesfortransdermalstudiesaretypicallyconstructedfromthemajorclassesoflipidsfoundinthisstratumcorneumsuchasceramides,cholesterolandfattyacids.Thegen-eralapproachinvolvesadjustingtherelativeconcentrationofindividuallipidspeciesandobservingthephasebehaviorandpermeability.Thestudiesweredesignedtoisolateaspeciclipidorcombinationoflipidsthatprovidesthedom-inantcontributiontotheoverallpermeabilitybarrier.Inaddition,theinuenceofpHandtemperatureonthemolecularorganizationofthemodellipidshasbeeninvestigated.Forexample,anincreaseinpHcanpromotethelongrangeorderingofthebilayers. 84 Thedevelopmentofmodelmembraneshashelpedtoidentifymanyofthephysicalprocessesgoverningtheinteractionsbetweenstratumcorneumlipids.Specically,insightregardingthephysicalinteractionsbetweenselectclassesofstratumcorneumlipidshasbeenobtainedusingthisapproach.Forexample,anincreaseintherelativeconcentrationofcholesterolresultedinanincreaseinthepermeabilityofamodellipidmembrane.Theobservedincreaseinpermeabil-

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18 ityofthecholesterolrichmembranewasonlyslightlyhigherthanthemembranecomposedoflipidsinproportionssimilartonormalstratumcorneumbilayers. 75 Althoughstandardproceduresareavailable,itisgenerallydifculttocon-structbilayerswithcompositionsandstructuralorganizationssimilartothoseofanatomicalstratumcorneumlipids.Despitethisexperimentallimitation,manyoftheimportantfeaturesofstratumcorneumlipidsthataffecttransdermaldiffu-sionhavebeenidentied.Amorecompleteunderstandingofthephysicalinterac-tionsthatoccurbetweenstratumcorneumlipidsandthecorneocytesisrequiredtocharacterizetransdermaldiffusioncompletely.Ageneraldescriptionofthemolec-ularforcesgoverningorganizationofstratumcorneumlipidsispresentedinthenextsection.2.4.4IntercellularLamellarLipidOrganizationTheintercellularlipidsofthestratumcorneumformbroad,sheet-likestruc-turesthatareparalleltothesurfaceoftheskin. 79 Thebilayersareverticallystackedintorepeatingunitsthatresultsinanoveralllamellararrangement.Rutheniumtetroxidexationstudieshaverevealedthattherelativethicknessoftherepeatinglipidunitsexhibitsalternatingbandsofbroadandnarrowregions. 38 , 91 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(93 Theunitcellfortherepeatinglamellarstructurewasidentiedasbeingbroad:narrow:broad.Thethicknessofthebroadandnarrowregionswasestimatedtobe13mand6m.ThealternatinglayerstructurehasbeenconrmedbyX-raydiffractionstudies. 94 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(96 Itwasproposedthatthebroadregionscorrespondedtothehydro-carbontailsoflipidbilayers.Incontrast,thenarrowregionswerebelievedtobehydrocarbontailsofmonolayers.Themacroscopicorganizationofthelamellarlipidsprovidesforacontinuoushydrophobicphasearoundthecorneocytes.Astructuralmodelwasdevelopedtoexplainthealternatingregionsofbroadandnarrowlipidlayers.Itwasproposedthatthelipidregionsofthefattyacids

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19 andsphingosinewerearrangedonoppositesidesofthepolarheadgroup.Thebroadregionscorrespondedtothelonghydrocarbontailsofthefattyacidsorthetailofasmallfattyacidinlinewiththerelativelyshortsphingosinetail.Forexample,the30-34carbontailofCeramide1couldformabroadregionandthelipophilicportionofthesphingosinewouldcorrespondtothenarrowregion.Thealternatingbroad:narrow:broadlipidstructureisillustratedinFigure 2-4 .Asingleunitcellispresentedwherethebroad:narrow:broadstructureiscovalentlyboundbetweentwocorneocytes.Inthestratumcorneum,theintercellularspacebetweenthecorneocytesislledwithmultipleunitcellsstackedontopofeachother.Apolarregionisprovidedtothelayeredlipidstructurebytheoxygenatomsofthefattyacidsandsphingosine. Figure2-4:Alternating-widthlayeredstructureofstratumcorneumlamellarlipids.Theboundingboxescorrespondtothepolarregionsofthestratumcorneumlipids.FigureadaptedfromSwartzendruber.38 Thesegregationofthelipophilicandhydrophilicregionsiscausedbyatrade-offbetweencompetingforces.Forexample,electrostaticinteractionsdominatenearthesurfaceofpolarheadgroupsandvanderWaalsforcesandhydrogenbondingareresponsibleforthecloselypackedarrangementsofthelipidhydro-carbontails. 17

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20 Itisgenerallyacceptedintheliteraturethatthelonghydrocarbontailsoftheceramidesandfattyacidsareideallysuitedtoformhighlyorganized,denselypackedmembranestructures. 12 Asmentionedearlier,extensiveresearchhasbeenconductedtocharacterizetheinteractionsbetweendiffusingmoleculesandthestratumcorneumlipids.Particularemphasishasbeenplacedonidentifyingtherelationshipbetweenlipidmicrostructureandthediffusionrateofcompounds.Thebiophysicalpropertiesofstratumcorneumlipids,suchasphasebehaviorandstructuralorganization,havebeenstudiedbyavarietyofexperimentaltechniquesincluding2Hnuclearmagneticresonance, 31 , 64 , 71 Ramanspectroscopy, 88 , 97 , 98 in-fraredspectroscopy, 54 , 99 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(104 differentialscanningcalorimetry, 88 , 99 , 103 , 105 , 106 freeze-fractureelectronmicroscopy, 36 , 59 , 71 , 94 , 107 rutheniumstaininganalysis 37 , 38 , 91 andx-raydiffractionstudies. 12 , 94 , 96 , 108 , 109 Animportantcharacteristicofstratumcorneumlipidsidentiedinthesestud-iesisthatorder-disorderphasetransitiontemperaturesaregenerallyhigherthanthenormalphysiologicaltemperatureof37C. 70 , 99 Incontrast,thelipidspresentinthecellularmembranesinotherregionsofthebodyhavetransitiontemperatureswhichareusuallylowerthan37C. 20 Thehightransitiontemperatureofstratumcorneumlipidsisconsistentwithmoreorderedpackingarrangementsatnormalphysiologicaltemperature.Therelativelyhighphasetransitiontemperaturesofstratumcorneumlipidsareduetothelargethermalenergyrequiredtouidizethelonghydrocarbontails.Forexample,atwocarbonincreaseinthelengthofhydrocarbontailofphospho-lipidsisaccompaniedbya20Cincreaseinthegeltoliquidcrystallinetransitiontemperature. 4 Thedenselypackedarrangementsofstratumcorneumlipidbilay-erstypicallyobservedatphysiologicaltemperaturesgreatlyrestrictsthediffusionofwaterandionicspeciesdirectlythroughthemembrane.

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21 Lipidpolymorphism.Themixtureoflipidsinthestratumcorneumbilayersexhibitcomplexphasebehavior.Forexample,thelipidsdemonstrateconsiderablelateralanisotropyinchemicalcompositionandstructuralorganization.Insteadofassemblingintoasinglephasewithuniformcomposition,thebilayersareorga-nizedintoclustereddomainswhicharearrangedindifferentpackingstates. 24 , 100 Withinagivenbilayer,stratumcorneumlipidsarepredominantlyassembledineitheralamellargelorlamellarliquid-crystallinestate. 69 , 97 Bothofthesephasescorrespondtohighlyorderedstructures;however,intheliquid-crystallinephasethehydrocarbontailsarelesstightlypacked. 73 , 85 Thecomparativelylooserpackingarrangementofliquid-crystallinelipidspro-videsforatwoorderofmagnitudeincreaseinmembraneuidityupontransitionfromthegelstate. 73 Athighertemperatures>80Chexagonalpackingofthelipidshasbeenobserved.Thehexagonalpackedstructureismuchmoreuidandporousthanthegelorliquid-crystallinephasewhichareassociatedwithlowertemperatures.AschematicofthestructuralorganizationofthevariousphasesobservedinstratumcorneumlipidsispresentedinFigure 2-5 . Figure2-5:Structuralorganizationofstratumcorneumlipidphases.Thelamellargelphase,liquid-crystallinephaseandhexagonalclose-packedphasearedenotedbythekeysa,bandc,respectively.FigureadaptedfromGennis.73 Theobservationofmultiplephaseswithinagivenbilayerisadeningcharac-teristicoflipidpolymorphism. 78 , 110 Polymorphismisawell-documentedpropertyoflipidswhichhasbeenusedtoprovideacausalrelationshipbetweenmolecularstructureandtheregulationfunctionofcellularmembranes.Polymorphismisob-

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22 servedinbilayerswithuniformlipidcompositionaswellasinmorechemicallydiversesystems. 73 , 110 Temperature,watercontent,pH,proteincontentandlocalcompositionoflipidsinuencethestructureofthelocalizedphasedomainsofthebilayers. 24 , 73 , 78 , 84 Animportantbiophysicalpropertyassociatedwithpolymorphismisthatlipidsareabletodiffuselaterallywithinagivenbilayer. 73 , 77 Therelativelyhighmobilityofcellularlipidbilayersobservedatphysiologicaltemperaturesisconsistentwiththeexibleanduidpackingarrangementsseenintheliquid-crystallinephase.Asthehydrocarbontailsofstratumcorneumlipidsaregenerallylongerthanincellularmembranelipids,itislikelythatthereislesslateraldiffusionintheskin.Intercellularwater.Waterisanimportantcontributortotheoveralllipidor-ganizationofthestratumcorneumbilayers.Theweightpercentageofwaterinthestratumcorneumisapproximately20%asopposedto70-80%inthestratumgranulosum. 111 , 112 Thereisalsoawaterconcentrationgradientacrossthestra-tumcorneum.Theconcentrationofwaterishighestintheinnermostlayersofthestratumcorneumandgraduallydecreasestowardthesurfaceoftheskin. 113 Mostofthewaterisboundtothecorneocyteproteins;however,resultsfromx-rayscatteringexperimentssuggestedthatsmallamountsofwaterwerepresentintheintercellularlipidmatrix. 95 Thewaterwasbelievedtoresidealongthepolarheadgroupsofthelipidbilayers. 95 , 114 Thestratumcorneumpossessesanamazingabilitytoabsorblargequantitiesofwater.Ithasbeenreportedthatwaterisabsorbedinquantitiesequaltothreetofourtimesthedryweightofthestratumcorneum. 59 Thehydrationprocessisnotinstantaneous.Asthewatercontentofthestratumcorneumincreasesovertimethecorneocytesbegintoswell.Experimentswithfullyhydratedskinrevealedthat

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23 corneocyteexpansiondoesnotleadtosignicantstructuralalterationofindivid-uallipidbilayers. 59 , 91 , 95 , 96 , 115 , 116 Thestudiesindicatedthatwaterwasgenerallyaggregatedintosmallpoolslocatednearthejaggedinterfacesoflipidregions.Thepoolsofwaterwerebe-lievedtohavebeencausedbyphaseseparationbetweenthehydrophobicregionsofthelipidbilayersandthewater. 59 Althoughnotdirectlyobserved,theauthorsproposedthatthepoolswereinterconnected.Suchaschemecouldresultinacontinuousnetworkofaqueouspathwaysfordiffusionofionicsubstances.2.4.5DomainMosaicModelAcompleteframeworkestablishingthelinkbetweenthemorphologicalstruc-tureandchemicalcompositionofstratumcorneumlipidsandthecorrespond-ingphysiologicalfunctionisnotyetcomplete.TheDomainMosaicModeldevel-opedbyForslindincorporatesthephysicochemicalpropertiesofstratumcorneumlipidswithmanyoftheobservedanatomicalfeaturesandphysiologicalfunc-tionsoftheskin. 24 Thismodelisanextensionofthebrick-and-mortarnetworkmodelproposedbyMichaelsetal. 45 Aninherentassumptionofthebrick-and-mortarmodelwasthattransportofmoleculesoccurredthroughthelipidmatrixandaroundthecorneocytes.Thecorneocyteswereassumedtobeimpermeable;however,absorptionofcompoundsalongtheoutsidesurfaceofthecellswascon-sidered.TheDomainMosaicmodelwasdevelopedwheretheinteractionsbetweendif-fusingcompoundsandstratumcorneumlipidswereemphasized.TheDomainMosaicmodelconsideredtheabsorptionofwaterintothecorneocytes.Forexam-ple,itwasarguedthatthecorneocytesrequireasmalluxofwatertopreventcellembrittlement.Themodelincludedamechanismfordiffusionofwaterthrough

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24 thelipidbilayers.Theproposedtransportpathwaywasconsistentwiththecom-positionandstructureofthelipidmatrixwasincorporatedintothemodel.Forslind'sDomainMosaicmodelisanadaptationoftheFluidMosaicmodelofphospholipidbilayersdevelopedbySingerandNicolson. 117 Lipidpolymorphismwasusedextensivelyinbothofthesemodelstoestablishtherelationshipbetweenmembranestructureandtransportproperties.Forslindappliedthermodynamicargumentstoproposethatstratumcorneumlipidsaggregateintocrystallinesub-domains.Thecompositionofeachsub-domainwouldinturnconsistoflipidswithhydrocarbontailsofsimilarlengths.Thehigh-energygrainboundariesattheinterfacebetweenthecrystallinesubdomainscouldprovideroutesofaqueoustransportacrossthelamellarlipids.Oncewaterdiffusedacrossagivenbilayeritcouldthentravellaterallyintheaqueousregionslocatedbetweenthepolarheadgroupsofthelamellarbilayers.Transportwouldcontinueparalleltothesurfaceoftheskindirectionuntilan-otherlipid-phasegrainboundarywasencountered.Thealternatingprocessoflat-eralandtransversediffusioncouldprovidefortransportacrosstheentirestratumcorneum.Animplicationofthismodelisthataqueoustransportoccursalongatortuousroute.Atortuouspathwaywouldrequirealongerdiffusionpathlengthincomparisontotransportdirectlythroughthestratumcorneum.Therelativelylowobservedtransportratesofwateracrosstheskinisconsis-tentwithextendeddiffusionpathway. 75 , 81 , 114 Forexample,diffusioncoefcientsobtainedfromexperimentswithfullyhydratedskinwere20-30%oftheircorre-spondingfreesolutionvalues. 59 , 118 Thelateraldiffusionofwateralongthepolarregionshasbeenshowntoberelativelyfast. 119 Therefore,theratelimitingstepintheoveralltransportprocesswilllikelybemovementfromonebilayertoanother.

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25 AlthoughtheDomainMosaicmodelisfairlysuccessfulinrelatingthecomplexstructureofstratumcorneumlipidstothebarrierpropertiesofskin,unresolvedissuesremain.Forexample,themodelcannotbedirectlyappliedforpredictionoftransportratesacrosstheskin.Itshouldbeemphasizedthatthemodelwasdevel-opedtoaccountforthetransportpropertiesofthestratumcorneumundernormalphysiologicalconditions.Itislikelythatthebilayerswillbesignicantlydisturbedbythepresenceofanelectriceldduringiontophoresis.Avarietyofpredictivemodelshavebeendevelopedtoaccountfortheinuenceoftheelectriceldonthetransportofspeciesthroughtheskin. 120 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(124 Mostofthepredictivemodelsarebasedonmacroscopictransporttheoryanddonotaccountfortherangeofinterac-tionsconsideredintheDomainMosaicmodel.AdditionaldiscussionofpredictivetransdermaltransportmodelsisprovidedinChapter 3 .2.5IntercellularAppendagesInterspersedthroughouttheskinisavarietyofappendagealstructureswhichprovidepassagewaysforwaterandmetabolitesfromthedermistothesurfaceoftheskin. 10 , 125 Thethreetypesofappendagesinhumanskinarehairfollicles,sebaceousglandsandsweatglands.ThestructureofthesedermalappendagesisillustratedinFigure 2-6 .Appendagesaccountforonly0.1%to1%ofthetotalsurfaceareaofskin. 6 , 126 Althoughappendagesmakeupsuchasmallfractionoftheoverallskinsurface,thesemacroscopicstructuresmayserveaspotentialroutesoftransportfortrans-dermaldrugdelivery.Theproposalisbasedontheobservationthatappendagesbypassthediffusionbarrierofthestratumcorneumandprovidedirectaccesstothedermis. 4 Abriefdiscussionoftheanatomicalstructureandphysiologicalactiv-ityoftheseappendagesisprovidedhere.Theobjectivewastodescribethetypes

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26 Figure2-6:Structureofskinappendagesthatpenetratethestratumcorneum.Fig-urereproducedfromOrkin.5 ofinteractionsthatdiffusingmoleculesmightencounterastheypassthroughtheappendages.2.5.1HairFolliclesHairfolliclesarecomposedofcloselypacked,proteinaceouscellsassembledintoalong,brouscylindricalshaft.Hairproteinsarepredominantlyarrangedinlamentsthatarecross-linkedbysulfurbonds. 6 Similartotheproteinsinthecorneocytes,hairproteinsarealsomadeofkeratin.Inthelowerregionsoftheskinthehairfollicleiscompletelysurroundedbycells.Thecellshelptoanchorthefollicleintheskinandpromotegrowthoftheshaft.Intheupperregionsofthedermisthehairfollicleislocatedintheannularspaceofthefollicularcanal.Thedensityofhairfolliclesvariesthroughoutthebody.Afolliculardensityof300-500/cm2isfoundonthescalp.Thescalphasthehighestdensityoffollicleswhich

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27 isinstarkcontrasttothesolesofthefeetwherethesestructuresareessentiallyabsent. 4 Associatedwithhairfolliclesaresebaceousglands.Sebaceousglandsarepouchshapedstructuresthatareconnectedviaductstothehairfolliclecanals.Similartohairfollicles,thedensityofsebaceousglandsalsovariesoverthesurfaceofthebody.Thehighestdensityofsebaceousglandsisfoundontheforeheadandupperregionsofthebody.Thismaximumglandulardensitycorrespondsto400to900glands/cm2.Theremainderofthebodyhasapproximately100sebaceousglands/cm2. 19 Sebaceousglandsexcreteanamorphousmixtureoflipids,knownassebum.Sebumisreleasedintothehairfolliclecanalsanddepositedonthesurfaceoftheskin.Thetypesoflipidspresentinsebumareprimarilycomposedoftriglycerides,waxestersandsmallamountsofcholesterolesters. 127 Thetriglyceridesarepar-tiallyhydrolyzedwhichmaintainstheacidicpH5ofsebum. 7 , 128 Theacidicnatureofsebumhelpstoprovideskinwithitsantimicrobialcharacter. 35 , 129 Thethicknessandcontentofsebumpresentonthesurfaceoftheskinvariesgreatlywithanatomicallocation. 127 Thehighlipidcontentofsebumwilllikelypreventthepassageofdrugsaltsthroughthehairfollicles.2.5.2SweatGlandsSweatglandsformthemajorityofappendagespresentonthesurfaceofthebody.Sweatglandsareclassiedasbeingeitherapocrinesweatglandsorec-crinesweatglands.Apocrinesweatglandsarepredominantlyfoundinthegeni-talandunderarmregionsandthereforewillnotlikelybesubjectedtoiontophor-esis.Eccrineglandscompriseapproximately80%ofthetotalsweatglands.Theyaredistributedovertheentirebodywithanaveragedensityofapproximately400glands/cm2. 4

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28 Themainfunctionofeccrinesweatglandsistofacilitatethermoregulationviasweating.Thestructureofsweatglandsconsistsofcoiledtubularbundleslocatedinthedermiswhichareattachedtocylindricalductswithopeningsontopofthestratumcorneumsee,forexample,Figure 2-6 .Thesecretionsfromsweatglandsare99%waterandhaveapHofapproximately5underrestconditionsand7undermaximumsweating. 130 Theefuxoftheaqueoussecretionsfromthesweatglandsmaypreventtheinuxofmaterialfromthesurfaceoftheskinintothebody.Itcouldalsobearguedthattheaqueousnatureofthesecretionsmightbefavorableforthetransportofioniccompounds.2.6InuenceofElectricFieldsonSkinPropertiesThematerialpresentedinSections 2 2.5 describedthepropertiesofskinun-derhomeostaticconditions.Duringiontophoresistheapplicationofcurrentwillinduceanonequilibriumelectriceldintheskin.Althoughanimposedcurrentcanincreasethetransdermaluxofchargedcompounds,skinpropertiesmaybealteredduringtheprocess.Theobjectofthissectionwastodescribethebehaviorofskinduringiontophoresis.2.6.1ElectricalPropertiesoftheStratumCorneumTheelectricalpropertiesofthestratumcorneumaredirectlylinkedtothechem-icalcompositionandstructuralarrangementofthemembrane'sconstituentmolecules.Itisgenerallyacceptedthatthestratumcorneumpossessesanetnegativeback-groundcharge. 114 , 120 , 131 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(135 Thenegativebackgroundchargefavorsthetransportofcationsoveranionsthroughtheskin.Thetransportofanionsisrestrictedinordertomaintainelectroneutralitywithinthemembrane.Transferencenumberexperimentswithmonovalentcationsofchloridesaltsprovidedtherstevidenceforthisconclusion. 131 , 133

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29 Althoughthenegativebackgroundchargeofskinisgenerallyacceptedintheliterature,theexactsourceofthechargeisstillunclear.Forexample,ithasbeenproposedthattheproteinresiduesinthecorneocytesprovidethenegativeback-groundcharge. 120 , 131 Thiswouldrequireanexcessofaminoacidresidueswithnegativechargessuchascarboxylicacidgroupsasopposedtopositivemoietiessuchasaminegroups. 131 Ithasalsobeenproposedthatasmallfractionofthenegativechargeresideswiththepolarheadgroupsofthelipidbilayers. 114 Theoverallchargeisprobablyconcentratedintheinteriorofthecorneocyteswithaminorcomponentdistributedthroughoutthelamellarlipidmatrix.Electroosmoticowofwaterthroughskinlipids.Inadditiontosupportingthepreferentialtransportofcations,thenegativebackgroundchargeofskincanalsofacilitatethebulkowofwaterduringiontophoresis.Themechanismforthesolventtransportisbasedontheassumptionthatthenegativechargeislocalizedalongthesurfaceofapproximatelycylindricalpores.Thenegativechargealongtheporewallswillintroduceadiffuseregionofpositivechargeintheadjacentelectrolytesolutiontomaintainsystemelectroneutrality.Thethicknessofthediffuseregionofchargeisinverselyrelatedtoionicstrengthoftheelectrolyteandthechargedensityonthesurfaceoftheporewalls.Whenavoltagedifferenceisappliedacrosstheskinduringiontophoresisanelectricalbodyforcewillbeexertedonthethinlayerofpositivelychargeduid.Theelec-tricforceonthepositivelychargedelectrolytewillcausebulkuidowthroughthesystem.Thistypeofelectricallyinducedowisreferredtoaselectroosmosiswhichisasubsetofthemoregeneralclassofbehaviorknownaselectrokineticphenomena. 136 , 137 ThemechanismfortheowofbulkwaterthroughskinwasrstproposedbyGrimnes. 138 Evidenceforelectroosmosisduringtransdermaliontophoresis

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30 wasprovidedbyexperimentswhereneutralspeciesweredeliveredthroughtheskin. 121 , 131 , 135 , 139 )]TJET1 0 0 1 6.447 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(146 Sophisticatedmathematicalmodelshavebeendevelopedtoaccountforelectroosmoticowthroughskin.ThemodelsaredescribedinmoredetailinSection 3.2 .Macroscopicelectricalpropertiesofthestratumcorneum.Skinhasaniso-electricpointatpHvaluesbetween3and4. 23 , 112 , 147 ThisimpliesthatskinwillbenegativelychargedwhenthepHofthesurroundingsolutionisabovethisvalueandpositivelychargedatmoreacidicpH.Theisoelectricpointmustbeconsid-eredwhencompilingdrugformulations.ImproperselectionofsolutionpHcouldleadtoneutralizationofthebackgroundchargewhichwouldproduceareversalofthecationselectivityofthemembrane.Asaresult,theiontophoreticdeliveryofthetargetmoleculewouldbecomemoredifcult. 148 Excisedstratumcorneumexhibitscharacteristicallyhighpolarizationresist-ancevalueswhicharegenerallyontheorderof100kW/cm2. 1 , 111 Theelectricalresistanceofwholeskin,asmeasuredinvivo,isgenerallyonetotwoordersofmagnitudehigher. 1 , 149 Thecauseforthedifferenceintheinvitroandinvivoval-uesofskinresistanceremainsunresolved.However,itislikelythattheproce-dureusedtoextractthestratumcorneumfromtheunderlyinglayersoftheskinislargelyresponsibleforthelowerelectricalresistanceofexcisedepidermaltissue.Therelativelyhighpercentageoflipidsandlowpercentageofwaterinthestra-tumcorneumisresponsibleforthehighelectricalresistanceofthemembrane.Ex-perimentshaveshownthattheelectricalresistanceisinverselyproportionaltothewatercontentofthestratumcorneum. 112 , 150 , 151 Anotherinterestingfeatureofskinisthattheimpedancecanvarydramaticallydependingonanatomicallocation. 16 , 44 Theinvivoimpedancevaluesfromadjacentskinsitesinthesameanatomicalre-gionhavebeenshowntodifferbyseveralordersofmagnitude. 152

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31 Skinalsoexhibitsanonlinearresponsetolargeapplied-currentsignals. 2 , 3 , 153 , 154 Thenonlinearpropertiesofskincorrespondtodecreasedvaluesofskinimped-ancewithincreasedvaluesofcurrentdensity.Therangeofapplied-currentden-sitiesfortheonsetofnonlinearbehaviorliesbetween0.1A/cm2and75A/cm2.Thepotentialdifferenceacrossthemembraneattheseapplied-currentdensitiesfallsbetween0.1Vand2V. 3 Thealterationstotheskinmayormaynotbere-versible.Thedegreeofreversibilitydependsontheskinhydration,theamplitudeoftheimposedcurrentandthedurationoftheappliedcurrent. 153 Thedecreaseinskinresistancetolargeelectricalsignalsstronglysuggeststhattheinternalstructureofthestratumcorneumhasbeenmodied.Suchstructuralmodicationsmayintroduceadditionalpathwaysforenhancedtransport.Avari-etyofmechanismshavebeenproposedfortheformationofnewpathwaysduringiontophoresis.Forexample,ithasbeenproposedthatelectricalburnsontheskinarecausedbylocalizedregionsofhighcurrentdensity. 3 Thehighcurrentden-sitypathwayswouldlikelyexperienceJouleheating.Iftheincreaseinthermalenergywaslargeenough,stratumcorneumlipidscouldundergophasetransi-tionstomoreuidandpermeablecongurations. 3 Thishypothesisissupportedbytheobservationofincreasedskinpermeabilityattemperaturesabovetheglasstransitiontemperatureofstratumcorneumlipids. 155 Inuenceofelectricaleldonskinlipids.Theeffectofelectriceldsonbi-ologicalmembranesisawellstudiedphenomenon.Forexample,thecouplingofconcentrationpolarizationandpotentialgradientsacrosscellmembranescanproduceshort-durationcurrentpulses.Thistypeofmechanismisresponsiblefortheconductionofnerveimpulsesandthecontractionofmusclebers. 156 , 157 Thestructuresandmechanismsresponsibleforphysiologicalandmetabolicprocessesarediverse.Forexample,electrochemicallycoupledtransmembraneexchangeof

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32 calciumincardiacmusclesoccursinhydrophilicproteinchannelsthatspanacrossthelipidbilayerswhichenclosethemusclecells. 156 Inthestratumcorneum,thelamellarlipidslackthesetypeofproteinchannelswhichhelpstoexplainthelowpermeabilityofskin.Anothermechanismresponsibleforexchangeofspeciesacrossmembranesre-quiresanadditionalcarriermoleculetocomplexwiththephysiologicallyactivecompound.Thecarriermoleculeservesasanescortthroughthemembraneinordertoovercometheotherwiseunfavorableinteractionsinthecellularlipidbi-layers.Thistypeoftransportisresponsiblefortheexchangeofglucoseacrosserythrocytemembranes. 73 Theconceptofcarriermoleculeswasusedtodevelopliposomesfortopicaldeliveryoftherapeuticcompounds. 158 , 159 Typicallyforliposomaltransporttheionicdrugisencapsulatedintheaqueousinnercoreofmicelles.Theouterlipophilicregionofthemicellesprovidesforen-ergeticallyfavorableinteractionsbetweentheliposomesandthelamellarbilayersofthestratumcorneum.Thereductionofhydrophilic-hydrophobicinteractionsbetweentheionicdrugandthelipidbilayersprovidesforenhancedtransportrates.Adramaticexampleofthetherapeuticuseofappliedelectriceldsforma-nipulatingbiologicalbilayersisprovidedbyelectroporation.Electroporationcon-sistsoftheapplicationofhigh-voltagepulsesinshortdurationtoreversiblyopenporesinlipidbilayersystems.Thetechniquewasdevelopedtointroducegeneticmaterialacrossthelipidbilayersofcellularmembranes. 160 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(162 Theelectriceldsappliedduringtransdermaliontophoresismightalsobeexpectedtocausetheformationofnewchannelsforaqueoustransport.However,themechanismforstructuralchangeswilllikelybedifferentiniontophoresisastheelectriceldsareappliedatmuchloweramplitudesforlongerperiodsoftime.

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33 Indirectsupportforelectricallyinducedalterationstothestratumcorneumwasprovidedbyconstant-currentiontophoresisexperimentswhereanincreaseinspeciesuxwasaccompaniedbydecreasedskinimpedance. 112 , 131 , 163 Thereisalsoconsiderableevidencethatareductioninskinimpedancehasnoeffectonthemagnitudeoftransdermalux. 133 , 164 Itispossiblethatcurrentmaydisruptthelamellarlipidsbutthemagnitudeofthealterationsmaynotbelargeenoughtopromoteenhancedtransport.2.6.2IontophoreticTransportPathwaysThereisconsiderablediscussionintheliteraturepertainingtotheroutethatdiffusingmoleculestravelastheypassthroughtheskinduringiontophoresis.Transportthroughthestratumcorneumcanbeenvisionedtooccuralongthefol-lowingpathways;intercellular,transcellularandappendageal.AschematicoftheproposedpathwaysfortransdermaldrugdeliveryispresentedinFigure 2-7 .The Figure2-7:Potentialroutesfortransportoftherapeuticcompoundsduringtrans-dermaliontophoresis.FigurereproducedfromBanga.10 intercellularpathwaycorrespondstodiffusionthroughthelipidmatrixofthestra-tumcorneum.Theintercellularpathwayalsoincludesthepossibilityofinduced

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34 poresorpathwayscausedbythealterationofthelipidbilayersduringthepassageofcurrent.Thetranscellularroutereferstotransportwhichalternatesbetweenthelipidregionanddirectlythroughthecorneocytes.Theappendagealpathwayisdescribedbytransportthroughthemacroscopicshuntsinthestratumcorneumsuchashairfolliclecanalsandsweatglands.Relativelylittleexperimentalevi-denceisavailableforthetranscellularroute;however,thereissignicantexper-imentalsupportforboththeintercellular 54 , 58 , 62 , 120 , 165 andtheappendagealpath-ways. 28 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(31 , 166 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(168 Duringtransdermaliontophoresis,itislikelythatbothintercell-ularandappendagealpathwayscontributetotheoveralluxofmoleculesacrosstheskin.Thephysicochemicalpropertiesofthediffusingspecieswillstronglyinuencethetransportrouteduringiontophoresis.Forexample,lipophiliccompoundswillmostlikelytravelthroughtheintercellularlipidmatrixwhereasstericallyhindered,highmolecularweightspeciesmightbeexpectedtopassthroughtheappendagealshuntpathways.Targetmoleculepropertiesforpredictingthemag-nitudeandlocationofiontophoretictransportincludecharge,molecularweight,molecularsize,pKaandlipid-waterpartitioncoefcient. 23 , 81 , 120 , 139 , 145 , 169 , 170 2.7SummaryofSkinPropertiesAffectingIontophoreticTransportInSections 2.1 2.5 thestructureandcompositionofhumanskinundernormalphysiologicalconditionswasdescribed.Adominantofthosesectionswasthatthephysicochemicalpropertiesofskinareextremelycomplex.Althoughtheanatomyandphysiologyofskiniscomplicated,someimportantgeneralizationsrelatedtopercutaneoustransportcanbemade.Forexample,thedominantbarriertotrans-dermaldrugdeliveryisthetop-mostlayeroftheskin,thestratumcorneum.Thethicknessacrosstheheterogeneousmembraneisonly10to20micronsovermost

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35 ofthebody.Thestratumcorneumiscomprisedofdiskshapedcellssurroundedbyalamellarlipidmatrix.Theuniquecompositionandrelativelyhighpercentageoflipidsinthestra-tumcorneumisgenerallyconsideredtoprovideamajorcontributiontothelowpermeabilitycharacteristicsofthemembrane.Althoughthecellsofthestratumcorneum,thecorneocytes,arenotcapableofmitoticdivisionthereisconsiderable,physiologicalandenzymaticactivityinthisregion. 55 Importantcharacteristicsofthestratumcorneumincludealowpermeabilitytohydrophiliccompoundsandarelativelylowpercentageofwater.Section 2.6 describestheelectricalpropertiesofthestratumcorneum.Majorfeaturesofthestratumcorneumunderhomeostaticconditionsincludeanegativebackgroundchargeandahighelectricalresistance.Anotherimportantcharacter-isticofstratumcorneumisthattheelectricalresistancedropsdramaticallywhentheappliedvoltageisgreaterthanthe0.1to2V.Itisimperativethattheseprop-ertiesbeconsideredforthedevelopmentoftransdermaldrugdeliverymodalitiessuchasiontophoresis.Althoughacomprehensivedescriptionoftheinteractionsandmechanismsinvolvediniontophoresisremainsunresolved,itisclearthatanimposedelectriceldcanenhancetransdermaldeliveryratesofbothionic 120 , 142 , 171 )]TJET1 0 0 1 6.447 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(179 anduncharged 121 , 131 , 135 , 139 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(146 , 178 compounds.

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CHAPTER3MODELSFORTRANSDERMALIONTOPHORESISAvarietyofmathematicalmodelshavebeendevelopedtoprovideinsightintotheimportantfactorsaffectingtransdermaliontophoresis.Thesemodelshavebeenusedforthepredictionoftransdermaldrugdeliveryratesforgivenvaluesofappliedcurrentandasatoolfortheidenticationofthemechanismsinvolvedinthetransportprocess.Theapproachesusedtoformulatethesemodelsaredi-verse,howevermostarebasedoncontinuum,hinderedtransport,nonequilibriumthermodynamic,orkineticrateconcepts.Thenalsectionsofthischaptersee,forexample,Sections 3.6.1 3.6.3 pro-videadiscussionofidealelectriccircuitmodelsdevelopedforthepredictionoftheimpedanceresponseofskin.ElectrochemicalImpedanceSpectroscopyEISiscommonlyusedtostudyskintransportpropertiesduringiontophoresis.Theformulationoftheoverallcircuitnetworkinvolvesthesemi-empiricaladditionofcircuitelementsuntilthemodelprovidesanaccuratedescriptionoftheskinimpedanceresponse.Upontheestablishmentofanappropriatenetwork,adeduc-tiveprocessisthenusedtorelatethepropertiesoftheskintotheindividualcircuitelementsthatcomprisetheoverallnetwork.Asummaryoftheassumptionsandlimitationsassociatedwitheachofthemodelingframeworksisprovided.3.1Nernst-PlanckContinuumModelsOneofthemostcommonapproachesformodelingtransdermaliontophoresisisbasedontheNernst-Planckdenitionofspeciesuxthroughhomogeneousmedia.Dilute-solutiontheoryisalsoappliedinthesederivations.Severalau36

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37 thorshaveimplementedtheNernst-Planckformalismtodeveloppredictiveex-pressionsofspeciesuxinsteady-state 122 , 132 , 140 , 144 , 145 , 180 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(182 andtimevaryingsys-tems. 27 , 121 , 140 , 183 , 184 Theoveralluxisdrivenbytheelectrochemicalpotentialgradientandbythenetowofthebulksolution.Theuxresultingfromtheelectrochemicalpotentialgradientistypicallydecoupledintoanelectromigrationtermthataccountsfortheforceoftheelectriceldonchargedmoleculesandadiffusiontermcorrespondingtoactivityorconcentrationgradientdrivenow.TheNernst-Planckux,thataccountforthesedrivingforces,ispresentedbyNi=)]TJ/F53 11.955 Tf 11.465 8.094 Td[(DiziF RTcirF)]TJ/F53 11.955 Tf 12.593 0 Td[(Dirci+vci-1whereNiistheuxdensity,Diisthediffusioncoefcient,ziisthechargenumberofthespeciesi,FisFaraday'sconstant,Ristheuniversalgasconstant,Tcorre-spondstotheabsolutetemperature,ciistheconcentrationofspeciesi,rFiselec-trostaticpotentialgradientandvisthenetvelocityofthesolution.ThetermsontherighthandsideofEquation 3-1 correspondtothecontributionstotheover-alluxfromelectromigration,diffusionandconvection,respectively.Transportthroughouttheentiresystemdomainisgenerallycharacterizedbyintegratingtheuxequationswithappropriateboundaryconditions.Theapproachleadstoex-pressionsforpotentialandconcentrationproleswithinthemembrane.Thenonlinearelectromigrationtermintheuxexpressionmakesdirectanaly-sisintractableexceptforinafewrestrictedcases.Asaresult,simplifyingassump-tionsareusuallyinvokedtoobtainananalyticalsolutiontotheuxequation.Formostofthemodelsavailableintheliteratureitisassumedthattheelectriceldthroughtheskinisconstantorthatthesystemiseverywhereelectricallyneutral.Theconstanteldassumptionremovesthenonlinearityintheelectromigrationterm.Thesimplicationallowsfordirectsolutionforthespeciesuxunderthe

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38 additionalassumptionofatimeinvariantsystem. 180 Analternativeapproachistorelaxtheconstanteldconditionandassumethesystemiselectricallyneutraleverywhere.Intherestrictedcasewheretheelectrolytesolutioniscomposedofasinglebinary1:1salt,suchasNaCl,applicationoftheelectroneutralityassumptionwillalsoleadtoasystemofequationsthatisamenabletoanalyticalsolution.Inclinicaliontophoreticdeliverysystems,drugformulationsareusuallybecomposedofdrugsalts,buffersandsupportingelectrolytes.Theelectroneutral-ityconditionisinsufcienttoprovidefordirectsolutionoftheuxexpressionscorrespondingtothesemorecomplexmixtures.Numericalmethodsmustbeim-plementedtoobtaintransdermalprolesofspeciesux,concentrationandpoten-tialfrommathematicalmodelsbasedontheNernst-Planckdenitionofux.Agoaloftheworkpresentedherewastoinvestigatetheeffectofsolutioncompo-sitiononthedrugdeliveryrateandtheconcentration,pHandpotentialproles.Inaccordancewiththisobjective,iterativenumericaltechniqueswereappliedinthedevelopmentofthemodelfortransdermaliontophoresis.ThedetailsoftheapproacharedescribedinChapter 10 .3.2HinderedTransportModelsAsdemonstratedinChapter1,skincannotbedescribedasbeingahomoge-neousmembrane.Inordertoaccountforthecomplexstructureoftheskinmanyauthorshaveutilizedhinderedtransporttheorytodevelopmathematicalmodelsfortransdermaliontophoresis. 120 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(124 HinderedtransporttheoryisanextensionoftheNernst-Planckdescriptionofuxwheretheeffectsofconstrainedowge-ometriesandelectrostaticinteractionsontheuidareconsidered.Aninherentassumptionmadeinthedevelopmentofmodelsfortransdermaliontophoresisbasedonhinderedtransporttheoryisthattransportoccursthroughaqueousporesinthestratumcorneum.Thehypothesizedporescouldbeconsideredtobeinte-

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39 gralstructuresoftheskinortemporarychannelsinducedupontheapplicationofcurrentduringiontophoresis.Thehinderedtransportorporerestrictionmodelframeworkwasoriginallydevelopedtocharacterizeowthroughlong,narrowpassagessuchascapillar-iesandstraightchanneledporousmembranes. 185 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(189 Thediffusingparticlesareassumedtobeofthesamedimensionsastheowchannels.Underthesecondi-tions,interparticleinteractionsandparticle-wallinteractionsconstituteasigni-cantfractionoftheoverallresistancetoowthroughthemembrane.Thesametypesofinteractionsarealsopresentinlargerchannels;however,inthissituation,therelativeinuenceonthehydrodynamicowprolecanusuallybeneglected.Theapproachhasprovidedforsuccessfulpredictionofspeciesuxthroughcap-illarysystems.Incontrast,directapplicationofthestandardNernst-Planckuxexpressionstosimilarconstrainednetworksoverpredictstransportratesascom-paredtoexperiment.Thegeneralformforspeciesuxbasedonhinderedtransporttheoryisdi-rectlyanalogoustothestandardNernst-Planckexpression.However,thecorrec-tionterms,HandWareintroducedtoaccountfortheadditionaltransportresist-ancethroughnarrowchannels.TheuxexpressionforhinderedtransporttheoryispresentedbyNi=)]TJ/F53 11.955 Tf 10.245 0 Td[(HDiziFci RTdF dx+dci dxWvxci-2wherethevoidfractionofthemembraneislumpedtogetherwiththetortuosityfactorintheparameter.HrepresentsthehindrancefactorfordiffusionandmigrationandWrepresentsthehindrancefactorforconvection.Onamolecularscale,theterm,H,accountsforstericandlong-rangeelectrostaticinteractions.Theterm,W,accountsfortheenhancedhydrodynamicdragonparticlescausedbythepresenceoftheporewall.

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40 Predictedvaluesforthehindrancefactors,HandW,areusuallyobtainedfromcorrelationsbasedontheratiooftheradiioftheuidparticlestotheradiioftheporewalls.Ingeneral,thecorrectionfactorsHandWincreaseasthesizeofthediffusingparticlesapproachesthesizeoftheporeopenings.Thestandardexpres-sionsforthehindrancefactors,HandW,developedbyAndersonandQuinn 185 forsphericalparticlesaregivenbyH=)]TJ/F11 12.457 Tf 12.116 0 Td[(2)]TJ/F20 11.955 Tf 11.996 0 Td[(2:144+2:0893)]TJ/F20 11.955 Tf 11.996 0 Td[(0:09485-3W=)]TJ/F11 12.457 Tf 12.116 0 Td[(2)]TJ/F20 11.955 Tf 11.996 0 Td[()]TJ/F11 12.457 Tf 12.115 0 Td[(2)]TJ/F20 11.955 Tf 13.191 8.094 Td[(2 32)]TJ/F20 11.955 Tf 11.996 0 Td[(0:1633-4wheretheindependentvariable,isdenedby=rparticle rpore-5whererparticleistheparticleradiusandrporeistheporeradius.3.3RenedHinderedTransportModels:SoluteInteractionswithPoreWallsAnattractivefeatureofthehinderedtransportformalismisthatthenegativebackgroundchargeofskincanbeconsidered.Itistypicallyassumedthatthechargeislocatedonthesurfaceofcylindricalporeswithlargeaspectratios.Thenegativechargeontheporewallcausesadiffuseregionofpositivechargetode-velopintheelectrolytesolutionadjacenttotheporesurface.ThefunctionofthepositivelychargedregionistomaintainsystemelectroneutralityTheDebyescreeninglengthprovidesanestimateforthicknessofthediffusechargeregion. 136 TheexpressionforcalculatingtheDebyelengthisgivenby=RT F2zi2ci;bulk-6where,R,TandFarethesolutionpermittivity,whichisalsoreferredtoasthedielectricconstant,universalgasconstant,absolutetemperatureandFaraday's

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41 constant.Thebulksolutionconcentrationandchargenumberofanionaresigni-edbyziandci;bulk.TheexpressionfortheDebyelengthstatesthatthethicknessofthediffuseregionisinverselyproportionaltoionicstrength.Whenanelectriceldisappliedacrossacharged,porousmembrane,anelec-tricalbodyforcewillbeexertedonthevolumeofionicsolutionlocatedinthedif-fusechargeregionadjacenttotheporewalls. 136 Iftheelectriceldistheorientedperpendicularlytotheporewalls,bulkuidowcanoccur.Thephenomenonofelectricallyinduceduidowisknownaselectroosmosis.AschematicofowthroughchargedcapillariesispresentedinFigure 3-1 .Theuidstreamlinescon-vergeatthemouthoftheporewhichdecreasetheprobabilitythatauidparticlewillenterthechannel. Figure3-1:Schematicrepresentationofuidowthroughconstrainedpores.Flowtrajectoriesoftheuidparticlesaredenotedbyarrows. Thesituationwithintheskinduringiontophoresisisgenerallyconsistentwiththeconditionsrequiredforelectroosmoticow.Forexample,itcanbeenvisionedthatthenegativebackgroundchargeofthestratumcorneumislocatedonthesurfaceofthestraightcylindricalaqueouspores.Althoughthereisconsiderableexperimentalevidencesuggestingthepresenceofaqueousporesduringionto-

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42 phoresis,theexactstructureoftheseporeshasnotbeencompletelycharacter-ized. 30 , 31 , 54 , 58 , 62 , 118 , 122 , 165 Theassumptionthattransportoccursthroughstraightchanneledporesseemsunrealisticgiventhecomplexmorphologicalstructureofskin.Eveniftransportdoesoccurthroughcylindricalporesitislikelythatthereisadistributionofporesizesinskin.Despitetheselimitationsthetypesofmolecularinteractionsconsideredinhinderedtransporttheorycanexplaintheobservationofelectroosmoticowduringiontophoresis.Manyauthorshaveappliedmodelsoftransdermaliontophoresisbasedonhin-deredtransporttheorytoestimateanequivalentporesizebasedonmeasureduxvalues. 120 , 123 Aspartofthecalculationprocess,theelectriceldthroughtheskinwasconsideredtobeuniform.Calculatedvaluesoftheporeradiiwereintherangeof8-30A.Theestimatesfortheporesizesprovidedintheliteraturecouldbeusedwiththecorrespondingmodelstopredictupperandlowerboundsofdrugdeliveryratesforagivencurrent.Thepredicteddimensionsofthecylindricalpathwaysaremuchsmallerthanthoseassociatedwiththeappendagealpathways.Thiscouldimplythattrans-portisoccurringintercellularlyorthattheeffectiveporesizespresentintheap-pendagesaresmallerthantheirstructuraldimensions.Modelsbasedonhinderedtransporttheoryhaveprovidedinsightintopotentialroutesoftransportthroughtheskinduringiontophoresis.Althoughapplicationofthehinderedtransportmodelssuggestmechanismsthataffecttransdermaliontophoresis,theapproachcannotbeapplieddirectlytoestimatespeciesuxes.Robertsetal.developedarenedmodeloftransdermaliontophoresisbasedonthehinderedtransportformalismwheretheeffectsofpartiallyionizedsolutesandirregularlyshapedparticleswereconsidered. 124 Themodelalsoaccountedforelectrostaticinteractionsbetweenthesolutionionsandachargedporewall.

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43 Thegeneralobjectiveofthemodelwastodevelopanexpressionforrelatingthemolecularvolumeofadrugtotheiontophoretictransportrate.ThespeciesuxcorrespondingtotherenedmodelwaspresentedbyNi=PCionto;ici-7wherePCionto;iistheoveralliontophoreticpermeabilitycoefcientandciisthesoluteconcentration.TheiontophoreticpermeabilitycoefcientisdenedbyPCionto;i=2uizibfiFITWPRTi ks;c+ks;ah1+cfuiui+)]TJ/F1 11.955 Tf 12.827 3.622 Td[(cfuiiii)]TJ/F11 12.457 Tf 12.116 0 Td[(ivsol-8wheretherstandsecondtermsontherighthandsidecorrespondtothecontribu-tionstotheoveralluxfromelectromigrationandconvection,respectively.Theparameterscontributingtothepermeabilitycoefcient,Equation 3-8 ,includedthesolutemobility,ui,specieschargenumber,zi,Faraday'sconstant,F,totalcur-rentthroughtheskin,ITandthepermselectivityofskin,W.Theothervariablesrequiredforcalculationoftheiontophoreticpermeabilitycoefcientincludedtheporerestrictionterm,PRTi,thedonorandreceptorsolutionconductivities,ks;dandks;r,thefractionsofionizedandunionizedsolute,iiandui,theporereectionco-efcient,iandthesolventvelocity,vsol.Alloftheparametersforthepermeabilitycoefcientwereknownorcouldbecalculatedbystandardcorrelationswiththeexceptionoftheporerestrictionterm,PRTi,andthecorrectedconvectioncoefcient,)]TJ/F11 12.457 Tf 12.276 0 Td[(i.Forexample,thefractionofionizedandunionizedsolutewerecalculatedfrompublishedpKavaluesandmeasuredsolutionpH.Theporerestrictiontermandcorrectedconvectioncoef-cientwerecalculatedaccordingtoEquations 3-3 and 3-5 whichareimplicitfunctionsoftheporeradius.Theporesizewasdeterminediterativelysuchthatdifferencebetweentheiontophoreticuxpredictedfromthemodelandtheuxdeterminedbyexperimentwasminimized.

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44 Alimitationoftherenedhinderedtransportmodelisthataprioriestima-tionofiontophoreticdruguxesisnotpossible.Thisisbecausetherelationshipbetweenporesizeanddrugphysicochemicalpropertiesofthedrugmustdeter-minedexperimentally.Bulksolutionvaluesofphysicochemicalproperties,suchassolutemobilityandpH,wereusedfortheregressionofEquation 3-7 totheuxdata.Itislikelythattheseparameterswillbedifferentintheconstrainedenvironmentofthenarrowpore.Althoughthesetypesoferrorswillleadtoinac-curateestimatesofporesizes,themodelaccountsfortheinteractionswhichareexpectedtobeimportantfortransdermaliontophoresis.3.4NonequilibriumThermodynamicModelsNumerousmathematicalmodelsbasedonnonequilibriumthermodynamicshavebeendevelopedformoleculartransportacrossbiologicalmembranes. 156 , 190 Modelsoftransdermaliontophoresisbasedonnonequilibriumthermodynamicsareattractivebecauseskinsubjectedtoconstantcurrentwillnotbeunderequilib-riumconditions.Althoughmanymodelsfortheexchangeofmetabolicspeciesacrosscellularmembraneshavebeendevelopedfromnonequilibriumthermo-dynamicsonlyalimitednumberofattemptshavebeenmadetoapplythein-frastructuretotransdermaliontophoresis. 172 , 175 , 191 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(193 Thegoalhereistoprovideasummaryoftheapplicationofnonequilibriumthermodynamicsforbiologicalmembranetransport.Anoutlineofthegoverningequationsandlimitationsofthetheoreticalinfrastructureisprovided.TheapplicationofnonequilibriumthermodynamicsformodelingbiologicalmembranetransportwaspioneeredbyKedemandKatchalsky. 194 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(196 Theobjec-tiveoftheirworkwastoaccountforspecicinteractionsbetweenthemembraneandtheelectrolytesolutioncomponents.Inthiswork,thesolventwasconsid-eredasadiffusingspecies.Therefore,bulkuidow,whichhasbeenobserved

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45 inbiologicalmembranetransport,wasconsideredexplicitly. 194 Thetreatmentrep-resentedapointofdeparturefromtheclassicalNernst-Planckformalismfordif-fusionprocesses.Thegoverningequationsformembranetransportdevelopedinthisworkarestillwidelyacceptedbythebiologicalcommunity.ThederivationoftheequationsformembranetransportbasedonnonequilibriumthermodynamicspresentedherelooselyfollowstheexplanationpresentedbyFriedman. 156 Anunderlyingassumptionofnonequilibriumthermodynamics,alsoknownasirreversiblethermodynamics,isthattheforcesanduxesofagivensystemaredirectlyrelated.Thisassumptionalsoholdsforequilibriumthermodynamics,however,theapproachfordeningtheuxequationsisdifferent.Forexample,theelectrochemicalpotentialgradientisconsideredtobethedrivingforcefortheuxintheNernst-Planckformalism.Theforcesanduxesfornonequilibriumthermodynamicsareconstrainedbythedissipationfunction.Theintegratedformofthedissipationfunctionanticipa-tionfunctionisdenedaccordingtoF=TZa0diS dtdx-9whereFistheintegratedformofthedissipationfunction,diS dtcorrespondstotherateofentropygenerationperunitvolumeofthemembraneandtheabsolutetemperature,T,isplacedoutsidetheintegralbecausebiologicalsystemsarees-sentiallyisothermal.Theintegratedformofthedissipationfunctionisusuallyappliedformembranetransportbecauseitisdifculttoassessthelocalforceswithintheinteriorofthemembrane.TheuxesarerelatedtothedissipationfunctionaccordingtoF=iJiXi-10

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46 wheretheJi'saretheuxesandtheXi'sarethedrivingforcesfortheuxes.Equa-tion 3-10 statesthattheuxescontributetotheentropyofthesystemataratethatisproportionaltothedrivingforce.Thegeneralformofspeciesuxforirre-versiblethermodynamics,subjecttotheconstraintdenedbyEquation 3-10 ,isdescribedbyJi=iLijXi-11wheretheonlynewvariable,Lij,isthephenomenologicalcoefcient.Thephe-nomenologicalcoefcientsareproportionalityconstantsthatrepresentthecontri-butiontothespeciesuxesfromagivenforce.Thesubscriptj,isincludedtoaccountfortheinteractionofspeciesi,withallothercomponentsinthesolution.Theapproachaccountsforinteractionsbetweenthesolventandthevarioussolutemolecules.Interactionswithmoleculesofthesametypearealsoconsideredi.e.wheni=j.Sinceexplicitconsiderationofallofthepossibleinteractionsbetweenthevari-ouscomponentsinthesystemisprovidedbythisframework,thenumberofphe-nomenologicalcoefcientsincreasesdramaticallyasthenumberofspeciesinagivensystemincreases.UponinspectionofEquation 3-11 thenumberofphe-nomenologicalcoefcientsnecessarytocharacterizethesystemshouldequaln2,wherenisthenumberofuniquecomponentsinthesystem.However,theOn-sagerreciprocalrelationstatesthatLij=Lji,whichreducesthenumberofuniquephenomenologicalcoefcientston2+n 2.Formulticomponentsolutionsitisusuallyassumedthattheinteractionsbetweenagivensoluteandtheremainingsolutesdonotaffecttheuxoftheselectedspecies.TheassumptionimpliesLij=0fori6=jwhichreducesthenumberofindependentcoefcientsto2n-1.Adifcultywiththismodelingapproachisthatthephenomenologicalcon-stantsmustbedeterminedexperimentally.Anymodicationtothesolutioncom-

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47 positionrequiresadditionalexperimentationtodetermineanewsetofphenomeno-logicalcoefcients.Themannerinwhichtheuxequationsforirreversiblether-modynamicsaredenedprovidesnoinformationregardingthetransportmecha-nisms. 156 Furthermore,thestructureofthephysicalsystemcannotbeassessedbynonequilibriumthermodynamics.Theapproachinsteadyieldsexpressionsforre-latingmasstransportacrossmembranestomeasurablequantitiessuchassolutioncompositions.Thelargenumberofparametersrequiredtocharacterizethesys-temcoupledwithlackofmechanisticinsightofthetransportprocessmayexplainthelimitedapplicationofirreversiblethermodynamicsformathematicalmodelsoftransdermaliontophoresis. 193 , 197 3.5KineticRateTheoryBasedModelsThemultilaminatestructureofthestratumcorneumhaspromptedthedevel-opmentofmathematicalmodelsfortransdermaldrugdeliverywhichassumethattheoveralltransportprocessiscomposedofaseriesofdiscretetransportevents. 60 , 154 , 198 Theapproachhasalsobeenappliedsuccessfullytomodeltrans-portthroughcellularmembranes. 199 Itisassumedthatdrugcompoundsmustovercomeaseriesofpotentialenergybarriersinordertopassthroughtheskin.Thespatialdistributionofthepotentialenergybarriersisgenerallyconsideredtobelocatedattheinterfacialregionbetweenthevariouslayersofthestratumcorneum.Formalrelationshipsbetweenthetransportrateacrosseachoftheen-ergybarriersandthelocalconcentrationisestablishedbytheapplicationofkineticratetheory,alsoreferredtoasthetheoryofactivatedrateprocesses. 60 Thegeneralapproachformodelingtransdermaltransportbythisformalismisoutlinedhere;however,themethodologywasnotappliedforinterpretingtheexperimentspre-sentedinthisreport.

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48 Anexpressionforspeciesuxcanbedevelopedbyassumingthatparticlesmoveacrossagivenenergybarrierinboththeforwardandbackwarddirections.Generallyauniqueamountofenergyisrequiredforparticlemovementfromeachsideofthebarrier.Theprobabilityforatransporteventtooccurisinverselypro-portionaltotheenergyrequiredtoovercomethebarrier.Inaddition,theprobabil-ityfortransportacrossanenergybarrierisdirectlyproportionaltothelocalcon-centrationofaspecies.Thevelocityofparticles,ortransportrate,overthebarrierisdirectlyrelatedtotheprobabilityassociatedwithmovementfromtherespectivedirection.Theexpressionsfortheforwardandbackwardvelocitiesbasedonthelocalconcentrationarevfi;j=Ki;jci;j-12vbi;j=Ki;j+1ci;j+1-13wherevfi;jandvbi;jarethevelocitiesofspeciesicrossingbarrierjintheforwardandbackwarddirection,respectively.TheforwardandbackwardrateconstantsaresigniedbyKi;jandKi;j+1.Theconcentrationsofspeciesitotheleftandrightofbarrierjareindicatedbyci;jandci;j+1.Thenetuxacrossagivenenergybarrier,denedintermsofthevelocitiesassociatedwitheachdirectionoftransport,isJi;j=vfi;j)]TJ/F53 11.955 Tf 12.116 0 Td[(vbi;j=Ki;jci;j)]TJ/F53 11.955 Tf 12.487 0 Td[(Ki;j+1ci;j+1-14whereJi;jistheuxofspeciesiacrossbarrierjandtheremainingtermsarede-nedaccordingtoEquations 3-12 and 3-13 .TherateconstantsKi;jandKi;j+1aretypicallyfunctionsofenergybarrierlength,temperature,andelectricalstateofthesystem.Thegeneralapproachforcalculatinguxthroughasystemistoin-cludeexpressionsoftheformpresentedinEquation 3-14 foreachenergybarrier.

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49 Theexpressionsareusedincombinationwiththemassconservationprincipletodeterminedtheoverallux.AnArrheniusformcanbeassignedtotherateconstantstoreectthedepen-denceonthestateofthesystem.Forexample,therateconstantsarecommonlypresentedbyKij=ki;je)]TJ/F60 5.978 Tf 4.836 0 Td[(DGi;j RT-15whereki;jistheproportionalityconstant,DGi;jistheGibbsfreeenergyandRTisthesystemthermalenergy.Theexponentialtermcorrespondstotheactivationenergyrequiredtocrossanenergybarrier.Itshouldbenotedthatproportionalityconstant,ki;j,hasanimplicitdependenceonthewidthoftheenergybarrier.TheGibbsfreeenergytermcanbedeconvolutedtoincludeadrivingforcebasedontheelectricalpotentialandatermcorrespondingtothechemicalpoten-tial.Withthistypeofseparationitispossibletoexaminetheeffectofelectricalpotentialonthetransportrateofchargedcompounds.AschematicrepresentingthesequenceoftransporteventswhichareassumedtooccurwithintheskinisshowninFigure 3-2 .Transportthroughtheskinisenvisionedasoccurringfromlefttoright.Theskinsurfaceislocatedattheleft-handsideofthegureandentranceintothecirculatorysystemisassumedtooccurattherighthandside.Theverticaldashedlinescorrespondtothelocationsofthepotentialenergybarriers.Anadvantageofmodelsfortransdermaliontophoresisdevelopedfromtheactivatedrateformalismisthatuxescanbepredictedintheabsenceofadi-rectmechanismforthetransportprocess.Thedifcultyliesinidentifyingcor-rectvaluesforeachoftheproportionalityconstants,ki;j.Furthermore,selectionofthenumberandspatiallocationsoftheenergybarrierspresentinthestratumcorneumiscompletelyarbitrary.Mostauthorshaveassumedthatthereare15-20

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50 Figure3-2:Proposedschemeforstep-wisetransportofdissolvedspeciesthroughthestratumcorneum.Thedashedlinesrepresentthelocationsofthepotentialcontrolledtransportevents. energybarriers,whichisconsistentwiththenumberofcorneocytelayersinthestratumcorneum.Althoughthischoiceseemslogicalitispossiblethatthereisanalternativedistributionoftransporteventswithintheskin.3.6ElectrochemicalImpedanceSpectroscopyAllofthemathematicalmodelsdiscusseduptothispointweredevelopedtocharacterizedrugdeliveryratesduringtransdermaliontophoresis.Formanyofthesemodelscarefulconsiderationwasgiventothephysicochemicalpropertiesoftheskin.Animplicitassumptionofthetransportmodelswasthatthepropertiesofskinremainedconstantduringiontophoresis.Thereisconsiderableevidencethatthetransportpropertiesofskinchangeduringiontophoresissee,forexam-pleSection 2.6 .AvarietyoftechniquesincludingTransepidermalWaterLossMeasurementsTEWL 150 , 152 , 200 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(202 andElectrochemicalImpedanceSpectroscopyEIS 44 , 150 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(152 , 163 , 200 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(207 havebeenappliedtostudytheinuenceofappliedcurrentonskintransportproperties.Bothofthesetechniqueshavebeenusedtoinvesti-gateskinpropertiesintheabsenceofappliedcurrents. 16 , 50 , 65 , 102 , 153 , 208 )]TJET1 0 0 1 6.447 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.499 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(210 Thema-

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51 terialpresentedheredescribestheapplicationofidealelectriccircuitnetworksformodelingtheimpedanceresponseofskin.3.6.1ElectricalCircuitModelsofSkinImpedanceResponseElectrochemicalImpedanceSpectroscopyEIShasbeenappliedextensivelyfortheinvestigationofskintransportproperties.ThewidespreaduseofEISismo-tivated,inpart,bythetechnique'seaseofapplicationcombinedwiththerelativelyshorttimerequiredtocollectaspectrum.Forexample,animpedancespectrumofskinwiththefrequencyrangeof65kHzto0.1Hzwith12measuringpointsperlogarithmicdecadecanbecollectedinlessthan10minutes.AmoredetaileddescriptionofthetheoreticalandpracticalaspectsofElectrochemicalImpedanceSpectroscopyisprovidedinSection 4.1 .Thissectionprovidesadiscussionofthemodelspresentedintheliteraturefortheinterpretationofskinimpedancedata.Theadvantagesandlimitationsofthevariousmodelsaredescribed.DespitetheextensiveapplicationofElectrochemicalImpedanceSpectroscopyfortransdermaldrugdeliveryresearch,unambiguousinterpretationofthedataisnotyetavailable.SinceEISisasmall-signal,frequencydomaintechniqueitisamenabletoanalysiswithequivalentelectriccircuits.Thegeneralapproachistocombineindividualcircuitelements,suchasresistorsincapacitors,inanitera-tivefashionuntilthenetworkproducesanimpedanceresponsethatisconsistentwiththeskinspectrum. 57 , 133 , 149 , 152 , 155 , 208 , 211 , 212 Uponformulationofanappropriateequivalentcircuit,theimportantfeaturesofskinarededucedfromtheindividualelementsofthenetwork.Asimplecircuitnetworkcommonlyusedtorepresenttheimpedanceresponseofstratumcorneum 50 , 133 , 155 , 213 consistsofaresistorinserieswithaparallelcom-binationofaresistorandacapacitor.AschematicrepresentationofthecircuitispresentedinFigure 3-3 .ForthesystemshowninFigure 3-3 ,theleadingresistorRe

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52 representstheelectrolytesolutionresistance,theparallelresistorRskinistheOhmicresistanceofskin,andCskin,correspondstothebulkcapacitanceofskin. Figure3-3:Equivalentcircuitmodelforstratumcorneumimpedance.Re,RskinandCskinrepresenttheelectrolytesolutionresistance,theresistanceofskinandthecapacitanceofskin,respectively. MorethanoneexplanationhasbeenofferedasaphysicaljusticationforthecapacitorCskinintheequivalentcircuitmodelofskin.Forexample,themacro-scopicstructureofthestratumcorneumisroughlyanalogoustothecongurationofaparallelplatecapacitor.Thehighconcentrationofstratumcorneumlipidsservesasthedielectricmaterialwhichprovidesfortheseparationofcharge. 133 , 155 Foratypicalimpedanceexperiment1-5cm2ofstratumcorneumisprobed.Therelativelylargesurfaceareaofthestratumcorneumincomparisontothemem-branethickness20misalsosimilartothegeometricalcongurationofaparallelcapacitor.Analternativeinterpretationforthecapacitoristhatitrepre-sentsthedoublelayerchargingcapacitanceofthetransportpathwaysthroughskin.Thechargingprocessisbelievedtobeassociatedwithabsorptionreactionsbetweentheionsinsolutionandthepermanentlychargedsitesofthestratumcorneum. 211 Thefrequency-dependentimpedanceresponseofthesimplethree-elementcir-cuit,intermsoftheindividualcircuitelements,isestablishedaccordingtoZR)]TJ/F53 7.97 Tf 6.495 0 Td[(CPE=Re+Rskin 1+)]TJ/F53 11.955 Tf 6.838 -9.689 Td[(j!-16where!istheangularfrequencyoftheACsignalandisthecharacteristictimeconstantforthesystem.Thetimeconstantisrelatedtotheindividualcircuitele-

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53 mentsaccordingto=RskinCskin.Thecharacteristicfrequency,!c,isequaltotheinverseofthetimeconstant,.Theexponent,isequaltooneforthesimplecircuitshownincircuitshowninFigure 3-3 .Whenisbetween0and1thecircuitisreferredtoasaconstantphaseelement.ThesignicanceoftheconstantphaseelementdiscussedinmoredetailinSection 3.6.2 .Ingeneral,parametervaluesforthecircuitelementsaredeterminedbyregressingthemodeltoskinimpedancedata.ComplexnonlinearleastsquaresCNLRregressionroutinesareusuallyimplementedwithacomputertoprovideforrapiddeterminationofthecircuitparameters.Atypicalplotofskinimpedancedatapresentedintheimpedance-planeisshowninFigure 3-4 .Animpedance-planeplotdisplaystheimaginarycompo-nentoftheimpedance,Zj,onthepositivey-axisandtherealpartoftheimped-ance,Zronthex-axis.ThistypeofplotissometimesreferredtoasaNyquistplot.Theimpedanceresponseofthethree-elementcircuitwiththesamecharac-teristicfrequencyandthesamepolarizationimpedanceofskin,asdeterminedbyexperiment,isdisplayedasthetopcurveofFigure 3-4 .Visualinspectionoftheimpedance-planeplotshowsthatthethree-elementcircuitisinsufcienttomodeltheskinimpedanceresponse.3.6.2RenedCircuitModelsIngeneral,CNLRregressionofthethree-elementcircuitshowninFigure 3-3 tomostskinimpedancespectrawillnotprovidestatisticallyadequatets.Atypi-calimpedance-planeplotofskinimpedancedata,asshowninFigure 3-4 ,exhibitsadepressedsemicirclewherethelocusofthesemicircleliesbelowtherealaxis.Thistypeofimpedanceresponseischaracteristicofasystemwithadistributionofrelaxationprocesses.Forexample,impedance-planeplotsofmetallicelectrodesoftenexhibitasimilardepression.Itisgenerallyacceptedthatmorphologicalin-

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54 Figure3-4:Impedance-planeplotofskinimmersedin50mMCaCl2.Experimentaldataissigniedbyopencircles.Thedashedlinerepresentsthethree-elementcircuitmodelttothedata.Thesolidlinecorrespondstoconstantphaseelementrepresentationofdata,where=0.695andthecharacteristicfrequency,!c,was442Hz. homogeneitiesonthemetallicsurfacecauseadistributionofresidualstressesatelectrode/electrolyteinterface.Thismorphologicalvariabilityresultsinadistri-butionofactivationenergiesassociatedwiththeinterfacialchargetransferreac-tionsand,hence,adistributionoftimeconstants. 214 Asthesimplethree-elementcircuitisinsufcienttomodelmostdistributedsystems,moresophisticatedcircuitnetworkshavebeendevelopedtodescribetheimpedanceresponseofskin.Therenedcircuitmodelsofskingenerallyfallintotwocategories;1Transmissionlinemodelsand2Constantphaseelementmodels.ThecircuitcorrespondingtotransmissionlinesconsistsofRCresistive-capacitiveelementscombinedwithinductorsandresistorsina”ladder”networkarrangement.Thecircuitdiagramforthegeneraltransmissionlinemodelispre-sentedinFigure 3.5a .Thetransmissionlinecircuitwasoriginallydevelopedtomodelpowerlossesthatoccuroverlongdistancesinhigh-voltagecables. 215 Thetransmissionlinecircuithasbeenadaptedforusewithheterogeneoussys-tems,suchasionicconductionthroughporouselectrodesandmembraneswith

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55 interconnectedpores. 216 , 217 Inpractice,theinductorsareomittedfromthetrans-missionlinemodelforskinimpedance. 212 AsaresultthetransmissionlinecircuitoftheskinreducestothenetworkshowninFigure 3.5b .TheparallelnetworkofinterconnectedRCelementscanbeinterpretedasaspatialdistributionofthephysicochemicalpropertiesoftheskin.Superpositionofthetimeconstantsas-sociatedwiththecircuitelementsleadstoanimpedanceresponsecanprovidestatisticallyvalidrepresentationsofskinimpedancespectra. 212 a bFigure3-5:Equivalentcircuitmodelsoftransmissionlines.aGeneraltransmis-sionlinecircuit.bTransmissionlinecircuitforstratumcorneum.Theinductorsareomittedasthereisnoobviousphysicalbasisforincorporatingtheelementsintothemodelforskin. Thesecondclassofcircuitmodelsfortheimpedanceofskinareconstructedbyreplacingthecapacitor,Cskin,inthethree-elementcircuitshowninFigure 3-3 withaconstantphaseelement.TheconstantphaseelementcircuitforskinispresentedbyFigure 3-6 .AsdescribedinSection 3.6.1 ,thecompleximpedanceexpressionfortheconstantphaseelementnetworkispresentedbyEquation 3-16 .Theimped-anceresponseofskincangenerallybedescribedbythisexpressionwhentheexpo-nentialparameter,,isintherangeof0:65<<1:0. 151 , 208 , 211 , 212 Themagnitudeofreectstherelativedisplacementofthesemicirclelocusfromtherealaxisin

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56 Figure3-6:Constantphaseelementnetworkrepresentationofstratumcorneumimpedance.SimilartothecircuitshowninFigure 3-3 ,Re,andRskinrepresenttheelectrolytesolutionresistanceandtheresistanceofskin,however,CPErepresentsaconstantphaseelement. theimpedance-planewheresmallervaluesofcorrespondtogreaterdegreesofsemicircledepression.Similartothetransmissionline,theconstantphaseelementnetworkcanmodelsystemswithadepressedsemicircularimpedanceresponse.Themajordifferenceisthattheconstantphaseelementcircuitprovidesforacontinuousdistributionoftimeconstants,whereasthetransmissionlinemodelleadstoadiscretedistri-bution.Furthermore,thetimeconstantsfortheconstantphaseelementaresym-metricallydistributedaboutthecriticalfrequency.Ithasbeenproposedthattheconstantphaseelementisrepresentativeofasizeorchargedistributionoftheaqueousporeswhichprovidethetransportpathwaysthroughskin. 211 3.6.3LimitationsofIdealCircuitModelsAlimitationofelectriccircuitmodelsisthatmultiplecircuitnetworkscanbeconstructedtoprovidestatisticallyvalidtsforagivenimpedancespectrum.Theindividualelementsofthecompetingnetworksarelikelytobecongureddiffer-ently.Therefore,assignmentofphysicalpropertiestotheelementsofeachnet-workcanleadtoverydifferentinterpretationsforskinimpedance.Knowledgeofskinphysicochemicalpropertiescanbeusedtojustifytheaccep-tanceofanappropriatemodel.Forexample,Konturrietal.foundthattransmis-sionlinesandconstantphaseelementnetworksprovidedsatisfactoryrepresenta-

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57 tionsofskinimpedance. 211 , 212 Theauthorsselectedtheconstantphasenetworkasthebettermodelbecausetheycouldnotndaphysicaljusticationfortheinclusionoftheinductor. 212 Althoughthistypeofdeductiveprocessseemedrea-sonable,abetterapproachwouldbetoapplycomplementaryexperimentalandmodelingtechniquestoselectthemostappropriatecircuitnetwork.Amethodol-ogyformodelingskinimpedanceisdescribedbrieyattheendofthissection.Aconstraintofidealcircuitmodelsisthattheelementswhichcomposetheoverallcircuitnetwork,i.e.,theresistors,thecapacitorsandtheinductors,etc.,areassumedtobehavelinearlywithrespecttopotential. 218 Thisimpliesthattheproportionalitybetweentheinputandoutputsignalsforagivenelementisinde-pendentofthepotentialacrosstheelement.Forrealsystems,thereisalimitedrangeofpotentialwherethedesignequationsforidealcircuitsareapplicable.Forskin,thisrangecorrespondsto0.1-2V, 3 forfurtherdiscussionseeSection 2.6 .Itshouldbenotedthatthepropertiesassociatedwithagivencircuitelement,suchasresistance,capacitanceandinductanceareestablishedwithoutclosere-gardtotheinternalstructureoftheelement.This”lumped-sum”descriptionofidealcircuitelementpropertiesgreatlylimitstheutilityofcircuitnetworksforinterpretationofthephysicalpropertiesandthekineticprocessesoftheskin.Amorerigorousmethodologyforinterpretingimpedancedataistodevelopdeter-ministicmodelsbasedonthegoverningequationswhichdescribethephysicsandchemistryofskin.Themodelcanthenberegressedtoskinimpedancespectratoobtainparameterestimatesforthephysicalpropertiesofthesystem.Thisap-proachhasbeenappliedsuccessfullyforalimitednumberofsystemssuchastheelectrodissolutionofcopper;however,themethodologyhasnotyetbeenappliedtocomplexsystemssuchashumanskin.Moredetaileddescriptionsofthegeneralprocedureareprovidedintheliterature. 219 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(223

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58 3.7SummaryTheliteratureprovidesawidearrayofmathematicalmodelsoftransdermaliontophoresiswithvaryingdegreesofsophistication.ThemodelsweredevelopedfromthetraditionalNernst-Planckequilibriumdescriptionoftransport,thefor-malismforhinderedtransportthroughconstrainedgeometries,nonequilibriumthermodynamicsandkineticratetheory.Thenumberofuniquechemicalspeciesincludedinthemodelsreviewedherewasusuallylimitedtotwoorthreeions.Resultsfromthesemodelsmustbeviewedcautiouslybecausethebodycontainsacomplexmixtureofioniccompounds.Predictionsoftheconcentrationandpo-tentialproleswithintheskincannotbeobtainedfromthesemodelswiththeexceptionofthesimplestmodelsbasedonNernst-Plancktheory.Acommonfeatureofmostofthesedevelopmentsisthattheelectriceldacrosstheskinisassumedtobeuniform.Althoughthisassumptiongreatlysimpliesthemathematicalanalysisofthegoverningequations,thephysicalbasisforthisassumptionisquestionableduetotheheterogeneousstructureoftheskin.De-spitetheselimitations,themathematicalmodelsdiscussedherehaveprovidedamethodtopredictdrugdeliveryratesforgivenappliedpotentialsandexternalelectrolytesolutioncompositions.Inadditiontothelargenumberofmodelsdevelopedtopredicttransdermaldrugdeliveryrates,avarietyofidealcircuitnetworkshavebeendevelopedtomodelthetransportpropertiesofskin.ElectrochemicalImpedanceSpectroscopyisacommonlyusedtechniquetostudythetransportpropertiesofskinandthecircuitnetworksweredevelopedtomodeltheimpedanceresponseofskin.Itisimportanttopointoutthatalthoughthevariouscircuitmodelsdescribedinthisreviewcanadequatelyrepresentskinimpedancedata,theapproachisseverelylimitedinthatthereisnotnecessarilyadirectconnectionbetweentheindivid-

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59 ualelementsofthecircuitnetworkandthephysicochemicalpropertiesoftheskin.Despitetheselimitations,theworkreviewedhereservesasagoodstartingpointforthedevelopmentofclinicalsystemsand/ormoresophisticatedmodelsoftransdermaldrugdelivery.

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CHAPTER4EXPERIMENTALMETHODOLOGYThedevelopmentofiontophoretictransdermaldrugdeliverydevicesrequiresafundamentalunderstandingoftheinuenceofcurrentontransdermaldrugdeliveryratesandskintransportproperties.ElectrochemicalImpedanceSpec-troscopyEISwasappliedinthisworktostudythemacroscopictransportprop-ertiesofheat-separatedcadaverskin.ThemodulationprotocolfortheEISstudieswasmodiedtopreventlargepotentialdifferencesfromoccurringacrosstheskin.TheEISworkwassupplementedbymonitoringtheresponseofskinwhensub-jectedtoappliedDCpotentialandcurrentbiases.Anarrayofpotentialandcur-rentbiasamplitudeswereappliedtodeterminetheeffectofthesecontrolvariablesonskintransportproperties.TheinuenceofcurrentontransdermaldrugdeliveryrateswasinvestigatedwithUV-visabsorptionspectroscopy.Theabsorptionspectroscopytechniqueal-lowedforconcentrationchanges,andhencedruguxes,tobeinferredfromchangesinthelightintensitypassingthroughthesystem.Acustomdual-beamspectrom-etersystemwasdevelopedtoaccountfordriftinthebaselineresponseoftheexperimentalapparatus.TheabsorptionspectroscopysystemwasdesignedforconcurrentuseofEISduringthetransdermaldeliverystudies.Thecombinedmethodologywasselectedbecauseskintransportpropertiesanddrugdeliveryratescouldbemeasuredsimultaneously.Theimpedancedatawereanalyzedtoidentifythestationaryandlinearportionsoftheimpedancespectra.Thekeyfea-turesoftheexperimentaltechniquesaredescribedinthischapter. 60

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61 4.1ElectrochemicalImpedanceSpectroscopyElectrochemicalImpedanceSpectroscopyEIShasbeenappliedfortheinves-tigationofawidevarietyofelectroactivesystemsincludingceramic,polymericandbiologicalmembranes. 222 , 224 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(231 ThenegativebackgroundchargeofskinmakesEISanattractivemethodologyforstudyingskinbecauseitcanbeappliedeas-ilyandinanoninvasivemanner.Abriefoverviewofelectrochemicalimpedancespectroscopyisprovidedbecausethetechniquewasusedextensivelyinthiswork.Detaileddiscussionsofthetechnicalandtheoreticalissuesassociatedwithelectro-chemicalimpedancespectroscopyareavailableelsewhere. 219 , 220 , 232 , 233 4.1.1PrinciplesofElectrochemicalImpedanceSpectroscopyElectrochemicalimpedancespectroscopyisasmall-signaltechniquewhereasinusoidalcurrentorpotentialperturbationisimposedonthesystemofinterestandthecorrespondingpotentialorcurrentresponseismeasured.Comparisonoftheinputandoutputsignalsprovidesforthemeasurementoftheimpedanceatagivenperturbationfrequency.AnappealingfeatureofEISisthatsystemswithcharacteristictimeconstantsdistributedoverawide-rangeoftimescalescanbestudied.Forexample,transientphenomena,suchasdiffusion,doublelayerchargingandchargetransferreactions,typicallyoccuroverperiodsof1-10)]TJ/F20 7.97 Tf 6.448 0 Td[(1s,10)]TJ/F20 7.97 Tf 6.448 0 Td[(2-10)]TJ/F20 7.97 Tf 6.447 0 Td[(3sand10)]TJ/F20 7.97 Tf 6.448 0 Td[(4s,respectively. 234 Investigationofthevariousprocessesisaccomplishedinatypicalexperimentbyincrementallyadjustingthefrequencyoftheincidentwaveformoverawiderangeandmeasuringtheimpedanceateachfrequency.Electrochemicalimpedancespectroscopyhasbeenappliedextensivelyforstudyinginterfacialelectrochemicalreactionssuchasinthecorrosionofmetals.Thetechniqueisalsosuitablefortheinvestigationofsolid-stateandmembranesystems.Ashortdiscussionofelectrochemicalreactionsisprovidedtointroduce

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62 Figure4-1:Polarizationplotforatypicalelectrochemicalsystem. thetheoreticalfoundationforimpedancespectroscopy.Thedrivingforceforatyp-icalelectrochemicalreactionisprovidedbytheelectrostaticpotential.Ameasureofthereactionrateisprovidedbythecurrent.Therateofatypicalelectrochemi-calreactiondisplaysanexponentialdependenceonpotentialasdescribedbytheclassicalButler-Volmerequation. 137 Therelationshipbetweenreactionrateandpotentialiscommonlydisplayedgraphicallywithpolarizationplots.Atypicalpolarizationcurve,asshowninFig-ure 4-1 ,isconstructedbyplottingcurrentdensityontheordinateandpotentialontheabscissa.Duringanimpedanceexperimentthesinusoidalpotentialorcur-rentperturbationisappliedaboutasetpointonthepolarizationcurve.Ideally,thesinusoidalperturbationissmallenoughtomaintainlinearityinthesystem.Displacementofthesystemfromthesteady-stateconditionallowsthecurrent-potentialrelationshiptobeprobedinanoninvasivemanner.Thetheoreticalframeworkofimpedancespectroscopyisderivedfromlinearsystemstheory. 220 Thegoverningequationsforelectrochemicalimpedancemi-croscopyarebasedontheassumptionthatlinearityismaintainedinthesystem

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63 overthecourseoftheexperiment.Theinstantaneousresponse,yt,ofalinearsystemisrelatedtotheforcingfunction,xt,accordingtob0dnyt dtn+b1dn)]TJ/F20 7.97 Tf 6.448 0 Td[(1yt dtn)]TJ/F20 7.97 Tf 6.447 0 Td[(1+:::+bnyt=a0dmxt dtm+a1dm)]TJ/F20 7.97 Tf 6.448 0 Td[(1xt dtm)]TJ/F20 7.97 Tf 6.448 0 Td[(1+:::+amxt-1wheretherightsideofEquation 4-1 isalinearcombinationofthetermsassoci-atedwiththeinputfunction.ThetermsontheleftsideofEquation 4-1 corre-spondtothecontributionstothesystemresponse.Inanelectrochemicalimpedancespectroscopyexperiment,theforcingfunc-tion,xt,correspondstoeitherthesinusoidalpotentialorcurrentinputsignalandtheresponse,yt,isthecurrentorpotentialoutputsignal.Foranexperi-mentconductedundergalvanostaticcontrol,thecurrentistheinputsignalandthepotentialistheresponsesignal.TheinstantaneousvalueoftheinputcurrentwaveformcanbeexpressedinpolarandCartesiancoordinates,respectively,ac-cordingtoIt=I0sin!t-2andtheresponsesignalcorrespondingtothepotentialattime,t,isVt=V0sin!t+-3whereI0andV0aretheamplitudesofthecurrentandpotentialsignals,respec-tively.Thefrequencyoftheperturbationisdenotedby!,jisp )]TJ/F20 11.955 Tf 9.672 0 Td[(1andisthephaselagoftheoutputresponse.ReplacementofI0withV0inEquation 4-2 ,theexpressionfortheinputsignal,andV0withI0inEquation 4-3 ,theexpressionfortheresponsesignal,providestheappropriaterelationshipforexperimentscon-ductedunderpotentiostaticmodulation.ThecompleximpedanceofthesystemisobtainedfromtheinputandoutputsignalsbywayofatransferfunctionwhichisanalogoustoOhm'slaw.InCarte-

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64 sianandpolarcoordinatestheimpedance,Z,iscalculatedbyZ=V I=V0sin!t+ I0sin!t=V0e I0=jZje-4ThecompleximpedancecanbeconvertedfrompolartoCartesiancoordinatesandviceversabyapplyingEuler'sidentity.TherelationshipisexpressedaccordingtojZjej=jZjcos+jsin-5TherealpartoftheimpedanceisdescribedbyZr=jZjcos-6andtheimaginarypartasZj=jZjsin-7Themodulusoftheimpedanceisrelatedtotherealandtheimaginarycompo-nentsaccordingtojZj=q Zr2+Zj2-8andthephaseangle,orphaselag,ofthesystemis=arctanZj Zr-9Avarietyofanalyticalandgraphicalapproacheshavebeendevelopedtointerpretimpedanceresponses.Thetechniquesgenerallyrelyupontheimpedancequan-titiesdenedinEquations 4-6 through 4-9 .AfewofthecommonlyappliedpresentationformatsforimpedancedataincludeBode,impedance-planeandad-mittanceplots.TheBoderepresentationdisplaysthemodulusoftheimpedanceandthephaseangleversusfrequency.Animpedance-planeplot,alsoknownasaNyquistplot,displaystheimaginarypartoftheimpedance,Zj,versustherealpartoftheimpedance,Zr.Atypicalimpedance-planeplotofhumanskinisshown

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65 Figure4-2:Impedance-planeplotofskinimmersedin100mMNaCl.Themax-imummagnitudesoftherealandimaginarycomponentsofthecompleximped-ancearepresentedbythedashedhorizontalandsolidverticallines,respectively. inFigure 4-2 .Theshapeoftheimpedanceresponseofskin,aspresentedintheimpedance-plane,isoftendescribedasbeinga”depressed”semicircle.Theterminology”depressed”semicirclehasbeenadoptedbecausethemaxi-mummagnitudeoftheimaginarycomponentoftheimpedance,-Zj;maxresponseislessthanonehalfofthemaximumoftherealpart,Zr;max.Thedepressedsemi-circularresponsecanusuallybemodeledbytheconstantphaseelementcircuitpresentedinSection 3.6.2 whichsuggeststhatskinpossessesadistributionofchar-acteristictimeconstants.Adepressedsemicircularshapedimpedanceresponseisgenerallyconsistentwithalinearsystemwithconstantproperties.Acombina-tionofimpedance-planeplotsandidealcircuitmodelscanprovideestimatesforthepolarizationimpedance,capacitanceandcharacteristicfrequencyofskin.TheproceduretoextractthecircuitparametersisdescribedinSection 3.6.1 .Theinverseofimpedance,knownastheadmittance,isfrequentlypresentedasanalternativemethodfordisplayingimpedancedata.Thegeneralformofad-mittanceplotsissimilartotheBodedisplayformatortheimpedance-planeplotpresentationofimpedancedata.Admittanceplotsareappealingbecausethead-mittancequantityissensitivetochangesathighfrequencies.

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66 Figure4-3:Bodemagnitudeplotofatypicalimpedanceresponseofskin.Thediamondsrepresentthemeasuredvaluesforthemodulusoftheimpedance.Thetrianglesrepresentthecomplexpotentialdifferenceacrosstheskininducedbythe10Acurrentperturbation. 4.1.2ModulationProcedureforEISExperimentsThedeliveryoftherapeuticdrugsbyiontophoresisisproportionaltocurrent;therefore,galvanostaticmodulationofEISisrequiredinordertokeepthebaselinecurrentatthedesiredvalue. 148 TraditionalgalvanostaticallymodulatedEISmea-surements,whichmaintainthecurrentperturbationamplitudeataxedlevel,willcausethevoltageresponsetoreachitsgreatestvalueatthelowfrequencieswhereskinexhibitsitsmaximumimpedancevaluesee,forexampleFigure 4-3 . 153 Thelargeinducedpotentialscanalterthepropertiesoftheskin.Topreventlargepotentialswingsduringtheexperiment,apredictivealgo-rithmwasdevelopedtoadjustthecurrentateachfrequencysuchthatthepotentialwouldnotexceedapredeterminedvalue. 235 Thealgorithmforvariable-amplitudegalvanostaticmodulationofimpedanceexperimentswasbasedonaTaylor'sse-riesexpansionaboutagivenpointonthepolarizationcurve.Customizedsubrou-tineswerewrittenintheLabVIEWGrforWindowsprogrammingenvironmenttoincorporatethealgorithmintotheexperimentalcontrolsoftware.AsummaryofthedesignequationsdevelopedforthealgorithmisprovidedinAppendix B .

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67 4.1.3MethodologyApreliminarystudywasconductedtodeterminetheefcacyofthetraditionalconstant-amplitudegalvanostaticmodulationmethodformeasuringskinprop-ertiesbyimpedancespectroscopy.Ideally,skinpropertiesshouldnotbealteredbytheexperimentasimpedancespectroscopywasdevelopedtobeanoninva-sivetechnique.Theapproachherewastocollectmultipleimpedancespectrabyconstant-amplitudemodulation.Theamplitudeofthecurrentperturbationwasadjustedbeforeeachspectrumwascollected.Theperturbationamplitudesfortheimpedancescanswerebetween10Aand100A.Theobjectivewastodeterminewhethertheskinimpedanceresponsewasindependentofthecurrentperturba-tionamplitude.TheresultsfromtheseexperimentsarepresentedinSection 5.1 .Forthenextportionofthiswork,twotypesofgalvanostaticallymodulatedEISexperimentswereconducted.Therstexperimentmaintainedtheamplitudesofperturbationatvaluesof1Aand10A.Forthesecondtypeofexperiment,thecurrentamplitudewasadjustedateachfrequencytomaintainthevoltagere-sponseoftheskinbelowapredeterminedvaluechosenatthebeginningoftheexperiment. 235 Inaccordancewiththevariable-amplitudegalvanostaticmodula-tionalgorithm,previouslymeasuredimpedancevalueswereusedtopredicttheimpedanceatthefrequencyofthemeasurementbeingconducted.Aseriesofvariable-amplitudeimpedanceexperimentswereconductedoneachsampleofskin,where,periodically,aseriesofconstant-currentgalvanostaticimped-ancemeasurementswereperformed.Tocomparethedifferencebetweenthetwotechniques,aseriesofreplicatevariable-amplitudeexperimentswasperformedsubsequenttotheconstant-amplitudestudies.Theideawastodeterminethemostappropriatemodulationstrategyforconductingskinimpedanceexperiments.

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68 BothmodulationtechniqueswereappliedtoskinsamplesimmersedinNaClsolutionandinCaCl2solution,respectively.TheACcurrentperturbationwassuperimposedaboutaDCcurrentbiasof0Amperes/cm2.TheskinimpedancespectracollectedfrombothmodulationtechniquesarediscussedinSection 5.2 .Ingeneral,12measurementsweretakenforlogarithmicdecadeforfrequenciesbetween65kHzand1Hz.Forsomeoftheimpedanceexperiments,thelow-frequencyportionofthespectrawasextendedto0.1HzThemethodologydescribeduptothispointwasdesignedtoidentifyanexper-imentalapproachforcollectingskinimpedancespectrainanoninvasivemanner.Forthenextphaseofthisstudy,impedanceexperimentswereperformedtodeter-minetheinuenceofprolongedelectrolyteexposureonskintransportproperties.Theapproachwastocollectskinimpedancespectraintermittentlyoveraperiodof24hours.Thevariable-amplitudegalvanostaticmodulationstrategywasappliedforthehydrationstudy.ThesinusoidalcurrentperturbationsweremodulatedaboutaDCbiasof0A/cm2.Thetargetamplitudeofthepotentialdropacrosstheskinwassetto10mV.Thestudyprovidedabaselinetoestimatethechangesinskintransportpropertiescausedbytheadditionofwaterintothemembrane.TheresultsfromthisinvestigationarepresentedinSection 6.2 .Ithasbeenproposedthattherecoveryofskinpropertiestolargeelectricalper-turbationsismorerapidindivalentcationsolutionsthaninmonovalentcationsolutions. 152 Theinuenceofsolutioncompositionontherecoveryofskinproper-tiesisdescribedinSection 6.3 .Adetaileddiscussionoftheexperimentalapproachforthestudyisprovidedthere.Ifitisshownthattherecoveryofskinpropertiesisenhancedinthepresenceofdivalentcations,theinformationcouldbeusedtode-veloptransdermaliontophoreticprotocols.Forexample,supportingelectrolytes

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69 withdivalentcationscouldbeincludedindrugformulationstoenhancethere-coveryrateofskinpropertiesafteriontophoresis.Theinuenceoflargepotentialswingsonskinpropertieswasalsostudiedbyelectrochemicalimpedancespectroscopy.Theapproachwastocollectaseriesofskinimpedancespectrabyvariable-amplitudegalvanostaticmodulation.Theamplitudeofthetargetpotentialwasadjustedincrementallyfrom50mVto1Vatthebeginningofeachexperiment.Fourspectrawerecollectedforeachsetofexperimentalconditions.TheresultsfromthestudiesaredescribedinSection 6.4 .DuringtransdermaliontophoresisaDCcurrentbiasisappliedtoenhancetheuxofionicdrugcompoundsintothebody.TheobjectiveofthenextinvestigationwastocharacterizetheimpedanceresponseofskinunderappliedDCcurrentconditions.Forthiswork,asinusoidalcurrentsignalwassuperimposedabouttheapplied-currentbias.Theamplitudesofthecurrentbiaseswerebetween0A/cm2and855A/cm2.Thisrangewasconsistentwiththecurrentsappliedbyclinicaliontophoreticsystems. 177 , 201 , 236 TheresultsoftheimpedancestudiesontheinuenceofDCcurrentonskinpropertiesarediscussedinSection 6.5 .Theliteratureindicatesthereisaregionalvariationinskinpropertiesforanygivenperson.Furthermore,skinpropertiesalsovaryfromperson-to-person.Alimitednumberofstudieshavebeenperformedtocharacterizethevariationintheelectricalandtransportpropertiesofskin.AdemonstrationofthelargeregionalvariationinskintransportpropertiesisprovidedinSection 6.6 .Themethodologyusedfortheinvestigationisdescribedthere.Althoughvisualinspectionofthespectrafromthevariouspiecesofskinrevealedalargevariationinepidermalproperties,rigorousstatisticalassessmentofthesourcescontributingtotheoverallvariationwasperformed.TheapproachforthestatisticalanalysisofthevariationintheimpedanceresponseofskinisdescribedinChapter 7 .

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70 4.1.4StatisticalAnalysisofImpedanceSpectraAmajorportionofthisworkwasfocusedonthedevelopmentofinexperimen-taltechniquesformonitoringskinpropertiesduringtransdermaliontophoresis.Biologicalmembranes,suchasskin,oftenexhibitnonlinearand/ornonstationarybehaviorwhensubjectedtolargeelectricelds.Thissituationislikelytooccurduringtransdermaliontophoresisbecauseofthecharacteristicallyhighresistanceofthestratumcorneum.Thetransportpropertiesofskinmayalsochangeastheionicsolutionpenetratesthemembrane.Itispossiblethatthesechangesoccurduringthetimeperiodrequiredtocompleteatransdermaliontophoresisexperi-ment.Theevolutionofthesystemwasmonitoredbyimpedancespectroscopyforalloftheexperimentsconductedhere.StatisticalanalysisoftheimpedancedatawasperformedtodeterminetheKramers-Kronigconsistentportionsofthespectra.TheKramers-Kronigrelationsareasetofintegralequationsthatcanbeusedtoconvertbetweentherealandtheimaginarycomponentsofthecompleximpedance.Impedancespectrathatarestationary,linear,causalandstableconformtotheKramers-Kronigrelations.TheMeasurementModelapproachdevelopedbyAgarwaletal. 237 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(239 wasap-pliedinthisworktoassessKramers-Kronigconsistentportionsoftheimpedancespectra.TheMeasurementModelselectedforthatdevelopmentwastheVoigtcir-cuitmodel. 237 TheVoigtmodelissimilartotheidealcircuitnetworkpresentedinFigure 3-3 withadditionalRCelementsconnectedinseries.Thecompleximped-anceexpressionfortheVoigtcircuitisdenedaccordingtoZ!=Z0+nkRk +jk!-10whereZ0istheelectrolytesolutionresistance,kandRkarethetimeconstantandresistanceforthekthRCelementandnisthemaximumnumberoflineshapesthat

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71 canbejustiedaccordingtothenoiseinthemeasurement.Equation 4-10 iscon-sistentwiththeKramers-Kronigrelations.Therefore,astatisticallysignicanttoftheVoigtmodeltoanimpedancespectrumimpliesthatthedataareconsistentwiththeKramers-Kronigrelations.TheMeasurementModelforeachimpedancespectrumwasbuiltiterativelybythesuccessiveadditionofRClineshapes.TheMeasurementModelToolssoft-waredevelopedbyOrazemetal. 240 wasusedtoregressthemeasurementmodeltotheimpedancespectra.ComplexnonlinearleastsquaresCNLSregressionwasappliedateachstepofthemodelbuildingproceduretoobtainparameteresti-mates.ThecondenceintervalsfortheparameterestimateswerecalculatedfromMonteCarlosimulations. 239 Thetotalnumberofparametersforthemodelwasconstrainedsuchthatthe95.4%condenceintervalsmustnotincludezeroforeachoftheparameterestimates.TheMeasurementModelapproachwasusedtodeterminethenatureofexper-imentalerrors.Theresidualerrorsfromtheregressionprocedureconsistofdeter-ministicandstochasticerrors.Forexample,deterministicerrorsmaybecausedbyaninsufcientorincompletemodel,nonstationarysystembehaviorand/orin-strumentalbias.Thestochasticerrorswereassumedtoberandomlydistributedwithameanvalueof0andastandarddeviation.ThecontributionstothetotalerrorfromtheregressionaredenedbyZ)]TJ/F1 11.955 Tf 13.592 3.133 Td[(bZ=lof+ns+instr+stoch-11whereZandbZarethecompleximpedancevaluesfromtheexperimentandthemodel,lofisthelackofterrorduetomodelinadequacy,nsistheerrorfromnonstationaryeffects,instristheerrorfrominstrumentalartifactsandstochisthestochasticerror.

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72 InaccordancewiththeMeasurementModeltechnique,replicateimpedancespectrawerecollectedforeachsetofexperimentalconditions.AMeasurementModelwasregressedtoeachimpedancespectraseparately.Theregressionswereweightedbythemodulusoftheimpedance.Eachofthemodelswasselectedtohavethesamenumberoflineshapesandtheregressionparameterswereadjustedforeachreplicate.Undertheassumptionthatthesystemwasevolvingslowly,thisapproachservedasalterforthenonstationarycomponentoftheregressionerror.ThelackofterrorswereassumedtobeconstantforalloftheregressionssincealloftheMeasurementModelspossessedthesamenumberoflineshapes.Instru-mentalerrorswerealsoassumedtobeconstantbecausethecontrolparametersfortheimpedanceapparatuswerekeptconstant.Thegeneralapproachofregressingameasurementmodeltoeachreplicatespectraresultedintheextractionofthestochasticcomponentofthetotalerror.Thestochasticcomponentoftheregressionerrortypicallyexhibitsastrongdependenceonfrequencyforimpedancedata.AsauniqueMeasurementModelwithanequalnumberofparameterswasregressedtoeachoftheimpedancespec-traseparately,afamilyoffrequency-dependentresidualerrorswasproducedforeachreplicate.Thevarianceandthemeanoftherealandimaginaryresidualer-rorswerecalculatedaccordingtob2r=kres;r;k)]TJET1 0 0 1 228.289 -466.347 cmq[]0 d0 J0.478 w0 0.239 m5.284 0.239 lSQ1 0 0 1 0.12 -6.79 cmBT/F11 12.457 Tf 0 0 Td[(2res;r N)]TJ/F20 11.955 Tf 11.996 0 Td[(1-12b2j=kres;j;k)]TJET1 0 0 1 25.373 -23.513 cmq[]0 d0 J0.478 w0 0.239 m5.284 0.239 lSQ1 0 0 1 0.12 -6.79 cmBT/F11 12.457 Tf 0 0 Td[(2res;j N)]TJ/F20 11.955 Tf 11.996 0 Td[(1-13whereb2isthevariance,Nisthenumberofdatapointscollectedateachfre-quency,istheregressionerrorand isthemeanttingerror.Themeanttingcanbefurtherdecoupledto =meanlof+instr-14

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73 wherelofisthecontributiontothettingerrorfrommodelinadequaciesandinstristhecontributionfromsystematicerrorsinthemeasuringequipment.Agarwaletal.developedamodelforthefrequency-dependent,stochasticcom-ponentoftheerror. 238 Forthedevelopmentoftheerrorstructuremodelitwasassumedthatthestandarddeviationoftherealandimaginarycomponentswereequal.ThisassumptionwassubsequentlyvalidatedbyDurbhaetal.forKramers-Kronigconsistentdatawheretherealandimaginarycomponentsoftheimped-ancearecollectedsimultaneously. 241 Theerrorstructuremodelaccountsforthemethodbywhichimpedancedataiscollectedandisdescribedaccordingtoj=r==jZjj+jZrj+jZj2 Rm+-15whereRmistheresistanceofthepotentiostatmeasuringresistor,and,,andarethemodelconstants.ParameterestimatesareobtainedbytheregressionoftheerrorstructuremodeltotheresidualerrorsobtainedfromtheMeasurementModelregressionprocedure.ImpedancespectrawereassessedforconsistencywiththeKramers-Kronigre-lationshipbyweightingtheMeasurementModelregressionwiththeexperimen-tallydeterminederrorstructure.Thisapproachisgenerallysuperiortomodulusweightingasanemphasisisplacedondatawithlessnoisecontentincomparisontodatawithmorenoisecontent.MeasurementModelparameterswereobtainedfromthecomplexnonlinearleastsquaresregressionbyminimizingtheobjectivefunctionJ=kZr;k)]TJ/F1 11.955 Tf 13.592 3.132 Td[(bZr;k2 2r;k+kZj;k)]TJ/F1 11.955 Tf 13.592 3.132 Td[(bZj;k2 2j;k-16whereZr;kandZj;karetherealandimaginarycomponentsoftheimpedance,whereas2r;kand2j;karetheerrorstructurevariancesoftherealandimaginarypartsofimpedanceateachfrequency.

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74 ThequalityofinformationobtainedfromimpedancedatawasincreasedbyregressingtheMeasurementModelaccordingtothenoiseinthemeasurement.Theregressionschemedescribedhereprovidedforstatisticallyrigorousevalua-tionoftheKramers-Kronigconsistentpartsofimpedancedata.Thisinformationwasusedtoidentifymeasuringfrequencieswheretheimpedanceresponseofskinwasnotcausal,stable,linearorstationary.Forexample,datathatdidnotconformtotheKramers-Kronigrelationswasassociatedwithchangesinskinproperties.AlloftheimpedancespectrapresentedinthisworkwereassessedforconsistencywiththeKramers-Kronigrelations.4.2PotentialandCurrentStep-ChangeStudiesThetransientresponseofskintoconstant-amplitudeDCpotentialandcurrentsignalswasmonitoredtosupplementtheimpedanceresults.Theobjectivewastoidentifytheresponseofskintotheprolongedapplicationofelectricalsignals.Twotypesofexperimentswereperformedforthestudy.Fortherstsetofexperi-mentsaconstantamplitudeDCpotentialbiaswasappliedacrosstheskinandthecurrentresponsewasmonitoredforaperiodof20minutes.Thecurrentresponsewassampledatarateof52.9mHz,whichcorrespondstothecollectionofonemeasurementevery20seconds.Theskinwasthenallowedtorelaxforatleast15minutesafterthepotentialbiaswasterminated.Theinuenceofthepotentialbiasamplitudeonskinpropertieswasassessedbyincrementallyincreasingthepotentialbiasoverarangeofvalues.Themag-nitudeoftheappliedbiaseswere10,50,100,250,500and1,000mV,respectively.Forthisstudy,thesmallestbiasamplitudewasappliedatthebeginningoftheexperiment.Theexperimentalprotocolwasrepeatedfourtimes,twicewithsam-plesofskinimmersedinNaClsolutionandtwicewithsamplesofskinimmersedinCaCl2solution.Theobjectivewastodeterminewhethertheeffectsofsolution

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75 cationchargeandappliedpotentialmagnitudeonthetransportpropertiesofskinwerecoupled.Theresultsfromthepotentialstep-changestudiesarepresentedinSection 8.1 .Forthesecondtypeofexperiment,skinwassubjectedtoaseriesofstep-changesincurrentandthepotentialresponsewasmonitored.TheamplitudesoftheDCcurrentsignalswere1.4A/cm2,14A/cm2and140A/cm2.Ingen-eral,thecurrentstep-changewasheldattheelevatedconditionfor40minutes.Four10mVvariable-amplitudegalvanostaticallymodulatedimpedancespectrawerecollectedbeforeandafterskinwassubjectedtotheelevatedDCcurrent.Theresultsfromthecurrentstep-changesstudiesarediscussedinSection 8.2 .4.3MaterialsHeat-separatedexcisedhumanskinwasthemodelmembranestudiedinalloftheexperiments.Theseparationprocedureinvolvedphysicalandmechanicalmanipulationstoextractthestratumcorneumandtheadjoininglayersoftheepi-dermisfromtheunderlyingdermis.Incompliancewiththestandardprotocol,deionizedwaterwastheonlysolventaddedduringtheprocess. 242 Acompletedescriptionoftheheat-separationprocedureispresentedinAppendix A .Thethicknessoftheepidermalmembraneswasapproximately100m.Theexcisedskinwasobtainedfromtheabdomenortheback.Thesampleswerepliableandsemi-translucenttovisiblelight.AmicrographofaskinspecimenisshowninFigure 4-4 .Theoutoffocusregionsofthepicturewerecausedbywaterbubblestrappedbetweentheslideglassandthemembrane.Theskinsamplesweremountedbetweenglassdiffusioncellspriortoeachimpedancestudyandreplaceduponchangingtheionicsolution.Theskinandthesolutionweremaintainedatconstanttemperaturewithawater-jacketeddiffusioncell.Thediffusioncellprovidedseparationbetweentheionicsolutionsandthe

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76 Figure4-4:Micrographofheat-separatedcadaverskin.Picturetakenatamagni-cationof92x. exteriorheatingbath.Magneticstirbarswereaddedtothediffusioncelltokeepthesolutionwellmixed.Theappliedbiassignalsforthestep-changeexperimentswereprovidedbyaSchlumberger1286potentiostat.TheelectrochemicalimpedancemeasurementswereconductedwithaSchlumberger1286/1250impedancecouple.Inordertomonitorconditionsacrosstheskinafour-electrodecongurationwasusedforallofthestudies.TheAg/AgClcounterandworkingelectrodeswereproducedbyInVivoMetric.TheAg/AgClreferenceelectrodeswerefabricatedbyMicroElectrodes,Inc.Theelectrochemicalimpedancespectroscopyexperimentsdesignedtodemon-stratetheefcacyofvariable-amplitudegalvanostaticmodulationwereconductedinsolutionsof100mMNaClatapHof5.23and100mMCaCl2solutionatapHof4.92.TheionicstrengthoftheCaCl2solutionwasafactor1.8greaterthantheNaClsolution.Sinceactivitycoefcientcorrectionsareproportionaltothesquarerootofionicstrengththisdifferencewasconsiderednegligible. 136 Thewaterbathfortheseexperimentswasmaintainedatroomtemperature.Theionicsolutionsusedfortheotherexperimentsinthisworkwereeither150mMNaCl/20mMHEPES,150mMKCl/20mMHEPES,50mMCaCl2/20mMHEPESor50mMMgCl2/20mMHEPES.ThepHofthesolutionswasapproxi-

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77 mately7.Thetemperatureoftheheatingbathwasmaintainedat32C.Thewaterbathtemperaturewasconsistentwiththesurfacetemperatureofskin.Toensurethatactivitycoefcientcorrectionswereroughlyequivalentforexperimentscon-ductedinthetwoelectrolytes,theelectrolyteconcentrationswerechosentoyieldthesameionicstrength.4.4UV-visAbsorptionSpectroscopyTransdermaldrugdeliveryratesunderapplied-currentconditionswerecal-culatedwithUV-visabsorptionspectroscopy.Theanesthetic,lidocaine,wasthemodeldrugmoleculestudiedinthiswork.Thearomaticgroupoflidocainepro-videsthemoleculewithlightabsorbancepropertiesintheUVportionoftheelec-tromagneticspectrum.Thetypicalabsorptionpeakforaromaticmoleculesoccursbetween200and300nm,wheretheadditionoffunctionalgroupsshiftstheab-sorptionpeaktolongerwavelengths. 243 Afundamentalassumptionofabsorptionspectroscopyisthattheabsorptionintensityisproportionaltothechromophorelightabsorbingmoleculeconcen-trationandthelengthofthelightpaththroughthesample.TheformalexpressionforrelatinglightabsorbancetochromophoreconcentrationconsistentwiththeBeer-Lambertlawispresentedby 243 A=logP0 P=bci-17whereAistheabsorbanceofspecies,P0istheenergyofelectromagneticradiationreachingthedetectorintheabsenceofthechromophoreandPistheenergyofradiationreachingthedetectorforachromophoreconcentrationofci.Thepath-lengththroughthesampleis,bandisthemolarextinctioncoefcient.AccordingtotheBeer-Lambertlaw,themolarextinctioncoefcientshouldthe-oreticallybeindependentofconcentration.Forrealsystems,thiscriteriaissatis-

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78 edonlyoveralimitedrangeofconcentrationsandmustbedeterminedexper-imentally.Ingeneral,theabsorbanceresponseisconsistentwithBeer-Lamberttheorywhentheconcentrationofthelightabsorbingmoleculeislessthan10mM.Abovethiscriticalthreshold,nonlinearbehaviorisobservedbecauseofspecicinteractionsbetweenthelightabsorbingspecies. 244 Philbrick 164 successfullyappliedUV-visabsorptionspectroscopyformeasure-mentoflidocainedrugdeliveryrates.ThemagnitudeofappliedDCcurrentsusedforthestudywas1Aand100A.Thecalibrationstudyperformedforthatworkprovidedaccuratemeasurementoflidocaineconcentrationintherangeof0.5Mto30M.Drugdeliveryrateswereestimatedfromthetimerateofchangeofli-docaineconcentration.Resultsfromthestudydemonstratedthatthetransdermaldeliveryrateoflidocaineincreasedinresponsetoappliedcurrent.Elevatedli-docaineuxvalueswereobservedafterthecurrentwasterminated.Thisresultsuggestedthattheskinservesasareservoirforthetemporarystorageoflidocaine.Apossibleexplanationforthesourceofthereservoircapacitywasthatabsorptionreactionswereoccurringbetweenthenegativebackgroundchargeoftheskinandthepositivelychargedlidocaineions.4.4.1InstrumentationandDataCollectionConsiderableemphasiswasplacedondevelopingaccurateandreliablemethod-ologiesformeasuringdrugdeliveryratesduringtransdermaliontophoresis.Theabsorptionspectroscopyapparatuswasdesignedincompliancewiththegeneralprincipleofadual-beamspectrophotometers. 245 Theadvantageofthedual-beamsystemoverasinglebeamunitisthatuctuationsinthelightsourceoutputaswellasdriftinthephotodiodearrayofthespectrometercanbemonitored.Themaincomponentsoftheabsorptionspectroscopyapparatusconsistedofalightsource,acustomizeddual-beamabsorptionspectroscopycell,aparallelcom-

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79 binationofmulti-wavelengthspectrophotometers,beropticcablesandacom-puterinterfacetocontroltheexperiment.Ablockdiagramofthedualspectrome-tersystemispresentedinFigure 4-5 . Figure4-5:Dualspectrometersystemconguration.Thecustomcoupledspec-troscopydiffusioncellisrepresentedbytheregionenclosedbythedashedlinesandisshownindetailinFigures 4-6 and 4-7 . AdeuteriumlampservedastheUV-vislightemissionsourcefortheabsorp-tionspectroscopyexperimentsModelNumber:AIS-UV-2,AnalyticalInstrumentsSystems,Inc.,Flemington,NJ.Incompliancewiththerecommendationsofthemanufacturer,thelampwasturnedon30minutespriortothestartofallabsorp-tionspectroscopyexperiments.Theradiationexitingthelamppassedthrougha200mdiameterbifurcatedber-opticcabletothedual-beamspectroscopiccell.Approximatelyhalfofthelightsourceoutputintensityenteredthereceptorcom-partmentofthecoupledspectroscopydiffusioncellandtheremainderwenttothereferencecell.Themajorcomponentsofthedual-beamspectroscopyapparatusconsistedofthecellhousingenclosureandthecoupledspectroscopydiffusioncell.ThecellhousingwasdesignedbyRiemerandMembrinoaspartofanindependentstudyproject.Theunitwasfabricatedfromanaluminumblockandsubsequentlyan-odizedtopreventatmosphericand/orenvironmentaloxidationTMREngineer-ing,Micanopy,FL.Themountingsurfacesfortheinletandoutletopticallensesweremadeparalleltomaximizelightthroughput.Annularchannelsweredrilled

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80 inthebaseplateofthecellhousingtoprovidefortemperaturecontrolviaacir-culating,constant-temperaturewaterbathModelNumber:1160,VWRScientic,Niles,IL.Thecoupledspectroscopydiffusioncellconsistedofadonorchamberandareceptorchamber.A1cmdiameterholewasdrilledintoeachofthechamberstoserveasapathwayfordiffusion.TheprototypeofthecoupledspectroscopydiffusioncellwasdevelopedbyPhilbrick. 164 Thedonorchamberforthemodelsystemwasfabricatedfrompolycarbonateandthereceptorchamberwasmadefromastandardopticalgradequartzcuvette.AtthebeginningofeachexperimentanO-ringwasplacedontheskinandbothwereinsertedbetweentheopeningofthedonorchamberandthereceptorchamber.Theentiresystemwasthenplacedundercompressiontoformagoodseal.Adifcultyencounteredherewasthatthestandardquartzcuvetteswereun-abletowithstandthelargecompressiveforces.Theoriginaldiffusioncelldesignwasmodiedtoimprovethestructuralintegrityoftheopticalcuvette.Themod-ieddesignconsistedofahollowrectangularpolycarbonatevesselwithopticalgradequartzwindowsinsertedintotwooppositelyfacingsides.Thepolycarbon-ateframewasdesignedtominimizetheamountofstressplacedonthequartzglass.ApathwayforthetransmissionofUV-visradiationwasprovidedbythequartzglasswindows.Aschematicandpictureofthedual-beamdiffusioncellareshowninFigures 4-6 and 4-7 ,respectively.ThelightexitingeachcompartmentofthecellwascollectedwithadedicatedspectrometerModelNumber:SU2000,OceanOpticInstruments,Dunedin,FL.Thephotodiodearrayofeachspectrometermeasuredthelightintensityat740equallyspacedwavelengthsbetween200and400nm.Thiswavelengthrange

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81 Figure4-6:Dualspectrometerdiffusioncellconguration. Figure4-7:Dualspectrometerdiffusioncellphotograph. wasselectedtocoincidewiththedeuteriumlampmanufacturer'sspecicationsformaximumstabilityandoutputefciency.TheabsorbancewascalculatedaftertheexperimentswerecompletedwithMi-crosoftExcelspreadsheetsoftware.Thegeneralformoftheabsorbancerelation-shipispresentedbyAi;k=logIi;0)]TJ/F20 11.955 Tf 11.996 0 Td[(Ii;dark Ii;k)]TJ/F20 11.955 Tf 11.996 0 Td[(Ii;dark-18whereAi;kistheabsorbanceatwavelengthiforspectrumk.Thelightintensityatwavelengthi,intheabsenceofthechromophoreisdenotedbyIi;0,andIi;dark

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82 istheintensityatwavelengthi,whenlightisabsentfromthespectrometer.Priortoeachdiffusionstudythelightsourcewasblockedwithablackmetalplateandspectrawerecollectedbythespectrophotometers.Thesespectraprovidedfordi-rectevaluationofthedarksignalandcorrespondedtothebaselineresponseofthephotodiodearray.4.4.2SoftwareControlTheLabVIEWGrsoftwaredriverforthespectrometers,aspurchasedfromOceanOpticInstruments,lackedanoptionforstorageoftheintensityspectrainspreadsheet-compatibleoutputles.TheLabVIEWGrdriverwasmodiedtoenablecollectionofthespectrafromthereferencecellandthediffusioncell.Anoptionwasaddedwhichallowedtheusertoselecttherangeofwavelengthsforthecollectionofintensitydata.Theoptionhelpedtoreducethesizeoftheoutputles.Anadditionaloptionallowedtheusertospecifythetimeintervalbetweencollectionofsubsequentspectra.ThechangestothesoftwaredriverfacilitatedthecontroloftheUV-visabsorptionspectroscopyexperimentandstorageofdatawiththecomputer.4.4.3CalibrationStudiesAmulti-stepcalibrationprocedurewascompletedpriortothetransdermaliontophoresisexperiments.Therstpartofthecalibrationwasdesignedtochar-acterizethetransientbehaviorofthespectrometers.Thiswasaccomplishedbyplacingdeionizedwaterinboththereferencecellandthediffusioncellandcol-lectingspectraintermittentlyfor2.4hours.Sincenochromophorewaspresent,anychangesintheabsorbanceresponsewereassumedtobecausedbysystem-aticchangesintheequipment.TheresultsfromtheassessmentofsystemdriftarepresentedinSection 9.1 .

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83 Thesecondpartofthecalibrationwasdesignedtoidentifytherangeoflido-caineconcentrationsforwhichtheabsorbanceresponsecouldbedescribedbyBeer-Lamberttheory.Thiswasaccomplishedbycollectingabsorptionspectrafromsolutionswithknownlidocaineconcentrations.Theapproachwastosucces-sivelyaddsmallaliquotsofconcentratedlidocainesolutiontoaninitiallydilutemixture.Allmixingwasperformedinthecoupledspectroscopydiffusioncellinordertoincorporatetheeffectsofthecellgeometryontheabsorptionresponse.Theconcentrationofthelidocainesolutionsrangedfrom0.5Mto1.8mM.TheextinctioncoefcientateachwavelengthinthespectrawascalculatedfromtheabsorbancedataaccordingtotheBeer-Lambertlaw.TheresultsofthelidocainecalibrationstudiesarepresentedinSection 9.2 .Anadditionalstudywasconductedtoidentifytheinuenceofprolongedim-mersionofskininelectrolytesolutionsontheabsorbanceresponse.Thegoalwastodeterminetherateatwhichchromophoricspeciesdiffusefromtheskin.Theapproachprovidedforthecalculationoftherelativecontributionsofskinspeciesandlidocainetotheoverallabsorbanceresponse.Forthestudy,skinwasplacedinthecoupledspectroscopydiffusioncellandimmersedinabufferedsolutionof150mMNaCl.Absorbancespectrawerecollectedoverapproximately2.5hoursatthree-minuteintervals.Thetemperatureofthediffusioncellwasmaintainedat32C.AdetaileddescriptionoftheworkisprovidedinSection 9.3 4.5InvestigationofTransdermalIontophoresiswithCoupledSpectroscopyThecoupledspectroscopymethodologywasappliedtoinvestigatetransder-maliontophoresisuponcompletionofthecalibrationstudies.Thesystemwasmaintainedat32C.Transdermaliontophoresiswassimulatedbyperiodicallyap-plyingaDCcurrentbiasof14mA/cm2andmonitoringtheabsorptionresponsewiththespectrometers.Atthestartoftheexperimentskinwasimmersedin

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84 buffered150mMNaCland3.5mlofthelidocainecocktailwereadded.Thetemperaturewasmaintainedat32Cbythecirculatingwaterbath.Replicateimpedancespectrawerecollectedwhilethecurrentwasmaintainedat0A/cm2.Theelectrochemicalimpedancespectroscopyexperimentswereconductedundervariable-amplitudegalvanostaticcontrol.TheexperimentalresultsaredescribedinSection 9.4 .

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CHAPTER5DEVELOPMENTOFVAGMODULATIONFORSKINIMPEDANCESTUDIESApreliminarygoalofthisresearchwastodevelopanappropriatemethod-ologyformeasuringskinpropertiesbyelectrochemicalimpedancespectroscopy.Ideally,intheabsenceofanappliedcurrentbiastheimpedancespectroscopyex-perimentshouldnotalterskinproperties.InSection 5.1 itisdemonstratedthatthetraditionalmethodologyforconductingskinimpedanceexperimentscanalterskintransportproperties.Anadaptivemodulationstrategywasimplementedtopreventtheimpedanceexperimentfromchangingskinproperties.DevelopmentandapplicationoftheadaptivemodulationstrategyisdescribedinSection 5.2 .Skinimpedancespectracollectedbytheadaptivemethodologywereshowntobeconsistentwithamembranewithunalteredproperties.Asaresult,theadap-tivemodulationtechniquewasappliedextensivelyinsubsequentskinimpedanceexperiments.5.1PreliminaryInvestigationofSkinImpedanceTheconventionalmethodologyforstudyingskintransportpropertiesbyelec-trochemicalimpedancespectroscopyistoapplyaconstant-amplitudesinusoidalcurrentsignalandmeasurethepotentialresponseoverawiderangeofpertur-bationfrequencies. 131 , 151 , 233 Apreliminarystudywasconductedtodeterminetheinuenceofcurrentmodulationamplitudeontheimpedanceresponseofskin.Theobjectiveofthepreliminaryworkwastodeterminewhetherskinimpedancespectraobtainedwiththetraditionalconstant-amplitudegalvanostaticmodula-tiontechniquewereconsistentwithamembranewithunalteredproperties.For 85

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86 example,theskinwasassumedtobeunalteredbytheimpedanceexperimentifthecorrespondingspectrumsatisedtheKramers-Kronigrelations.Thereisageneralconsensusintheliteraturethatthestratumcorneumexhibitsanonlinearresponsetoelectricalimpulsesbetween0.1Vand2V,especiallyatfre-quenciesbelow10Hz. 2 , 3 , 153 , 154 Inaliteraturesurvey,Prausnitzreportedthatdirectcurrentdensitiesbetween0.1/cm2and75/cm2canalsointroduceanonlinearresponseinskinforamorecompletediscussionsee,forexample,Section 2.6 . 3 Theobjectiveofthisinvestigationwastodeterminethethresholdvalueofcurrentorpotentialfortheonsetofnonlinearbehavior.Thiswasaccomplishedbyadjustingtheamplitudeoftheapplied-currentperturbationandcheckingtheimpedanceresponseforconsistencywiththeKramers-KronigKKrelations.AsdescribedinSection 4.1.4 ,theKramers-Kronigrelationsareasetofintegralequa-tionswhichtransformtherealandimaginarycomponentsofcomplexquantities.DatathatconformtotheKramers-Kronigrelationsarelinear,stationary,causalandstable.Therefore,spectrathatwerefoundtobeconsistentwiththeKramers-Kronigrelationswereassociatedwithamembranewithconstanttransportprop-erties.Itispossiblethatthenonlinearskinimpedanceresponsedescribedintheliter-aturewasinducedbytheappliedelectricalperturbation.Thepreliminaryimped-ancestudiesweredesignedtoidentifyasetofexperimentalinputparameterswhichcouldyieldaskinimpedanceresponsethatwaslinearforthemajorityofthefrequencyrange.Theapproachwastocollectaseriesofeightconstant-amplitudegalvanostaticimpedancescans,allwithdifferentappliedperturbationamplitudes,fromthesamepieceofskin.Theskinwasimmersedin150mMNaClelectrolytesolutionwhichwasbufferedatapHofapproximately7.Themodu-lationamplitudesfortheimpedanceexperimentswereadjustedbetween10and

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87 100A.Inaccordancewiththeconstant-amplitudegalvanostaticmodulationmethod,themagnitudeofthecurrentperturbationwasheldconstantforallmeasuringfrequencieswithinagivenscan.Thecurrentperturbationfortherstscanwas10Aandtheperturbationmagnitudewasadjustedincrementallyatthestartofeachimpedanceexperiment.Theimpedance-planeplotofselectedskinimpedancespectrafromthestudyispresentedinFigure 5-1 foramorecompletediscussionofimpedancedatapresen-tation,pleaserefertoSection 4.1.1 .Thehigh-frequencyasymptotesoftheimped-ancewereapproximatelyuniformforallspectracollected.Thehigh-frequencyasymptotecorrespondstotheelectrolytesolutionresistanceislocatedneartheoriginoftheimpedance-planeplot.Theimpedancespectradisplayedthetypicaldepressedsemicircularshapeformodulationvalueslessthanorequalto30A.Thedepressedsemicircularshapesuggestedthattheskinpossessedadistributionofcharacteristictimeconstants. Figure5-1:Impedanceresponseofskinwhensubjectedtoaseriesofconstant-amplitudemodulatedexperiments.Theamplitudesofthecurrentperturbationsareindicatedbythelegend.Theresultsarepresentedintemporalorder. Thespectracollectedatmodulationamplitudesabove30Aexhibitedacon-tinuousdecreaseinskinimpedanceastheperturbationfrequencywassweptbe-low100Hz.Thereductionofskinimpedancecanbeobservedbytheasymmetric

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88 ”curl”or”hook”inthedatalocatedinthelowerrighthandregionofFigure 5-1 .Thecurvatureofthe”hook”wasproportionaltotheperturbationamplitude.Thedatapointsassociatedwiththe”hook”representthelow-frequencyimpedanceresponseofskin.Thelow-frequencyasymptoteoftheimpedancecorrespondstothepolarizationresistanceofskin.Ideally,asystemwithlineartransportprop-ertiesshouldhaveapolarizationresistancewhichisindependentoftheappliedcurrent.Thedecreaseinpolarizationresistanceassociatedwithperturbationampli-tudesgreaterthan30Asuggestedthatskinpropertieshadbeenaltered.Rig-oroussupportfortheproposedeffectoftheperturbationsonskinpropertieswasprovidedbyassessingthedataforconsistencywiththeKramers-Kronigrelations.Thedetailsoftheassessmentprocedurearepresentedinthenextsection.5.1.1Kramers-KronigConsistencyCheckofPreliminaryImpedanceDataTheimpedancespectrawereassessedforconsistencywiththeKramers-KronigrelationsbyregressingtheVoigtcircuitMeasurementModeltothedata.Detailedexamplesoftheassessmentprocedureareprovidedhere.However,amorecom-pletediscussionoftheapproachusedtoapplytheMeasurementModelforassess-ingimpedancedataforconsistencywiththeKramers-KronigrelationsisprovidedinSection 4.1.4 .Fortherstpartoftheassessmentprocedure,complextsoftheMeasurementModeltothespectrayieldedamaximumof2lineshapes.Thelim-itednumberoflineshapesresultedinlargettingerrors.Visualinspectionoftheimpedance-planeplotofskinimpedancerevealedthatthehigh-frequencyasymptote,whichcorrespondstotheelectrolytesolutionresist-ance,wasnegative.Anapparentnegativesolutionresistanceisacommonsymp-tomofinstrumentalartifact.ThedifcultywascircumventedbyperforminganimaginarytoftheMeasurementModeltothe10Amodulatedspectrum.The

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89 solutionresistanceforthisregressionwassetto0W.Anappropriatesolutionresistancewasselectedbyiterativelyadjustingthesolutionresistanceuntilthenormalizedrealresidualerrorsfromtheregressionwerenormallydistributedaboutameanof0W.Thenormalizedresidualerrorswerecalculatedateachfrequencybydividingthettingerrorsbytheimpedancemagnitudeoftherealandimaginarycompo-nentsaccordingtoRealresidualerror=Zr;data)]TJ/F20 11.955 Tf 11.996 0 Td[(Zr;model Zr;data-1Imaginaryresidualerror=Zj;data)]TJ/F20 11.955 Tf 11.997 0 Td[(Zj;model Zj;data-2whereZr;dataandZj;datarepresentthemeasuredvaluesoftherealandimaginaryimpedancecomponents.ThetermsZr;modelandZj;modelcorrespondtothecalcu-latedvaluesfortherealandimaginaryimpedancequantities.Itwasdeterminedthatanelectrolytesolutionresistanceof-55Wyieldedthebestdistributionofresid-ualerrorsforthe10Amodulatedexperiment.Therefore,theelectrolytesolutionresistancewassetto-55Wforallofthesubsequentregressions.Asimilarap-proachwasappliedforregressingtheMeasurementModeltootherimpedancespectrawithanapparentnegativesolutionresistance.Theselectionofanegativesolutionresistancefortheregressionswasnotcon-sistentwiththestateofthesystem.However,thegoalherewastodevelopamethodforobtainingimprovedtsoftheVoigtcircuitmodeltoskinimpedancespectra.Forthisdiscussion,animprovedtwasassociatedwithanincreaseinthenumberofmodelparametersusedtorepresenttheimpedancespectrum.Theaddedlineshapeshelpedtoreducethemagnitudeofthenormalizedresidualttingerrors.Forexample,theregressionswheretheelectrolytesolutionresist-ancewassetto-55Wyieldedaminimumof6shapesforalloftheimpedance

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90 spectra.Thettingerrorsfortheregressionswerewithinthenoiselevelofthemeasurements.TheimprovedtsoftheMeasurementModelmadeitpossibletodeterminewhetherthelow-frequencyimpedanceresponseofskinsatisedtheKramers-Kronigrelations.Anemphasiswasplacedonthelow-frequencyportionofthespectrabecausethedatacontainsinformationonskinpropertieswhichareaffectedbyiontophoresis.Thelow-frequencyportionsoftheskinimpedancespectrawereassessedforconsistencywiththeKramers-KronigrelationsbyregressingtheMeasurementModeltotheimaginarycomponentoftheexperimentaldata.Thecircuitelementparametersobtainedfromtheregressionswereusedtoestimatetherealcompo-nentateachfrequency.Normalizedrealresidualerrorswhichfelloutsidethe95.4%condenceintervalwereconsideredtobeinconsistentwiththeKramers-Kronigrelations.Asampleplotforthefrequency-dependentrealresidualerrorsfromanimaginarytoftheMeasurementModeltothespectrumcollectedbythe50AperturbationispresentedinFigure 5-2 .Thesolidyellowcirclescorrespond Figure5-2:NormalizedrealresidualerrorsfromanimaginarytoftheMeasure-mentModeltothe50Aspectrum.Redlinesindicatethe95.4%condenceinter-val.

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91 tothenormalizederrorsforthepredictionoftherealcomponentofskinimped-ance.Theredlinesrepresentthe95.4%condenceinterval.Theresidualerrorsfelloutsidethecondenceintervalatfrequenciesbelow44.3Hzandtherefore,wereconsideredtobeinconsistentwiththeKramers-Kronigrelations.Thisprocedurewasrepeatedforeachimpedancespectrumcollectedinthisinvestigation.Theregressionsrevealedthatthespectracollectedwithcurrentperturbationmagnitudeslessthan35AwereconsistentwiththeKramers-Kronigrelationsovertheentirefrequencyrange.Theconformityofthedataimpliedthatskinprop-ertieswerenotchangedbytheexperiment.Athighercurrentperturbationampli-tudestherewasacriticalfrequency,belowwhichdatawereinconsistentwiththeKramers-Kronigrelations.Theinconsistentdataimpliedthatskinpropertieshadchanged.ThemeasuringfrequenciesatwhichskinpropertiesbegantochangeforeachcurrentperturbationamplitudearelistedinTable 5-1 . Table5-1:MinimumfrequenciesandassociatedmembranepotentialdifferencesforKramers-Kronigconsistentportionsofskinimpedancespectra. CurrentPerturbationAmplitude/A Parameter 10 100 75 50 25 30 35 30 LowFreq. Cut-off/Hz 0.1 2056 249 44.3 0.1 0.116 0.37 0.1 Potentialat Cut-off/V 0.32 0.65 1.32 1.25 0.69 0.84 0.94 0.86 5.1.2ProposedDrivingForceforSkinPropertyChangesIthasbeenreportedintheliteraturethatskinpropertiesbegintochangewhenthepotentialdifferenceacrossthemembraneexceedsacriticalvalue. 3 Galvanos-taticorsquarewavecurrentcontrolwasappliedinthosestudies.Theliteratureresultswereusedtoformulateaworkinghypothesisthatthechangesinmem-branepropertiesobservedinthepreliminaryimpedancespectroscopystudywerecausedbylargepotentialdifferencesacrosstheskin.

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92 Skinimpedanceexperimentsemployingthetraditionalconstant-amplitudegal-vanostaticmodulationmethodmaintainthecurrentperturbationamplitudeataconstantvalueovertheentirefrequency-range.Astheexperimentprogressesfromhigh-frequencytolow-frequencytheimpedanceofskintypicallyincreasesinmagnitudefromapproximately50Wcm2toashighas250kWcm2.Sinceauniformcurrentperturbationamplitudeisusedthroughouttheexperiment,thelargestpotentialdropacrossthemembranewillbeobservedinthelow-frequencyportionoftheimpedancespectrum.Sincethecurrentperturbationismaintainedatauniformamplitude,deviationsfromlinearityinthelow-frequencyimped-anceresponseofskinwouldbeconsistentwiththeconceptofpotentialasbeingthecauseofchangestotheepidermis.ThevoltagedifferencefortheexperimentspresentedinSection 5.1 wascalcu-latedaccordingtoOhm'slawbymultiplyingthecurrentmodulationamplitudebythecompleximpedanceateachfrequency.ThepotentialdifferenceacrossskinatthethresholdfrequenciesforwhichpropertychangeswereobservedispresentedinTable 5-1 .Theresultsindicatethatskinpropertieswereconstantforpotentialdropslessthanapproximately800mV.Thefrequency-dependentpotentialdropacrosstheepidermisassociatedwiththeimpedancedatadisplayedinFigure 5-1 ispresentedinFigure 5-3 .Thepo-tentialdifferenceacrosstheskininresponsetothe100Aperturbationincreasedcontinuouslyastheexperimentprogressedfromhigh-frequencytolow-frequencyuntilamaximumvalueof2.23Vwasobservedat24Hz.Forfrequenciesbe-lowthismaximum,thepotentialdifferencedecreasedfortheremainderoftheimpedancescan.Asimilartrendwasobservedforthe75Ascan,however,themaximumpotentialdifferenceof1.77Voccurredat11.5Hz.Amaximumpoten-tialdifferenceof1.27Vwasobservedforthe50Aperturbationat3.65Hz.The

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93 maximumpotentialdifferenceforthescansconductedatmodulationvaluesof10and25Awereapproximately300mVand700mV,respectively.Themaxi-mumpotentialdropsassociatedwiththeseperturbationamplitudesoccurredattheminimumperturbationfrequencyof0.1Hz. Figure5-3:Potentialdifferenceacrosstheskinasafunctionoffrequency.ThedatacorrespondstotheimpedanceexperimentspresentedinFigure 5-1 .Thecurrentperturbationamplitudesusedtoinducetothevoltagedropsacrosstheepidermisareindicatedbythelegend.Theresultsarepresentedintemporalorder. Theobservationofamaximumpotentialdifferenceacrossthemembraneatanintermediatefrequencyforscansconductedwithcurrentmodulationamplitudesof35Aandgreatersuggestedthatthepropertiesofskinchangedcontinuouslyforallsubsequentperturbationfrequencies.ThedrivingforceforthechangeswaslikelyprovidedbythelargeamplitudeelectriceldsinducedbytheACcurrentperturbation.Forexample,theinternalstructureofthestratumcorneummayhavebeentemporarilyrearranged.5.1.3DeviationinPotentialResponsefromLinearityTheregressionsoftheMeasurementModeltotheimaginarycomponentoftheimpedanceprovidedestimatesforthepolarizationresistanceofskin.Thiswasac-complishedbyextrapolatingtheKramers-Kronigconsistentportionoftheimped-

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94 anceresponsetozero-frequencyi.e.,theD.C.currentresponse.Theregressedvaluesofpolarizationresistanceweremultipliedbythecurrentperturbationam-plitudesusedfortherespectiveimpedancescanstocalculatetheexpectedpoten-tialdropsacrosstheskinatzero-frequency.Similarly,theactualpotentialdiffer-enceacrossskinwasestimatedbymultiplyingthemodulusoftheimpedanceatthelowestmeasuringfrequency.1Hzbytheamplitudeofthecurrentpertur-bation.Bothestimatesforpotentialdropacrosstheepidermisateachcurrentper-turbationamplitudearepresentedinFigure 5-4 .Theopensquaresrepresenttheexpectedpotentialdifferenceatzero-frequencyandthesolidsquarescorrespondtothemeasuredpotentialdropacrosstheskinat0.1Hz. Figure5-4:CalculatedDClimitofpotentialdifferenceacrossskininresponsetoaseriesofconstant-amplitudegalvanostaticimpedancescans.Thetrianglesrepresenttherelativedeviationinthemeasuredlow-frequencyvoltagedifferenceacrossskinascomparedtothevoltagedifferenceacrossamembranewithapolar-izationresistanceindependentofpotential. ItwasshowninSection 5.1.1 thatskinimpedancespectracollectedatperturba-tionmagnitudeslessthan35AconformedtotheKramers-Kronigrelationsovertheentirefrequencyrange.SincethespectrawereconsistentwiththeKramers-Kronigrelations,itwasimpliedthatskintransportpropertieswerenotaltered

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95 bytheimpedanceexperiments.TheextrapolatedpolarizationresistancevaluesassociatedwiththeKramers-Kronigconsistentspectracollectedwithcurrentper-turbationslessthan35Awereusedtocalculatetheexpectedpotentialresponseofamembranewithconstantelectricalpropertiestocurrentperturbationampli-tudesgreaterthan35A.Theapproachwastoplottheestimatedpotentialdifferencesfromtheimped-anceexperimentswithperturbationmagnitudeslessthan35Aasafunctionofcurrent.Alinearmodelwasregressedtothedataset.Theslopeandinterceptcalculatedfromtheregressionwere2.7x103Wand3.97V,respectively.Ther2cor-relationparameterfortheregressionwas0.966indicatingthatthedatasetwasreasonablydescribedbyalinearmodel.Thelinearmodelfortheexpectedpoten-tialdifferenceacrossskinasafunctionofcurrentispresentedbythesolidblacklineinFigure 5-4 .Thepotentialdifferenceacrossskincalculatedfromthelinearmodelateachperturbationamplitudewasselectedasareferenceforcomparisonwiththecal-culatedpotentialdifferencefromtheimpedanceexperiments.Thedeviationofskinimpedancefromlinearitywascalculatedbysubtractingthemeasuredpoten-tialdifferenceacrossskinfromthepotentialdifferenceobtainedfromthelinearmodelaccordingtoRelativeerrorDVskin=DVcalculated)]TJ/F60 11.955 Tf 11.996 0 Td[(DVmodel DVcalculatedx100%-3whereDVcalculatedisvoltagedifferenceacrossskincalculatedfromtheimpedanceat0.1HzortheextrapolatedpolarizationresistanceandDVmodelisthevoltagedifferenceacrossskinpredictedbythelinearmodel.Thedifferenceinvoltagequantitiesateachperturbationcurrentrepresentedthedeviationinthemeasuredvoltageresponsefromtheresponseexpectedfromskinwithconstantproperties.

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96 TherelativedeviationsinthepotentialdropsacrosstheepidermalmembranearealsopresentedasafunctionofthecurrentperturbationmagnitudeinFigure 5-4 .Thelledtrianglesrepresentthepercentrelativedeviationinthepotentialre-sponseat0.1Hztotheexpectedresponseofskinwithpropertiesindependentofpotential.TheopentrianglescorrespondtotherelativepercentdifferenceinthepotentialresponseestimatedbytheKramers-KronigconsistentpolarizationimpedanceobtainedfromregressionoftheMeasurementModeltoeachspectrumfromconstantskinproperties.Therelativepercentdifferencesinthelow-frequencypotentialresponsesforthespectracollectedwithcurrentperturbationamplitudesbelow35Awerealllessthan10%.Thedeviationinthemeasuredpotentialdifferencefromtheidealresponsewasproportionaltothecurrentforperturbationamplitudesgreaterthan35A.Furthermore,therelativedeviationsinthepotentialresponseestimatedfromtheimpedanceat0.1HzweregenerallylargerthanforpotentialdifferencecalculatedfromtheKramers-Kronigconsistentpolarizationresistance.Thisstudyindicatedthattraditionalconstant-amplitudegalvanostaticmodu-lationofimpedancespectroscopyexperimentscanalterthepropertiesofskin.Aworkinghypothesiswasproposedthatthereisacriticalvalueofpotentialdiffer-enceacrossthemembraneatwhichskinpropertiesbegintochange.Anadaptivemodulationstrategywasdevelopedtomaintainthepotentialdifferenceacrossthemembranebelowthecriticalvalue.Thedevelopmentoftheadaptivemodulationprotocolisdiscussedinthenextsection.5.2DevelopmentofVAGModulationTechniqueThepreliminaryconstant-amplitudegalvanostaticimpedancestudiesindicatedthatskinpropertiescanchangeduringanexperiment.Thechangesoccurredathighcurrentperturbationamplitudeswheretheinducedpotentialdifferences

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97 acrosstheskinwereontheorderof1V.Anadaptivemodulationtechniqueforcollectingimpedancespectrawasimplementedtopreventtheexperimentfromalteringskinproperties.Theadaptivemethodforcollectingimpedancespectraappliedvariable-amplitudegalvanostaticVAGmodulation. 235 Thedevelopmentofthevariable-amplitudegalvanostaticmodulationtechniqueisdescribedinSec-tion 4.1.2 andAppendix B .Impedanceexperimentswereconductedtoverifytheefcacyofthevariable-amplitudegalvanostaticmodulationinpreventingchangestoskinproperties.Theapproachwastocollectreplicateskinimpedancespectraundervariable-amplitudegalvanostaticandconstant-amplitudemodulation.Multipleperturbationampli-tudeswereselectedforeachmodulationtechnique.Thespectrafromtherespec-tivemodulationstrategieswereassessedforconsistencywiththeKramers-Kronigrelations.Theconsistentportionsofthespectraassociatedwitheachmodulationtechniquewerecomparedtodeterminewhichapproachdidnotalterskinproper-ties.TheexperimentalapproachwasrepeatedforsamplesofskinimmersedinbufferedsolutionsofCaCl2andNaCl.Theresultsfromtheimpedanceexperi-mentsofskininCaCl2electrolytearedescribedindetail.TheresultsfromtheimpedancestudiesofskininNaClarenotpresentedastheywerecomparabletotheCaCl2experiments.MinordifferencesintheskinimpedanceresultsforthetwoelectrolytesolutionsaredescribedinSection 5.2.2 Theimpedancespectraobtainedbythetwomodulationtechniquesarepre-sentedintheimpedance-planeinFigure 5-5 .Theshapesoftheskinimpedancespectraweredirectlyrelatedtothemodulationtechniqueandthemagnitudeofthecurrentperturbation.Forexample,thespectracorrespondingtothe1Aconstant-amplitudeand10mVVAGexperimentsexhibitedasemicircularshape.

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98 Incontrast,thespectracorrespondingtothe10Axed-amplitudegalvanos-taticexperimentsdisplayedadistinctive”hook”inthelow-frequencyrange.The”hook”shapewassimilartotheskinimpedanceresponseobservedintheexperi-mentsdiscussedinSection 5.1 . Figure5-5:ImpedanceresponseofskinasmeasuredbyVAGandconstant-amplitudegalvanostaticmodulation.TheskinwasimmersedinbufferedCaCl2electrolyte. Thespectrafortherstseriesof10mVVAGexperiments,denotedbythesoliddiamondsinFigure 5-5 ,displayedthehighestimpedancevalues.Thefrequency-dependentimpedanceresponsesofthethreespectraobtainedbyVAGmodulationwereapproximatelyuniform.Spectracollectedwitha1Aconstant-amplitudecurrentperturbationareindicatedbythecrossmarksinFigure 5-5 .Theimped-anceresponseofskinatthe1Aperturbationamplitudewassimilartothespectracollectedby10mVVAGmodulation.Theresultsfromthe10Aconstant-amplitudeimpedanceexperimentsareshownbythesolidtrianglesinFigure 5-5 .Astheconstant-amplitudecurrentperturbationwasincreasedfrom1Ato10A,theimpedancedecreaseddramat-icallyinthelow-frequencyportionofthespectra.Thedecreaseinskinimpedance

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99 wascharacterizedbythe”hook”shapeofthelow-frequencyportionofthe10Aspectra.Spectrafromsubsequentconstant-amplitude10Ashowedacontinuousdecreaseinimpedancefromexperimenttoexperiment.Thedecreaseinimped-ancefromscantoscansuggestedthatskinpropertieshadbeenchanged.Therecoveryofskintothe10Aperturbationswasmonitoredbycollectingthree10mVVAGimpedancespectrawhichareindicatedbythecurveswithlledsquaresinFigure 5-5 .Asthemodulationtechniquewasswitchedfrom10Aconstant-amplitudegalvanostaticcontrolto10mVVAGcontrol,theshapeoftheimpedancespectrachangedfroma”hook”backtoasemi-circle.Subsequent10mVVAGscansdemonstratedacontinuousincreaseinskinimpedanceforagivenfrequency.Theincreaseinskinimpedance,asmeasuredbythethree10mVVAGscans,suggestedthatthemembranepropertieshadrecovered.However,there-coverytowardtheimpedanceresponsemeasuredfromtherst10mVVAGscanwasincompleteoverthecourseoftheexperiment.Aquantitativeassessmentoftherelativerecoveryofskinpropertieswasmadebycomparingthecalculatedpolarizationresistanceofeachspectratothepolar-izationimpedanceassociatedwiththerst10mVVAGscan.Thisspectrumwasusedasthereferenceresponsebecausethelargestmagnitudesofskinimpedancewereobservedforthisdataset.Therecoveryoftheimpedanceresponsefollowingtherstgroupof10Aconstant-amplitudegalvanostaticscans,asmeasuredbya10mVVAGtechnique,was85%,89%and91%,respectively.Thespectrafromthesecondsetof10Aconstant-amplitudegalvanostati-callymodulatedexperimentsispresentedbythesolidcirclesinFigure 5-5 .Uponchangingmodulationtechniquebackto10Aconstant-amplitudegalvanostaticcontrol,theimpedanceresponseonceagainexhibiteda”hook”inthelow-frequencyregion.Successivereplicatescollectedby10Aconstant-amplitudegalvanostatic

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100 modulationdecreasedcontinuouslyinthelow-frequencyportionsofthespectra.Thelow-frequencyimpedanceofskincorrespondingtothesecondsetof10Aconstant-amplitudegalvanostaticscanswaslessthantheresponseassociatedwiththerstsetof10Aconstant-amplitudegalvanostaticscans.The10mVVAGmodulatedimpedancescanscollectedafterthesecondsetofconstant-amplitudegalvanostaticimpedancespectraindicatedskinimpedancehadpartiallyrecovered.Therelativerecoveryinthelow-frequencyregionoftheimpedancespectrawas77%,80%and83%,respectively.Theanalysisdescribedherestronglysuggestedthatskinpropertieswerealteredbythe10Aconstant-amplitudegalvanostaticallymodulatedimpedanceexperiments.Aninterestingresultofthisstudy,wasthatthechangesinskinpropertiesoc-curredatlowerperturbationamplitudesthantheexperimentsdescribedinSection 5.1 .Thedifferencecanbeexplainedbythehigherimpedanceresponseoftheskinsam-pleusedforthisinvestigation.Foragivencurrentperturbationamplitude,thepotentialdifferenceacrossthehighimpedanceskinwashigherthanforthelowimpedanceskinstudiedinSection 5.1 .Thisobservationwasconsistentwiththehypothesisthatskinpropertiesbegintochangeaboveacriticalpotential.Rigoroussupportfortheapparentchangesinskinpropertiescausedbythe10Aconstant-amplitudeimpedanceexperimentswasprovidedbyassessingthespectraforconsistencywiththeKramers-Kronigrelations.Thespectrafromthe10mVVAGmodulatedexperimentswerealsoevaluatedforconsistencywiththeKramers-Kronigrelationstodeterminewhethertheadaptivemodulationtech-niquemeasuredskinpropertiesinanoninvasivemanner.5.2.1Kramers-KronigConsistencyCheckofImpedanceSpectraTheMeasurementModelapproachdevelopedbyAgarwaletal. 237 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(239 wasap-pliedtocheckimpedancespectraforconsistencywiththeKramers-Kronigrela-

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101 tions.TheKramers-Kronigrelationsmustbesatisedforspectrathatarelinear,causal,stationary,andstable.DatathatconformstotheKramers-Kronigrelationsisconsistentwithasystemwithconstantproperties.Incontrast,datathatdoesnotsatisfytheKramers-Kronigrelationsindicatesthatthesystemhaschanged.TheMeasurementModelwasregressedtothecompleximpedanceofthespec-traobtainedbytheconstant-amplitudeandvariable-amplitudegalvanostaticmod-ulationtechniques.Sincereplicateimpedancespectrawerecollectedforeachex-perimentalprotocolthefrequency-dependenterrorstructuresweredetermined.SubsequentregressionsoftheMeasurementModeltothedatasetwasweightedaccordingtotheerrorstructureofthemeasurement.Forexample,datawithlargestandarddeviationvaluesareweightedlessthandatawithsmallstandarddevi-ations.Errorstructureweightinggenerallyenhancestheamountofinformationwhichcanbeextractedfromthedata.Theerrorstructurewascalculatedforeachsetofexperimentalconditions.TheparametervaluescorrespondingtotheerrorstructuremodelshowninEquation 4-15 arepresentedinTable 5-2 . Table5-2:Errorstructureparametersofskinimpedancespectra.SkinsamplewasimmersedinCaCl2solutionandparametersarelistedintemporalorderofexper-iments. ModulationMethod ErrorStructure 10mVVAG =1.48x10)]TJ/F20 7.97 Tf 6.448 0 Td[(31.28x10)]TJ/F20 7.97 Tf 6.447 0 Td[(5;=4.36x10)]TJ/F20 7.97 Tf 6.448 0 Td[(36.23x10)]TJ/F20 7.97 Tf 6.448 0 Td[(6 1AGalv. =1.81x10)]TJ/F20 7.97 Tf 6.448 0 Td[(36.89x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5;=1.72x10)]TJ/F20 7.97 Tf 6.448 0 Td[(45.51x10)]TJ/F20 7.97 Tf 6.448 0 Td[(6 D=7.07x10)]TJ/F20 7.97 Tf 6.448 0 Td[(13.32x10)]TJ/F20 7.97 Tf 6.448 0 Td[(4 10AGalv. =3.98x10)]TJ/F20 7.97 Tf 6.447 0 Td[(34.41x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5;=2.91x10)]TJ/F20 7.97 Tf 6.448 0 Td[(41.42x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5 10mVVAG =1.55x10)]TJ/F20 7.97 Tf 6.447 0 Td[(37.68x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5;=3.98x10)]TJ/F20 7.97 Tf 6.448 0 Td[(42.00x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5 10AGalv. =1.84x10)]TJ/F20 7.97 Tf 6.448 0 Td[(33.51x10)]TJ/F20 7.97 Tf 6.447 0 Td[(5;=1.84x10)]TJ/F20 7.97 Tf 6.448 0 Td[(31.55x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5 10mVVAG =5.42x10)]TJ/F20 7.97 Tf 6.448 0 Td[(42.47x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5;=4.04x10)]TJ/F20 7.97 Tf 6.448 0 Td[(31.08x10)]TJ/F20 7.97 Tf 6.448 0 Td[(5 Aftertheerrorstructurewasdetermined,theMeasurementModelwasre-gressedtothespectratolteroutKramers-Kroniginconsistentdata.Theregres-sionswereweightedaccordingtotheerrorstructure.Therststepwastoper-formarealttothedataandpredicttheimaginarypart.Datalocatedoutside

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102 thecondenceintervalathighfrequencieswasconsideredtobeinconsistentwiththeKramers-Kronigrelations.Theinconsistenthigh-frequencydatapointswereomittedfromsubsequentregressions.Low-frequencydatacorrespondingtotherealcomponentoftheimpedancelocatedoutsideofthecondenceintervalwasconsiderednottosatisfyKramers-Kronigrelations.Theanalysisofthespectraobtainedfromeachmodulationtechniqueisdiscussedseparatelybelow.KKconsistencycheckfor10mVVAGspectra.ThenormalizedrealresidualerrorsforatoftheMeasurementModeltotherealpartoftheimpedancedataarepresentedinFigure 5.6a .Therealresidualerrorsareindicatedbythesolidcirclesandthenoiselevelofthemeasurementisillustratedbythedashedgreenlines.Therealresidualerrorsweregenerallyontheorderof1%andweremostlywithinthenoiselevelofthemeasurement.Astheresidualerrorsweresmallandrandomlydistributedabout0,itwasconcludedthatagoodtofthemodeltothedatahadbeenobtained.ThenormalizedresidualerrorsfromthepredictionoftheimaginarypartoftheimpedancearepresentedinFigure 5.6b .Thesolidtrianglescorrespondtotheimaginaryresidualerrorsandthedashedredlinescorrespondtothe95.4%conferenceinterval.Theresidualerrorswerelessthan5%ofthemeasurementvalueandwerecontainedwithinthe95.4%condenceintervalathigh-frequency.Therefore,theentiredatasetwasincludedfortheimaginaryt.Thesolutionresistancecalculatedfromtherealtwassettoaconstantvaluefortheimaginaryt.Thesameprocedureforeliminatinginconsistenthigh-frequencydatawasap-pliedtotheotherskinimpedancespectradescribedinthiswork.ThenormalizedresidualttingerrorscorrespondingtotheregressionoftheMeasurementModeltotheimaginarycomponentofskinimpedancearedisplayedinFigure 5.7a .Theimaginaryresidualerrorswerealllessthan5%ofthemea-

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103 a bFigure5-6:NormalizedresidualerrorsfromrealtoftheMeasurementModeltoa10mVVAGscanofskininCaCl2electrolyte.aFittingerrorsbErrorsfrompredictionofimaginarypartoftheimpedance.

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104 surementvalues,randomlydistributedandcompletelycontainedwithinthenoiselevelofthemeasurement.TheseresultsindicatedthattheMeasurementModelprovidedagoodttotheskinimpedancedata.Thepredictionoftherealpartoftheimpedancefromthettotheimagi-narycomponentofimpedanceisillustratedinFigure 5.7b .Thenormalizedrealresidualerrorswereallcontainedwithinthe95.4%condenceinterval.Thisob-servationledtotheconclusionthattheentirespectrumwasconsistentwiththeKramers-Kronigrelations.ConsistencywiththeKramers-Kronigrelationswasobservedforallimpedancespectracollectedbythe10mVVAGmodulationtech-nique.Althoughnotpresentedhere,theimpedancespectracollectedby1Aconstant-amplitudegalvanostaticmodulationwerealsoconsistentwiththeKramers-Kronigrelationsovertheentirefrequencyrange.Theconsistencyofimpedancespectracollectedatthe1Aperturbationamplitudeindicatedthatthepropertiesofskinwerenotalteredbythemeasurementtechnique.Animportantaspectoftheseexperimentswasthatthepotentialdifferenceacrosstheskinwasnotlargerthan0.55V.Thetransdermalvoltagedropsassociatedwiththe1Aspectraaresigni-cantlysmallerthanforthe10Aconstant-amplitudegalvanostaticallymodulatedspectradiscussedinthenextsection.KKconsistencycheckfor10Aconstant-amplitudegalvanostaticspectra.TheprocedureforidentifyingdatathatisnotconsistentwiththeKramers-KronigrelationsdescribedinSection 5.2.1 wasappliedhere.ThenormalizedrealresidualerrorsforattotherealpartofthedataarepresentedinFigure 5.8a .Theresid-ualerrorsdemonstratedsignicanttrendingandwereontheorderof10%ofthemeasurement.Furthermore,manyoftheresidualerrorswerelocatedoutsidethe

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105 a bFigure5-7:NormalizedresidualerrorsfromanimaginarytoftheMeasurementModeltoa10mVVAGscanofskininCaCl2electrolyte.aFittingerrorsbPredictionofrealpartoftheimpedance.

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106 noiselevelofthemeasurement.Thedistributioncharacteristicsoftherealresidualerrorswereconsistentwithapoort.TheresidualerrorsassociatedwiththepredictionoftheimaginarypartoftheimpedanceareshowninFigure 5.8b .Theimaginaryresidualerrorswereapprox-imatelyequalto10percentoftheimpedanceatfrequenciesgreaterthan100Hz.Theresidualsassociatedwithfrequenciesbelow100Hzwereaslargeas200%ofthemeasurementvalue.Theskinimpedancedatacollectedatfrequenciesabove10kHzfellwithinthe95.4%condenceinterval.Despitetherelativelypoorqual-ityofthist,theentirespectrumwasincludedforthetofthemeasurementmodeltotheimaginarypartoftheimpedance.ThenormalizedresidualerrorsforthetoftheMeasurementModeltotheimaginarypartoftheimpedancearepresentedinFigure 5.9a .Alloftheresid-ualerrorsfellwithinthenoiselevelofthemeasurementandwereapproximatelyequalto1%ofthemeasurement.TheresidualsfromthepredictionoftherealpartoftheimpedancearepresentedinFigure 5.9b .Therealresidualerrorsforfrequencieslessthan100Hzwerelocatedoutsidethecondenceinterval.Further-more,themagnitudeoftheresidualerrorsincreasedwithdecreasingfrequency.Therefore,theimpedancedatacollectedatfrequenciesbelow100Hzwereconsid-eredtobeinconsistentwiththeKramers-Kronigrelations.Theinconsistentdatapointswereobtainedwhenthepotentialvariationacrosstheskinexceeded1.06Vwhichcorrespondedtothemeasurementat100Hz.Dur-ingtheimpedanceexperiment,thepotentialdifferenceacrossthemembranecon-tinuedtoincreaseuntil5Hzwhereamaximumofapproximately4.97Vwasob-served.Therangeofpotentialforwhichchangesinmembranepropertieswereobservedwasconsistentwiththereportedthresholdofvoltageforskinchangesof0.1to2V. 3

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107 a bFigure5-8:NormalizedresidualerrorsfromatoftheMeasurementModeltotherealpartofa10Aconstant-amplitudegalvanostaticscanofskininCaCl2electrolyte.aFittingerrorsbErrorsfrompredictionofimaginarypartoftheimpedance.

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108 a bFigure5-9:NormalizedresidualerrorsfromatoftheMeasurementModeltotheimaginarypartofaselected10Aconstant-amplitudegalvanostaticscanofskininCaCl2electrolyte.aFittingerrorsbPredictionofrealpartoftheimpedance.

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109 5.2.2ComparisonofModulationMethodsThemagnitudeofskinimpedanceasmeasuredbythe10mVVAGand10Aconstant-amplitudegalvanostaticmodulationmethodspresentedtheprevioussec-tionsareplottedasafunctionoffrequencyinFigure 5-10 .Thesolidcirclesand Figure5-10:SkinimpedanceasafunctionoffrequencycollectedbybothVAGandconstant-amplitudemodulation.Thelledcirclesandlleddiamondscorre-spondtospectracollectedby10mVVAGand10Aconstant-amplitudemodula-tion.ThesolidlinesrepresentthetsoftheMeasurementModeltothedata.Theopendiamondscorrespondtothepotentialdropacrossskininducedbythe10Acurrentperturbation. soliddiamondscorrespondtotheresponsesmeasuredbythe10mVVAGand10Aconstant-amplitudegalvanostaticmodulationtechniques,respectively.TheregressionoftheMeasurementModeltothe10mVVAGspectrum,illustratedbythesolidblackline,demonstratedexcellentagreementwiththedata.Theen-tiredatasetwaslocatedwithinthecondenceintervalwhichissigniedbythedashedlines.TheMeasurementModelttothespectrumcollectedby10Agalvanostaticcontrol,shownbythesolidlinewithverticalcrossmarks,didnotcoincidewiththedataatfrequenciesbelow150Hz.Thedatacorrespondingtothislow-frequency

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110 rangewerelocatedoutsidethecondenceintervalfortheKramers-Kronigconsis-tentpredictionforskinimpedance.Theinconsistentdataprovidedanindicationthatskinpropertieswerealteredbythe10Aconstant-amplitudegalvanostati-callymodulatedimpedanceexperiment.Thepotentialdifferenceacrossskininducedbythe10Aperturbationsisde-notedbytheopendiamondsinFigure 5-10 .Theverticaldashedlinelocatedat150Hzrepresentsthecriticalfrequencybelowwhichskinpropertiesbegantochange.Thevoltagedifferenceacrossthemembraneatthisfrequencywas580mVwhichwasconsistentwiththeconceptthatlargeelectriceldscanalterthepropertiesofskin.ThepotentialdifferencedropacrossskinassociatedwiththeKramers-Kronigconsistent10mVVAGspectrumisnotshownasamaximumamplitudeof10mVwasmaintainedovertheentirefrequencyrange.Insummary,itwasdemonstratedthatimpedancespectracollectedby10mVvariable-amplitudegalvanostaticVAGmodulationand1Aconstant-amplitudegalvanostaticmodulationwereconsistentwiththeKramers-Kronigrelations.Thisimpliedthattheimpedanceexperimentdidnotsignicantlyalter,inastatisticalsense,skintransportproperties.Incontrast,spectracollectedbythetraditionalconstant-amplitudegalvanostaticmodulationmethodatthe10AperturbationamplitudewerenotconsistentwiththeKramers-Kronigrelations.Theinconsis-tentdatapointswerelocatedinthelow-frequencyportionofthespectra.ThefailureofthedatatoconformwiththeKramers-Kronigrelationsimpliedthatskinpropertieshadbeenaltered.Subsequentspectracollectedbyvariable-amplitudegalvanostaticmodulationwereconsistentwiththeKramers-Kronigrelations.Thedatafromthe10Aconstant-amplitudegalvanostaticallymodulatedex-perimentswhichdidnotsatisfytheKramers-Kronigrelationswereobservedwhenthepotentialdifferenceacrosstheskinexceededapproximately0.5V.Thisobser-

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111 vationwasconsistentwiththeconceptthatthepropertiesofskinbegintochangeaboveacriticalpotential.Therangeofpotentialforwhichskinchangeswerede-tectedinthisstudywasinagreementwiththepotentialandcurrentstep-changeexperimentsdiscussedinSection 8.1 ofthisreport.Althoughtheimpedancespectrafromthe10Aconstant-amplitudegalvano-staticscansdidnotconformtotheKramers-KronigrelationsfortheskinsamplesimmersedinNaClandCaCl2electrolytes,differenceswerenotedintherecoveryofepidermalpropertiesfollowingthelargecurrentperturbationexperiments.Forexample,impedancespectracollectedby10mVvariable-amplitudegalvanostaticmodulationfollowingthe10Aexperimentsindicatedthattheskinimpedancerecovered66%inNaClelectrolyteand80%inCaCl2electrolyte.Thediffer-enceintherecoveryofskinimpedancetothe10Aperturbationssuggestedthatdivalentcationscanreducetheeffectoflargeelectriceldsonepidermaltransportproperties.TheimprovedrecoveryofskininCaCl2electrolyteasopposedtoNaClelectrolytehasalsobeenreportedintheliterature. 152 5.3ComparisonofExperimentswithLiteratureResultsThemajorityofskinimpedancespectradescribedintheliteraturewerecol-lectedbyeitherconstant-amplitudepotentiostatic 133 , 205 , 211 orconstant-amplitudegalvanostaticmodulation. 150 , 152 , 151 , 207 Impedancedataobtainedwiththesemodu-lationmethodsmaybecorruptedbynonlinearornonstationaryphenomena.Forexample,transientprocesses,suchasskinhydrationsee,forexample,Section 6.2 ,cancausetheopen-circuitpotentialacrossthemembranetochange.Ingen-eral,potentiostaticimpedanceexperimentsareconductedbymodulatingasinu-soidalconstant-amplitudevoltageperturbationabouttheopen-circuitpotentialmeasuredatthebeginningoftheexperiment.Therefore,changesintheopen-

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112 circuitpotentialthatoccurwithinthetimerequiredtocompleteaperturbationcyclecanintroduceartifactsintheimpedancemeasurements.Manyresearchershaveadoptedtheconstant-amplitudegalvanostaticmodu-lationtechniquetomitigatetheinuenceofchangesintheopen-circuitpotentialonskinimpedancemeasurements. 151 , 152 Theoretically,thenetcurrentacrossasys-temwillbezeroattheopen-circuitcondition.Bymodulatingthesinusoidalcur-rentperturbationabouta0A/cm2DCcurrentbias,theopen-circuitpotentialismaintainedoverthecourseoftheimpedanceexperiment.Despitethisattractivefeature,theregulationofskinimpedanceexperimentsbytheconstant-amplitudegalvanostaticmethodcanbeproblematic.Forexample,theconstant-amplitudecurrentperturbationcancausethevoltagedifferenceacrossskintosurpass1V.Theliteratureindicatesthatskinpropertiesbegintochangewhenthepotentialacrossthemembraneexceeds0.1-2V. 3 Kaliaetal.developedamodulationtechniquetoreducetheimpactoftheimpedanceexperimentonskintransportproperties. 152 A2MWresistorwasplacedinserieswiththeskin.Inthisconguration,the1Vsinusoidalpotentialper-turbationusedtoprobethesystemproduceda0.25AnA/cm2constant-amplitudecurrentsignal.Theapproachhadtheadvantagethatthecriticalpoten-tialformembranealterationscouldbeavoidedwhentheskinpolarizationresist-ancewaslessthan1MW/cm2.Theefcacyoftheimpedanceregulationmethodforpreventingchangestoskintransportpropertieswasdemonstratedforinvivoexperiments. 152 Thedevelopmentofthenovelvariable-amplitudegalvanostaticVAGmod-ulationmethodforskinimpedanceexperimentswasdescribedinthischapter.Theregulationtechniqueprovidedspectrathatwerenotsubjectedtolargepoten-tialswingsacrossthemembrane.Skinimpedancespectrawerecollectedinthis

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113 workbyVAGregulationandbythetraditionalconstant-amplitudegalvanos-taticmodulationstrategy.Theresultswerecomparedtoassesstheinuenceofeachmodulationtechniqueonskinproperties.TheVoigtcircuitmeasurementmodelwasregressedtoeachtypeofspectra.AsthemodelwasconsistentwiththeKramers-Kronigrelations,datacorruptedbynonlinearornonstationarybehaviorcouldbeidentied.Spectracollectedwiththeconstant-amplitudegalvanostatictechniquedidnotconformtotheKramers-Kronigrelations.Incontrast,spectraobtainedbyvariable-amplitudegalvano-staticmodulationwereconsistentwiththeKramers-Kronigrelationswhichim-pliedthattheskinwasnotalteredbytheexperiment.Bypreventinglargepoten-tialdifferencesacrossskin,theelectricalandtransportpropertiesofthemembraneweremeasuredinanoninvasivemanner.Electricalcircuitmodelshavebeenusedextensivelyintheliteraturetoanalyzeskinimpedancedata. 133 , 211 )]TJET1 0 0 1 6.448 0 cm1 1 1 1 k 1 1 1 1 K1 0 0 1 0.498 0 cm0.0353 0.451 0.098 rg 0.0353 0.451 0.098 RGBT/F20 7.97 Tf 0 0 Td[(213 AsdescribedinSection 3.6.1 ,thegeneralprocedureistoassignsystemphysicalpropertiestotheindividualelementsofthecircuit.Thereareseveralawsinthisapproach.Forexample,electriccircuitanalogsarenotunique,whichcanleadtomultipleinterpretationsofskinimpedancespectra.Furthermore,thecircuitelementsareassumedtoreactlinearlyindependentoftimeandappliedpotential.Theseconditionscannotbeguaranteedaprioriforhumanskinimpedancedata.Theworkpresentedheremarkedtherstapplicationofelectriccircuitmodelsfordeterminingthemeasurementcharacteristicsofskinimpedancedata.Portionsofthespectrathatwerefreeofinstrumentalartifactandnonstationarybehaviorwereidentied.Theresultsindicatedthatthemodulationofskinimpedanceex-perimentsbythenovelvariable-amplitudegalvanostaticmethodologyprovidesformoreaccurateassessmentoftheelectricalandtransportpropertiesofskin.

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CHAPTER6RESULTSANDDISCUSSIONOFSKINIMPEDANCESTUDIESThedevelopmentofthevariable-amplitudegalvanostaticmodulationtech-niqueforelectrochemicalimpedancespectroscopywasdescribedinChapter 5 .Itwasdemonstratedthatskinimpedancespectracollectedbytheadaptivemodu-lationstrategywereconsistentwiththeKramers-Kronigrelations.Thisindicatedthatthemacroscopicelectricalandtransportpropertiesofthemembranewerenotalteredbytheexperiment.Therefore,thevariable-amplitudegalvanostaticmod-ulationstrategywasappliedextensivelyinthestudiesdiscussedhere.Asstatedearlier,anobjectiveoftheimpedancestudieswastocharacterizein-uenceofcurrentandpotentialonskinproperties.Theexperimentspresentedhereweredesignedtoidentifytheimpedanceresponseofskinunderopen-circuitandapplied-currentconditions.Theopen-circuitimpedancestudiesprovidedin-formationonthedynamicsofskinhydrationandtherecoveryoftheskinprop-ertiesaftertheappliedcurrentwasterminated.Theimpedancespectracollectedunderiontophoreticconditionsrevealedtheinuenceofappliedcurrentonskinproperties.Theresultsfromtheapplied-currentstudyarepresentedinSection 6.5 .Manyoftheimpedancespectracollectedintheinitialstudieshadnegativevaluesfortherealpartoftheimpedanceathighfrequencies.Thehigh-frequencyasymptoteoftherealpartoftheimpedancecorrespondstothesolutionresistance.Thenegativesolutionresistancemeasurementswerethoughttobeaninstrumen-talartifact.Theworkperformedtodeterminethesourceofthehigh-frequencyartifactisdescribedinSection 6.1 . 114

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115 TheimpedanceexperimentsaimedatidentifyingtheinuenceofprolongedelectrolyteexposureonskintransportpropertiesarepresentedinSection 6.2 .Theobjectivewastocharacterizethedynamicsofskinhydration.Thestudyprovidedabaselineforevaluatingchangesinskinpropertiescausedbytheadditionofwa-terintothemembrane.Ithasbeenproposedthattherecoveryofskinpropertiesafterlargeelectricalperturbationsismorerapidindivalentcationsolutionsthaninmonovalentcationsolutions. 152 TheinuenceofsolutioncompositiononskinpropertiesisdescribedinSection 6.3 .ItwasshowninChapter 5 thatlargepotentialswingscanalterskinelectricalandtransportproperties.Thelargepotentialdropsacrosstheskinwereinducedbytheconstantamplitude-galvanostaticmodulationtechnique.Asupplemen-talimpedancestudyusingvariable-amplitudegalvanostaticmodulationwasper-formedtoconrmthatskincanbealteredbylargepotentialsignals.TheresultsfromtheinvestigationarepresentedinSection 6.4 .TransdermaliontophoresiswassimulatedduringtheimpedancestudiesbymodulatingthesinusoidalcurrentperturbationaboutaDCcurrentbias.Theamplitudeofthedirectcurrentsignalswereconsistentwithclinicaliontophoresissystems. 177 , 201 , 236 AdiscussionofthisworkisprovidedinSection 6.5 .Thenalstudydescribedinthischapterwasdesignedtoidentifytheregionalvariationintheimpedanceresponseofheat-separatedexcisedhumanskin.Formostoftheexperimentsperformedinthiswork,piecesofskinwereextractedfromadjacentlocationsofagivendonorsample.TheexperimentsdescribedinSection 6.6 provideanestimateofthevariationinskinpropertiesassociatedwiththemembranesusedforthiswork.

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116 6.1InuenceofReferenceElectrodeonHigh-FrequencyImpedanceResponseAsmentionedearlier,themajorityofskinimpedancespectracollectedinthisworkwereobtainedbyVariable-AmplitudeGalvanostaticVAGmodulationcon-trol.Forthesestudies,Ag/AgClmicro-referenceelectrodeswereused.Formanyofthespectra,therealcomponentoftheimpedanceathighfrequencieswasnega-tive.Foratypicalfour-electrodemeasurementofmembraneimpedance,thehigh-frequencyasymptoteoftherealpartoftheimpedanceshouldbeequaltotheelec-trolytesolutionresistance.Itwashypothesizedthatthenonidealbehaviorathigh-frequencywascausedbythemicro-referenceelectrodes.Forexample,thesmallsurfaceareaofthemicro-referenceelectrodesmayrestricttherangeofappliedpotentialforwhicheithertheideallynonpolarizableelectrodeassumptionorthereversibleequilibriumstateisvalid. 137 Analternativeexplanationisthatthenegativeelectrolytesolutionresist-ancevalueswereanartifactofthepotentiostatortheFrequencyResponseAn-alyzer.Measurementorbiaserrorsfromtheimpedanceequipmentareusuallycausedbylimitationsoftheinternalcircuitryandarecommonlyobservedathighfrequenciesforlowimpedancesystems.Duringiontophoresistheelectricalandtransportpropertiesofskinwillbein-uencedbyanappliedDCcurrentbias.Changesinskinpropertieswillmostlikelyappearinthelow-frequencyportionoftheimpedancespectra.Therefore,impedancespectrawithnegativehigh-frequencyasymptotesfortherealcompo-nentofthecompleximpedanceshouldstillcontaintheessentialinformationonskintransportproperties.Themainlimitationposedbytheapparentnegativeso-lutionresistancewasthatonlyoneortwolineshapescouldbeobtainedfromtheregressionoftheMeasurementModeltotheimpedancedatasee,forexample,Section 4.1.4 .Thesmallnumberoflineshapesoftenresultedinlargettinger-

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117 rors.ThepoorttingbehaviormadeitdifculttodeterminewhetheraparticularimpedancespectrawasconsistentwiththeKramers-Kronigrelations.Thislim-itedtheinterpretivepoweroftheMeasurementModeltechniqueforassessingtheinuenceofagivensetofexperimentalcontrolvariablesonskinproperties.Theobjectofthisstudywastodeterminetheinuenceofreferenceelectrodesonthehigh-frequencyimpedanceresponseofskin.TheapproachwastocollectreplicateimpedancespectraundersimilarexperimentalconditionsusingbothAg/AgClmicro-referenceelectrodesandcalomelreferenceelectrodes.SpectracollectedwiththecalomelelectrodeswerecomparedtothedatacollectedwiththeAg/AgClmicro-referenceelectrodes.Calomelreferenceelectrodeswereselectedforthecomparisonastheyarecommonlyusedforelectrochemicalmeasurementsandarestableoverawiderangeofpotentials. 136 Theimpedanceexperimentswereconductedunderconstant-amplitudegal-vanostaticcontrol.Perturbationamplitudesof100Aand10Aweresuperim-posedabouta0ADCcurrentbiastoproducefoursetsofsevenreplicatescans.Theskinwassoakedfor48hoursin50mMCaCl2bufferedelectrolytepriortothestudytoallowthemembranetobecomefullyhydrated.Thesamepieceofskinandsameelectrolyticsolutionwereusedforallexperiments.Acustom,two-compartmentdiffusioncellwasconstructedfrompolycarbonatesheetingtoac-commodatethelargerdimensionsofthecalomelreferenceelectrodes.Alloftheimpedanceexperimentswereperformedwiththecustomcell.Theresultsfromthe10Aexperimentsarenotpresented,asthetrendsweresimilartothe100Astudiesdiscussedbelow.SelectedimpedancespectracollectedwitheachtypeofreferenceelectrodewerethenassessedwiththeKramers-Kronigrelationsaccordingtomethodologyde-scribedinSection 4.1.4 .Theentirefrequencyrangeofthespectrawerecheckedfor

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118 consistencywiththeKramers-Kronigrelations.InconsistencywiththeKramers-Kronigrelationswasassumedtobecausedbyinstrumentalartifacts.6.1.1ResultsTheimpedanceresponseofskintothe100AperturbationsmeasuredbythecalomelandAg/AgClmicro-referenceelectrodesarepresentedinimpedance-planeformbyFigures 6.1b and 6.1a ,respectively.Thehigh-frequencyasymp-totesoftherealpartoftheimpedancearelocatedneartheoriginofthegures.Thespectracollectedbythecalomelreferenceelectrodes,showninFigure 6.1b ,displayedpositiveimpedancevaluesinthehigh-frequencyregion.Incontrast,thehigh-frequencyasymptotesoftheimpedancespectracollectedwiththeAg/AgClmicro-referenceelectrodes,displayedinFigure 6.1a ,werenegative.Thelow-frequencyimpedanceofthispieceofskinwasapproximately5kWcm2regardlessofthereferenceelectrodetype.Thelowpolarizationresistancevalueswereprobablycausedbyprolongedexposuretowater.Sincethefocusofthestudywastoanalyzethehigh-frequencyresponseofthereferenceelectrodes,thelowpolarizationresistancevalueswerenotconsideredtobeprohibitive.6.1.2K-KConsistencyCheckforCalomelElectrodeDataComplextsoftheMeasurementModelwereperformedforalloftheimped-ancespectracollectedbythe100Agalvanostaticmodulation.Modulusweight-ingwasappliedfortheregressions.Sevenlineshapeswereobtainedforalloftheimpedancespectra.Ingeneral,thelineshapemodelshowedgoodagreementwiththedataobtainedwiththecalomelreferenceelectrodes.Theerrorstructureforthemeasurements,asdenedbyEquation 4-15 ,wascalculated.Theparametersandwereincludedinthemodelandwereequalto4.17x10)]TJ/F20 7.97 Tf 6.448 0 Td[(4and7.63x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2,re-spectively.

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119 a bFigure6-1:Impedance-planeplotsofsuccessive100Aimpedancescansoffullyhydratedskin.aMeasuredwithAg/AgClmicro-referenceelectrodes.bMea-suredwithcalomelreferenceelectrodes.

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120 a bFigure6-2:NormalizedresidualerrorsfromatoftheMeasurementModeltotherealpartofskinimpedance.SpectrumwasobtainedfromhydratedskininbufferedCaCl2electrolyteandcollectedwithcalomelreferenceelectrodes.aRe-gressionttingerrors.bErrorsfrompredictionofimaginarypartoftheimped-ance.

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121 Thefourthspectrumcollectedwiththecalomelreferenceelectrodeswasas-sessedforconsistencywithKramers-Kronigrelations.TheregressionsoftheMea-surementModeltothedatawereweightedbytheerrorstructure.Thettotherealpartofthecompleximpedanceyielded8lineshapes.ThenormalizedresidualttingerrorsfromtheregressionaredisplayedinFigure 6.2a .Thesolidcirclesandsolidlinescorrespondtothettingerrorsandthenoiselevelofthemeasure-ment,respectively.Theresidualerrorsweregenerallylessthan1%oftherealpartoftheimpedanceandfellwithinthenoiselevelofthemeasurement.Inaddition,theresidualerrorswerenormallydistributedaboutthex-axis.Therelativelysmallmagnitudeandnormaldistributionoftheresidualerrorsindicatedagoodtofthemodeltothedata.Theresidualerrorsforthepredictionoftheimaginarycomponentoftheimped-ancearepresentedinFigure 6.2b .Theresidualerrorscorrespondtothesolidtrianglesandthe95.4%condenceintervalisshownbythedashedlines.Theer-rorswereontheorderof10%ofthemeasuredimpedanceforfrequenciesabove10Hz.Thenormalizedresidualerrorsforfrequenciesabove5Hzwerewithinthecondenceintervalindicatingthatthehigh-frequencydataconformedtotheKramers-Kronigrelations.TheMeasurementModelwasregressedtotheimaginarycomponentoftheimpedance.Theobjectivewastodeterminewhetherthelow-frequencyportionofthespectrumalsosatisedtheKramers-Kronigrelations.Eightlineshapeswereobtainedfromtheimaginaryt.ThenormalizedttingerrorsarepresentedinFigure 6.3a .Thenoiselevelforthemeasurementisindicatedbythesolidlineandtheresidualerrorsareshownbythesolidtriangles.Thettingerrorswerealllessthanvepercentoftheimaginarycomponentoftheimpedance.Thenoiselevelfortheimaginarytwasapproximately40%oftheimpedanceat1Hz.Thenoise

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122 a bFigure6-3:NormalizedresidualerrorsfromanimaginarytoftheMeasurementModeltoaselectedimpedancespectrumofhydratedskinmeasuredwithcalomelreferenceelectrodes.aNormalizedttingerrorsfromregression.bErrorsforpredictionoftherealcomponentoftheimpedance.

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123 levelgraduallydecreasedwithincreasingfrequency,reachinganasymptoticvalueof5%oftheimpedanceforfrequenciesgreaterthan100Hz.Alloftheresidualerrorswerelocatedwithinthenoiselevelofthemeasurementwhichimpliedthatastatisticallyvalidthadbeenobtained.Therelativeresidualerrorsfromthepredictionoftherealpartoftheimped-ancearepresentedinFigure 6.3b .Thenormalizedresidualsareindicatedbythesolidtrianglesandthe95.4%condenceintervalisshownbythedashedredlines.Theresidualerrorswerealllessthan2%ofthemeasurementandfellwithinthe95.4%condenceinterval.ThisindicatedthattheimpedancespectrumcollectedwiththecalomelreferenceelectrodeswasconsistentwiththeKramers-Kronigre-lations.Therefore,itwasconcludedthattheelectricalandtransportpropertiesofskinwerenotalteredbythelow-frequencyperturbations.6.1.3K-KConsistencyCheckforMicro-ReferenceElectrodeDataRegressionoftheMeasurementModeltoimpedancespectracollectedwiththeAg/AgClmicro-referenceelectrodesprovedtobeproblematic.Forexample,complextsweightedbythemodulusofimpedanceyieldedonlyonelineshape.Thefrequency-dependenterrorstructuremodelpresentedbyEquation 4-15 wasregressedtotheresidualerrorsfromthecomplexts.Theappropriateerrorstruc-tureforthemeasurementsincludedthemodelparametersandwhichwereequalto2.35x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3and4.73,respectively.ThefourthimpedancespectrumwasthenassessedforconsistencywiththeKramers-Kronigrelations.TheregressionsoftheMeasurementModelwereweightedbytheerrorstructure.Arealttothedatayieldedthreelineshapes.ThenormalizedttingerrorsarepresentedinFigure 6.4a .Theresidualerrorsexhibitedsignicanttrendingandfelloutsidethenoiselevelathighfrequencies.Themagnitudeofthettingerrorswereaslargeas75%oftherealpartoftheimpedanceathighfrequencies.

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124 Thelargettingerrorsathighfrequencieswereprobablycausedbythenegativevaluesoftherealpartoftheimpedance.Theresidualerrorsforthepredictionoftheimaginarypartoftheimpedance,showninFigure 6.4b ,alsodemonstratedsignicanttrending.Manyoftheresid-ualerrorswerelocatedoutsidethecondenceinterval.Thethreedatapointsout-sidethecondenceintervalathigh-frequencywereconsideredinconsistentwiththeKramers-Kronigrelations.TheinconsistentdatapointswerenotincludedforthetoftheMeasurementModeltotheimaginarypartoftheimpedance.NinelineshapeswereobtainedfromtheimaginaryttoaskinimpedancespectrumcollectedwiththeAg/AgClmicro-referenceelectrodes.TheresidualttingerrorsarepresentedasafunctionoffrequencyinFigure 6.5a .Theer-rorswerenormallydistributedandwerelessthan5%oftheimaginarypartoftheimpedance.ThenormalizederrorsfromthepredictionoftherealimpedancearepresentedinFigure 6.5b .Theresidualerrorswerebetween2%and10%forfre-quenciesabove5kHz.Theremainderoftheerrorswereallontheorderof1%.Sinceallofthedatafellwithinthecondenceinterval,thisportionofspectrumwasconsideredtobeconsistentwiththeKramers-Kronigrelations.6.1.4ComparisonofCalomelandMicro-ReferenceElectrodesThelow-frequencyportionsofthespectracollectedwiththecalomelandtheAg/AgClmicro-referenceelectrodessatisedtheKramers-Kronigrelations.How-ever,onlythedatacollectedwiththecalomelelectrodesconformedtotheKramers-Kronigrelationsathigh-frequency.Itisemphasizedthatallofthespectrawerecollectedunderidenticalconditionswiththeexceptionofthereferenceelectrodetype.Therefore,theinconsistentdatainthehigh-frequencyportionsofthespectracollectedwiththemicro-referenceelectrodeswasassumedtobecausedbyinstru-mentalartifact.

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125 a bFigure6-4:NormalizedresidualerrorsfromarealtoftheMeasurementModeltoaselectedimpedancespectrumofhydratedskinmeasuredwithAg/AgClmicro-referenceelectrodes.aRegressionttingerrors.bErrorsfrompredictionoftheimaginarycomponentoftheimpedance.

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126 a bFigure6-5:Normalizedresidualerrorsfromanimaginaryttoaselectedimped-ancespectrumofhydratedskinmeasuredwithAg/AgClmicro-referenceelec-trodes.aNormalizedttingerrors.bErrorsforpredictionofrealpartoftheimpedance.

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127 Thedifcultyinmeasuringthehigh-frequencyresponseofskinwithAg/AgClmicro-referenceelectrodesmaybeassociatedwiththelowimpedanceofthesys-tem.Forexample,mostelectrochemicalsystems,includingskin,displaythelow-estvaluesofimpedanceathigh-frequency.Therefore,thevoltagedropinducedbythehigh-frequencycurrentperturbationwasalsosmall.Itislikely,thattherelativelysmallmagnitudeofthevoltageresponsewaspartlyresponsibleforthehigh-frequencyartifact.Forexample,thesmallerdimensionsofAg/AgClmicro-referenceelectrodesmaynothavebeenadequatetosensethehigh-frequencyre-sponseofthesystem.Thepotentialdifferenceacrosstheskininducedbythecurrentperturbationwasapproximatelyequalfortheexperimentsconductedwithbothtypesofelec-trodes.However,thelargerdimensionsofthecalomelelectrodesmayhavebeensufcienttoovercomethehypothesizedsignal-to-noisedifculties.Thestudyde-scribedhereidentied,atleastinpart,thesourceofthehigh-frequencyartifactobservedinskinimpedancemeasurements.Animportantoutcomeofthisstudywasthatthehigh-frequencyartifactassociatedwiththeAg/AgClmicro-referenceelectrodesdidnoteffectthequalityofthelow-frequencyskinimpedancedata.Therefore,themajorityofrelevantinformationonskintransportpropertieswasincludedintheimpedancespectracollectedwithAg/AgClmicro-referenceelec-trodes.6.2InuenceofHydrationonSkinImpedanceThelocalenvironmentoftheheat-separatedskinchangedsignicantlywhenthesampleswereplacedinthediffusioncell.Forexample,theslightlymoistenedepidermiswasstoredinbetweentwosheetsofpolymerlmintherefrigerator.AtthestartofatypicalexperimenttheskinwasremovedfromtherefrigeratorandwasimmersedinawarmCsaltsolutionwithapproximatelythesamepH

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128 andionicstrengthastheelectrolyticuidwithinthebody. 246 Thegoalofthisstudywastocharacterizethetransientresponseofskintothechangeofenvironment.Inaccordancewiththisobjective,thetimerequiredforthesystemtoachievesteady-statewasidentied.ReplicateelectrochemicalimpedancespectrawerecollectedperiodicallybyVariable-AmplitudeGalvanostaticVAGmodulationtotrackthechanges.Thesinusoidalcurrentperturbationwassuperimposedabouta0ADCcurrentbiasandtheamplitudeofthevoltageresponseacrosstheskinwasmaintainedat10mV.Theopen-circuitpotentialacrossthemembranewasmeasuredbeforeandaftereachimpedancescan.Uponcompletionofanimpedancescantheskinwasal-lowedtorelaxforthreeminutesbeforethenextspectrumwascollected.Separatestudieswereperformedontwopiecesofskinextractedfromthesamedonorsample.Onepiecewasimmersedin50mMCaCl2electrolyteandtheotherin150mMNaClelectrolyte.Theskinimpedancespectrawerecollectedperiodi-callyfor24hours.Thecontrolparameterswereuniformforalloftheexperiments.Therstpartofthisstudyinvolvedthecollectionof40impedancespectraoverveandahalfhours.Theskinwasleftinsolutionovernightand15additionalscanswerecollectedonthefollowingday.AllofthespectrawerecheckedforconsistencywiththeKramers-Kronigrelations.Theselectedconditionforsteady-staterequiredthatthelow-frequencyportionsof2consecutiveimpedancespectraconformtotheKramers-Kronigrelations.Acompletedescriptionoftheresultsforthepieceofskininthe50mMCaCl2electrolytesolutionisprovided.Selectedresultsforthestudyoftheskinin150mMNaClarealsodescribed.6.2.1DirectAnalysisofHydrationDataSelectedimpedancespectracorrespondingtoeveryfthimpedancescanfromtheexperimentsofskininCaCl2arepresentedinFigure 6.6a .Theimpedance

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129 responsedemonstratedagradualandcontinuousdecreasethroughouttheen-tireobservationperiod.ThespectracorrespondingtoeveryfthimpedancescancollectedaftertheskinwassoakedovernightarepresentedinFigure 6.6b .TheaxislimitsonFigure 6.6b arethesameasforFigure 6.6a toprovidefordirectcomparisonwiththespectracollectedatbeginningoftheexperiment.Thelow-frequencyasymptotesofthelastspectrumcollectedinrst5.5hoursofthestudyandtherstspectrumobtainedaftertheskinwasleftinsolutionovernightwerecompared.Theresultsindicatedthepolarizationresistanceofthemembranehadrecoveredtoapproximately85%ofthevaluemeasuredatthestartoftheexperi-ment.Thepartialrecoverysuggestedthattheimpedanceexperimenthadasmalleffectonskinproperties.Subsequentspectracollectedontheseconddayexhib-itedacontinuousdecreaseinskinimpedance.Theopen-circuitpotentialmeasurementsarepresentedasafunctionoftimeinFigure 6-7 .Theopen-circuitpotentialatthestartoftheexperimentswas120.1mV.Thepotentialdifferenceacrossthemembraneincreasedtoamaximumof151.9mVduringthersthalfhourofthisstudy.Theopen-circuitpotentialasymptot-icallydecreasedto1mVoverthecourseofthenexthour.The1mVpotentialdifferencewasapproximatelyequaltothepotentialdropmeasuredbyamultime-terinanidenticalelectrolytesolutionintheabsenceofskin.Itislikelythatthedramaticchangesinopen-circuitpotentialwerecausedbytheformationofaque-ousionicchannelsinthestratumcorneum.Astheconductivityoftheelectrolytesolutionswasontheorderof0.01S/cm,awellhydratedion-exchangemembrane,suchasskin,willnotlikelyexhibitasignicantopen-circuitpotential.Althoughtheopen-circuitpotentialacrosstheskinremainedconstantafter1.5hours,theimpedanceresponsecontinuedtochangeovertheentirecourseoftheinvestigationsee,forexample,Figures 6.6b and 6.6a .Therefore,thepolariza-

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130 a bFigure6-6:SelectedsequentialimpedancescansofskinhydrationinbufferedCaCl2electrolyte.aResponseduringtheinitial5.5hoursofhydration.bRe-sponseafterskinwassoakedovernight. Figure6-7:Open-circuitpotentialacrossskinduringthehydrationstudy.

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131 tionresistancewasselectedasasimpleparameterforcharacterizingchangesinskinproperties.Skinresistancevalueswerenormalizedbythefollowingrelation-shipRp?=Rp)]TJ/F20 11.955 Tf 11.996 0 Td[(Rp;1 Rp;0)]TJ/F20 11.955 Tf 11.997 0 Td[(Rp;1-1whereRp;1istheestimatedasymptoticpolarizationresistanceastimegoestoin-nityandRp;0isthepolarizationresistanceatthestartoftheexperiment.Twoestimatesforthepolarizationresistancewerecalculated.Therstcorrespondedtothemodulusofskinimpedanceatthelowestmeasuringfrequency.1Hz.ThesecondestimatewastheKramers-KronigconsistentpolarizationresistancecalculatedfromatoftheMeasurementModeltotheexperimentaldata.ThenormalizedpolarizationresistanceofskinindivalentandmonovalentelectrolytesarepresentedinFigures 6.8a and 6.8b ,respectively.Thesolidcir-clesandthesolidtrianglesrepresentthenormalizedmodulusofskinimpedanceat0.1HzandtheKramers-Kronigconsistentpolarizationresistance.Thesolidredlineandthesolidblacklinecorrespondtothetsofanexponentialdecaymodeltobothsetsofestimatesforskinresistance.Theresultsindicatedtheskinimpedancedecreasedcontinuouslyoverthecourseoftheexperimentforbothskinsamples.Theresistanceoftheskinspecimensimmersedinthedivalentandmonovalentelectrolytesolutionsdecreasedbyap-proximately65%and80%respectively.Foragivenperturbationfrequency,theKramers-Kronigconsistentpolarizationresistanceofskinwasgenerallylowerthanthemodulusofskinimpedanceatthelowestmeasuringfrequency.Thedif-ferencebetweenthetwoestimatesofskinresistanceimpliedthattheresponsepredictedforatimeinvariantskinsamplewasslightlylowerthanthemeasuredquantity.

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132 a bFigure6-8:Normalizedpolarizationresistanceplotsofskin.aSkininbufferedCaCl2electrolyte.bSkininbufferedNaClelectrolyte.

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133 6.2.2InuenceofCationChargeonSkinHydrationTheMeasurementModelapproachdevelopedbyAgarwaletal. 238 , 239 wasappliedtoassessselectedimpedancespectraforconsistencywiththeKramers-Kronigrelations.Asstatedearlier,theassessmentprocedurewasusedtoiden-tifywhenthepropertiesofskinachievedsteady-state.ThemethodologyfortheassessmentprocedureisdescribedinSection 4.1.4 .ThepieceofskinimmersedinCaCl2solutiondidnotachievesteady-stateuntilaftertheskinwassoakedovernight.Incontrast,thepropertiesofskininNaClelectrolytechangedcontinu-ouslyoverthecourseoftheexperiment.AsproposedinSection 5.2.2 ,itispossi-blethatthechargeoftheelectrolytecationsinuencedthehydrationdynamicsofskin.Itisunlikelythattheimpedanceexperimentswereresponsiblefortheslowap-proachtowardsteady-state,sincethepotentialdifferencesacrossthemembraneinducedbythecurrentperturbationswereontheorderof10mV.Despitethecontinuouschangesintheskinsamplesstudiedhere,themajorityofskinspeci-mensstudiedbyelectrochemicalimpedancespectroscopyinthisworkdisplayedastationaryresponsewithinthersthourofbeingimmersedinelectrolytesee,forexample,Section 5.2.1 .6.3InuenceofElectrolyteCationChargeonSkinImpedanceTheliteraturesuggeststhatthechargeofelectrolytecationsinuencestheef-ciencyofiontophoretictransport. 20 , 131 , 133 , 247 Forexample,thetransportnumberscorrespondingtoaseriesofdifferentinorganicunivalentcationswerefoundtobeapproximately0.6.Incontrast,thetransportnumbersofvariousinorganicdi-valentcationswereintherangeof0.2-0.4.Theresultssuggestedthatspecicinteractions,suchaselectrostaticbinding,occurbetweendivalentcationsandthenegativebackgroundchargesitesofthestratumcorneum.Additionaliontophor-

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134 eticstudiesindicatedthattherecoveryofskinimpedancetoelectriccurrentisen-hancedinthepresenceofdivalentcationsincomparisontomonovalentcations. 152 TheresultsdescribedinSections 5.2.2 and 6.2.2 areconsistentwiththeseobserva-tions.Apossiblemechanisticexplanationfortheenhancementofskinrecoveryratesbydivalentcationsisderivedfromelectrostatictheory.Forexample,theforcebetweenanegativechargeandadivalentcationistwicethatofmonovalentcation.Theenhanceddrivingforceassociatedwiththedivalentcationscouldprovideforpreferentialadsorptiononthenegativelychargedregionsofthestratumcorneum.Thelargerelectrostaticinteractionsintheinteriorofstratumcorneummayreducetheimpactoflargeelectriceldsonskinproperties.Theobjectofthisstudywastoinvestigatetheeffectofelectrolytecationchargeontherecoveryofskintolargeelectricelds.Anadditionalgoaloftheinvestiga-tionwastoconrmthatskintransportpropertiescanbemonitorednonnivasivelybyvariable-amplitudegalvanostaticmodulatedimpedancespectroscopy.Theob-jectiveswereaccomplishedbysubjecting2piecesofskin,oneimmersedmono-valentcationelectrolyteandtheotherindivalentelectrolyte,toasimilarseriesofimpedanceexperiments.Theapproachwastocollect10mVVAGmodulatedimpedancespectrainter-mittentlyoverthecourseofthreehourstomonitorskinhydration.Largeelectriceldswereinducedacrosstheskinbythesubsequentcollectionoffour10Aconstant-amplitudegalvanostaticallymodulatedimpedancespectra.Therecov-eryofskinpropertiestothelargeperturbationswasmonitoredthroughthecol-lectionoffour10mVVAGmodulatedimpedancespectra.TheDCcurrentbiaswas0A/cm2foralloftheexperiments.TheMeasurementModel,describedinSection 4.1.4 ,wasregressedtothedatatoidentifyportionsofthespectraofthat

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135 wereinconsistentwiththeKramers-Kronigrelations.Theinconsistentdatawasassumedtobecausedbychangesinskinproperties.Theepidermalmembraneswereextractedfromadjacentlocationsonthesameskinsampletominimizeintra-individualvariability.Therstsamplewasim-mersedinbuffered150mMNaClbufferedelectrolyteandthesecondsampleinbuffered50mMCaCl2electrolyte.Theconcentrationofthesolutionswasconsis-tentwiththeionicstrengthoftheelectrolyticuidwithinthehumanbody. 246 6.3.1ImpedanceofSkinImmersedinMonovalentElectrolyteTheimpedancespectrafromtheskinimmersedinNaClelectrolytesolutionareshownintheimpedance-planeinFigure 6-9 .Thebandofspectrawiththe Figure6-9:Impedance-planeplotofskinimmersedin150mMNaClbufferedelectrolyte.ThelledsymbolstotheleftofmarkerA.correspondtospectracollectedby10mVVAGmodulation.ThehollowsymbolstotherightofmarkerB.representthe10Amodulatedexperiments. solidsymbolslocatedtotheleftofmarkerA.correspondtotheexperimentsconductedbyVAGcontrol.ThegroupofspectratotherightofmarkerB.werecollectedby10Amodulation.Visualcomparisonofthedatarevealedthattheskinimpedancemeasuredbythe10AperturbationwaslowerthantheresponsemeasuredbyVAGcontrol.Duringtherstthreehoursofthestudy,skinimped-anceincreasedgraduallyunderVAGcontrol.Uponchangingto10Aconstant-amplitudegalvanostaticcontrol,theimpedancedroppeddramatically.The10mV

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136 VAGmodulatedimpedancespectracollectedduringthehouraftertheconstant-amplitudeexperimentsrevealedapartialrecoveryoftheskinimpedanceresponse.Sincemorethan30impedancespectrawerecollectedinthisinvestigation,itwasdifculttoevaluatethetemporalevolutionofthesystemdirectlyfromtheimpedance-planeplot.TheKramers-Kronigconsistentpolarizationresistanceofskinwasonceagainselectedasasimpleparametertorepresentmembraneprop-erties.TheresultsfromtheassessmentprocedurearedescribedinSection 6.3.3 .SkinpolarizationresistanceisplottedasafunctionoftimeinFigure 6-10 .Thesolidcirclesandsolidtrianglesrepresentthedatacollectedby10mVVAGmod-ulationand10Aconstant-amplitudegalvanostaticcontrol,respectively.Thepo-tentialdifferenceacrosstheskinattheminimummeasuringfrequencyisshownbytheopensymbolsofFigure 6-10 . Figure6-10:Polarizationimpedanceandpotentialdifferenceacrossskinim-mersedinbuffered150mMNaClelectrolyte.Thesolidcirclesandsolidtrian-glescorrespondtothepolarizationresistanceofskinismeasuredbyVAGandconstant-amplitudegalvanostaticmodulation,respectively.Similarly,theopencirclesandopentrianglesrefertothemembranepotentialdifferenceatthelow-estperturbationfrequencyfortheVAGandconstant-amplitudegalvanostaticallymodulatedexperiments. Thepolarizationresistanceoftheskinapproachedanasymptoteof75kWcm2duringtherstthreehoursofthisstudy.InaccordancewiththeVAGmodu-

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137 lationprocedure,thepotentialdropacrosstheskinwasapproximately10mVwhilethespectrawerecollected.Asthemodulationstrategywaschangedto10Aconstant-amplitudecontrol,thepolarizationresistancedroppedtoapprox-imately50kWcm2.Themaximumpotentialdifferenceacrossskinfortheconstant-amplitudestudieswasapproximately1V.Thepolarizationimpedancerecoveredtowithin90%ofitsoriginalvaluewhilethenextseriesofVAGexperimentswasperformed.Theincompleterecoveryofskinimpedancesuggestedthatthealter-ationsinducedbythelargeelectriceldswereirreversibleonthe1hourtimescaleoftheseexperiments.6.3.2ImpedanceofSkinImmersedinDivalentElectrolyteTheimpedancespectraoftheskinsampleimmersedinbufferedCaCl2elec-trolytearepresentedintheimpedance-planeinFigure 6-11 .ThebandofspectrawiththesolidsymbolslocatedtotheleftofmarkerA.correspondtotheexperi-mentsconductedbyVAGcontrol.ThegroupofspectratotherightofmarkerB.werecollectedby10Amodulation.Theimpedanceofskincollectedbyconstant-amplitudemodulationwasalwaysless10mVVAGcontrolmeasurements.ThedifferenceintheimpedanceresponsesofthetwomodulationstrategieswasmorepronouncedthanforthespectraofskininNaClelectrolyte.Theskinimpedancespectrawereapproximatelyuniforminmagnitudeafteronehour.Theapproachtowardasteady-stateimpedanceresponsewasmorerapidinthiselectrolytethanfortheskinimmersedinNaClelectrolyte.Uponchangingthemodulationtechniqueto10Acontroltheimpedanceofskinde-creased.Theskinimpedancerecoveredrapidlywhenthemodulationstrategywasswitchedbackto10mVVAGcontrol.Sincetherecoveryofskinwassorapid,asecondsetof10Aimpedanceexperimentswasperformed.Thespectraas-sociatedwiththe10Aexperimentsalsodemonstratedadramaticreductionin

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138 Figure6-11:Impedance-planeplotofskinimmersedin50mMCaCl2bufferedelectrolyte.ThelledsymbolstotheleftofmarkerA.correspondtospectracollectedby10mVVAGmodulation.ThehollowsymbolstotherightofmarkerB.representthe10Amodulatedexperiments. skinimpedance.Therecoveryprocesswasonceagainmonitoredby10mVVAGmodulatedimpedancespectroscopy.ThespectrafromtheVAGexperimentsin-dicatedthattheelectricalandtransportpropertiesofskinhadalmostcompletelyrecovered.ThetemporalevolutionofthepolarizationresistanceofskininCaCl2elec-trolyteispresentedinFigure 6-12 .Theinitialvalueofskinpolarizationresistancewas75kWcm2.Theresistancedidnotchangesignicantlyduringthethree-hourintervalwhereskinpropertiesweremonitoredby10mVVAGmodulatedimped-ancespectroscopy.Uponswitchingthemodulationstrategyto10Aconstant-amplitudecontrolthepolarizationresistancedroppedtoapproximately65kWcm2andcontinuedtodecreaseassubsequent10Aspectrawerecollected.Thedif-ferenceinpolarizationresistancemeasuredbythetwomodulationstrategieswassmallerthanforthespecimenimmersedinNaClsolution.Themaximumpoten-tialdropacrosstheskinduringtheconstant-amplitudescanswasalsoontheorderof1V.Thepolarizationresistanceincreasedto74kWcm2whenthemodulationtech-niquewasswitchedto10mVVAGcontrol.SubsequentspectracollectedbytheVAGmodulationmethoddemonstratedsimilarpolarizationresistancevalues.The

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139 Figure6-12:Polarizationimpedanceandpotentialdifferenceacrossskinim-mersedinbuffered50mMCaCl2electrolyte.Thesolidcirclesandsolidtrian-glescorrespondtothepolarizationresistanceofskinasmeasuredbyVAGandconstant-amplitudegalvanostaticmodulation,respectively.Similarly,theopencirclesandopentrianglesrefertothemembranepotentialdifferenceatthelow-estperturbationfrequencyfortheVAGandconstant-amplitudegalvanostaticallymodulatedexperiments. uniformmagnitudeofthelow-frequencyresponseassociatedwiththeseimped-ancespectrawereconsistentwithacompleterecoveryofskinproperties.6.3.3Kramers-KronigConsistencyAssessmentInSections 6.3.1 and 6.3.2 itwasdemonstratedthattheimpedanceresponsesofskinmeasuredby10mVVAGand10Aconstant-amplitudegalvanostaticmod-ulationweredifferent.Thepotentialdifferenceacrossskininthelow-frequencyportionsoftheimpedancespectracollectedby10Aconstant-amplitudegalvano-staticmodulationwereontheorderof1V,whereas,theVAGmodulationstud-iesmaintainedthepotentialdropatamagnitudeof10mV.Theinuenceofthelargepotentialperturbationsinducedbythe10Aconstant-amplitudegalvanos-taticcontroltechniqueonskinpropertieswasassessedbycheckingtheimpedancespectraforconsistencywiththeKramers-Kronigrelations.Inaddition,thespec-

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140 traobtainedunder10mVVAGcontrolwereevaluatedforcompliancewiththeKramers-Kronigrelations.Theresultsfromtheassessmentprocedurearesummarizedhere.Thelow-frequencyportionsoftheVAGspectraofskininmonovalentanddivalentso-lutionssatisedtheKramers-Kronigrelationswithinonehourafterbeingim-mersedinelectrolyte.Incontrast,thespectraofskinin150mMNaClcollectedby10Aconstant-amplitudegalvanostaticmodulationwereinconsistentwiththeKramers-Kronigrelationsatfrequenciesbelow25Hz.Similarly,thespectraofskininCaCl2electrolytewereinconsistentatfrequenciesbelow100Hz.There-sultsfromthe10Aconstant-amplitudestudiesimpliedthatskinpropertieswerealtered.Thealterationswereassociatedwithpotentialswingsontheorderof1V.Thegreatestinuenceofcationchargeontheimpedanceresponseofskinwasobservedforthespectracollectedafterthe10Aconstant-amplitudegalvano-staticmodulatedscans.Forexample,theimpedancespectraofskininCaCl2electrolytewereconsistentwiththeKramers-Kronigrelationswhereasthespec-traassociatedwiththeskininNaClelectrolytewerenot.TheKramers-KronigconsistentspectracollectedfromthespecimeninCaCl2electrolytewerecompati-blewiththehypothesisthatskinpropertiesrecovermorerapidlyandcompletelyinthepresenceofdivalentcationssee,forexample,Section 5.2.2 .6.4InuenceofLarge-AmplitudeACPotentialSwingsonSkinItwasdemonstratedinSections 5.1.1 , 5.2.1 ,and 6.3.3 thatskinimpedancedatacollectedbyconstant-amplitudegalvanostaticmodulationwasinconsistentwiththeKramers-Kronigrelations.Theinconsistentdatapointsweregenerallylocatedinthelow-frequencyportionsofthespectrawhereskinexhibitsitslargestimped-ance.Forskinsampleswithapolarizationresistanceontheorderof100kWcm2,theconstant-amplitudemodulationtechniquecaninducepotentialswingswhich

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141 exceed1V.Electrochemicalsystemstypicallydemonstratenonlinearbehavioratelevatedpotentials; 137 therefore,itwashypothesizedthatpotential,andnotcur-rent,wasresponsibleforthechangeinskinimpedance.Theinuenceofpotentialonskinpropertieswasinvestigatedherebycollect-ingreplicateimpedancespectrabyvariable-amplitudegalvanostaticmodulation.Theapproachwastoperiodicallyincreasethetargetpotentialdropacrosstheepi-dermisfrom10mVto1V.Therelativelylargerangeofpotentialwasselectedtoidentifythethresholdamplitudeatwhichthepropertiesofskinbegintochange.TheimpedancespectrawereassessedforconsistencywiththeKramers-Kronigrelationstoidentifycorrupteddata.Itwasassumedfortheseexperimentsthatthe10mVtargetperturbationampli-tudewassufcientlylowasnottochangethepropertiesofskin.TheassumptionwaslatervalidatedbyconrmingthatthespectracollectedatthistargetpotentialamplitudesatisedtheKramers-Kronigrelations.The10mVVAGskinprotocolwasusedtomonitortherecoveryofskinfollowingeachsetofelevatedtargetamplitudeexperiments.Fourreplicateswerecollectedforeachsetofexperimen-talconditions.Themagnitudesofthetargetpotentialdifferenceacrosstheskinforthereplicatescanswere50,100,250,500and1000mV.TheimpedancespectracollectedattheprescribedtargetvoltagesarepresentedinFigure 6-13 .ThespectrawithopendiamondstotheleftofmarkerArepre-senttheinitialgroupof10mVVAGimpedancescans.Thedataindicatedthattheimpedanceofskinwaslargestatthebeginningoftheexperiment.ThespectrawithsolidyellowdiamondstotheleftofmarkerBrepresenttheimpedancere-sponsetothe50mVtargetperturbation.ThespectrawithopencirclestotheleftandrightofsymbolCcorrespondtothe100mVtargetperturbationmeasure-ments.ThespectrawithsolidyellowtrianglestotheleftofmarkerDrepresent

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142 Figure6-13:Impedance-planeplotofskinwherethetargetpotentialdropacrosstheskinwasincreasedperiodically.ThespectratotheleftofmarkersA-Drep-resentthemeasurementscollectedbytheVAGmodulationtechniquewithtargetvoltagesof10,50,100,and250mV,respectively. thedatacollectedatthe250mVamplitude.Thesolidbluediamondsandthesolidbluetrianglescorrespondtothespectracollectedatthe500mVand1Vtargetam-plitudes.Ingeneral,themagnitudeoftheimpedancedecreasedastheamplitudeoftar-getperturbationswasincreased.Furthermore,fortargetamplitudesgreaterthanorequalto250mVtheimpedanceofsuccessiveskinspectradecreasedwithtime.Theresultssuggestedthatskintransportpropertieswerealteredbythelargepo-tentialsignals.TherecoveryofskinimpedancetotheelevatedpotentialswingsispresentedinFigure 6-14 .TheopendiamondstotheleftofmarkerAcorrespondtotheini-tialgroupof10mVVAGimpedancespectra.Thisgroupofreplicatesservedasabaselineforcomparisonwithsubsequentspectra.ThespectradenotedbythesolidcirclestotheleftofmarkerBwerecollectedafterthe50mVVAGmeasurements.TheopentrianglestotherightofmarkerCwerecollectedafterthe100mVVAGimpedancescanswerecompleted.Thesolidtriangles,opencirclesandlleddi-amondsrepresenttheimpedanceresponseofskinfollowingthe250mV,500mVand1Vimpedanceexperiments.Ageneraltrendwasobservedwhereskinimped-

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143 anceincreasedasthetargetpotentialoftheVAGimpedancescanswasswitchedto10mVaftertheapplicationofthehigheramplitudesignals.Theimpedancecon-tinuedtoincreaseassuccessive10mVVAGspectrawerecollectedwhichimpliedthatthechangesinducedbythelargepotentialswingswerepartlyreversible. Figure6-14:Skinpolarizationresistanceuponcompletionoftheelevatedtargetpotentialimpedancescans.ThespectratotheleftofmarkersAandBcorre-spondtothe10mVVAGscanscollectedatthestartoftheexperimentandafterthe50mVVAGexperiments,respectively.ThebandofspectratotherightofCcorrespondtothe10mVVAGexperimentsconductedafterthe100mVVAGscans. SelectedspectrafromeachsetofexperimentalconditionswereassessedwiththeKramers-Kronigrelations.Impedancedatacollectedatmeasuringfrequen-ciesbelow5Hzatthe10mVtargetperturbationlevelweregenerallyinconsistentwiththeKramers-Kronigrelations.Theinconsistentbehaviorwaslikelycausedbynonstationaryeffects;e.g.hydrationofthemembraneortherecoveryofskinpropertiestothehighamplitudepotentialswings.Alargerportionofthelow-frequencydatacollectedatthehighertargetper-turbationamplitudeswasinconsistentwiththeKramers-Kronigrelations.Forex-ample,thespectracollectedwithatargetperturbationof1Vwereinconsistentatfrequenciesbelow200Hz.Theresultsareinagreementwiththeproposalthatskinpropertiesbegintochangeatacriticalpotential.Themagnitudeofthevolt-ageacrossskinwherethepropertiesbegantochangeinthisworkwas250mV.

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144 ThedatapresentedinFigures 6-13 and 6-14 clearlyindicatedthattherewasastrongeffectofpotentialonskinproperties.However,itwasdifculttoassessfromtheimpedance-planeplotsthemagnitudeandcharacterofthechangesinskinpropertiesinducedbythe500mVand1Vpotentialswings.Astheinu-enceofpotentialperturbationsonskinisgreatestatlow-frequencies,thepolar-izationresistancewasselectedasasimpleparameterforevaluatingalterationstothemembrane.ThepolarizationresistanceandpotentialdifferenceacrosstheskinaredisplayedasafunctionoftimeinFigure 6-15 .Thelleddiamondscorrespondtoskinpolarizationresistanceandthelledcirclesrepresentthepotentialdropacrossthemembrane. Figure6-15:Polarizationresistancesolidbluediamondsandvoltagedropacrosstheskinsolidyellowcirclesfortheelevatedtargetpotentialimpedancescans. Thepolarizationresistanceofskindecreasedasthepotentialdifferenceacrossthemembraneincreased.Thegreatestchangesinskinpolarizationresistancewereobservedwhenthetargetpotentialwassetto500mVand1V.Thepolarizationresistanceassociatedwiththesespectrawasanorderofmagnitudelowerthantheresistancemeasuredafter10mVVAGscansatthestartoftheexperiment.Skin

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145 polarizationresistance,measuredbythe10mVVAGmodulationtechnique,in-creasedpseudoexponentiallywithtimefollowingtheexperimentscollectedwithtargetvoltagesgreaterthan50mV.The10mVVAGresultsindicatedthatthechangesinmembranepropertiesinducedbythelargepotentialswingswerepar-tiallyreversible.Presentationoftheimpedancedatainthisfashionallowedforeasierinterpretationoftheinuenceofpotentialonskinproperties.6.5InuenceofDCCurrentBiasonSkinImpedanceDuringtransdermaliontophoresisDCcurrentisappliedtoprovideanad-ditionaldrivingforcetoenhancethedeliveryratesoftherapeuticcompoundsacrosstheskin.TheobjectiveofthisstudywastodeterminetheeffectofDCcur-rentonskintransportproperties.Theresponseofthemembraneunderapplied-currentconditionsandtherecoveryofskinpropertieswerestudiedbyimpedancespectroscopy.SixamplitudesofappliedDCcurrentintherangeof0A/cm2to855A/cm2werestudied.Thecurrentrangeusedforthestudywasconsistentwiththecurrentsappliedbyclinicaliontophoretictransdermaldevices.Amini-mumoffourimpedancescanswerecollectedunderconstant-amplitudegalvano-staticcontrolforeachapplied-currentmagnitude.Thesinusoidalcurrentpertur-bationwasequalto7.5%oftheDCbiasamplitudetooptimizethesignal-to-noiseratioofthepotentialresponse.Atthestartoftheexperiment,fourVAGmodulatedimpedancescanswithatargetpotentialdifferenceof10mVwerecollected.Thespectraprovidedabaselineofskinpropertiesandtheinitialhydrationstateofthemembrane.Theskinwasallowedtorelaxattheopen-circuitconditionforaminimumofsixmin-utesbeforecollectingsubsequentspectra.Afterskinhydrationwasstudied,fourimpedancespectrawerecollectedatthe71A/cm2appliedbiascondition.TherecoveryofskintoDCcurrentwasmonitoredthroughthecollectionoffour10mV

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146 VAGspectra.TheprocedureofalternatingthemodulationmethodforsuccessiveimpedancescanswasrepeatedastheDCcurrentbiasamplitudewasincreasedincrementally.6.5.1ComparisonofSkinImpedanceSpectraTheimpedance-planeplotcorrespondingtoimpedanceresponseofskinim-mersedinbuffered50mMCaCl2solutionunderapplied-currentconditionsispre-sentedinFigure 6.16a .Thesolidbluesymbolscorrespondtothespectracol-lectedatthebeginningoftheexperimentatanappliedbiasof0A/cm2.Thesolidyellowsymbolsandsolidredsymbolscorrespondtothemeasurementsob-tainedatappliedbiasamplitudesof71A/cm2and140A/cm2.Thesolidpur-plesymbolsarespectracollectedunderthe285A/cm2appliedbias.Theopenreddiamondsandsolidgreendiamondsarethemeasurementscollectedwithbiasamplitudesof570A/cm2and855A/cm2.Alloftheskinspectraexhibitedadepressedsemicircularshapeintheimpedance-plane.Asthecurrentwasincreased,thepolarizationresistanceandthecharac-teristictimeconstantforthesystemdecreased.Asecondaryprocessinthelow-frequencyregionofthespectrawasobservedfortheexperimentsconductedwithapplied-currentdensitiesgreaterthan71A/cm2.Thevariable-amplitudegalvanostaticmodulatedspectracollectedastheskinrecoveredfromtheappliedcurrentsarepresentedinFigure 6.16b .Thesymbolsforthespectraarecodedinthesamemannerastheapplied-currentbiasscanspresentedinFigure 6.16a .Withtheexceptionofthehydrationspectra,skinimpedanceincreasedassuccessivereplicateswerecollectedatthe10mVtargetperturbationamplitude.Thistrendindicatedthatskinpropertieswererecoveringfromtheapplied-currents.Therecoveryofskinimpedancewasincompleteoverthe4hoursofthisstudy.

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147 a bFigure6-16:ImpedancespectracollectedtodeterminetheinuenceofDCcurrentonskinproperties.Thecurrentbiasamplitudesareindicatedbythelegends.aSkinimpedanceunderapplied-currentconditions.bRecoveryofskinimped-ancetoappliedcurrentbias.

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148 6.5.2IdenticationofCorruptedDataSelectedimpedancespectraforeachsetofexperimentalconditionswereas-sessedforconsistencywiththeKramers-Kronigrelationsaccordingtothemethod-ologydescribedinSection 4.1.4 .Forexample,theMeasurementModelwasttothefourspectracollectedunderthe255/cm2DCbiascondition.Theerrorstruc-tureassociatedwiththissetofdatawasdetermined.TheerrorstructurewasusedtoweightsubsequentregressionstoidentifyportionsoftheimpedancespectrathatwereinconsistentwiththeKramers-Kronigrelations.Asmentionedearlier,thisprocesswasrepeatedforthespectracollectedundereachsetofexperimentalconditions.Ingeneral,thespectrawereconsistentwiththeKramers-Kronigrelationsovertheentirefrequencyrange.Thisbehaviorwasobservedregardlessoftheappliedcurrent.Thegeneralformoftheskinimpedanceresponsewascorrelatedtotheexperimentalmethodologyi.e.,whetherthesystemwasprobedunderanapplied-currentbiasorattheopen-circuitcondition.Forexample,asecondaryprocess,intheformofasmallcapacitiveloop,wasobservedinthelow-frequencyportionsoftheapplied-currentspectra.Theattributebecamemoreprominentasthecur-rentamplitudewasintensied.Incontrast,thesecondarypeakwasabsentinthemajorityofspectracollectedatthe0/cm2biasamplitude.ThedataassociatedwiththesecondarypeakwereconsistentwiththeKramers-Kronigrelations;however,acompletemechanisticexplanationforthefeatureisnotknown.SincetheresponsewasobservedexclusivelyinthespectracollectedunderaDCcurrentbias,itislikelythatthelargestationaryelectriceldsinducedbytheappliedcurrentinteractedwiththeskindifferentlythanthesignicantlysmallereldsduringthe10mVVAGexperiments.

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149 6.5.3PolarizationResistanceandOpen-circuitPotentialDataTheKramers-KronigconsistentpolarizationresistancewasusedtotracktherecoveryofskinpropertiesafterDCcurrentwasapplied.Thepolarizationresist-ance,themeasuredimpedanceat1Hzandthecorrespondingvoltagedropacrossskinarepresentedbythecircles,trianglesanddiamonds,respectively,inFigure 6-17 .Theimpedanceat1Hzis,ingeneral,approximatelyequaltothepolarizationresistanceofheat-separatedcadaverskin. 3 , 233 Figure6-17:Skinpolarizationresistanceinresponseto6amplitudesofappliedcurrent.OpensymbolscorrespondtomeasurementscollectedunderVAGmod-ulation.Solidsymbolsrepresentthemeasurementstakenduringapplied-currentbiasconditions.Thecirclesandtrianglesaretheimpedanceat1Hzandpolariza-tionresistanceofskin,respectively.Theopenandsoliddiamondsrepresentthepotentialdropacrosstheskin. Thepredictedpolarizationresistanceandimpedanceat1Hzfromtherstse-riesof10mVVAGimpedancescanswasapproximately23kWcm2.Thepolariza-tionresistanceassociatedwiththissetofimpedanceexperimentscorrespondedtothemaximumforthestudy.Ingeneral,skinpolarizationresistancedecreasedastheappliedbiaswasincreased.Thereductioninpolarizationresistancewasproportionaltotheapplied-currentdensity.Atapplied-currentdensitiesgreaterthan285A/cm2,thepolarizationresistancedecreasedcontinuouslyasconsecu-

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150 tiveimpedancescanswerecollected.Thereductioninskinresistanceindicatedthatthemembranehadbeenaltered.Thepolarizationresistanceofskinassociatedwiththe10mVVAGimpedanceexperimentsdemonstratedslightlymorecomplexbehavior.Forexample,afterthespectrawerecollectedatthe71A/cm2biascurrent,skinresistancewasap-proximately21kWcm2.Thisquantitywasapproximatelyequaltothepolarizationresistanceassociatedwiththe71A/cm2biasspectra.Asthepolarizationresist-ancewasidenticalforthetwoexperimentalconditions,theresultstronglysug-gestedthatthe71A/cm2currentbiashadnotsignicantlyalteredskinproper-ties.Spectracollectedbyvariable-amplitudegalvanostaticmodulationafterskinwassubjectedtothelargerDCcurrentbiassignalsdemonstratedanincreaseinpolarizationresistancewithtime.Thetrendindicatedthatthealterationsinducedbytheelevatedcurrentswerepartiallyreversible.Theopen-circuitpotentialacrosstheskinwasmeasuredbeforeandaftereachimpedanceexperiment.Theopen-circuitmeasurementsarepresentedasafunc-tionoftimeinFigure 6-18 .Ingeneral,theopen-circuitpotentialpriortothe10mVVAGmodulatedimpedancescanswasgreaterthanthevaluemeasuredafterthespectrawerecollected.Theoppositetrendwasobservedforalloftheimpedancespectracollectedunderappliedbiasconditions.Thereductionintheopen-circuitpotentialassociatedwiththe10mVVAGwaslikelycausedbytheintroductionofelectrolytesolutionintothemembrane.Theincreaseinpotentialdifferenceacrosstheskinfortheappliedbiasstudieswasgreatestfortherstgroupofspectracollectedaftercompletionofthe10mVVAGmodulatedexperiments.Forexample,theopen-circuitpotentialincreasedby131mVduringtherstimpedancescanwiththe71A/cm2.Thedifferenceinopen-circuitpotentialsmeasuredbeforeandafterthecollectionofsubsequent

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151 Figure6-18:Open-circuitpotentialdifferenceacrossthestratumcorneumbeforeandafterimpedancescans.Opencirclesandopentrianglescorrespondtomea-surementscollectedbeforeandafterthe10mVVAGimpedancescans,respec-tively.Solidcirclesandsolidtrianglescorrespondtomeasurementscollectedbe-foreandafterconstant-amplitudeimpedancescanswithanapplied-currentbias,respectively. impedancespectraatthiscurrentbiaswasapproximately85mV.Theincreaseinopen-circuitpotentialafterapplicationoftheDCcurrentsuggestedthatthemembranehadbeencharged.Theopen-circuitpotentialrecoveredto110mVatthestartoftherstVAGmodulatedimpedanceexperimentuponcompletionofthe71A/cm2appliedbiasstudy.Theopen-circuitpotentialassociatedwiththenextthree10mVVAGspectrawereapproximatelyequaltothe80mVdifferencemeasuredatthestartofthisstudy.Astheappliedbiaswasincreasedto142A/cm2theopen-circuitpotentialincreased280mV.Duringthesixminuterestpriortothenextimped-ancescanthepotentialdifferencedecreasedto180mV.Afterthesecondimped-ancespectrumatthe142A/cm2biasamplitudewascollected,theopen-circuitpotentialincreasedto300mV.Asimilarbefore-and-aftertrendwasobservedforremainingspectracollectedunderthe142A/cm2currentbias.

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152 Theopen-circuitpotentialmeasurementscorrespondingtotheimpedancespec-tracollectedwith10mVVAGmodulationwereapproximatelyequalto80mV.Af-tertherstimpedancespectrumatthe285A/cm2biasamplitudewasobtained,theopen-circuitpotentialincreasedto310mV.Astheskinwasallowedtorelaxafterthisscan,theopen-circuitpotentialdecreasedto190mV.Uponcompletionofthenextspectrumatthe285A/cm2currentcondition,theopen-circuitpotentialincreasedto300mV.Thesamebehaviorwasobservedfortheremainingspectracollectedwiththe285A/cm2currentbias.Theopen-circuitpotentialmeasurementsassociatedwiththe10mVVAGimped-ancespectracollectedafterthe285A/cm2biasexperimentsdecreasedsteadilywithtime.Themeasurementscollectedwiththefourth10mVVAGspectrumwereapproximatelyequalto80mV.Thismagnitudewasapproximatelyequaltotheopen-circuitpotentialmeasuredatthebeginningofthisstudy.Itshouldbenotedthatthepotentialdifferenceinducedbythe285A/cm2currentbiaswasgreaterthan3V.Theopen-circuitpotentialdifferencemeasuredwiththe570A/cm2and855A/cm2biasspectrawerealllessthan80mV.Furthermore,themagnitudeofthemeasurementsdecreasedwithtime.Undertheseapplied-currentconditions,thepotentialdifferenceacrosstheskinwasgreaterthan4-5Vatthelowestperturbationfrequenciesoftheimpedancescan.Therelativelysmallopen-circuitpotentialsassociatedwiththeimpedancespec-tracollectedatbiasamplitudesgreaterthanorequalto285A/cm2suggestedthattheinternalstructureoftheskinhadbeenalteredbythelargeelectriceld.Modicationstotheinternalstructureoftheskincouldprovideforeasieraccessoftheelectrolytesolutionintotheinteriorofthemembrane.Theintegrationofelectrolytewouldcausetheconductivityofskintoincreaseandtheopen-circuitpotentialtodecrease.Thelowopen-circuitpotentialsandtherelativelysmallpo-

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153 larizationresistanceofskinassociatedwiththesehighcurrentbiasexperimentswereconsistentwiththeproposedstructuralmodications.Insummary,itwasshownthattherewasasignicanteffectofcurrentonthetransportpropertiesofskin.Theimpedancestudiesindicatedthatthepolarizationresistanceofskindecreasedinresponsetoanincreaseincurrent.Acomparisonoftheopen-circuitpotentialacrossskinbeforeandafterimpedancespectrawerecol-lectedstronglysuggestedthattheepidermisbecamechargedwhentheDCcurrentbiaswasbetween71A/cm2and285A/cm2.Theexperimentsdescribedhereprovidedanestimateofthepolarizationbe-haviorofskinunderapplied-currentconditions.Forthesestudies,thecurrentbiaswasappliedforapproximately3to4minutes,whichcorrespondedtothetimerequiredtocollectancompleteimpedancespectrum.Asthepermeabilityofskintomosttherapeuticcompoundsistypicallysmall,clinicalprotocolsfortrans-dermaliontophoresiswilllikelyrequirethatcurrentbeappliedformuchlongerperiodsoftime.TheresponseofcadaverskintotheprolongedapplicationofDCcurrentisdiscussedinChapter 8 .6.6VariationofPropertieswithLocationTheliteratureindicatesthatskinpropertiesvarywithbodylocation. 14 , 15 , 16 , 17 , 18 Theexperimentsdescribedhereprovidedaninitialestimateofthevariationinthetransportpropertiesoftheskinsamplesusedforthisbodyofwork.Fourpiecesofskinwereextractedfromadjacentlocationsofthesamedonorsample.Theskinwasinspectedwithamagnifyingglasstoconrmthatmacroscopicholeswerenotpresent.Thesamplewasessentiallyfreeofhairfolliclesandthesurfacetexturewasrelativelyuniform.Theimpedanceresponseofeachpieceofskinwasmeasured.Theimped-ancespectrawerecollectedbyVAGmodulationcontrolwherethetargetpoten-

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154 tialacrossthemembranewassetto25mV.Fourimpedancespectrawerecol-lectedforeachpieceofskinstudied.Theskinsampleswereimmersedinbuffered50mMCaCl2.Theimpedance-planeplotforasinglespectrumforeachpieceofskinispresentedinFigure 6.19a .AschematicoftherelativespatiallocationswherethepiecesofskinwereextractedisshowninFigure 6.19b .Thepolarizationresistancevaluesforthespecimenslistedaccordingtoextrac-tionsitewereapproximately180,10,20and120kWcm2.Thedistributionofimped-ancevaluesclearlydemonstratedthatskinpropertiesdidnottrackcontinuouslywiththespatialoriginofthesamples.Largevariabilityinskinimpedancewasalsoobservedforpiecesoftheheat-separatedcadaverskinobtainedfromdiffer-entdonors.Sincealargedatabaseofimpedancemeasurementswascollectedinthiswork,astatisticalanalysisofvariancewasperformedtoestimatethecon-tributionsfromeachsourcetothetotalvariationinskinproperties.AdetaileddiscussionofthestatisticalanalysisisprovidedinChapter 7 .6.7ComparisonofImpedanceDatawithLiteratureResultsTheworkpresentedinSection 6.2 describedthedetailedanalysisoftheinu-enceofmembranehydrationonskintransportproperties.Open-circuitpoten-tialmeasurementsandskinimpedancespectrawerecollectedtoinferwhenthesystemhadachievedsteady-state.Theopen-circuitpotentialacrosstheskinde-creasedfrom120mVtoauniformreadingof1mVwithintherst1.5hoursoftheexperiment.Theimpedancespectraindicatedthatskinpolarizationresist-ancedecreasedcontinuouslyoverthe5hourtime-frameoftheexperiment.ThespectradidnotconformtotheKramers-Kronigrelationsatlowfrequencieswhichindicatedthatthesystemwasstillevolving.ImpedancespectracollectedonthenextdaysatisedtheKramers-Kronigrelations;therefore,theskinwasassumedtobecompletelyhydrated.

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155 a bFigure6-19:Impedancespectraandtherelativelocationforskinsampleextractionoffourpiecesofskin.aImpedanceresponseof4piecesofheat-separatedskintakenfromadjacentlocationsofthesamedonorsample.bSchematicoftherelativelocationforskinsampleextraction.

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156 Animportantimplicationofthestudywasthattheelectrochemicalimpedancespectroscopytechniqueismoresensitivetochangesinskinhydrationthanopen-circuitpotentialmeasurements.Althoughapproximately24hourswererequiredfortheskinusedintheseexperimentstoachievesteady-state,themajorityofotherskinsamplespresentedintheremainderofthisworkdemonstratedauniformresponsewithinonehourofbeingimmersedinelectrolyte.Alimitednumberofreportswhichdescribetheinuenceofhydrationonskinimpedanceareavailableintheliterature. 152 , 206 Thecontinuousdecreaseinimped-anceasafunctionofimmersiontimeobservedinthisworkisconsistentwiththereportedresults. 152 , 206 Successiveskinimpedancecollectedinthoseinvesti-gationswerecomparedvisuallytoidentifywhentheskinhydrationprocesswascomplete.AuniquefeatureoftheworkpresentedherewasthatskinspectraweretestedforconsistencywithKramers-Kronigrelationstodeterminethesteady-statecondition.TheadvantageofthisapproachisthatdatamustbestationaryinordertosatisfytheKramers-Kronigrelations.Theassessmentproceduredescribedinthisworkprovidesformoreaccurateidenticationofthesteady-statecondition.Theinuenceoflargesinusoidalvoltageswingsonskinimpedancewasde-scribedinSection 6.4 .Variable-amplitudegalvanostaticVAGmodulationwasappliedtomaintaintheamplitudeofthepotentialperturbationsatprescribedlev-els.Skinpolarizationresistancewasfoundtobeinverselyproportionaltothepo-tentialperturbationamplitude.Impedancespectracollectedby10mVVAGmod-ulationfollowingthelargeperturbationamplitudeexperimentsdemonstratedanincreaseinskinpolarizationresistancewithtime.Theimpedancerecoveryratewasnotcorrelatedtothevoltageperturbationamplitude.Thetrendssuggestthattherelativelylargeelectriceldscausedtheinter-nalstructureoftheepidermistobecomemoreporous.Themoreopenarrange-

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157 mentcouldprovideforadditionalioniccurrentpathwayswhichwouldreducethemembraneresistance.Thetransientincreaseinresistanceobservedafterthelargepotentialswingswereterminatedisconsistentwiththerelaxationofthestruc-turalalterations.Theincompleterecoveryofthepolarizationimpedancefollow-ingthelargevoltageexperimentsimplythatthetime-constantfortherelaxationoftheproposedstructuralalterationsislargeincomparisontothetimescaleoftheexperiment.Analternativeexplanationisthatthechangeswerepartiallyirre-versible.ThebehaviordescribedinSection 6.4 isgenerallyconsistentwithasimilarDCpotentiometricstudyofexcisedhumanskin. 248 Oneimportantdifferencenotedinthatworkwasthattherecoveryrateofskinimpedancewasproportionaltotheappliedvoltage.Thediscrepancycanbeexplainedbythetypeofvoltagesignalusedfortheinvestigation.Forexample,aprescribedamplitudeofDCvoltagewasappliedforaminimumof10minutes.Theelectriceldwithintheskininducedbytheappliedvoltagewouldbepermanentlyoriented.Consistentwiththehy-pothesisthattheinternalstructureofskinwasmodiedbytheelectriceld,theextentofmembranepolarizationinresponsetotheDCvoltagewouldbeexpectedtobelargerthanforanalternatingsignalofthesameamplitude.Thesmallerrel-ativechangesinskinimpedancedescribedinSection 6.4 areconsistentwiththisscenario.Theuseofelectrochemicalimpedancespectroscopyintransdermaliontophor-esisresearchhasbeengenerallylimitedtothemeasurementofskintransportpropertiesduringhydrationandaftertheapplicationofDCcurrent. 150 , 152 , 166 , 205 , 248 AuniqueaspectoftheworkdescribedinSection 6.5 wasthatskinimpedancespectrawerealsocollectedunderapplied-currentconditions.Theadvantageof

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158 thisapproachisthattheinuenceoftheD.C.currentbiasontheelectricalproper-tiesofskincouldbeassesseddirectly.Thespectracollectedusingthismethodologydemonstratedthatskinimped-ancedecreasesinresponsetoanappliedDCcurrent.Thereductioninskinimped-ancewasproportionaltotheamplitudeofappliedcurrent.Theobservedbehaviorisconsistentwithreportedinvivo 150 , 152 , 206 andinvitroresults. 166 , 205 , 248 Thelitera-tureindicatesthatspectracollectedaftercurrentapplicationdemonstratealargerandmorerapidreductionofskinimpedanceinvivothaninvitro. 206 Thedynam-icsofskinimpedancechangesdescribedinSection 6.5 areconsistentwiththere-portedbehavior.Theprocedureforextractingtheepidermisfromthedermishasbeendescribedasapotentialsourcefortheslowerkineticsandsmallerquantitativeamountsofreducedimpedanceobservedintheinvitrostudiesthanfortheinvivoinvestiga-tions. 206 Forexample,theelevatedtemperatureatwhichtheepidermisisextractedmayalterorevenclosesomeofthecurrentconductingpathwaysoftheepidermis.Thecurrentbiasexperimentsdemonstratedthatskinimpedanceincreasedaf-terappliedcurrentwasterminated.Therecoveryprocesswassignicantlyslowerthanthemorerapidreductionobservedunderappliedbiasconditions.Asde-scribedearlier,itislikelythattheDCcurrentbyhiscausedthemembranetobecomepolarized.Theresultsareconsistentwithaslowrelaxationprocess.TheexperimentsdescribedinSection 6.5 arealsoinagreementwiththeliterature. 206 , 248 Insummary,theresultspresentedinthischapterweregenerallyconsistentwiththeliterature.Additionalcharacteristicsofskinimpedanceweredetectedunderavarietyofexperimentalcontrolconditions.Animportantaspectofthisworkwasthatasmallcapacitiveloopwasobservedinthelow-frequencypor-tionsofspectracollectedunderappliedbiasconditions.Thedistinctiveattribute

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159 wasabsentinspectracollectedattheopen-circuitcondition.Thesecondarypeakisnotmentionedintheliterature.Thefeaturecouldnotbedetectedinthoseex-perimentsbecauseimpedancespectrawerenotcollectedwhileanappliedcurrentbiaswasactive.Itwouldbeinterestingtorepeatthecurrentbiasexperimentsinvivotodetermineifthelow-frequencyfeatureisalsopresent.Theabsenceofalow-frequencycapacitiveloopwouldimplytheepidermalextractionprocedurealtersskin.

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CHAPTER7STATISTICALANALYSISOFVARIATIONINSKINIMPEDANCEAlargedatabaseofimpedancespectrawasassembledduringthecourseofthiswork.Themeasurementswerecollectedfrompiecesofheat-separatedcadaverskinfromavarietyofdifferentdonors.Foragivendonorsample,theimped-anceresponsesfrommultiplepiecesofskinweremeasured.AsdemonstratedinSection 6.6 ,skinpropertiesfromthesamedonordisplayedawidedistributionofimpedancevalues.Asimilarvariabilitywasalsonotedwhentheimpedancere-sponseofskinfromdifferentdonorswascompared.Theobjectiveofthisanalysiswastoapplystandardstatisticalmethodstocomparethesample-to-samplevari-ationinskinimpedancewiththevariationofpiecestakenfromthesamedonorsample.Adiscussionoftheanalysisofvarianceinskinimpedancedataispro-videdinSection 7.1 .Inaddition,theeffectofelectrolytecationchargeonskinimpedancewasassessedinaseparateanalysis.TheworkfortheinuenceofcationchargeisdescribedinSection 7.5 .Theimpedancespectraanalyzedherewerecollectedbyvariable-amplitudegalvanostaticVAGmodulation.Thetargetpotentialdropacrosstheskinwassetto25mVorlessandtheDCcurrentbiaswasxedat0A/cm2.Itwasdemon-stratedearlierinthisworkpleaserefertoSections 5.2 and 6.3 thatVAGmodu-lationofskinimpedancemeasurementscanbenoninvasive,especiallywhenthetargetvoltageresponseiskeptbelow250mV.Thespectrawereassessedforcon-sistencywiththeKramers-Kronigrelationstoestimatethepolarizationresistanceofskinwithconstantproperties.Therefore,itwasassumedthattheobserveddis160

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161 tributionofimpedancevaluescouldbeattributedtoinherentdifferencesinthevariouspiecesofskin.Forthediscussionpresentedhere,theterminologydonorsamplereferstothecompleteportionofskinobtainedfromagivendonorandpiecereferstoasmallsegmentofskintakenfromthesample.TheclassicationschemeisillustratedinFigure 7-1 .Theepidermalmembraneswereextractedfromthedorsalandab-dominalregionsofhumancadavers.Astheskinspecimensweretakenfromthesameregionsofthebodyitwasassumedthatthedistributionofskinpropertieswasassociatedwithdifferencesbetweenindividualsand/ordifferenceswithinthesample.Theobjectiveofthestatisticalanalysiswastodeterminethecontri-butiontotheoverallvarianceinskinpropertiesfromeacheffect.Alternativelystated,theaimherewastodeterminewhethertheinter-individualdistributionofpropertieswasdifferentfromtheintra-individualvariation. Figure7-1:Proposedsourcesofvariationinskinproperties. Theobservationsetsfortheanalysiscorrespondedtoimpedancemeasure-mentscollectedimmediatelyaftertheskinwasimmersedinelectrolyte.Aseriesof3-5impedancespectrawascollectedforeachpieceofskinduringthehydra-

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162 tionperiod.Theskinsampleswereprovidedby18differentdonorsfromwhich127pieceswereextractedtoperformtheexperiments.Atotalof32pieceswereimmersedindivalentcationelectrolytesolutionsand95inmonovalentcationso-lutions.Theentireobservationsetconsistedof508impedancespectra.Asampleofskinwasconsideredintheanalysisonlyifstudieswereconductedonpiecesofskinthatwereimmersedinbothmonovalentanddivalentelectrolytes.Astheionicstrengthofthemonovalentanddivalentelectrolytesolutionswasuniform,theeffectofcationchargeonskinimpedancewasassessedbyperformingStu-dent'st-testsandF-tests.FurtherdiscussionoftherespectivetestproceduresisprovidedinSection 7.5 .7.1StatisticalModelforSkinImpedanceDataTheGeneralizedLinearModelGLMwasusedtorepresenttheexperimentaldatabecauseadeterministicprocessmodelofskinimpedanceisnotyetavailable.TheGLMmodelisastatisticalmodelthatdescribespopulationswhicharenor-mallydistributedaboutameanvalue.TheselectionoftheGLMmodelwasbasedontheassumptionthatdonorsampleswerechosenatrandomfromthegeneralpopulation.Furthermore,itwasalsoassumedthatpiecesofskincutfromagivendonorsamplewererandomlyselected.Undertheseassumptions,deviationsfromthemeanvaluearecausedbyeitherdonor-to-donorvariations,site-to-sitevaria-tionswithinasample,orrandomlydistributedmeasurementerrors.Thelocationfromwhichapieceofskinwasselectedwasasubsetofthedonorsample;therefore,thenestedformoftheGeneralizedLinearModel 249 wasap-plied.ThenestedformoftheGeneralizedLinearModelisrepresentedbyyijk=+i+ij+ijk-1whereisthemeanvalueforthepopulation,ii=1;2:::aarethecontributionstotheobservationsduethedonorsampleandijk=1;2:::barethecontribu-

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163 tionsfromthelocationsonagivendonorsample.Theterm,ijkk=1;2:::n,representsthemeasurementerror.Itisassumedthattheparameters,i,ijandijkarenormallydistributedwithmeanvaluesof0andrespectivevariancesof2,2and2.ThetotalvarianceintheimpedancedatafortheGeneralizedLinearModelcanbedecoupledaccordingto2Total=2Donor+2LocationDonor+2Residual-2where2Totalisthetotalvarianceofthepopulation.Theterm,2Donorcor-respondstothecontributiontothevarianceinskinpropertiesfromthedifferentdonorsamples.Similarly,2LocationDonoristhevarianceinskinpropertieswithinsamedonorsample.Thenalterm,2Residual,isthevarianceoftheresidualerrors.Thevariancemodelwasappliedtothepolarizationresistanceandcriticalfrequencydatasetsforeachelectrolytetype.Therelativemagnitudeofthedonor-to-donorandsite-to-sitevariationswerethencomparedtothevarianceintheresidualerror.Theapproachmadeitpossibletodeterminewhetherthevarianceinskinpropertiesamongthedonorsamplesandthevarianceforpiecesofskinfromthesamesampleweresignicantlylargerthanthevarianceintheresidualerror.TherelativecontributionstothetotalvariancefromthevarioustermsoftheGeneralizedLinearModelwereassessedthroughSAScv8.0software.Separateanalyseswereperformedwherethepolarizationresistanceandthecriticalfre-quencywereselectedchosenasthedependentvariables.TypeIIIstatisticalanal-ysiswasimplementedsincethedatasetwasunbalanced,i.e.,moreskinsamplesweretestedinmonovalentelectrolytethanindivalentelectrolyte. 250 TheoutputfromtheSASprocedurewaspresentedinstandardANOVAtabularformat.Thetablecolumnscorrespondtotheindependentvariablename,degreesoffreedom,

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164 meansquareoftheregressionerrors,F-testparameterandone-sidedprobabilityforacceptanceofthenullhypothesis.ThenullhypothesisandalternativehypothesisfortheeffectofdonorsampleandlocationfromwhichtheskinwasobtainedonthepolarizationresistancearepresentedinTable 7-1 .Acceptanceofthenullhypothesisfordonortypeimpliesthatthevarianceofpropertyvaluesamongthedonorsampleswasinsignicant.Similarly,acceptanceofthenullhypothesisfortheeffectoflocationonpolariza-tionresistanceimpliesthatthesitefromwhichtheskinwasobtainedprovidednosignicantdifferenceinpropertyvalues. Table7-1:Proposedhypothesesformodeleffectsonpolarizationresistance Variable Hypothesistype Equation Donor Null H0:2DonorRp=0 Donor Alternative Ha:2DonorRp6=0 LocationDonor Null H0:2LocationDonorRp=0 LocationDonor Alternative Ha:2LocationDonorRp6=0 7.2AnalysisofSkinImpedanceDataforNormalDistributionCharacteristicsTheanalysisofvarianceprocedureisextremelysensitivetotheconditionofnormality. 251 Consistencycheckswereperformedpriortotheanalysistoverifythatdatasetswerenormallydistributed.Anexampleofthevariationinskinimpedanceisprovidedbythehistogramofcriticalfrequencyforpiecesofskinim-mersedinmonovalentelectrolytepresentedinFigure 7.2a .Thedatapointswereclusteredneartheoriginandclearlywasnotnormallydistributed.Thehistogramfortheexperimentallydeterminedcriticalfrequencyofskinindivalentelectrolyteexhibitedsimilarbehavior.Thedistributionsofskinpolarizationresistanceinbothtypesofelectrolytealsodemonstratedgrossdeparturesfromnormality.Astatisticalmethodwhichiscommonlyappliedtoshiftdistributionstowardnormalityistoscaletheexperimentaldatabythesquarerootorlogarithmof

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165 themeasuredquantities. 252 Bothtransformationswereappliedtothepolarizationresistanceandcriticalfrequencydatabutthelogarithmictransformationprovideddistributionsthatmostcloselyapproximatedthenormaldistribution.Anexampleoftheshifttowardnormalityproducedbythelogarithmictransformationisillus-tratedbythehistogramofskincriticalfrequencymeasuredinmonovalentelec-trolytespresentedinFigure 7.2b .Anequalnumberofsamplingintervalswasselectedforbothhistogramstoensurethatthescalingwasuniform.Thenormaldistributionscorrespondingtotheobservedmeanandstandarddeviationforbothdatasetsareshownbytheredlines.ThemeasuredskincriticalfrequencydatasetwasclusteredneartheoriginofFigure 7.2a .Thenormaldistributioncurvewascenteredtotherightofthemedianvaluewhichindicatedthatthepopulationwasnotnormallydistributed.Incontrast,thehistogramofthetransformedcriticalfrequenciesillustratedthatthedataweredistributedoverawiderrange.Further-more,thenormaldistributioncurvewascenteredwithin4%ofthemedianvalue.Althoughtheseobservationsstronglysuggestedthatthelogarithmictransfor-mationproducednormallydistributeddata,theapproximationtonormalitywasalsoassessedbythekurtosisandskewnesscoefcientsofthepopulation.Thekur-tosismeasuresthe”atness”or”peakedness”ofapopulationrelativetothenor-maldistribution.Anegativekurtosiscoefcientimpliesthedistributionisatterthannormal,whereasapositivevalueimpliesamorepeakeddistribution.ThekurtosiscoefcientiscalculatedaccordingtoKurtosisnn+1 n)]TJ/F20 11.955 Tf 11.997 0 Td[(1n)]TJ/F20 11.955 Tf 11.996 0 Td[(2n)]TJ/F20 11.955 Tf 11.996 0 Td[(3ni=1xi)]TJ/F20 11.955 Tf 13.09 0.03 Td[(x 4)]TJ/F20 11.955 Tf 25.571 8.093 Td[(3n)]TJ/F20 11.955 Tf 11.996 0 Td[(12 n)]TJ/F20 11.955 Tf 11.996 0 Td[(1n)]TJ/F20 11.955 Tf 11.996 0 Td[(2-3wheren,xandarethetotalnumberofobservations,themeanandthestan-darddeviationofthedataset,respectively.Theanalysisofvarianceprocedureisextremelysensitivetothekurtosiscoefcient.Forexample,theprobabilityofrejectionunderthenullhypothesisofaatdistributiongreatlyexceedsaselected

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166 a bFigure7-2:Histogramsofthecriticalfrequencyofheat-separatedepidermis.aDistributionofmeasuredcriticalfrequencyvalues.bDatatransformedbythebase10logarithm.

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167 signicancelevel,,andforapeakeddistributiontheprobabilityisconsiderablylessthan. 251 Theskewnessrepresentstheasymmetryofthedatarelativetothenormaldis-tribution.Theeffectofskewnessonthesignicancelevelsofvariancetestsismuchlessextremethantheeffectofthekurtosiscoefcient. 251 Positiveskewnessindi-catesanasymmetricdistributionwherethetailisstretchedtowardmorepositivevalues,i.e.,totherightsideofthemean.Alternatively,anegativeskewnesscoef-cientcorrespondstoadistributionthatextendstowardmorenegativevalues,i.e.,totheleftsideofthemean.TheskewnessisdenedbySkewnessn n)]TJ/F20 11.955 Tf 11.997 0 Td[(1n)]TJ/F20 11.955 Tf 11.996 0 Td[(2ni=1xi)]TJ/F20 11.955 Tf 13.09 0.03 Td[(x 3-4wheren,xandaredenedinthesamemannerasforthekurtosiscoefcient.Theskewnessandkurtosiscoefcientsforthemeasuredandlogrithmicallytrans-formedcriticalfrequencydatafromimpedanceexperimentsofskinimmersedinmonovalentanddivalentelectrolytearepresentedinTables 7-2 and 7-3 ,respec-tively.Similardistributionstatistictablesforthemeasuredandlogarithmictrans-formedpolarizationresistancedatasetsarepresentedinAppendix C .Also,in-cludedinAppendix C arethesquareroottransformeddistributionstatistics.Theskewnessandkurtosiscoefcientsdescribingthedistributionofexperi-mentallydeterminedcriticalfrequenciesofskinimmersedinmonovalentelec-trolytewere20.79and4.35,respectively.Therelativelylargemagnitudeofthedistributionparametersindicatedthatthepopulationwaspeakedandseverelyskewedtowardmorepositivevaluesincomparisontothenormaldistribution.Thehistogramcorrespondingtothetransformedvaluesillustratedthatthedatasetswasapproximatelynormallydistributed.Theskewnessandkurtosiscoef-cientswere-6.13x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3and-4.82x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1,respectively.Thedistributionparametersindicatedthatthetransformeddatasetwasessentiallycenteredaboutthemean

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168 Table7-2:Distributionstatisticsforcriticalfrequencyasafunctionofelectrolytetype Variable Divalent Monovalent Mean 435.33 715.66 StandardError 93.54 77.57 Median 78.75 169.66 Mode 53.65 954.10 StandardDeviation 1020.44 1547.50 SampleVariance 1.04x106 2.39x106 Kurtosis 14.04 20.79 Skewness 3.67 4.35 Minimum 11.56 3.66 Maximum 5.37x103 1.16x104 Sum 5.18x104 2.85x105 DegreesofFreedom 119 398 CondenceLevel.0% 185.24 152.50 andslightlydepressedrelativetothenormaldistribution.Thetransformedpolar-izationresistancedatasetsdisplayedsimilartrendsformeasurementscollectedwithmonovalentanddivalentelectrolytes.Insummary,thelogarithmictransfor-mationoftheexperimentaldataproduceddistributionsthatwereapproximatelynormalandthussatisedtherequiredconditionsforproperinterpretationoftheANOVAinvestigations.7.3VarianceComponentsofPolarizationResistanceThevariancecomponentsofthelog10transformedskinpolarizationimped-ancedataforsamplesimmersedinmonovalentanddivalentelectrolytesolutionsarepresentedinTable 7-4 .Theresultsforthemonovalentanddivalentskinpop-ulationswereverysimilar.Forexample,thesample-to-samplecontributionstotheoverallvarianceforthemonovalentanddivalentdatasetswere20%and17%,respectively.Thewithin-samplevarianceprovidedthelargestcontributiontothetotalvarianceofskinpolarizationresistance.Therelativecontributionsforthemonovalentanddivalentdatawere76%and82%,respectively.Thevarianceintheresidualerrorsforbothelectrolytetypesprovidedlessthan4%ofthetotal.

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169 Table7-3:Distributionstatisticsforlog10ofcriticalfrequencyasafunctionofelec-trolytetype Variable Divalent Monovalent Mean 2.03 2.30 StandardError 6.01x10)]TJ/F20 7.97 Tf 6.447 0 Td[(2 3.72x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 Median 1.90 2.23 Mode 1.73 2.98 StandardDeviation 6.55x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 7.33x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 SampleVariance 4.30x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 5.38x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Kurtosis 1.55x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 -4.82x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Skewness 8.53x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 -6.13x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3 Minimum 1.06 0.56 Maximum 3.73 4.06 Sum 241.90 891.90 DegreesofFreedom 119 388 CondenceLevel.0% 0.119 0.073 Theresultsindicatedthattheintra-individualvariabilityinthetransformedpo-larizationresistancedatawasgreaterthantheinter-individualvariability. Table7-4:Calculatedcontributionstotheoverallvarianceinthelog10ofskinpo-larizationresistance Electrolyte 2Total 2Donor 2LocationDonor 2Residual Monovalent 0.239 6.04x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 0.229 1.01x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 Divalent 0.225 4.70x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 0.223 1.98x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3 Theanalysisofvarianceparametersfordeterminingwhetherthevariancecom-ponentswerestatisticallysignicantarepresentedinTables 7-5 and 7-6 .Thesig-nicancelevel,,forthecomparisonswas0.05.TheF-testparameterandproba-bilityvaluesforacceptanceofthenullhypothesisfortheeffectofthedonorfromwhichapieceofskinwasextractedonthepolarizationresistanceofthespecimensimmersedinmonovalentelectrolytewere2.45and0.46%,respectively.TheF-testparameterandprobabilityvaluesforeffectoflocationfromwhichapieceofskinwasobtainedwere89.93andlessthan0.01%.Thenullhypothesiscouldnotbeacceptedforbotheffects,asF-testprobabilitiesforacceptanceofthenullhypoth-esiswereextremelysmall.Theresultsimpliedthatcontributionstotheoverall

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170 varianceinthepolarizationimpedancedatacausedbydifferencesinthedonorsamplesandvariationsinagivensampleassociatedwithspecimenlocationweresignicantforskinimmersedinmonovalentelectrolyte. Table7-5:Calculatedcontributionstothetotalvarianceinthelog10ofskinpolar-izationresistance.Resultsfrompiecesimmersedinmonovalentelectrolyte Variable DOF TypeIIISS MeanSq. F-stat Pr>F Donortype 16 32.96 2.06 2.45 0.0046 MSErrorDonor 79.14 66.53 0.841 LocationDonor 79 71.75 0.908 89.93 <0.0001 MSErrorLocationDonor 292 2.95 0.0101 Table7-6:Calculatedcontributionstothetotalvarianceofthelog10ofskinpolar-izationresistanceforpiecesimmersedindivalentelectrolyte Variable DOF TypeIIISS MeanSq. F-stat Pr>F Donortype 11 19.93 1.74 2.32 0.0488 MSErrorDonor 19.99 14.96 0.748 LocationDonor 20 13.66 0.683 345.96 <0.0001 MSErrorLocationDonor 87 0.172 1.98x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3 Similarresultswereobtainedfromthevariancemodelfortheobservationsetofskinimmersedindivalentelectrolyte.TheF-statisticandprobabilityforac-ceptanceofthenullhypothesisfortheeffectofdonorsampleonthevariationinpolarizationresistancewere2.32and4.88%,respectively.Theregressionparam-etersfortheeffectofextractionsitewithinadonorsampleonthevariationinpolarizationimpedancewere345.96and0.01%,respectively.Thenullhypothesiswasrejectedforbotheffects.Thisimpliedthatvariationinpolarizationresist-anceofskinspecimensindivalentsolutionswaslarge.Furthermore,thevariationinpolarizationresistancewithinagivendonorwasatleastaslargeastheinter-individualvariation.7.4VarianceComponentsofCriticalFrequencyThevariancecomponentsofthelog10transformedskincriticalfrequencydataforsamplesimmersedinmonovalentanddivalentelectrolytesolutionsarepre-

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171 sentedinTable 7-7 .Thesample-to-samplecontributionstotheoverallvarianceinthetransformedcriticalfrequencydataforthemonovalentanddivalentdatasetswere24%and10%,respectively.Thewithin-samplevarianceprovidedthelargestcontributiontothetotalvarianceofskincriticalfrequency.Forexample,theintra-individualvarianceofthemonovalentanddivalentdatacomprised74%and89%ofthetotalvariance.Thevarianceintheresidualerrorsforbothelectrolytetypesprovidedlessthan3%ofthetotal.Theresultsindicatedthattheintra-individualvariabilityinthetransformedcriticalfrequencydatawasgreaterthantheinter-individualvariability. Table7-7:Calculatedcontributionstotheoverallvarianceinthelog10ofskincrit-icalfrequency Electrolyte 2Total 2Donor 2LocationDonor 2Residual Monovalent 0.400 0.124 0.388 1.22x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 Divalent 0.385 4.21x10)]TJ/F20 11.955 Tf 9.672 0 Td[(2 0.379 6.42x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3 Thestatisticalsignicanceofthecontributionstotheoverallvarianceinskincriticalfrequency,asdescribedbythevariancemodelofEquation 7-2 ,waseval-uated.TheparametersfortheanalysisofvarianceinskincriticalfrequencyforsamplesimmersedinmonovalentanddivalentelectrolytesolutionsarepresentedinTables 7-8 and 7-9 ,respectively.A5%signicancelevelwasselectedforthecomparisons.Thenullhypothesisfortheanalysisproposedthattherewasanin-signicanteffectofdonorsampleonthetotalvarianceofcriticalfrequencydatasetofskinimmersedinmonovalentelectrolyte. Table7-8:Calculatedcontributionstothetotalvarianceofthelog10ofskincriticalfrequencyforpiecesimmersedinmonovalentelectrolyte Variable DOF TypeIIISS MeanSq. F-stat Pr>F Donortype 16 66.23 4.14 2.91 0.0009 MSErrorDonor 79.10 112.33 1.42 LocationDonor 79 121.24 1.535 125.97 <0.0001 MSErrorLocationDonor 292 3.56 1.22x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 -

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172 Table7-9:Calculatedcontributionstothetotalvarianceofthelog10ofskincriticalfrequencyforpiecesimmersedindivalentelectrolyte Variable DOF TypeIIISS MeanSq. F-stat Pr>F Donortype 11 25.61 2.33 1.72 0.14 MSErrorDonor 19.98 27.00 1.351 LocationDonor 20 24.68 1.234 192.21 <0.0001 MSErrorLocationDonor 87 0.558 6.42x10)]TJ/F20 7.97 Tf 6.447 0 Td[(3 TheF-testparameterandprobabilityvaluesforacceptanceofthenullhypoth-esiswere2.91and0.09%,respectively.Similarly,theF-testparameterandprob-abilityvaluesforeffectoflocationfromwhichapieceofskinwasobtainedwere192.21andlessthan0.01%.Thenullhypothesisfortheeffectofdonorsampleonthecriticalfrequencyforskinimmersedinmonovalentelectrolytewasrejected,astherewasonlya0.09%chanceofselectingtwopiecesofskinfromdifferentdonorswithsimilarcriticalfrequencies.Alternativelystated,thevariationincriticalfre-quencyattributedtodifferencesinskinfromthedonorpopulationwassignicant.TheF-parameterandprobabilityvaluefortheeffectofdonorsampleofskinimmersedindivalentelectrolytewere1.72and14.0%,respectively.Therefore,thenullhypothesiscouldnotberejectedunconditionally.TheF-statisticandprobabil-ityvalueforthesite-to-sitevariationofcriticalfrequencywere192.21andlessthan0.01%,respectively;hence,thenullhypothesiswasrejected.Thisimpliedthevari-ationincriticalfrequencyofskinimmersedindivalentelectrolyteassociatedwithsite-to-sitedifferenceswasgreaterthanvariationcausedbysample-to-sampledif-ferences.Insummary,theanalysisofvariancestudyindicatedthattherewasasigni-cantvariationinthelog10polarizationimpedanceandcriticalfrequencyofskinforpiecesobtainedfromthesamedonorsampleandforpiecestakenfromdifferentdonors.Thevariationinpropertieswassimilarirrespectiveofthecationchargeintheelectrolyte.Inotherwords,theintra-individualvariationofskinproperties

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173 wasasgreatorgreaterthantheinter-individualvariation.Theresultsindicatedthatpiecesofskintakenfromthesamedonorcannotbeconsideredasidenticalspecimens.Furthermore,thevariabilityinthepropertiesofexcisedskinextractedfromdifferentdonorswasalsolargeenoughtorestrictdirectcomparisonofanytworandomlyselectedsamples.Thecharacteristicsofthevariationinskinprop-ertiesdescribedabovearecomparedwiththeliteratureinSection 7.7 .7.5EffectofElectrolyteonSkinPropertiesTheresultsdescribedinSections 5.2.2 , 6.2.2 and 6.3 indicatedthatthechargeofthecationintheionicsolutionsusedforanexperimentcaninuencetheimped-anceresponseoftheskin.Themeanvaluesandvariancesofthepolarizationresistanceandcriticalfrequencydatacorrespondingtoskinspecimensimmersedinmonovalentanddivalentsolutionswerecomparedtoassessthestatisticalsig-nicanceoftheeffectofelectrolytecompositiononskinimpedance.Thedatasetswereclassiedaccordingtoelectrolytetype.Student'st-testsandF-testswereappliedtoeachclassofmeasurements.Asthesetestsrequiretheobservationsettobenormallydistributed,thebase10logarithmictransformeddatasetswereselectedforanalysis.ThenullhypothesesfortheStudent'st-testandtheF-testwerethattherespec-tivemeansandvariancesofthemonovalentanddivalentdatasetswereequal.Acceptanceofthenullhypothesiswouldimplythattherewasnoeffectofcationchargeontheimpedanceresponseofskin.ThenullandalternativehypothesesfortheStudent'st-testandF-testarepresentedinTables 7-10 and 7-11 . Table7-10:Proposedhypothesesforcomparisonofmeans Variable Hypothesistype Equation Rporfc Null H0:1=2 Rporfc Alternative Ha:16=2

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174 Table7-11:Proposedhypothesesforcomparisonofvariance Variable Hypothesistype Equation Rporfc Null H0:12=22 Rporfc Ha:12>22 Thesubscript1correspondstoskintransportpropertiesinmonovalentelec-trolyteand,similarly,subscript2correspondstosimilarskinparametervaluesindivalentelectrolyte.Therewasnoapriorijusticationforassuminganequal-ityofvariances,thereforetheF-testwasappliedrst.TheinformationobtainedfromtheF-testguidedtheselectionofanappropriatet-testsinceitcanbeappliedundertheassumptionofequalorunequalvariances.TheinputparametersfortheF-testswerethedegreeoffreedomforeachclassofmeasurementsandtheF-statisticwhichisdenedbytheratioofvarianceindataset1tovarianceindataset2.TheF-testparametersforcomparisonofthetransformedpolarizationresist-anceandcriticalfrequencyvariancesarepresentedinTables 7-12 and 7-13 ,respec-tively.AsthecalculatedF-statisticwaslessthanthecriticalF-valueforthe95%signicancelevelinbothcasesthenullhypothesiscouldnotberejected.Therewasa31.8%chancethatthecalculatedF-statisticforthepolarizationresistancewaslessthanthecriticalF-valueandtherewasa7.32%chancethatthecriticalfrequencyF-statisticwaslessthanthecriticalF-value.AlthoughtheF-testssug-gestedthattherewasasmallpossibilitythatthevariancesinskinpropertiesforeachtypeofelectrolytewereequal,theStudent'st-testwasappliedassumingun-equalvariances.TheinputparametersfortheStudent'st-testweretheadjusteddegreeoffree-domandthet-statisticwhichisthedifferencebetweenthetwomeansdividedbytheweightedstandarddeviationoftheentiresamplepopulation.Theparametersforthet-testsofpolarizationresistancemeansandcriticalfrequencymeansfor

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175 Table7-12:F-teststatisticsforcomparisonofvariancesinthelog10ofpolarizationresistanceforeachelectrolytetype Statistic Monovalent Divalent Mean 4.46 4.73 SampleVariance 3.02x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 2.80x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 Observations 388 119 DegreesofFreedom 387 118 F-statistic 1.08 PrF
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176 Table7-14:Student'st-testoutputstatisticsforcomparisonofmeansinthelog10ofpolarizationresistanceforeachelectrolytetype Statistic Monovalent Divalent Mean 4.46 4.73 SampleVariance 3.02x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 2.80x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Observations 388 119 HypothesizedMeanDifference 0 DegreesofFreedom 202 t-valuetwo-tailed 4.84 Prt
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177 Figure7-3:Relationshipofcharacteristicskinimpedanceparameters,log10fcandlog10Rp. wherelog10fcandlog10Rpcorrespondtothelogarithmictransformationsofthecriticalfrequencyandthepolarizationresistanceofskin.ThePearson'scorrelationcoefcientfortheregressionwas-0.936whichindicatedthatadecreaseincriticalfrequencyisassociatedwithadecreaseinthepolarizationresistance.Thecorrelationbetweenlog10fcandlog10Rpmaysuggestthatasingletimeconstantcanbeusedtodescribetheentiresystem.Althoughthistypeofsimplerelationshipisattractive,caremustbetakenbeforeassigningasingleparametertodescribetheskinsystem.Forexample,thedepressedsemicircularimpedanceresponseofskinimpliesthatthereisadistributionofrelaxationprocessesinthesystem.Thishaspromptedtheapplicationofconstantphaseelementsformodel-ingskinimpedance.Amajorrestrictionofthistypeofdistributedmodelisthatthetimeconstantsforthesystemmustbesymmetricallydistributedaboutthecriticalfrequency.

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178 7.7ComparisonofVariationinSkinImpedancewithLiteratureResultsTheliteratureindicatesthatstratumcorneumproperties,suchasthicknessandlipidcomposition,displayconsiderablevariationwithlocationonthebodyinter-individualvariation. 13 , 14 , 16 , 17 , 253 andbetweenindividualsforagivenanatomi-calregioninter-individualvariation. 16 Thereisageneralconsensusthatdiffer-encesinthecompositionandstructureofstratumcorneumlipidsareresponsibleforvariationsinthepermeabilityandimpedanceinskin. 13 , 24 , 35 , 46 , 67 Despitethisconsensus,therelationshipbetweenthestateofstratumcorneumlipidsandthemacroscopictransportpropertiesofthemembranehasnotbeencompletelychar-acterized. 16 Statisticalanalysiswasappliedtoinvivoskindatatodeterminethattheinter-individualvariabilityofstratumcorneumlipidcomponentswassignicantlylargerthantheintra-individualvariability. 16 Theregionalvariationinskinimpedancewasalsofoundtobesignicant;however,thevariationbetweenindividualswasnotassessed.Intheworkdescribedinthischapter,thenestedformoftheGen-eralizedLinearModel 249 wasappliedtoevaluatesimilarsourcesofvariationinimpedancedatafromthehydrationofheat-separatedcadaverskin.Theresultsindicatedthattheintra-individualvariabilityinskinimpedancewasgreaterthantheperson-to-personvariability.Thelargevariabilityinskinimpedancecouldhavesignicantimpactonthedesignandplacementoftransdermaliontophoresisdevicesifsimilarresultsarefoundforinvivohumanskin.Forexample,lowskinimpedancehasbeenassoci-atedwithrelativelyhighmembranepermeability. 112 , 131 , 163 Identicationoftheselowimpedancesitescouldguidetheplacementoftransdermaldeliverydevicesonthebody.Thistypeofplacementstrategyhasotheradvantages.Itwasdemon-stratedearlierinthistextsee,forexample,Section 5.2 thatlargepotentialdif-

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179 ferencescanalterskinproperties.Topicalirritationduringclinicaltransdermaliontophoresisstudieshasbeenassociatedwithhighimpedanceskin. 254 Therefore,placementoftheiontophoretictransdermalpatchoverlowimpedanceskinmaypreventpatientdiscomfort.Statisticalanalysistechniques,suchasStudent'st-testsandF-tests,wereim-plementedinthisworktoidentifytheinuenceofelectrolytecationchargeontheimpedanceofheat-separatedcadaverskin.Theevaluationsrevealedthattheimpedanceresponseofskininmonovalentcationsolutionswasdifferentfromtheresponseindivalentcationelectrolyte.Theresultthatcationtypeinuencesskinimpedanceisinagreement 152 andinconict 207 withreportedndings.Theinconsistentliteratureresultswereobtainedbythesameresearchgroupusingasimilarmethodology.Forexample,electriccircuitmodelswereregressedtotheimpedancespectratoobtainrepresentativequantitiesforskinresistanceandca-pacitance.Theeffectofcationtypeontherecoveryofskintoiontophoresiswasassessedusingcircuitparameters.Despitethesimilaroftheexperimentalapproach,importantdifferenceswerepresentinthetwoinvestigations.Forexample,adifferentcircuitnetworkwasregressedtoeachsetofskinimpedancedata.Thestandarddeviationsofthere-gressedcircuitelementswereapproximately10-20%oftheparametervalues.Inaddition,thenumberofskinsamplesprobedinthestudieswere2and5,respec-tively.Thereisastrongpossibilitythattherelativelylargeuncertaintyinthecir-cuitparameterscoupledwiththesmallsamplesizesledtoerroneousconclusionsfortheeffectofcationtypeonskinimpedance.Theworkpresentedinthischap-terwasmuchlesssusceptibletothesetypeoferrorsbecausethenumberofskinsamplesinvestigatedwasatanorderofmagnitudelarger.Thelargersamplesizewouldimprovethecondenceofthestatisticalofregressions.

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CHAPTER8POTENTIALANDCURRENTSTEP-CHANGESTUDIESTheinuenceofalternatingcurrentandpotentialonthepropertiesofskinwasdemonstratedinChapters 5 and 6 .Theresultsindicatedthatskinpropertiesbegintochangeatacriticalpotential.Themajorityoftheimpedancestudieswerecon-ductedwithazeroDCcurrentbias,i.e.,attheopen-circuitcondition.Undersuchconditionstheskinwasallowedtopartiallydepolarizeduringeachcompleteper-turbationcycleoftheimpedancescan.Sinceanonzerocurrentbiasisapplieddur-ingtransdermaliontophoresistoenhancedrugdeliveryrates,itislikelythattheskinwillbecomepolarized.Theinuenceofanonzerocurrentbiasonskinprop-ertieswasinvestigatedbyimpedancespectroscopysee,forexampleSection 6.5 ,however,thecurrentwasonlyappliedforapproximatelyveminutes.Transdermaliontophoreticdeliveryratesaretypicallysmall; 133 , 255 therefore,protocolsforcommercialiontophoreticdeviceswilllikelyrequirecurrenttobeappliedformuchlongerperiodsoftime.Thepurposeofthisworkwastodeter-minetheresponseofskintoelevatedDCcurrentandpotentialsignals.ThemajordifferenceofthisstudyfromthepreviousworkdescribedinthistextisthattheDCbiassignalswereappliedforlongertimeintervals.Thegeneralapproachwastoperturbtheskinfromtheopen-circuitconditionwithastep-changeinDCcur-rentorpotential.Thesystemresponsewasmonitoredattheelevatedconditionforaminimumof20minutes.Theskinwasthenallowedtorelaxattheopen-circuitcondition.Theresultsforthepotentialandcurrentstep-changestudiesarepresentedinSections 8.1 and 8.2 ,respectively. 180

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181 8.1PotentialStep-ChangeResultsTheexperimentaldatapresentedherewereobtainedaccordingtothemethod-ologydescribedinSection 4.2 .Impedancespectrawerenotcollectedforthesestudies.Electricalproperties,suchasthepolarizationimpedance,wereestimatedbyregressingalinearmodeltothecurrent-potentialdatacollectedatpotentialsbetween10and100mV.Itwasassumedthatskinpropertieswerenotalteredattheserelativelylowperturbationamplitudes.MicrosoftExcelcwasusedfortheregressionswherecurrentwasselectedastheindependentvariableandpotentialasthedependentvariable.AtofthelinearmodeltothedatayieldedestimatesfortheDCelectricalpropertiesofskin.Forexample,theslopeofthelinearmodelrepresentsthepolarizationresistanceandtheinterceptistheopen-circuitpoten-tial.Condenceinthelinearmodelwasprovidedbyther2correlationparameterforeachregression.8.1.1ModelPredictionsofSkinPolarizationResistanceThelinearmodelwasregressedtothelow-amplitudepotentialbiasdataforallfoursetsofexperiments.Asampleplotofthecurrent-potentialdatawiththeregressionlineisprovidedbyFigure 8-1 .Thepolarizationresistance,open-circuitpotentialandr2coefcientsforthefoursetsofexperimentsarepresentedinTable 8-1 .Thelinearmodelprovidedexcellenttstothedatasets,asther2coefcientswereallgreaterthan0.997.Theestimatedvaluesofthepolarizationimpedancerangedfrom14.6kWcm2to25.1kWcm2.Theopen-circuitpotentialsobtainedfromthetswerebetween12.7mVand25.3mV.Thepolarizationimpedanceandopen-circuitpotentialvaluesfromtheregressionswerecomparabletothemea-surementsobtainedinimpedancespectroscopystudies.

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182 Figure8-1:Sampleregressionoflinearmodeltopotentialstep-changedatatopredictskinproperties. Table8-1:Regressionparametersforestimationofskinproperties Sample Rpol,Wcm2, VOC,mV r2 NaClI 25182 12.7 0.9972NaClII 14623 22.7 0.9999CaCl2I 21328 19.7 0.9992CaCl2II 21239 25.3 0.9997 8.1.2CalculatedDeviationFromConstantPropertiesThepolarizationresistanceofasystemwithconstantelectrochemicalproper-tiesshouldbeindependentoftheappliedcurrentorpotential.Ideally,iontophor-eticdevicesshouldnotalterthepropertiesofskin.Anacceptablealternativere-quiresthatelectricallyinducedchangesbereversiblewithinalimitedtimeframe.Thegoalofthisanalysiswastodeterminethedeviationofthemeasuredcurrentresponseincomparisontoasystemwithconstantproperties.Forexample,skinwithapotentialindependentpolarizationresistanceshouldexhibitaproportionalincreaseinmeasuredcurrentforagivenincreaseofpotential.Thepolarizationresistanceistheconstantofproportionalitythatrelatesthecurrentdensitytotheelectrostaticpotential.

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183 Thedeviationfromconstantpropertieswasassessedbycomparingthemea-suredcurrenttotheresponseexpectedfromskinwithapotentialindependentpolarizationresistance.Theapproachherewastopredictthecurrentresponsetopotentialstep-changesgreaterthan100mVfromthepolarizationresistancecalcu-latedbytheregressionproceduredescribedinSection 8.1 .ThepredictedcurrentforskinwithconstantpropertieswascalculatedaccordingtoIpredict;linear=Vapplied)]TJ/F20 11.955 Tf 11.996 0 Td[(VOC Rpol-1whereVappliedistheappliedpotentialinvolts,VOCistheopen-circuitpotentialinvoltsandRpolisthepolarizationresistanceinunitsofohm-squarecentimeters.Thedifferencebetweenthepredictedcurrentandthemeasuredcurrentwascal-culatedforallofthestep-changestudies.Thisdifferenceprovidedameasureofthedeparturefromalinearresponseinskinpropertiesinducedbythepotentialstep-change.Theaveragedifferenceincurrentoverthepotentialbiasintervalwasalsocalculated.Thestandarddeviationofthedifferenceprovidedameasureofthenonlinearandnonstationaryconditionofthecurrentresponse.Thedeviationinthemeasuredcurrentresponsefromskinwithaconstantpo-larizationresistanceispresentedasafunctionoftimeandpotentialinFigure 8-2 .Thedeviationincurrentisplottedontheleftordinateandtheappliedpotentialisplottedontherightordinate.Forpotentialstep-changeslowerthan250mV,theobserveddeviationinthemeasuredcurrentresponsewasgenerallylessthan100nA/cm2.Astheappliedpotentialwasincreasedto250mV,thedeviationsinthecurrentresponseincreasedtoapproximately1A/cm2.Forthe500mVex-perimentsthecurrentdeviationwas,ingeneral,smallestimmediatelyafterthestep-changewasappliedandincreasedcontinuouslyforapproximately10min-utes.Fortheremainderofthe500mVbiasintervalthedeviationincurrentrangedfrom2-6A/cm2.Atthe500mVbiaslevelthedeviationsincurrentresponsefrom

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184 skinwithconstantpropertiesweregenerallygreaterformembranesimmersedinNaClsolutionthanthesamplesinCaCl2solution. Figure8-2:Deviationinthemeasuredcurrentfromthecurrentassociatedwithpotentialindependentpolarizationresistanceskin. Thelargestdeviationsinmeasuredcurrentwereobservedforthe1Vstep-changes.Forexample,thedeviationsinthecurrentresponserangedbetween5A/cm2and55A/cm2.Duringthe1VbiasintervalsthedeviationsincurrentincreasedcontinuouslywiththeexceptionofthesecondbiasintervaloftherstskinsampleimmersedinNaClsolution.Similartothe500mVbiasresults,themagnitudeofthecurrentdeviationswere,ingeneral,largerforskinsamplesim-mersedinNaClsolutionthanthoseinCaCl2solution.Theresultsindicatedthatthereisacriticalpotentialbetween100mVand250mVwherethepropertiesofskinbegintochange.Therangeofpotentialatwhichskinpropertiesbecomealteredwasconsistentwiththeimpedancespectroscopystudies.Asthemagnitudeofthepotentialstep-changewasincreasedabovethisrangethemeasuredcurrentresponsewashigherthanexpectedforskinwithaconstantpolarizationresistance.Forappliedbiasamplitudesabovethecritical

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185 potential,themagnitudeofthedeviationincurrentincreasednonlinearlywithincreasingvaluesofpotentialbias.Ingeneral,therelativedeviationinmeasuredcurrentresponsefromaconstantpropertysystemwasgreaterforskinimmersedinNaClelectrolytethaninCaCl2electrolyte.ThelargerdeviationsobservedforthemonovalentelectrolytesolutionswasalsoconsistentwiththeelectrochemicalimpedancespectroscopystudiespresentedinSections 5.2.2 , 6.2.2 and 6.3 .8.2CurrentStep-ChangeResultsTheelectrochemicalimpedancestudiesandthepotentialstep-changeexperi-mentsdescribedinSections 5.2 and 8.1 ,respectively,indicatedthatskinpropertiesbecomealteredaboveacriticalpotential.Theobjectiveofthisstudywastodeter-minewhetherskinpropertieschangeaboveacriticalcurrent.Theapproachherewastosubjectskintoaseriesofstep-changesincurrentandmonitorthepotentialresponse.Theamplitudesofthecurrentstepsignalswere1.4A/cm2,14A/cm2and140A/cm2.Ingeneral,thecurrentstep-changewasheldattheelevatedcon-ditionfor40minutes.TheexperimentalprotocolofthestudiespresentedherewasanalogoustothemethodologydescribedinSection 8.1 .However,inthiscase,acurrentstep-changewasappliedacrosstheskinandthepotentialresponsewasmeasured.Twopiecesofskinwereextractedfromthesamedonorsampleandsubjectedtothesameseriesofcurrentstep-changes.Theamplitudeandsequenceoftheapplied-currentsignalswereidentical.Theskinspecimenswereimmersedinbuffered150mMNaClelectrolyte.Aseriesoffour10mVVAGimpedancespectrawerecollectedattheopen-circuitconditioni.e.,iDC;applied=0,beforeandaftertheappliedDCcurrentsteps.Thespectraprovidedinformationontherecoveryofskinpropertiestotheelevatedcurrentsignals.Theresultsfromthestudieswith

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186 rstskinsamplearedescribedindetailinSections 8.2.1 and 8.2.2 .AcomparisonoftheresponsesforbothpiecesofskinisprovidedinSection 8.2.3 .8.2.1MeasuredPotentialDifferenceAcrosstheSkinThepotentialdifferenceacrosstherstpieceofskinforeachapplied-currentamplitudeispresentedasafunctionoftimeinFigure 8-3 .ThedatacorrespondingtoIntervals1-8representthepotentialmeasurementscollectedwhilethecurrentstep-changeswereapplied.Thesolidgreendiamondsandopenblackdiamondscorrespondtotheopen-circuitpotentialsmeasuredbeforeandaftertheimpedancespectrawerecollected. Figure8-3:Potentialdifferenceacrossepidermis.Theamplitudesofthecurrentstepchangescausingthevoltagedropsareindicatedinthelegend.Thesolidgreendiamondsandopenblackdiamondscorrespondtotheopen-circuitpoten-tialmeasurementscollectedbeforeandaftertheimpedancescans. Priortotheapplicationoftherst1.4A/cm2currentstep-changetheopen-circuitpotentialdifferenceacrosstheskinwasontheorderof5mV.Immediatelyafterthe1.4A/cm2currentwasterminatedthepotentialdifferenceacrossthemembranewas51mV.Whilea1.4A/cm2currentsignalwasappliedduring

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187 Intervals2and3thepotentialdifferenceacrosstheskingraduallyincreasedto86mV.Theincreaseinthepotentialdifferencewasconsistentwithanincreaseinthepolarizationresistanceofskin.Theopen-circuitpotentialmeasurementscollectedaftertheappliedcurrentwasterminatedwereapproximately5mV.Theopen-circuitpotentialdecreasedwithtimeduringalloftherecoveryperiodsfol-lowingthecurrentstep-changes.Therelaxationofopen-circuitpotentialsug-gestedthattheskinhadbecomeslightlychargedwhilethestep-changewasap-plied.Intervals4and5correspondtothevoltageresponsestothe14A/cm2per-turbations.Themembranepotentialdifferencewas627mVimmediatelyafterthecurrentstep-changewasapplied.Thepotentialdifferenceacrossthemembranedecreasedcontinuouslywhilethecurrentwasapplied.Thepotentialdropattheendofstep-changeInterval4was569mV.Agradualdecreaseinthepotentialdif-ferenceacrosstheskinwasalsoobservedduringInterval5.Forexample,thevolt-agedifferenceacrosstheepidermiswas638mVimmediatelyafterthe14A/cm2signalwasappliedand567mVjustbeforethecurrentwasterminated.Thegrad-ualdecreaseinthepotentialdifferenceacrossskinindicatedthatthemembranepolarizationresistancehaddecreased.Theresultswereconsistentwiththehy-pothesisthatskinpropertiesbegintochangeasthepotentialdifferenceacrossthemembraneexceeds250mV.Theopen-circuitpotentialsmeasuredimmediatelyafterthe14A/cm2cur-rentwasterminatedwereontheorderof20mV.Duringagivenrecoveryperiod,theopen-circuitpotentialdecreasedovertime.Thedecayintheopen-circuitpo-tentialresponsesuggestedthatthestateand/ordistributionofchargewithintheskinchangedduringtheapplicationofthe14A/cm2currentsignal.Forexam-ple,itispossiblethatthepassageofcurrentmodiedtheinternalstructureof

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188 theepidermistoprovidegreateraccessforthecationsandneutralizethenegativebackgroundchargeofskin.Thistypeofprocesscouldhavetheeffectofreducingtheopen-circuitpotential.Intervals6and7correspondtothepotentialdropsacrosstheskininducedbythe140A/cm2step-changes.Similartothe14A/cm2results,themembranepotentialdifferencealsodeclinedcontinuouslywhilethecurrentwasapplied.Forexample,thepotentialdifferencedecreasedfrom2.62Vto1.60VduringInter-val6.Similarly,thevoltagedropacrosstheskindecreasedfrom2.11Vto1.55VduringInterval7.Theopen-circuitpotentialswerealsoapproximately20mVafterthe140A/cm2step-changesignals.Theopen-circuitpotentialdecreasedforeachsubsequentmeasurementcollectedafterelevatedcurrentsignalhadbeenterminated.Theamplitudeofthenalcurrentstep-change,representedbyInterval8,was1.4mA/cm2.Thepotentialdifferencedecreasedfrom5.18Vto4.07Vwhilethecurrentwasheldattheelevatedcondition.Thepotentialdifferenceinducedbythelargeststep-changewassignicantlylargerthehypothesizedvoltagethresh-oldforonsetofchangesinskinproperties.Ingeneral,thereductioninpotentialdifferencewithtimeforallcurrentstep-changesabove1.4A/cm2stronglysug-gestedthatthepolarizationresistanceofskinhaddecreased.Theprocedureusedtocalculatethepolarizationresistanceisdescribedinthenextsection.8.2.2CalculatedPolarizationResistanceSkinpolarizationresistancewascalculatedaccordingtoOhm'slawbydivid-ingthemeasuredpotentialdifferencebytheappliedcurrent.Thepolarizationresistanceshouldbeindependentofcurrentandtimeforasystemwithconstantproperties.ThecalculatedpolarizationresistanceofskinisillustratedinFig-ure 8-4 .ThedataindicatedbyIntervals1-8correspondtotheskinresistance

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189 atthedifferentcurrentstep-changeamplitudes.ThesoliddiamondsrepresenttheKramers-Kronigconsistentpolarizationresistancescalculatedfromtheimped-ancespectra. Figure8-4:Calculatedpolarizationresistanceofskin.Thecurrentstep-changeamplitudesareindicatedbythelegend. Thepolarizationresistancecorrespondingtotherstimpedancescancollectedbeforethestartofthe1.4A/cm2step-changewas43.5kWcm2.Subsequentmea-surementscollectedattheopen-circuitconditionwereapproximately43kWcm2.Thecalculatedpolarizationresistanceduringtherst1.4A/cm2step-changein-creasedfrom43.9kWcm2to50.3kWcm2.DuringInterval2,wheretheappliedcurrentwasalso1.4A/cm2,theskinresistanceincreasedfrom44.1kWcm2to49.3kWcm2.Theestimatedpolarizationresistancesfromthefourimpedancespec-tracollectedafterInterval2wereallapproximately49kWcm2.Theskinresistancealsoincreasedoverthecourseofthenal1.4A/cm2step-changeInterval3.Immediatelyafterthe1.4A/cm2signalwasappliedtheskinresistancewas45.6kWcm2.AttheendofInterval3theresistanceincreasedto

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190 52.8kWcm2.TheimpedancespectracollectedafterInterval3indicatedthatthepolarizationresistancewasapproximately51kWcm2.TheentirespectrumforeachofthefourreplicatescollectedwasconsistentwiththeKramers-Kronigrelations.Asthemagnitudeofthestep-changewasincreasedto14A/cm2forIntervals4and5,thetime-dependenttrendofthepolarizationresistancereversed.Forex-ample,theskinresistancedecreasedcontinuouslyfrom43.7kWcm2to39.6kWcm2duringInterval4.Similarly,thecalculatedpolarizationresistancewas44.5kWcm2asthe14A/cm2step-changewasappliedatthestartofInterval5and39.5kWcm2justbeforetheappliedcurrentwasstopped.Adramaticreductionintheskinresistancewasobservedwhenthe140A/cm2currentwasappliedduringIntervals6and7.AtthestartofInterval6,thepolar-izationresistancewas18.4kWcm2.Thiscorrespondedtoa61%reductioninthepolarizationresistanceincomparisontotheresistancecalculatedfromthenalimpedancespectracollectedafterInterval5.OverthecourseofInterval5theskinresistancedecreasedcontinuouslytoanalvalueof11.2kWcm2justbeforethecurrentwasstopped.Theskinrecoveredpartiallywhiletheimpedancespectrawerecollectedinbe-tweenIntervals6and7.Forexample,theKramers-Kronigconsistentpolarizationresistanceincreasedfrom21.4kWcm2to28.6kWcm2whiletheskinwasallowedtorelaxattheopen-circuitcondition.AtthestartofInterval7theskinresistancedroppedto14.8kWcm2.Thiscorrespondedtoa48%decreasetheskinresistanceincomparisontotheopen-circuitcondition.Thenalskinresistancemeasurementfromthe140A/cm2currentsignalwas10.9kWcm2.Theskinresistanceestimatesfromtheimpedancespectracollectedattheopen-circuitconditionafterInterval7indicatedapartialrecoveryofmembraneprop-erties.Forexample,theresistancejustafterthe140A/cm2currentbiaswaster-

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191 minatedwas17.8kWcm2.Theresistanceestimatedfromthelastimpedancescanmeasuredattheopen-circuitconditionwas23.2kWcm2.Asthe1.4mA/cm2step-changewasappliedduringInterval8,thepolarizationresistancedroppedto3.6kWcm2.Whiletheskinwasheldattheelevatedcurrenttheresistancecontinuedtodecreaseto2.8kWcm2.Theresultsindicatedthatthepolarizationresistancewasanorderofmagnitudelowerthantheresistancemea-suredintheabsenceofcurrent.Thecalculatedpolarizationresistancedatademonstratedthatskinbehavesnonlinearlyinresponsetocurrentstep-changes.Thecharacteroftheresponseisrelatedtothemagnitudeoftheappliedcurrent.Forexample,theskinresist-anceincreasedwhilethe1.4A/cm2step-changeswereapplied.Thepotentialdifferenceacrosstheskinatthiscurrentwasalwayslessthan90mV.Thispoten-tialdifferencewaslessthantheproposedthresholdfortheonsetofchangestoskinproperties.Theskinresistancedecreasedwithtimeforstep-changeslargerthan1.4A/cm2.Themagnitudeandrelativedegreeofthechangeinresistancewasproportionaltotheappliedcurrent.Thepotentialdropacrosstheskininducedbytheappliedcurrentatamplitudesgreaterthan1.4A/cm2wasatleast0.55V.Thismagni-tudeofpotentialdifferencewasabovetheproposedthresholdforthealterationofskinproperties.Simplystated,thedeparturefromthelinearresponsewaspro-portionaltotheamplitudeofthecurrentstep-change.Wherelargechangestoskinpropertieswereobserved,thepotentialdifferenceacrosstheskinwasgreaterthan250mV.8.2.3ComparisonofResponsesforSkinSamples1and2.TheresponseofSkinSamples1and2tothe14A/cm2and140A/cm2cur-rentstep-changeswerecompared.Theobjectivewastodeterminewhetherthe

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192 amplitudeoftheappliedcurrentwasadeterminantfortheonsetofskinpropertychanges.Itshouldbenotedthattheskinspecimensweresubjectedto1.4A/cm2step-changespriortothecollectionofthedatapresentedhere.Theresponsesofbothpiecesofskintothe1.4A/cm2signalsremainedconstantwhilecurrentwasapplied.Theimpedancespectracollectedafterthe1.4A/cm2currentstepwereconsistentwiththeKramers-Kronigrelationswhichimpliedthatskinpropertieshadnotbeenaltered.Themeasuredpotentialdifferencesacrossbothskinsamplesduringtheappli-cationoftherst14A/cm2step-changesareshowninFigure 8.5a .ThesolidredlineanddashedbluelinecorrespondtothepotentialdifferencesacrossSkinSamples1and2,respectively.ThepotentialresponsesofSample1decayedinapseudoexponentialmanner,whereasthepotentialremainedessentiallyconstantforSkinSample2.ThemagnitudeofthepotentialdifferenceacrossSkinSample2waslessthan100mVoverthecourseoftheentirestep-change.Incontrast,po-tentialdifferenceacrossSkinSample1measuredduringtheapplicationofcurrentwasgreaterthan500mV.Theeffectofthecurrentstep-changesoneachpieceofskinwasassessedbyexaminingthetimedependenceofthepolarizationresistance.Thecalculatedpo-larizationresistanceforeachpieceofskinduringthe14A/cm2step-changesarepresentedinFigure 8.5b .Thesolidtrianglesandsoliddiamondscorrespondtotheresistancescalculatedfromtheimpedancespectra.Asstatedearlier,thespec-tracollectedpriortotheapplicationofcurrentwereconsistentwiththeKramers-Kronigrelations.ThepolarizationresistanceofSkinSample1estimatedfromtheimpedancespectrumcollectedpriortotheapplicationofcurrentwas49.9kWcm2.Immedi-atelyafterthestep-changewasappliedtheresistancedroppedto43.7kWcm2and

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193 decreasedexponentiallywhilecurrentamplitudewasheldat14A/cm2.There-ductioninskinresistanceindicatedthattheepidermishadbeenaltered.Theseresultsareconsistentwiththehypothesisthatskinpropertiesbegintochangeasthemembranepotentialdifferenceexceedsapproximately250mV.TheresistanceofSample2remainedconstantatapproximately2.9kWcm2throughouttheentirestep-changeInterval.Theskinresistancecalculatedfromtheimpedancespectracollectedpriortothecurrentstep-changewasalsoequalto2.9kWcm2.TheconstantresistanceobservedforSkinSample2impliedthatthe14A/cm2currenthadnotalteredthemacroscopictransportpropertiesofthemembrane.ThemembranepotentialdifferenceofSkinSamples1and2inresponsetothe140A/cm2step-changesispresentedbyFigure 8.6a .Similartothe14A/cm2results,thepotentialresponseofSkinSample1decreasedexponentiallywithtime.Althoughnotvisibleatthisscale,thepotentialacrossSkinSample2alsodecayedwithtime.Themagnitudeofthemembranepotentialdifferencewasapproxi-mately300mV.ThevariationofresistancewithtimesuggestedthatthepropertiesofSkinSample2hadbeenaltered.Theinuenceoftheappliedcurrentonthepolarizationresistanceisshownin 8.6b .TheresistanceofSkinSample1droppedfrom46.7kWcm2to18.4kWcm2asthe140A/cm2step-changewasapplied.Theresistancecontinuedtodecreasewhiletheskinwassubjectedtothecurrent.Althoughnotvisibleatthisscale,theresistanceofSkinSample2alsodecayedwithtime.Theresistancechangesinbothsamplesoccurredwhilethepotentialdifferenceacrossthemembranewasgreaterthan250mV.Thelow-frequencyportionsofimpedancespectracollectedafterthe140A/cm2step-changeswerenotconsistentwiththeKramers-Kronigrelations.Theincon-

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194 sistentimpedancedataindicatedthatskinpropertieshadbeenchanged.Thecom-binationoftheimpedanceandstep-changeresultswereconsistentwiththepro-posed250mVthresholdforpotentialinducedpropertychanges.Insummary,thepropertiesofheat-separatedskincouldbealteredbytheapplicationofcurrent.However,changeswerenotobserveduntilthepotentialacrosstheskinexceeded250mV.

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195 a bFigure8-5:Responseofskinsamplesto14/cm2step-change.Thesolidredlineanddashedbluelinerepresenttheresponsesfortherstandsecondpieceofskin.aPotentialdifferenceacrossepidermis.bCalculatedpolarizationresistanceofskin.

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196 a bFigure8-6:Responseofskinsamplestoa140/cm2step-change.Thesolidredlineanddashedbluelinerepresenttheresponsesfortherstandsecondpieceofskin.aPotentialdifferenceacrossepidermis.bCalculatedpolarizationresist-anceofskin.

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CHAPTER9TRANSDERMALLIDOCAINEFLUXMEASUREMENTSPriortotheinvestigationoftransdermallidocainedeliveryratesunderapplied-currentconditions,thestabilityofthedual-beamUV-visabsorptionspectroscopysystemwascharacterized.Therstpartofthestudyidentiedthedriftinslaveandmasterchannelsofthedual-beamspectroscopysystemforamoredetaileddescriptionoftheexperimentalapparatus,pleaserefertoSection 4.4.1 .Thetimedependentbehaviorofthespectrometerswasdeterminedandastrategywasde-velopedtoaccountforthenaturaldriftoftheUV-visapparatusinthelightab-sorbancecalculations.Oncethetemporalcharacteristicsofthemeasurementsys-temwereidentied,acalibrationcurvewasdevelopedtorelatelidocainecon-centrationwiththeabsorbanceresponse.Absorbancespectrafromaseriesofli-docainesolutionswithconcentrationsintherangeof0Mto1.8mMwerecol-lected.Linearregressionswereperformedontheabsorbancedataatselectedwavelengthstoobtainafamilyoflidocaineextinctioncoefcients.TherangeofconcentrationsforwhichtheabsorbanceresponseobeyedBeer-Lamberttheorywasdeterminedforadditionaldiscussion,pleaserefertoSection 4.4 .9.1SpectroscopySystemStabilityAseriesof51spectrawerecollectedatthreeminuteintervalsover2.4hourstoidentifythestabilityoftheUV-vislightsourceandthe2spectrometerchannels.Forthestudy,the2outputbersofthe100mbifurcatedcablewereconnectedtotheinletreferenceandreceptorportsoftheopticallycoupledspectroscopycell.A200mberopticcablewasconnectedfromthelight-pathoutletsoftheoptically 197

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198 coupledspectroscopycelltotheentranceportsofthespectrometer.Themasterandslavechannelsmeasuredthelightintensitythroughthereferenceandrecep-torcompartments,respectively.AschematicoftheexperimentalcongurationisprovidedbyFigure 4-5 .Theintegrationtimerequiredforcollectionofthespectrawas300ms.Atthebeginningoftheexperimentthreespectrawerecollectedwiththelightsourceblockedtodeterminethebaselineresponseofthespectrometers.Theav-erageintensityofthedarkspectrawassubtractedfromthemeasuredintensityoftheremainingspectratocalculatedthelightthroughputateachwavelength.Forexample,thedark-correctedintensitywascalculatedaccordingtoIi=Ii)]TJET1 0 0 1 105.057 -179.138 cmq[]0 d0 J0.478 w0 0.239 m4.029 0.239 lSQ1 0 0 1 0 -9.779 cmBT/F20 11.955 Tf 0 0 Td[(Ii;dark-1whereIiand Ii;darkarethemeasuredintensityandtheaverageintensitywiththelightsourceblockedateachwavelength.Meanvaluesoftheadjustedintensitywerecalculatedasafunctionofwave-lengthfromthe51spectracollectedwitheachspectrometer.TheaverageadjustedintensitiesfortheslavechannelandmasterchannelarepresentedbythelledtrianglesandlledcirclesinFigure 9-1 .Theaverageintensityforbothchannelswasnegligibleatwavelengthsbelow180nm.Thesignalresponseincreasedfromapproximately250intensityunitsto3800intensityunitsforwavelengthsrangingfrom215nmto255nm.Theintensityofbothspectrometerchannelsgraduallydecreasedto1000intensityunitsforwavelengthsbetween255nmand475nm.Theintensityofthespectrafrombothspectrometersdisplayedsimilarshapeandmagnitudeovertherangeofwavelengthsstudied.Theconsistencybetweenthetwosignalssuggestedthatoneofspectrometerchannelscouldserveasareferenceforsystemdrift.

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199 Themeasureofsystemdriftwascalculatedbythepercentrelativestandarddeviation.TheexpressionappliedheretoquantifysignaldriftwasdenedbyRelativeStandardDeviation=Ii Iix100%-2whereIiandIiarethestandarddeviationandmeanvalueoftheadjustedintensityateachwavelength,respectively.Therelativestandarddeviationsofthedark-correctedintensitiesforbothspectrometers,shownbyemptysymbolsinFigure 9-1 ,werealsocorrelated. Figure9-1:Meanvaluesforthedark-correctedtransmissionintensityspectracol-lectedover2.4hours. Thelargestrelativestandarddeviationswereobservedbetween180and195nm.Themaximumrelativestandarddeviationofthespectracollectedonthemasterchannelwasequalto16%ofthesignalamplitude.Themaximumwasob-servedat180nmwhichcorrespondedtotheshortestwavelengthofthespectrum.Thenormalizedstandarddeviationofthemasterspectrometerdecreasedrapidlybetween180nmand200nmtolessthan3%ofthedark-correctedintensity.Therelativestandarddeviationofslavespectrometerwaslessthan3%overtheentire

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200 rangeofwavelengths.Thelowerrelativestandarddeviationsassociatedwiththeslavespectrometerindicatedthatthischannelwasmorestablethanthemasterchannel.Althoughthestabilityoftheslavespectrometerwasgreaterthanthemasterspectrometer,theerroranalysisindicatedthatbothlightsignalsthroughthespec-troscopysystemwere,toagoodapproximation,stationaryoverthe2.4hourcol-lectioninterval.Sincethemagnitudeandstandarddeviationofbothspectrome-terswerecorrelated,theratioofslavespectrometerandmasterspectrometerin-tensitieswasusedtoassessreductioninsignalintensityduringthetransdermaliontophoresisexperiments.Theapproachwastomonitorthereceptorchamberofthediffusioncellwiththeslavespectrometer.ThemasterspectrometermeasuredthesignalresponseofUV-vislightthroughacuvetteofdeionizedwater.Duringatypicaltransdermaliontophoresisstudylidocaineistransportedfromthedonorchamberintothereceptorcompartmentoftheopticallycoupledspec-troscopycell.Aslidocaineaccumulatesinthereceptorcompartment,theintensityoftheslavechannelwilldecreaseinresponsetotheadditionofthechromophore.Incontrast,deionizedwaterdoesnotabsorblightintheUV-visportionoftheelectromagneticspectrum.Therefore,changesinsignalintensitymeasuredbythemasterspectrometerwerecausedbyrandomuctuationsorbyashiftinthebase-lineresponseofthischannel.Theratioofthetwosignalsactedasalterforthenonstationarycomponentofthemeasurement.Theratiosofthedark-correctedintensitysignalsfromeachspectrometerwerecalculatedforallofthespectracollectedinthestudy.Therelativestandarddevi-ationandmeanvaluesfromtheadjustedintensityarepresentedasafunctionofwavelengthinFigure 9-2 .Thestandarddeviationoftheintensityratioexhibitedamaximumvalueofat180nmwhichcorrespondedto10%ofthesignalmagnitude.

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201 Therelativestandarddeviationdecreasedsharplyandcontinuouslybetween180nmand200nmto3%oftheintensityratio.Forwavelengthslongerthan210nm,therelativestandarddeviationsoftheintensityratiowerelessthan1%ofthesig-nal.Ingeneral,thestandarddeviationsoftheintensityratiowerebetweenthedeviationsoftheslaveandmasterspectrometersshowninFigure 9-1 .Theresultwasnotsurprisingsincethestabilityoftheintensityratioshouldbeweightedbytheerrorcontributionsfromeachchannel. Figure9-2:Ratioofslaveandmasterspectrometertransmissionintensities. Theerroranalysisdescribedabovedemonstratedthattheratioofthelightintensitysignalscollectedfromeachspectrometercouldaccountforthenaturalevolutionofthemeasurementsystem.Therefore,theintensityratiowasusedtocalculatethelidocaineextinctioncoefcientsandtodeterminethedeliveryratesoflidocainebytransdermaliontophoresis.9.2LidocaineCalibrationStudy.Theresultsfromthecalibrationexperimentsforrelatinglidocaineconcentra-tiontothesignalintensitiesoftheabsorbancespectrometersarepresentedhere.

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202 LidocaineextinctioncoefcientswerecalculatedaccordingtoBeer-Lambertthe-ory. 243 Accordingtothetheory,theextinctioncoefcientisalinearproportional-ityconstantwhichrelateschromophoricconcentrationtolightabsorbancemagni-tudeforamorecompletediscussionofthesubject,pleaserefertoSection 4.4 .Inpractice,theabsorbanceresponseislinearoveralimitedrangeofchromophoricconcentrations.Thelinearresponserangeforthissystemwasdeterminedexperi-mentallybycollectingspectrafromaseriesofsolutionswithknownlidocainecon-centrations.Theconcentrationofthelidocainesolutionswasvariedincrementallybetween0.5Mand1.8mM.Theopticallycoupleddiffusioncellwasmonitoredbytheslavechannelandthereferencecuvette,lledwithdeionizedwater,wasmonitoredbythemasterchannel.Threespectrawerecollectedforeachlidocaineconcentration.TheanalysispresentedinSection 9.1 indicatedthatthedriftinthe2spectrom-eterswascorrelated.Theabsorbanceforthedual-beamsystematagivenwave-lengthisdenedbyA=log10Is;0)]TJ/F20 11.955 Tf 11.996 0 Td[(Is;dark Im;0)]TJ/F20 11.955 Tf 11.996 0 Td[(Im;dark)]TJ/F20 11.955 Tf 11.996 0 Td[(log10Is)]TJ/F20 11.955 Tf 11.996 0 Td[(Is;dark Im)]TJ/F20 11.955 Tf 11.996 0 Td[(Im;dark-3wheretherstlogarithmictermcorrespondstotheintensityratioofthetwospec-trometersatzeroconcentration.Thesecondlogarithmictermistheratioofdark-correctedsignalintensitiesatagivenlidocaineconcentration.Thedifferencebe-tweenthelogarithmicratiosyieldsanabsorbancewhichaccountsforthetimedependentsignaldrift.9.2.1ComparisonofAbsorbanceSpectra.Thefamilyofcalculatedabsorbancespectrafromthecalibrationstudyarepre-sentedinFigure 9-3 .Theabsorbanceincreasedsignicantlyasthelidocainecon-centrationwasincreasedforspectralwavelengthsbetween210and280nm.The

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203 changeinabsorbanceatlowlidocaineconcentrationswasgreatestinthe215-230nmportionofthespectra.Forlidocaineconcentrationsgreaterthan200Mabroad,secondaryabsorbancepeakdevelopedinthe240-275nmregionoftheab-sorbancespectra. Figure9-3:Normalizedabsorbancespectraforcalibrationoflidocaineconcentra-tion. Astheconcentrationoflidocainewasincreased,theabsorbancemeasurementsbecamescatterednearthemaximumabsorbanceofagivenwavelength.Theran-domlydistributeddatapointswerelocatedatwavelengthsbetween180and240nm.Thescatteredabsorbancevalueswererstobservedattheshortestwave-lengthswhenthelidocaineconcentrationwasbelow25M.Randomlydistributedabsorbancevaluesappearedatlongerwavelengthsasthechromophoricconcen-trationwasincreased.Thescatteredabsorbancedatawascausedbythereductionofthelightthrough-putintensityofthereceptorchambertothedarksignalamplitude.Astheeffectivesignalintensitywasequaltozero,theadditionofmorechromophoretothesys-temcouldnotchangetheabsorbanceresponse.Variationsintheabsorbanceafter

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204 thelightthroughputsignalhadbeenextinguished,wereproportionaltothenoiselevelofthemeasurement.9.2.2DeterminationofLidocaineExtinctionCoefcients.Asstatedabove,extinctioncoefcientscan,inprinciple,becalculateddirectlybydividingthemeasuredabsorbanceresponseofachromophorebyitsconcentra-tion.Theabsorbanceforthissystemwasafunctionofelectromagneticradiationwavelength.Therefore,aspectrumofwavelength-dependentextinctioncoef-cientswascalculatedaccordingtothemethodologydescribedabove.Theaccu-racyoftheextinctioncoefcientswasassessedbydividingselectedabsorbancespectrawithknownlidocaineconcentrationsbythespectrumofcalculatedextinc-tioncoefcients.Theapproachyieldedafamilyoflidocaineconcentrationswhichwereafunctionofwavelength.Thestandarddeviationofthelidocaineconcen-trationswasgreaterthanthemeanvalueforsomeofthespectra;therefore,analternativemethodologywasdevelopedtodeterminetheextinctioncoefcients.Theapproachusedandthisworktoidentifythelinearresponserangeplottheabsorbanceatagivenwavelengthasafunctionoflidocaineconcentrationandsubsequentlyregressingalinetothedatatocalculatetheextinctioncoefcient.ThecalculatedabsorbanceatselectedwavelengthsispresentedasafunctionoflidocaineconcentrationinFigure 9-4 .Theabsorbancedataforagivenwavelengthdemonstratedabimodallinearprole.Alternativelystated,thereweretworegionsoflinearitywithdifferingslopes.Forexample,alinearrelationshipwasobservedfortheabsorbancemea-surementscorrespondingtolidocaineconcentrationslessthan200M.Athigherconcentrationsthedatapointswerealsolinear,however,theslopewasgreaterthantheslopeforlow-concentrations.ThedataanalysistoolboxofMicrosoftExcelcwasusedtoregressalinearmodeltotheabsorbancedata.Theslopeof

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205 Figure9-4:Absorbanceasafunctionoflidocaineconcentrationatselectedwave-lengths. thelinedrawnthroughtheabsorbanceresponseforagivenwavelengthcorre-spondedtotheextinctioncoefcient.Sincetheabsorbanceshouldbezerointheabsenceofachromophore,thex-interceptofthelineshouldbezeroforaproperlycalibratedsystem.Regressionofalinearmodeltotheentirecollectionofabsorbance-concentrationdatawasintractablebecauseofthebimodalstructuredescribedabove.Thealter-nativeregressionstrategyimplementedhere,involveddividingtheabsorbance-concentrationdatasetintotwoportions.Forexample,separateregressionswereperformedontheabsorbancemeasurementscorrespondingtolidocaineconcen-trationsupto200Mandforthedatasetassociatedwithconcentrationsgreaterthan200M.Theconcentrationrangesassociatedwiththetruncateddatasetsroughlycorrespondedtothetworegionsoflinearityobservedinthecompletecollectionofabsorbance-concentrationdata.Theregressionparameterscorrespondingtoabsorbancedatacorrespondingtolidocainesolutionswithconcentrationsgreaterthan200MareshowninTable 9-1 .

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206 Table9-1:Regressionparametersforcalculationofextinctioncoefcientsfromabsorbancedataoflidocainesolutionswithconcentrationsgreaterthan200M Wavelength/nm Slope/M)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Intercept r2 210.0 160.17 1.2684 0.7099 215 189.57 1.3816 0.6288 220.3 340 1.3973 0.5079 225.2 557.93 1.21 0.5615 230.2 942.18 0.8444 0.7407 235.1 1376.3 0.2793 0.9089 240 1431.2 -0.1127 0.9407 245.3 1201.8 -0.2439 0.9169 250.1 960.57 -0.2026 0.9086 255 951.67 -0.2019 0.9072 260.3 1047.2 -0.2187 0.9113 265.2 960.8 -0.1991 0.9094 270 822.94 -0.1645 0.9096 275.2 156.46 -0.0067 0.9119 280.1 28.544 0.0215 0.9101 Thecolumnsofthetablecorrespondtoradiationwavelength,slope,whichisequivalenttotheextinctioncoefcient,x-interceptandlinearcorrelationcoef-cient,respectively.Ther2valuesfromthemodeltstotheabsorbancedatacorre-spondingtowavelengthsshorterthan235nm,asindicatedinbold,werelessthan0.9.Therelativelysmallmagnitudeofthecorrelationcoefcientsindicatedthatthelinearmodelprovidedpoortstotheshorterwavelengthdata.Thisimpliedthatcorrespondingextinctioncoefcientsdatashouldnotbeincludedintheesti-mationoflidocaineconcentrationsgreaterthan175M.Incontrast,ther2param-etersforwavelengthsgreaterthan235nmallexceeded0.9.Thelarger2valuesforwavelengthsbetween235nmand280nmimpliedthattheextinctioncoefcientsassociatedwiththeselongerwavelengthsweresuitableforcalculatingalidocaineconcentrationsgreaterthan175M.Asecondfamilyofextinctioncoefcientswasdeterminedbyregressingthelinearmodeltotheabsorbancedataobtainedfromthelidocainesolutionswithconcentrationsfrom0Mto200M.Themodelwasregressedtotheabsorbance

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207 Table9-2:Extinctioncoefcientsandregressionparameterscalculatedfromab-sorbancedataoflidocainesolutionswithconcentrationslessthan175M Wavelength/nm Slope/M)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Intercept r2 210.0 6833.9 -0.0341 0.9513 215 5912 -0.046 0.9431 220.3 4036.2 -0.0358 0.9232 225.2 2859.8 -0.0263 0.9243 230.2 2054.9 -0.0172 0.9278 235.1 1339.2 -0.0094 0.9305 240 854.68 -0.0046 0.9449 245.3 558.9 -0.0018 0.9549 250.1 466.95 -0.001 0.9599 255 465.63 -0.0011 0.9567 260.3 506.43 -0.0017 0.957 265.2 479.95 -0.0027 0.9538 270 433.01 -0.0014 0.9566 275.2 210.28 0.0002 0.9663 280.1 143.76 0.0016 0.9277 dataatthesamewavelengthsanalyzedforthehigh-concentrationsolutions.Themodelparametersretainedfromthelow-concentrationdatasetarepresentedinTable 9-2 .Theminimumcorrelationcoefcientassociatedwiththelow-concentrationspec-trawas0.948whichcorrespondedtothe225nmabsorbancedata.Thelargecor-relationcoefcientsassociatedwiththisdataindicatedthatofthemodeltsweregood.Thelargestmagnitudeoftheinterceptswas1.19x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2whichcorrespondedtothe220nmabsorbancedata.Ingeneral,thex-interceptswereatleastfouror-dersofmagnitudesmallerthantheextinctioncoefcient.Theexcellentttingcharacteristicsoftheregressionparametersimpliedthattheentirecollectionofcalculatedextinctioncoefcientswassuitableforforcalculatinglidocaineconcen-trationsfromabsorbancespectra.Theresultswereconsistentwithaproperlycal-ibratedabsorptionspectroscopysystem.Sincetworegionsoflinearity,correspondingtolow-concentrationandhigh-concentrationlidocainesolutions,wereobservedintheabsorbancedata,atwo-

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208 stepprocedurewasdevelopedforcalculatinglidocaineconcentrationsfromthecoupledspectroscopytransdermaldeliverystudies.Whilethepredictedlidocaineconcentrationswerelessthan200MthefamilyofextinctioncoefcientslistedinTable 9-2 wereused.Oncetheconcentrationexceeded200Mtheextinctionco-efcientsinTable 9-1 wereselectedforcalculatinglidocaineconcentrations.Thestrategyprovidedforthedeterminationofreceptorcompartmentlidocainecon-centrationsintherangeof0.5Mto1.8mM.Analternativepresentationoftheextinctioncoefcientsobtainedfromthetwo-stepregressionprocedureisshowninFigure 9-5 .Theextinctioncoefcientsassociatedwiththelow-concentrationandhigh-concentrationdatasetsareindi-catedbythelledtrianglesandopencircles,respectively.Theplotwasintendedtoprovideagraphicalillustrationofthedistributionoflidocaineextinctioncoef-cients.Thegeneralstructureofthetwogroupswassimilarforwavelengthslongerthan235nm.IntheshorterwavelengthregionsofFigure 9-5 theextinctioncoefcientsfromthetodatasetsdiverged.Forexample,thelow-concentrationdatatrendeddown-wardswithincreasingwavelengths,whereas,thehigh-concentrationvaluesin-creased.Thedetailedanalysisoftheregressionparametersdescribedabovemadeitpossibletodeterminethattheshortwavelengthextinctioncoefcientsassoci-atedwiththehigh-concentrationmeasurementswerenotappropriateforcalcu-latinglidocaineconcentrations.Thecalibrationproceduredescribedhereincreasedtherangeoflidocainecon-centrationsforwhichtheabsorbanceresponseobeyedBeer-Lamberttheorybyafactorof7incomparisontoearlierwork. 164 Theexpandedconcentrationrangeforthelinearabsorbanceresponsesuggestedthattheadditionofthesecondaryreferencecellhadproperlyaccountedforsystemdrift.

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209 Figure9-5:Dependenceofcalculatedextinctioncoefcientonlightwavelength.Thesolidtrianglesandopencirclescorrespondtothecalculatedextinctioncoef-cients 9.3AbsorbanceChangesfromSkinSpeciesThemethodologydescribedinSection 4.4.3 wasappliedfortheexperimentspresentedhere.Inpreviousopticallycoupledtransdermaluxexperimentsabroadsecondaryabsorbancepeakwasobservedatwavelengthsbetween240nmand300nm. 164 Thesecondarypeakwasnotobservedinthelidocainecalibra-tionstudiesforthatwork.Therefore,itwasconcludedthatchromophoricspecieswereemanatingfromtheskin.Theobjectofthisworkwastodeterminethetimedependentabsorbanceresponseofexcisedhumanepidermisintheabsenceofelectricalcurrent.Theideawastoextractthecontributionofskinchromophorestotheoverallabsorbanceresponseofthetransdermaliontophoresisexperiments.Themethodologyusedheremadeitpossibletodeterminewhetherthebroadsecondarypeakobservedatlongerwavelengthsintheearlierworkwasarepro-duciblephenomena.TheskinabsorbancespectrafromthehydrationstudyarepresentedinFigure 9-6 .Thelargestabsorbanceresponseoccurredatwavelengthsbelow220nm.The

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210 datapointswerediscontinuousandrandomlydistributedforthisrangeofwave-lengths.ThebehaviorwassimilartotheresultsdescribedinSection 9.2 whenthelightthroughputsignalatagivenwavelengthwasextinguished.Theabsorbancewasessentiallyzeroatwavelengthsgreaterthan320nm. Figure9-6:AbsorbancespectraofskinimmersedinbufferedNaClsolution. Astheskinwassoakedintheelectrolyteabroadabsorbancepeakappearedbetween225nmand320nm.Themaximumabsorbancewas0.03correspondingtoawavelengthof262nm.Themaximumabsorbancerepresenteda6%changeinthesignalresponseoverthecourseof2.5hours.Incomparison,theabsorbancefromthelidocainecalibrationexperimentsexceeded0.03whenthechromophoricconcentrationwasgreaterthan75M.Ifthelidocaineuxislargeenoughduringtransdermaliontophoresisthecontributionoftheskinchromophorestotheover-allabsorbanceresponseshouldbenegligible.Although,itispossiblethatcurrentcouldenhancethediffusionrateofchromophoriccompoundsfromtheskin.Anexperimentwasconductedwhereskinwassubjectedtoa-500A/cm2for30minutes.Forthestudy,NaClelectrolytewasinsertedinbothchambersofthe

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211 diffusioncell.Theskinsamplewassoakedintheelectrolytefor30minutesbeforecurrentwasapplied.Althoughnotpresentedhere,themaximumabsorbanceatwavelengthsbetween225nmand320nmwasapproximately0.02.Therateofab-sorbancechangeinthisportionofthespectrawasuniformregardlessofwhethercurrentwasapplied.A50%increaseinabsorbancewasobservedinthespectracollectedaftercur-rentwasterminated.Theresultssuggestthatthechromophoricskinspecieswerediffusingbackintothedonorchamberbyeithermigrationorelectroosmosisinre-sponsetotheelectriceld.Asthepotentialdifferenceacrosstheskinwasgreaterthan5VitisquitelikelythattheskinhadbeenalteredbytheappliedDCcurrent.Uponterminationofthecurrent,theelectriceldbegantorelaxandskinchro-mophoreswerefreetodiffuseintothereceptorchamber.Despitetheincreaseinabsorbanceassociatedwiththeapplicationofcurrent,therelativemagnitudewasnegligibleincomparisontotheabsorbanceresponseobservedinthecalibrationstudieswhenthelidocaineconcentrationexceeded100M.9.4TransdermalDeliveryofLidocainebyIontophoresisApreliminaryexperimentwasperformedtoverifytheefcacyofthecoupledspectroscopyapproachformeasuringtransdermaldeliveryratesoflidocaineun-deriontophoreticconditions.ThemethodologydescribedinSection 9.4 wasap-pliedforthiswork.Thetemporalsequenceoftheappliedcurrentsfortheinvesti-gationislistedinTable 9-3 .The60absorbancespectraobtainedfromthetransdermaliontophoresisstudyareillustratedinFigure 9-7 .Theabsorbanceresponsebetween200and280nmispresentedbecausesignicantdifferencesinsignalintensitywerenotdetectedatotherwavelengths.Ingeneral,theabsorbanceincreasedwithtimewheretherateofchangedependedonwavelengthandmagnitudeofappliedcurrent.Thetrends

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212 Table9-3:Opticallycoupledspectroscopyexperimentsettings Time/min Current/mA/cm2 Comments 0-9 0 SkinHydration 10-35 0 LidocaineAdded 35-67 0.71 CurrentOn 67-86 0 CurrentOff 86-111 1.4 CurrentOn 111-134 2.8 ” 134-181 5.6 ” observedinthedatawereconsistentwithtransportofthelidocainechromophoreacrossskin. Figure9-7:Evolutionoftheabsorbanceresponseduringthetransdermalionto-phoresisexperiment. Aspecicfeatureofthespectraldatasetwasthattheabsorbanceresponseremainedconstantovertherst50minutesoftheexperiment.Aftertheinitialstationaryperiod,thesignalintensitybegantoincreasewithtimeatwavelengthsbetween200and220nm.Thechangeinabsorbanceresponsecorrespondedtoa15minutedelaybetweentheapplicationofthe0.71A/cm2currentbiasandthedetectionoflidocaine.Theresultssuggestthattheskinhadnotbecomefullysaturatedwiththelidocainechromophoreduringthepassiveiapplied=0A/cm2segmentoftheexperiment.

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213 Theevolutionoftheabsorbancespectraassociatedwithremainderoftheex-perimentisnotdescribedbecausespecictrendsaredifculttoidentifyatthescalepresentedinFigure 9-7 .Instead,macroscopictransportquantities,suchaslidocaineconcentrationandtransdermalux,werecalculatedusingMicrosoftExcelcspreadsheetsoftware.Forexample,theabsorbanceatselectedwavelengthsofeachspectraweredividedbytheextinctioncoefcientscalculatedinSection 9.2.2 todeterminelidocaineconcentration.Theprocedurewasrepeatedforeachspectratoproduceafamilyof60chromophoreconcentrationswhichwereafunc-tionoftime.ThecalculatedlidocaineconcentrationproleispresentedbytheopencirclesinFigure 9-8 .Theredlinecorrespondstoacombinationoflinearandparabolictstothedata.Ageneraltrendofincreasingconcentrationwithtimewasobserved.Therelativedegreeofchangewasproportionaltotheamplitudeofappliedcurrent.Thetrendsindicatedthatlidocainewasbeingtransportedacrosstheskinbythecurrent.TheconcentrationscalculatedaccordingtoBeer-Lamberttheoryweresubse-quentlyusedtoestimatelidocaineux.Forexample,theaveragelidocaineuxoverthetimeintervalrequiredtocollecttwospectrawascalculatedbyNit=Dci DtV A-4whereVisthereceptorcellvolume,Aisthecross-sectionalareaofskinavailablefortransport,andDciisthechangeinchromophoreconcentrationoverthetimeinterval,Dt.Lidocaineuxeswerecalculatedforallsuccessivepairsofabsorbancespectra.Someoftheestimateduxeswerefoundtobenegative,especiallyduringtherst85minutesofthestudy.Thistimeperiodcorrespondedtotheskinhydration,therstiontophoreticiapp=0.71A/cm2andthesubsequentpassivediffusionportionsoftheinvestigation.Therelativelysmallchangesintheabsorbancespec-

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214 Figure9-8:Temporalevolutionofthecalculatedlidocaineconcentrationanduxinthereceptorcell. trawereinagreementwiththesmalldrivingforcesfortransdermaltransport.Astransportwasunfavorableattheseexperimentalconditions,itisreasonabletoassumethatchangesintheabsorbancesignalwereprimarilycausedbyran-domuctuationsinthespectrometer.Thestochasticerrorsassociatedwiththesespectrawouldthenpropagatethroughtotheconcentrationanduxcalculations.Thenegativeuxesobservedatthestartoftheexperimentareconsistentwiththisassumption.Althoughnegativeuxeswerecalculatedfromthelow-currentiontophoreticspectra,lidocaineconcentrationgenerallyincreasedovertheentireinterval;there-fore,theaverageuxovertheentireobservationalperiodwascalculatedratherthanovertheshortertimeintervalscorrespondingtothecollectionofsuccessivespectra.Duringthelatterportionsoftheexperimentwhentheiontophoreticcur-rentamplitudewasgreaterthanorequalto1.4A/cm2theabsorbanceincreased

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215 morerapidlyfromspectrum-to-spectrumwhichwasconsistentwithincreasedtransdermallidocainetransport.Furthermore,thelargerelativechangesinab-sorbanceassociatedwiththeseexperimentshelpedtoimprovethesignal-to-noiseratioofthemeasurement.Theuxproles,ascalculatedbyEquation 9-4 arepresentedbythesolidlineswithverticalcrossmarksinFigure 9-8 .Themagnitudeoflidocaineuxisdenotedbytheright-handordinateoftheplot.Theuxwasapproximately30-40mol/cm2/minduringthepassiveportionoftheexperimentwhentheionto-phoreticcurrentwas0mA/cm2.Asthecurrentwasincreasedto0.71mA/cm2,theuxincreasedinstantaneouslytoapproximately55mol/cm2/min.Theuxthendecreasedto30mol/cm2/minduringtherecoveryperiodaftertherstin-tervalofiontophoretictransport.Theslightincreaseindeliveryrateduringthe0.71mA/cm2currentapplicationcyclesuggestedthattheiontophoresisprotocolhadenhancedthetransportoflidocaine.Thetransdermallidocaineuxincreasedsignicantlyduringthe1.4mA/cm2iontophoresistreatmentinterval.Forexample,auniformdeliveryrateofap-proximately150mol/cm2/minwasobservedforthersttwelveminutesof1.4mA/cm2appliedcurrent.Theuxovertheremainderofthistreatmentcyclein-creasedcontinuouslytoanalamplitudeof340mol/cm2/min.Theuxesasso-ciatedwiththisportionoftheexperimentwere,ataminimum,threetimeslargerthanthelidocainedeliveryratesmeasuredduringthe0.71mA/cm2iontophoreticsegmentofthestudy.Alternativelystated,themagnitudeoflidocaineuxhadtripledbydoublingthecurrent.Thetransdermaldeliveryrateoflidocainealsoincreasedcontinuouslyfrom340mol/cm2/minto1.3mmol/cm2/minoverthecourseofthe2.8and5.6mA/cm2currenttreatments.Theuxmeasurementsindicatedthattheapplicationofcur-

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216 rentincreasedthetransdermaluxoflidocaine;however,thedeliveryrateswerenotcontrolledataconstantlevel.Skinpolarizationresistancewasselectedasasimpleparametertoevaluatetheinuenceoftheappliedcurrentsonmembranetransportproperties.TheprolescorrespondingtoskinpolarizationresistanceandtransdermallidocaineuxarepresentedinFigure 9-9 .ThesolidyellowcirclesandthesolidlinescorrespondtothepolarizationimpedancemeasuredbyimpedancespectroscopyandbytheSolartron1286potentiostat,respectively.Thebluelineswithverticalhashmarkssignifythetransdermaldeliveryratesoflidocaine. Figure9-9:Temporalevolutionofskinpolarizationresistanceandtransdermallidocaineux. Thepolarizationresistanceofskinwasapproximately400kW/cm2atthestartoftheexperiment.Asthe0.71mA/cm2iontophoreticcurrentwasapplied,theresistancedecreasedbyoveranorderofmagnitudetoapproximately20kW/cm2.Overthecourseofthistransdermaliontophoresistreatmentcycle,skinresistance

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217 droppedto15kW/cm2.Thetransdermalvoltagedifferenceassociatedwiththe0.71mA/cm2currentalsodecreasedfrom14Vtoapproximately12V.Itislikelythatthelargepotentialdifferencesinducedbythecurrentalteredthepropertiesoftheskin.ThetransdermalvoltagedifferencesmeasuredinthisworkwerewellabovethethresholdforpotentiallyinducedchangesinskinpropertiesobservedinSections 5.2 and 8.1 ofthisworkandreportedintheliterature. 3 Theimpedancespectracollectedafterthe0.71mA/cm2currentbiaswaster-minated,indicatedthatskinpolarizationresistanceincreasedfrom60kW/cm2to100kW/cm2.Theresistanceassociatedwiththethirdimpedancespectrumwasapproximatelyone-fourthofthemagnitudemeasuredatthebeginningoftheex-periment.Theslowandincompleterecoverysuggestedthatthechangesinskinpropertieswerenotcompletelyreversibleoverthetimescaleofoverthisportionoftheexperiment.Theapplicationofthe1.4mA/cm2,2.8mA/cm2,and5.6mA/cm2iontophor-eticcurrentscausedthepolarizationresistanceofskintodecreasetoapproxi-mately10,5,and2kW/cm2,respectively.Thetrendrepresentedasimplelinearrelationshipbetweencurrentamplitudeandskinpolarizationresistance.Therel-ativereductionsinskinresistancewereapproximatelyafactorof5smallerthandecreaseassociatedwiththe0.71mA/cm2and1.4mA/cm2currents.Thecom-binedresultssuggestthatthereisanasymptoticlimitforthereductionofskinpolarizationresistanceundertheinuenceofappliedcurrent.Thelidocaineuxesobservedinthisworkwereapproximatelyanorderofmagnitudesmallerthanthedeliveryratesreportedintheliteratureundersim-ilarexperimentalconditions. 143 ThediscrepancyintheresultscanbepartiallyexplainedbythehigherlidocaineconcentrationmMandlowerpH.5ofthedonorcompartmentsolutionusedforthatstudy.Forexample,thelower

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218 pHwouldincreasetheconcentrationofioniclidocainewhichwouldimprovethetransportefciencyoftheiontophoreticcurrent.ThetransdermaldeliveryratesoflidocainereportedbyPhilbrickwereseveralordersofmagnitudelowerthantheuxesmeasuredinthiswork. 164 Therangeofapplied-currentbiasesforthisinvestigationwasinagreementwithclinicalther-apeuticprotocols;however,theiontophoreticcurrentswereapproximatelytwoordersofmagnitudelargerthanforthestudydescribedabove.Inaddition,thepotentialdifferenceacrosstheskinfortheexperimentswasatleast14Vwhichwaswellabovethethresholdforchangestothemembranetransportproperties. 3 Therefore,theenhancediontophoreticdeliveryoflidocaineobservedherewasprobablycausedbyacouplingofthesetwoeffects.Insummary,theworkpresentedhereindicatesthatthecouplingofUV-visabsorptionspectroscopywithelectrochemicalimpedancespectroscopycanbeapotentiallyusefulmethodologyforstudyingtransdermaliontophoresis.Electro-chemicalimpedancespectroscopyprovidedforthemeasurementofskinelectri-calandtransportpropertiesandUV-visabsorbancespectroscopyprovidedforthemeasurementoftransdermallidocaineux.Inthepreviouschaptersitwasshownthatelectrochemicalimpedancespectroscopyisarobusttechniqueformonitor-ingskinproperties.Therstthreesectionsofthischapterdemonstratedthatthedual-beamUV-visspectroscopysystemdevelopedforthisworkwasproperlycal-ibrated.Thetransdermaliontophoresisexperimentspresentedabovearepreliminaryresultswhichclearlydemonstratethattheapplicationofelectricalcurrentincreasestransdermallidocaineux.Thedifcultyinobtainingconstanttransdermaldeliv-eryratesduringiontophoresismayhavebeenassociatedwiththelimitationsinthepotentiostatfordrivingcontrolledcurrentsatlargepotentials.Forexample,

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219 thevoltagedifferenceacrosstheskininducedbytheiontophoreticcurrentwasbetween12and14volts.Thiscorrespondstotheupperstabilitylimitofthe1286potentiostat.Althoughthepotentiostatreportedcurrentwasbeingdeliveredattheprescribedlevel,itislikelythatthesignal-to-noiseratioofthecurrentsignalwasnotoptimal.RecommendationsareprovidedinChapter 13 toimprovetheaccuracyoftheopticallycoupledspectroscopicmeasurements.

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CHAPTER10MATHEMATICALMODELOFTRANSDERMALIONTOPHORESISAmathematicalmodelwasdevelopedtosimulatesteady-statetransdermaliontophoresis.Undertheassumptionthatthestratumcorneumisthedominantbarriertotransdermaldrugdelivery,onlythemacroscopictransportpropertiesofthissectionoftheepidermiswereconsidered.Forexample,thelowpermeability,highelectricalresistanceandnegativebackgroundchargeofthestratumcorneumwereexplicitlyincorporatedintothemodel.Thesystemgeometrywasdesignedtomimiciontophoretictransportwithintheexperimentaldiffusioncell.Anicefeatureofthemodelpresentedhereisthatitcanbeadaptedtosimulateclinicaliontophoreticsystemsbyadjustingtheinputparameters.Theobjectiveofthisworkwastocalculatetheinuenceofcontrolledvari-ablesontheconcentration,uxandpotentialproleswithintheskin.Thisworkwasintendedtoprovideinsightintotheinuenceofskinproperties,suchasback-groundcharge,onthetransportprocess.ResultsfromthemodelsimulationswerealsocomparedwiththeuxesobtainedfromUV-visabsorptionspectroscopyex-periments. 164 ThetransdermaliontophoresissimulationresultsarepresentedinChapter 11 .10.1SystemDescriptionThesimulatedtransdermaliontophoresissystemconsistedofthreedistinctre-gions:adonorsolution,theskinandareceptorsolution.Thedimensionsofthesimulatedsystemwereconsistentwiththeexperimentalapparatus.Forexample,thereceptoranddonorcompartmentswere2cmlongandtheskinwasmod220

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221 eledasbeing20mthick.AschematicofthesimulatedsystemisprovidedbyFigure 10-1 . Figure10-1:Dimensionsofthesimulatedsystemfortransdermaliontophoresis.Figurenottoscale. Thegoverningequationsforeachregionwereformulatedtoreectthephys-icalcharacteristicsofthesystem.Forexample,theskinwasassumedtoconsistofauniformlychargedbarrier.Thediffusionpathlengththroughtheskinwasassumedtobelongerthanthethicknessofthemembraneduetothehighlycom-plexstructureofthemembrane. 256 , 257 Atortuosityfactorwasintroducedintothegoverningequationstoaccountfortheextendedpathlength. 258 Thediffusionco-efcientsofallionicspecieswerereducedbythetortuosity.Theionicselectivecharacteroftheskinwasthereforeassociatedsolelywiththetendencyforexclusionofionicspeciesoflikecharge.Underconditionsofionto-phoreticoperation,therapeuticagentsaredrivenfromthedonorsolutiontothereceptorsolution.TheboundariesofthesystemrepresenttheAg/AgClworkingelectrodesthatdrivecurrentthroughthesystem.Thetotalcurrentthroughoutthesystemwasassumedtobeuniform.Thegoverningequationsforthemodelwerederivedfrommacroscopictrans-porttheoryfordilutesolutions. 136 TheseequationsarediscussedinmoredetailintheGoverningEquationssectionofthischapter.Theuxofionicspeciesac-countedfortransportbymigrationanddiffusion.Themodelisgeneralinthe

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222 sensethatitcanaccountforanynumberofionicspecies.Partialdissociationofionicspecieswasdescribedbyequilibratedhomogeneousreactions.Inthisway,dissociationofwaterandbufferswastreatedexplicitly.ThespeciespresentinthesimulatedsystemwereCa2+,Na+,Cl)]TJ/F20 11.955 Tf 6.946 -4.34 Td[(,H+,OH)]TJ/F20 11.955 Tf 6.946 -4.34 Td[(,lidocainecation,dissociatedHEPESbufferanion,undissociatedHEPESbufferandthexednegativechargesiteswithintheskin.Theinorganicspeciescorrespondtothemajorioniccomponentspresentinthehumanbody. 246 Inaddition,thechargeoftheskinwastreatedtobeanimmobileionicspecies.Localelectroneutralitywasassumedtoapply.Thelistofdependentvariablesincludedtheconcentrationofeachspeciesandtheelectricalpotential.Thus,fornindependentspecies,asetofn+1nonlinearordinarydifferentialequationsandalgebraicequationsweresolvedusingaNewton-Raphsoniterativescheme.10.2BoundaryConditionsTheboundaryconditionsinthedonorandreceptorphasesrequiredthattheconcentrationsofthespeciesapproachedthebulkvalues.Continuityofconcen-trationanduxwasassumedtoapplyattheboundariesbetweenregions.Poten-tialwasspeciedatthedonorboundary.Theboundaryconditionscorrespondtothelocationoftheelectrodes.TheelectrodesusedtodrivecurrentthroughtheskinwereassumedtobeAg/AgCl,whichisreversibletothechlorideions.Sincechlorideionsweretheonlyspeciesreactingattheelectrodes,chloridewastheonlyspecieswithanonzerouxattheelectrode.TheheterogeneousreactionattheanodewasAg+Cl)]TJ/F14 12.457 Tf 9.935 -5.633 Td[(!AgCl+e)]TJ/F20 11.955 Tf 130.791 -4.938 Td[(-1wheresilverwasoxidized.Theboundaryconditionatthecathodecorrespondedtothereductionofthesilverion.ThecathodicreactionisdescribedbyAgCl+e)]TJ/F14 12.457 Tf 9.934 -4.937 Td[(!Ag+Cl)]TJ/F20 11.955 Tf 130.791 -5.633 Td[(-2

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223 TherelationshipdescribingtheuxofchlorideionsattheelectrodesurfaceispresentedbyNCl)]TJ/F8 12.457 Tf 8.82 -0.274 Td[(=itotal FzCl)]TJ/F20 11.955 Tf 158.266 7.927 Td[(-3whereitotalistheapplied-currentdensity.Theboundaryconditionstatesthatallofthecurrentwascarriedbytheuxofchlorideionsattheelectrode.10.3BulkSolutionCompositionsThecompositionofthedonorsolutioncanhaveasignicantinuenceonthetransportratesofthetherapeuticagent. 148 , 81 , 170 , 259 Inthisregiontherearerela-tivelyhighconcentrationsoftheactiveagents.Thisallowsforexibilityinevalu-atingthetransportratesofavarietyofdifferentactivespecies.Therapeuticcom-poundswilloftenhavemolecularweightsthatareordersofmagnitudelargerthantheionsusedincludedinthismodel.Tocompensateforthedisparityinmolecularweightsamodeldrugspecieswasselectedwithadiffusioncoefcientanorderofmagnitudelowerthantheremainingspecies.Thebulkconcentrationsofionicspeciespresentinthedonorsolutionandthereceptorsolutionwereselectedtobeconsistentwiththeioniccontentofthebodyanddrugformulations,respectively. 246 TheidealsolutiondiffusioncoefcientscorrespondingtoeachofthesespeciesarepresentedinTable 10-1 .Thediffu-sioncoefcientsofthelidocaineion,theHEPESbufferionandtheundissociatedHEPESspecieswerecalculatedusingtheWilke-Changcorrelation. 260 Evaluationofthediffusioncoefcientbythismethodrequiresthemolalvolumeofthesoluteatthenormalboilingpointasaninputparameter.Themolalvolumewasesti-matedusingSchroeder'sAdditiveMethod. 260 Thismethodprovidesestimatesformolalvolumes,whichareaccuratetowithinthreepercent.

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224 Table10-1:Diffusioncoefcientsandbulksolutionconcentrationsforthespeciespresentinthetransdermaliontophoreticsimulation Species Di/ DonorSolution ReceptorSolution 105cm2s)]TJ/F20 7.97 Tf 6.447 0 Td[(1 ci;bulk/M ci;bulk/M Na+ 1.3341 0.250 0.14 Ca2+ 0.792 0.100 0.050 Lidocaine+ 0.59y 5.0010)]TJ/F20 7.97 Tf 6.447 0 Td[(3 1.0010)]TJ/F20 7.97 Tf 6.448 0 Td[(6 Cl)]TJET1 0 0 1 44.733 -4.334 cmq[]0 d0 J0.398 w0.199 0 m0.199 14.804 lSQ1 0 0 1 25.451 4.334 cmBT/F20 11.955 Tf 0 0 Td[(2.032 0.453 0.256 H+ 9.31 1.0010)]TJ/F20 7.97 Tf 6.447 0 Td[(7 3.8910)]TJ/F20 7.97 Tf 6.448 0 Td[(8 OH)]TJET1 0 0 1 48.428 -4.334 cmq[]0 d0 J0.398 w0.199 0 m0.199 14.571 lSQ1 0 0 1 28.44 4.334 cmBT/F20 11.955 Tf 0 0 Td[(5.26 1.0010)]TJ/F20 7.97 Tf 6.447 0 Td[(7 2.5710)]TJ/F20 7.97 Tf 6.448 0 Td[(7 HEPES+ 0.734 2.2010)]TJ/F20 7.97 Tf 6.447 0 Td[(3 4.2010)]TJ/F20 7.97 Tf 6.448 0 Td[(3 HEPES 0.720 7.8010)]TJ/F20 7.97 Tf 6.447 0 Td[(3 5:8010)]TJ/F20 7.97 Tf 6.448 0 Td[(3 10.4GoverningEquationsThegoverningequationsforthesteady-statemodeloftransdermaliontophor-esisweredevelopedaccordingtodilutesolutiontheory. 136 , 137 Theionicstrengthofthesolutionssimulatedinthesystemwaslessthan0.5M;therefore,specicinter-actionsbetweenindividualionswereconsideredtobenegligible.Theentiresys-temwassimulatedasbeingelectricallyneutralandatequilibrium.Theapproachprovidedforconcentration,uxandelectrostaticpotentialprolesthroughouttheentiretransdermaliontophoreticsystemdomain.10.4.1MolarFluxThemolaruxofthespecieswasassumedtoobeyNernst-Planckbehavior.Theuxdensityofspeciesi,isrepresentedbyNi=)]TJ/F53 11.955 Tf 9.791 0 Td[(uiziFcirF)]TJ/F53 11.955 Tf 12.594 0 Td[(Dirci+vci-4thetermsassociatedwiththeuxequationcorrespondtothequantitiesdenedinEquation 3-1 .Forexample,thetotaluxwasassumedtobecomposedofcontributionsfrommigration,diffusionandconvection,respectively.ThemobilityofthespeciesinsolutionwasrelatedtodiffusivitybytheNernst-Einsteinrelation

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225 Di=uiRT-5whereuiisthemobilityofspecies,i,R,istheuniversalgasconstantandTistheabsolutetemperature.Theuxesdeterminedbyexperimentcorrespondtosurfaceaveragedquanti-ties,therefore,thedesignequationsforthemodelwerecastinone-dimensionalform.Theone-dimensionalformulationledtoamodelappropriateforprobingvariationsinpotential,ux,pHandconcentrationinthedirectionofiontophor-etictransport.Migration,diffusionandconvectiontermswereincludedintheux.Anassumptionwasmadeinthisworkthatthecontributionfromconvectiontothetotaluxwasnegligibleincomparisontothecontributionsfrommigrationanddiffusion.Thecompleteexpressionforuxdensityinthedirectionoftrans-portisdescribedbyNix=)]TJ/F53 11.955 Tf 9.791 0 Td[(uiziFcidF dx)]TJ/F53 11.955 Tf 12.594 0 Td[(Didci dx-6where,asstatedearlier,convectioninthedirectionoftransportwasassumedtobenegligible.10.4.2MaterialBalanceExpressionsThegeneralexpressionfortheconservationofmassforthecomponentsinthesystemisdescribedby@ci @t=)2(rNi+Ri-7where)2(rNiisthevolumeaveragedaccumulationrate.Sincethesystemwasatsteady-statethersttermintheconservationequationwaszero.ThetermcorrespondingtoRirepresentstheproductionratefromhomogeneousreactionsinvolvingspeciesi.Homogeneousreactionsconsideredinthissystemarethedis-sociationofwaterandmoderationofpHbytheHEPESbuffer.

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226 Adetaileddescriptionofthetreatmentofthehomogeneousreactionsispro-videdbelow.Provisionwasmadeinthedonorsolutionforreplenishmentofspeciesandinthereceptorforclearanceofthetransportedspecies.Theappro-priateexpressionforthedivergenceuxoftheiontophoreticsystemconsideredhereispresentedby)2(rNi=)]TJ/F53 11.955 Tf 10.987 8.093 Td[(dNix dx)]TJ/F53 11.955 Tf 13.312 8.655 Td[(dNiy dy-8Contributionstothetotaldivergencearedividedintotwocomponents.Thersttermcorrespondstotransportinthedirectionofiontophoresis.Thesecondterm,inthey-direction,correspondstoconvectiveuxinthedirectionperpendiculartocurrentow.They-componentoftheuxallowedfortheadditionofmaterialtothedonorsolutionandtheremovalofmaterialfromthereceptorsolution.Conservationofmasswasobeyedbecausethetotalamountofmaterialenter-ingthedonorsolutionwasequaltotheamountofmaterialleavingthereceptorsolution.TheowofspeciesthroughthesystemisillustratedinFigure 10-2 .Theverticalarrowscorrespondtothespeciesuxinthedirectionnormaltoiontophor-etictransport.Thehorizontalarrowsrepresenttheiontophoreticowofmaterialthroughthesolutionchambersandtheskin. Figure10-2:Flowpatternofdissolvedspeciesthroughthesystemdomain.Figurenottoscale.

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227 They-componentofthedivergencewascalculatedbyaddingatermtotheuxexpressionwhichwasproportionaltothedifferenceinthelocalandbulksolutionconcentrations.Thedivergenceofuxinthey-directionisgivenby)]TJ/F53 11.955 Tf 10.987 8.655 Td[(dNiy dy=)]TJ/F53 11.955 Tf 9.791 0 Td[(vydci dy-9wherevyisthebulksolutionvelocityinthedirectionnormaltoiontophoretictransport.Numericalevaluationoftheuxderivativeinthey-directionproceededaccordingto)]TJ/F53 11.955 Tf 10.986 8.655 Td[(dNiy dy=)]TJ/F53 11.955 Tf 9.791 0 Td[(vyci)]TJ/F53 11.955 Tf 12.116 0 Td[(ci;bulk Dy-10whereci;bulkisthebulkconcentrationofthespeciesofinterest,Dyrepresentsthelineardistancerequiredforcitoequalci;bulkandvyisthey-componentvelocity.Forthesimulationspresentedheretheratioofvelocityandcharacteristicdistance,Dy,wasconsideredtobeconstant.Thistermprovidedadrivingforcefortransportinthedirectionnormaltotheiontophoreticux.10.4.3HomogeneousReactionsTheelectrolyticsolutionsassociatedwiththeiontophoreticsystemcontainedbufferstomoderatechangesinpH.Inaddition,thedissociationofwaterwasin-cludedinthemodel.Thereactionswereconsideredtobeinequilibrium.Theho-mogeneousreactionswerenotexplicitlyevaluatedwiththeuxdivergencetermsintheconservationequations.Instead,algebraicmanipulationswereperformedtoeliminatethereactionterms.Themanipulationsallowedfortheuxdivergencetermsandthereactiontermstobeevaluatedseparately.Adetailedaccountofthisprocedureisprovidedbelow.Thegeneralstoichiometricexpressionforthedissociationofa1:1buffersaltisdescribedaccordingtoHBuffH++Buff)]TJ/F20 11.955 Tf 131.442 -5.633 Td[(-11

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228 whereHBuffrepresentstheundissociatedbuffer,H+isthedissolvedhydrogenionandBuff)]TJ/F20 11.955 Tf 9.935 -4.34 Td[(representsthebaseofthedissociatedbuffer.TheequilibriumrelationshipforthebufferreactioniscH+cBuff)]TJET1 0 0 1 169.983 -85.046 cmq[]0 d0 J0.478 w0 0.239 m43.345 0.239 lSQ1 0 0 1 8.255 -10.951 cmBT/F53 11.955 Tf 0 0 Td[(cHBuff=KBuffer-12TheotherhomogeneousreactioncorrespondstothedissociationofwaterwhichproceedsaccordingtoH2OH++OH)]TJ/F20 11.955 Tf 136.433 -5.4 Td[(-13Similartothebufferreaction,theequilibriumrelationshipforthewaterdissocia-tionreactioniscH+cOH)]TJ/F8 12.457 Tf 8.821 -0.273 Td[(=Kw-14Sincethereactionsforthedissociationofwateranddissociationofbufferwereassumedtobeequilibrated,Equations 10-14 and 10-12 mustbesatisedsimul-taneously.Forasystematsteady-statethematerialbalanceequationsforthespeciesin-volvedinthehomogeneousreactionsarepresentedby)2(rNH++RH+=0-15)2(rNOH)]TJ/F8 12.457 Tf 8.157 -0.274 Td[(+ROH)]TJ/F8 12.457 Tf 8.821 -0.274 Td[(=0-16)2(rNBuff)]TJ/F8 12.457 Tf 8.157 -0.274 Td[(+RBuff)]TJ/F8 12.457 Tf 8.821 -0.274 Td[(=0-17)2(rNHBuff+RHBuff=0-18Sincethebufferdissociationreactionwasassumedtobeatequilibrium,theconsumptionrateoftheundissociatedbufferwasequaltotheproductionrateof

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229 dissociatedbufferion.ThisrelationshipisdescribedbyRHBuff=)]TJ/F53 11.955 Tf 10.269 0 Td[(RBuff)]TJ/F20 11.955 Tf 142.278 -0.274 Td[(-19whereRHBuffandRHBuff)]TJ/F20 11.955 Tf 8.103 -0.274 Td[(aretheproductionratesoftheundissociatedbuffermoleculesandbufferions,respectively.Thehomogeneousproductionrateinthematerialbalanceexpressionfortheundissociatedbuffer,Equation 10-18 ,canbereplacedbyEquation 10-19 .Theequivalentformoftheundissociatedbuffermassconservationequationcanbeaddedtomaterialbalanceexpressionforthebufferion,Equation 10-17 ,toyield)2(rNHBuff)-185(rNBuff)]TJ/F8 12.457 Tf 8.821 -0.274 Td[(=0-20Themanipulationsdescribedabovecombinedthemassconservationequationsfortheundissociatedbufferandbufferionsintoasingleexpression.Algebraiceliminationoftheremainingreactionratetermsfromthematerialbalanceexpressionswasperformedbyequatingthehydroniumionproductionratetotheproductionratesofhydroxideionsplusbufferanions.Forexample,theproductionrateofhydroniumionsisdescribedaccordingtoRH+=ROH)]TJ/F8 12.457 Tf 8.156 -0.273 Td[(+RBuff)]TJ/F20 11.955 Tf 130.997 -0.273 Td[(-21whichimpliesthatthedissociationofwatermoleculesandbuffersaltscontributetotheformationofhydroniumions.Thenetproductionrateofhydroniumions,describedbyEquation 10-21 ,wasusedtoeliminatethehomogeneousreactiontermsinmaterialbalanceequationsforthehydronium,hydroxideandbufferions.TheapproachwastosubtractEquations 10-16 and 10-17 fromEquation 10-15 .TheexpressionobtainedfromthemanipulationconsistedoftheuxdivergencesfortheH+,OH)]TJ/F20 11.955 Tf 11.709 -4.34 Td[(and

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230 Buff)]TJ/F20 11.955 Tf 9.934 -4.339 Td[(ions.Thecombinationofthematerialbalanceequationsisdescribedby)2(rNH++rNOH)]TJ/F8 12.457 Tf 8.156 -0.274 Td[(+rNBuff)]TJ/F8 12.457 Tf 8.821 -0.274 Td[(=0-22whichstatesthattheaccumulationrateofthehydrogenionswasequaltotheproductionratesofhydroniumionsplusbufferions.Thealgebraiceliminationstrategypresentedherereducedthenumberofin-dependentrelationshipsfromfourtotwo.ThenaltworelationshipsrequiredforsolutionofthesystemofequationsweretheequilibriumreactionexpressionspresentedinEquations 10-12 and 10-14 .10.4.4ElectroneutralityTheentiredomainofthissystemwasconsideredtobeelectricallyneutral.Theexpressionforelectroneutralityisizici-23whichstatesthatthesumoftheionicconcentrationsmultipliedbytherespectiveionicchargenumbersisequaltozero.Electroneutralityisavalidapproximationformoderatelydilutesystems.Theelectroneutralityconditionisgenerallysatis-edinthebulkphasesofelectrochemicalsystemsbecauseofthelargeelectricalforcesrequiredtoseparatecharge.10.4.5NumericalMethodThesystemofdifferentialequationswascastinnite-differenceformandwassolvednumericallyusingtheBANDroutinedevelopedbyNewman. 261 TheBANDalgorithmwasimplementedbecauseitreducesthecomputationaleffortrequiredtosolvesystemswithtridiagonalcoefcientmatrices.Inordertoaccountfordif-ferencesinscalebetweentheskin,whichhasathicknessontheorderof10-20microns,andthedonorandreceptorchambers,themeshsizewasexpandedin

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231 thedonorandreceptorchambers.Allequationswerewrittentobeoftheorderofthesquareofthemeshsize,andconvergencewasquadratic.

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CHAPTER11MODELSIMULATIONRESULTSThesimulationresultsfromthemathematicalmodeloftransdermaliontophor-esisdescribedinChapter 10 arepresentedhere.Aseriesofsimulationswasper-formedwithskinofdifferentresistancevaluesundera100A/cm2appliedDCbias.Thepredictedpotentialproleswithinthestratumcorneumfromthesim-ulationsarepresentedinFigure 11-1 .Theskinwithpolarizationresistancesof2.9kWcm2and4.1kWcm2displayednonlinearpotentialproles.Ageneralfeatureoftheresultswasthatthedecreaseddiffusivityofthemobilespeciesassociatedwiththeassumedtortuositycausedtheskintoserveasthedominantresistanceinthesystem. Figure11-1:Potentialprolewithinthestratumcorneum. Akeyresultwasthattheelectriceldwithintheskinwassignicantlylargerthaninthesurroundingionicsolutions.Forexample,theeldstrengthwithinthe 232

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233 skinwiththe4.1kWcm2polarizationresistancewasapproximately20.7kV/cm.Theelectriceldwithintheskinwiththelowestpolarizationresistancewasap-proximately1.7kV/cm.Thelargeelectriceldwithintheskinprovidedthedom-inantdrivingforceforthetransportofionicspecies.11.1CalculatedFluxProlesTheuxprolesfortheskinwiththe4.1kWcm2polarizationresistancearepresentedinFigure 11-2 .Theuxesofthecalciumandsodiumionsareindicatedbytheblackandbluecurves.Themagnitudesofthecalciumandsodiumuxesareindicatedbytheleft-handordinate.Theredtriangularsymbolscorrespondtotheuxofchlorideions.Themagnitudeofchlorideionuxisindicatedbytherighthandordinate. Figure11-2:Calculateduxprolesofthemajorionicspeciesthroughoutsystemdomain. Theuxesofallspeciesexceptforthechlorideionwereequaltozeroattheboundariesofthesystem.Throughouttheinteriorofthesystemdomain,allspeciesuxeswerenonzerowiththehighestvaluesobservedneartheskinsur-face.Thisresult,whichmimicsthebehavioroftheexperimentalsystem,wasmadepossiblebytheinclusionoftermstoaccountforreplenishmentofspecies

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234 Figure11-3:Calculateduxproleoflidocainethroughoutsystemdomain. inthedonorsolutionandforclearanceofspeciesinthereceptor.Overallconser-vationofmassandchargeforcedtheiontophoreticuxestobenonzero.ThesimulateddruguxproleisindicatedbythesolidgreencirclesinFigure 11-3 .Thedrugux,calculatedfromthissimulation,washighestatthesur-faceoftheskinfacingthedonorsolution.Thedruguxproleintheadjacentre-ceptorsolutionshowsadramaticdecreaseasthedistancefromtheinteriorsurfaceoftheskinincreases.Thisobservationwasconsistentwiththeexpectedbehaviorofaspeciesentranceintothereceptorcompartmentandsubsequentremovalbyconvection.Asimilarbehaviordescribedbytheseresultsisthatthedrugentersthebodyandiscarriedawaybythecirculatorysystemofthepatient.TheuxproleforthesimulatedsystemwasseveralordersofmagnitudelowerthanforthetransdermaliontophoreticdeliveryratesoflidocainedescribedinSection 9.4 .Inaddition,themodelpredicteddruguxesthatwereapprox-imatelyanorderofmagnitudelowerthantheuxesreportedintheworkofPhilbrick. 164 Thediscrepancybetweenthepredictedandmeasuredtransdermaldruguxesmayhavebeencausedbyaninaccuratepredictionofthelidocaine

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235 diffusioncoefcient.Furthermore,thepredictionsobtainedhereareforskinex-hibitingpolarizationresistancevaluesthatareapproximatelyanorderofmagni-tudelowerthantypicallymeasuredvalues. 1 , 111 Numericaldifcultiespresentattheinterfacebetweentheskinsurfaceandadjacentelectrolytesolutionspreventedsimulationofmorerealisticvaluesofskinimpedance.11.2InuenceofBufferonpHWithinStratumCorneumAseparatestudywasconductedwithunbufferedandbufferedsystems.Forthesimulationsanarrayofskinresistancevalueswasselected.TheobjectivewastodeterminetheinuenceofthebufferinmediatingsolutionpH.TheresultsfromthebufferedandunbufferedsystemsarepresentedinFigure 11.4a andFigure 11.4b ,respectively.Aninterestingfeatureofthisworkisthattheconcentrationproleswithintheskinweresignicantlydifferentthaninthesurroundingsolutions.Forex-ample,thecouplingbetweentheelectroneutralityconditionwhichaccountedforthexedbackgroundcharge,thehomogeneousreactions,andthespeciesuxescausedthepHtohavealocalmaximumwithintheskinthatwashigherthaninthesurroundingsolutions.LocalmaximaofpHwereobservedforboththeunbufferedandbufferedsystems.Asexpected,themaximumpHvaluefortheunbufferedsystemwashigherthanforthebufferedsystem.ThemagnitudeofthemaximumpHwashighestforskinwiththehighestimpedancevalues.IthasbeenproposedthatextremesinpHcanbeasourceofskinirritation. 148 , 158 TheresultsheredemonstratethatextremesinpHmaybepredictedbyaccountingforthecouplingofphysicalphenomena.ThisworksuggeststhatsimulationsofskinwithhigherpolarizationimpedancewillyieldlargerobservedvaluesoflocalpHmaximawithintheskin.

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236 a bFigure11-4:CalculatedpHproleswithinstratumcorneum.aBufferedelec-trolytesystem.bUnbufferedelectrolytesystem.

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CHAPTER12CONCLUSIONSAnobjectofthisworkwastodeterminetheinuenceofappliedelectricalsig-nalsonskintransportproperties.Theworkwasdesignedtosupportthedevelop-mentofdevicesfortransdermaldeliveryoftherapeuticcompoundsbyiontophor-esis.Inaccordancewiththisgoal,electrochemicalimpedancespectroscopywasimplementedtomonitortheelectricalandtransportpropertiesofheat-separatedcadaverskinunderavarietyofconditions.Forexample,experimentswerecon-ductedwhereanonzeroDCcurrentbiaswasappliedacrossheat-separatedhu-mancadaverskintosimulateinvivotransdermaliontophoresis.Recoveryofskinpropertiestoappliedcurrentwasmonitoredbyimpedancespectroscopyatopen-circuitconditionscorrespondingtotheapplicationofa0A/cm2DCbias.Twomodulationstrategieswereimplementedfortheelectrochemicalimped-ancespectroscopystudiesofhumanskin:constant-amplitudegalvanostaticmodulationandvariable-amplitudegalvanostaticmodulation.Constant-am-plitudegalvanostaticmodulationisthetraditionalcontrolmethodusedforskinimpedanceexperiments.Foratypicalexperiment,aconstant-amplitudesinu-soidalcurrentperturbationisappliedandthepotentialresponseismeasuredoverawiderangeoffrequencies.Skinexhibitsacharacteristicallyhighimpedanceinthelow-frequencyportionsoftheimpedancespectra.Therefore,atlowfrequen-ciestheconstant-amplitudesinusoidalcurrentperturbationcaninducepotentialswingsacrossthemembranewhichoftenexceed1V.Statisticalerroranalysisofskinimpedancespectraobtainedbythismethodologyprovedtobeinconsistent 237

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238 withtheKramers-Kronigrelations.Theinconsistentdatapointswerelocatedinthelow-frequencyportionsofthespectra.Theresultsimpliedthatskinpropertieshadbeenaltered.Variable-amplitudegalvanostaticmodulationwasimplementedasthesecondcontrolstrategyfortheskinimpedanceexperiments.Theapproachwastopredic-tivelyadjusttheamplitudeofthecurrentperturbationtopreventlargepotentialswingsacrossthemembrane.Impedancespectracollectedbytheadaptivemod-ulationstrategywereshowntobeconsistentwiththeKramers-Kronigrelationswhichindicatedthatskinpropertieswerenotmodiedbytheexperiment.Theworkstronglysuggeststhatpotentialperturbationsontheorder1Vcanalterskinproperties.Asthevariable-amplitudegalvanostaticcontrolstrategyavoidslargepotentialuctuations,themethodologyshouldbeappliedformonitoringskintransportpropertiesbyelectrochemicalimpedancespectroscopy.Theworkdescribeduptothispointestablishedthatvariable-amplitudegal-vanostaticmodulationofimpedancespectroscopyprovidesfornoninvasivemea-surementofskintransportpropertiesattheopen-circuitcondition.Themethod-ologywasappliedforsubsequentelectrochemicalimpedancespectroscopyandstep-changeexperimentsdesignedtoidentifytheinuenceofanappliedDCelec-tricalbiasonskin.Forthestep-changestudiesbothapplied-currentandpotentialsignalswereappliedacrosstheepidermisforatleast20minutes.TheamplitudeoftheDCbiaswasincreasedperiodicallytodeterminethepotentialorcurrentatwhichskinpropertiesbegintochange.Theresultsindicatedthatalterationsoc-curredwhenthepotentialdifferenceacrossthemembraneexceeded100-250mV.Thedeviationintheresponsesignalfromamembranewithconstantelectricalpropertieswasproportionaltothemagnitudeofthepotentialdifferenceacrossskin.

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239 Theinuenceofsolutioncompositionontherecoveryofskinpropertiestolargeelectricalsignalswasassessed.Impedancespectroscopyexperimentswereconductedonskinspecimensimmersedinelectrolytesolutionswithmonovalentanddivalentcations.Anidenticalmethodologywasusedtostudytheskinineachtypeofelectrolyte.Therecoveryofskinpropertiestolargeelectricalperturbationswasfoundtobemorecompleteandmorerapidforthesampleimmersedintheso-lutionwithdivalentcations.Thisobservationcouldhaveimportantimplicationsforthedevelopmentofiontophoreticdrugformulations.Forexample,ifthesamebehaviorisidentiedinvivodivalentcationsaltscouldbeaddedassupportingelectrolytetothetherapeuticmixturesofiontophoreticsystems.Anotherimportantaspectofthisworkidentiedthesourcesofvariationintheelectricalandtransportpropertiesofheat-separatedcadaverskin.Alargebodyofimpedancedatawascollectedinthiswork.Forexample,127piecesofheat-separatedhumanepidermisfrom18cadaverswerestudiedbyelectrochemicalimpedancespectroscopy.Thesamplesdisplayedawidedistributionofimped-anceresponses.Statisticalanalysiswasperformedtodeterminethecontributionstotheoverallvariationinproperties.Theimpedancedataincludedintheanalysiswasobtainedfromtheskinhydrationstudieswhichwereconductedunderiden-ticalexperimentalconditions.Therefore,thesourcescontributingtothevariationwereassumedtobecausedbydifferencesbetweenthecadaversandbyvariationswithinagivenskinsample.Ageneralizedlinearmodelwasusedtoextractthecontributionstotheover-allvariationofskinproperties.Thevariationofskinimpedancewithinagivensamplewasfoundtobelargerthanthevariationassociatedwithdifferencesbe-tweenthecadavers.Theanalysissuggeststhatcautionshouldbeexercisedwhencomparingtheimpedanceresultsfromtwopiecesofskin.

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240 Amathematicalmodelwasdevelopedtosimulatetransdermaliontophoresis.Theobjectofthisworkwastocalculatetheinuenceofcontrolledvariablesontheconcentrationanduxproleswithintheskin.Theuxofionicspecieswasassumedtobedrivenbybothmigrationanddiffusion.Auniquefeatureofthisworkwasthatthepotentialprolewithintheskinwascalculatedexplicitly.Equi-libratedhomogeneousreactionswereincludedtoaccountforpartialdissociationofwaterandbuffers.ThespeciespresentinthesimulatedsystemwereassumedtobeCa2+,Na+,Cl)]TJ/F20 11.955 Tf 6.946 -4.34 Td[(,H+,OH)]TJ/F20 11.955 Tf 9.672 0 Td[(,drugcation,drugcounteranion,anddissociatedandundissociatedbufferspecies.Inaddition,thechargeoftheskinwastreatedtobeanimmobileionicspecies.Aninterestingfeatureofthisworkisthattheconcentrationproleswithintheskinweresignicantlydifferentthaninthesurroundingsolutions.Forex-ample,thecouplingbetweentheelectroneutralityconditionwhichaccountedforthexedbackgroundcharge,thehomogeneousreactions,andthespeciesuxescausedthepHtohavealocalmaximumwithintheskinthatwashigherthanei-therofthesurroundingsolutions.ThelargestlocalpHmaximawereobservedinthesimulationsofskinwiththelargestpolarizationresistances.TransdermaldeliveryratesofthemodeldruglidocaineweremeasuredbyUV-visspectroscopy.Acustomdual-channelspectrometerapparatuswasdevelopedtoprovideforthesimultaneousmeasurementoftransdermallidocaineuxandskintransportpropertiesunderiontophoreticconditions.Theabsorptionspec-troscopysystemwasshowntobeproperlycalibrated.Thecalibrationprocedureprovideforthecalculationoflidocainedeliveryratesacrosstheskin.Itwasdemonstratedinthisworkthatthetransdermaluxoflidocainewasincreasedbyoveranorderofmagnitudewhencurrentwasapplied.Thelargesttransder-maldeliveryrateswereobservedatthelargestamplitudesofappliedcurrent.The

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241 resultsindicatethationtophoresiscanimprovethedeliveryefciencyofchargedtherapeuticcompoundsacrossskin.Insummary,theexperimentalworkdescribedinthistextidentiedthein-uenceofcontrolledvariablessuchascurrent,potentialandsolutioncomposi-tionontheelectricalandtransportpropertiesofheat-separatedhumanskin.ThedeliveryratesoflidocaineacrosstheskinweremeasuredbyUV-visabsorptionspectroscopy.Theresultsindicatedthattheappliedelectricalcurrentenhancedthetransdermaluxoflidocaine.Themathematicalmodeloftransdermalionto-phoresisprovidedinformationontheeffectofcoupledphenomena,suchasequi-librateddissociationreactionsandelectroneutrality,ontheconcentrationanduxproleswithinahomogeneousmembranewithpropertiessimilartohumanstra-tumcorneum.

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CHAPTER13SUGGESTEDRESEARCHAlargedatabaseofimpedancespectrawascollectedinthisworktodeterminetheeffectofappliedelectricalsignalsonskintransportproperties.ThespectrawereregressedtotheVoigtcircuitmodeltoidentifydatathatwasinconsistentwiththeKramers-Kronigrelations.Identicationoftheinconsistentdatapro-videdameansfordeterminingchangesinskinproperties.Inthismanner,theinuenceofagivensetofexperimentalparametersonmembranepropertiescouldbedetermined.Althoughthisapproachisrobust,additionalinformationcouldbeextractedbyregressingaprocessmodeltotheimpedancespectracollectedinthiswork.Theprocessmodelwouldlikelyincludetermsassociatedwiththemasstransferresist-anceofionsenteringandexitingthestratumcorneum.Inaddition,theadsorptionofelectrolytecationstothenegativebackgroundchargeofskincouldprovideamechanismfortheobservedcapacitanceofthemembrane.Themodelparametersassociatedwiththistypeofformulationwoulddirectlycorrespondtothephysicalpropertiesoftheskin.Regressionofthemodeltotheimpedancespectracollectedinthisworkwouldprovidefordirectcalculationoftheinuenceofelectricalsig-nalsonthephysicalpropertiesoftheskin.Heat-separatedhumancadaverskinwasusedasthemodelmembraneforthisstudy.Theprimarytransportbarrierforthedeliveryoftherapeuticcompoundsisthestratumcorneum.Theentirestratumcorneumwascontainedintheepider-malmembranesusedforthisstudy.Theworkpresentedinthisreportaddressed 242

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243 andidentiedmanyoftheimportantfactorsaffectingdrugtransportacrossintacthumanskinduringiontophoresis.However,therearedifferencesbetweenheat-separatedhumancadaverskinandintacthumanskin. 97 , 152 , 148 , 206 , 207 Forexample,thepolarizationimpedanceofhumancadaverskinwasfoundtobeapproximatelyanorderofmagnitudelowerthanforhumanskininvivo. 152 Thesedifferencessug-gestthattheexperimentalmethodspresentedinthisworkshouldbeappliedforinvivotransdermaliontophoresisinvestigationstoidentifytheinuenceofcon-trolledvariablesontheefciencyofdrugtransport.ItwasdemonstratedinChapter 9 thatthecouplingofUV-visabsorptionspec-troscopywithelectrochemicalimpedancespectroscopyrepresentsapromisingmethodologyformonitoringtransdermaliontophoresis.TheUV-visabsorptionspectroscopysystemwasshowntobeproperlycalibrated.Preliminarytrans-dermaliontophoresisexperimentsindicatedthatelectricalcurrentenhancedli-docaineux.DespitethesuccessfulapplicationofUV-visabsorptionspectroscopyforthemeasurementofthelidocainedeliveryratesacrossskin,thereremainunresolvedissues.Forexample,someoftheabsorptionmeasurementsthatindicatedlido-caineconcentrationdecreasedforshortintervalsduringthetransdermaluxex-periments.Aspassivediffusionwassmallandpositiveacrosstheskin,theun-usualresultwasprobablycausedbymeasurementerror.Hence,itisrecom-mendedthatadditionaltransdermaliontophoresisexperimentsbeperformedtodeterminethesourceoftheanomalousbehavior.Inaddition,UV-visabsorp-tionspectroscopyisaninferentialtechnique,therefore,supplementalexperimen-talmethods,suchasmassspectroscopyorhigh-performanceliquidchromatogra-phy,shouldbeimplementedtodirectlymeasurelidocaineconcentrationsinthereceptorchamberofthediffusioncell.Thisapproachcouldbeusedtovalidate

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244 theaccuracyandprecisionoftheUV-visabsorptionspectroscopymeasurementsunderiontophoreticconditions.Theinuenceofcontrolledvariablessuchassolutioncompositionandappliedcurrentonthedeliveryofamodeldrugacrossthestratumcorneumwasassessedbythesteady-statemodelofthetransdermaliontophoresis.Thestratumcorneumwassimulatedasahomogeneousmembranewithuniformproperties.Theac-tualstructureandcompositionofhumanstratumcorneumismuchmorecomplexthanforthetransdermalsystemsimulatedhere.Despitethislimitation,theim-portantfactorsaffectingtransdermaldeliveryofionicdrugcompoundsbyionto-phoresis,suchasthenegativebackgroundchargeandlowpermeabilityofstratumcorneum,wereconsidered.Interactionswiththenegativebackgroundchargeofthestratumcorneumwerecoupledthroughtheelectroneutralitycondition.Specicinteractions,suchasthebindingofsolutioncationswiththenegativebackgroundchargeofskin,werenotconsidered.Amechanismforbindingcouldbeincludedinthemodelbyintro-ducingaGibbsadsorptionisothermattheinterfacebetweenthenegativechargesitesoftheskinandtheelectrolytesolution.Thedrivingforcefortheadsorptionreactionsshouldbeproportionaltotheelectrostaticpotentialdifferenceatthein-terface.Themodelcouldalsoberenedtoaccountforadditionalequilibratedhomogeneousreactionssuchasthedissociationofstratumcorneumfattyacids.Thesetypesofrenementswouldprovideforanimprovedmodeloftransdermaliontophoresis.

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APPENDIXAPREPARATIONOFEPIDERMISHeatseparatedhumancadaverskinwasusedforalloftheexperimentalstud-ies.Thethicknessoftheskinsampleswasontheorderof100mwhichcorre-spondedtotheuppermostlayersoftheepidermis.Thestratumcorneumcom-posedthetop20mofthemembranes.TheskinsampleswereextractedfromthecadaversatALZACorporationandwereshippedbyover-nightexpressmailininsulatedcontainers.Theprocedureforseparatingtheepidermisfromthedermisisdescribedhere. 262 1. Iffrozenskinwasused,itwasallowedtopartiallythaw.Thepartiallythawedskinwascutinto10cmx15cmpieces.Halfoftheunderlyingtis-sueandfatweretrimmedwithascalpelorscissorssuchthatthedermisandepidermisremainedintact. 2. Thefull-thicknessskinwasrinsedinapanofroom-temperaturedeionizedwaterforseveralminutes. 3. Thefull-thicknessskinwasthenrinsedinapanof32Cdeionizedwaterandallowedtosoakforseveralminutes. 4. Thefull-thicknessskinwastransferredtoalargebeakerorpanofdeionizedwaterwithaninitialtemperatureof62.0C.Theskinwassubmergedwithaglassstirringrodforoneminute.Thetimeandtemperatureweremeasuredbyastopwatchanddigitalthermometer,respectively. 245

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246 5. Thewarmskinwastransferredontoplasticsheetingorapieceoflab-benchlinerforseparationoftheepidermis.Atthestartoftheseparationproce-duretheedgeofthedermiswasheldwithtweezersandtheepidermiswithlightlyimpactedwiththeedgeofaround-tippedspatula.Afterapproxi-mately4cm2oftheepidermiswasseparated,thedermiswashelddownwithaglovedhandandtheepidermispushedawaywiththespatulaorglovednger. 6. Theepidermiswasplacedapanofdeionizedwater,oatingtheepidermiswiththedermalsidefacingthewatertorinsetheepidermis.Thisstepwasrepeatedseveraltimestoremoveexcessfatfromtheskin.Theepidermiswasshippedforuseorwasstoredforlateruse. 7. Theepidermiswaspreparedforstoragebyoatingitinapanofwaterandplacingapieceofreleaselinerpolymersheetingundertheepidermis.Thereleaselinerwasusedtopickuptheepidermisandwrinklesinthemem-braneremoved.Theepidermiswasplacedbetweenasecondpieceofreleaselinerandgentlyagitatedtoremoveexcesswater.Theepidermiswaspack-agedinplasticbag,sealed,andstoredat4Cforaperiodnotlongerthan3weeks.

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APPENDIXBVAGMODULATIONFORIMPEDANCESPECTROSCOPYInordertomaintainlinearityinanelectrochemicalsystem,thepotentialmustbekeptbelowacriticalvaluewhichischaracteristictothesystemunderstudy.Atypicalimpedancescanstartsathighfrequencyandthefrequencyisdecreasedincrementallyuntiltheminimummeasuringfrequencyisattained.Electrochem-icalsystemsfrequentlyexhibitathreeorderofmagnitudeincreaseinimpedanceasthefrequencyissweptfromhightolow.Foraconstant-amplitudegalvanostat-icallymodulatedexperiment,thepotentialdifferencewillreachitsgreatestvaluewheretheimpedanceexhibitsitsgreatestvalue.Wojciketal. 235 developedanalgorithmtoadjustthecurrentperturbationateachmeasuringfrequencytopre-ventlargepotentialdifferencesduringthecourseofanelectrochemicalimpedancespectroscopyexperiment.B.1DesignEquationsTherstsetofoperationsperformedinthepredictivealgorithmestimatetheimpedancevalueatthenextmeasuringfrequencyinthescan.Forallbuttherst3measuringfrequencies,thepredictedimpedanceisobtainedfromasecondorderaccuracylinearextrapolationofthepreviouslymeasuredimpedancevalues.Throughoutthecourseofanexperiment,thepredictedimpedancevalueisusedwithasetvalueforthedesiredpotentialdifferenceinthesystemtocalculatethecurrentperturbationatthenextmeasuringfrequencyaccordingtoDeI!=DeVtarget jZ!jestimatedB-1 247

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248 whereDeVtargetisthedesiredpotentialresponseandjZ!jestimatedistheguessvaluefortherstimpedancemeasurement.Agoodestimatefortherstvalueoftheimpedanceistheelectrolyticsolutionresistance.Theimpedancevaluemeasuredattherstfrequencyisthenusedtopredicttheappearanceatthesecondfre-quencyaccordingtoZ!k=Z!k)]TJ/F20 7.97 Tf 6.448 0 Td[(1+Olog!k !k)]TJ/F20 7.97 Tf 6.447 0 Td[(12B-2Forthethirdmeasuringfrequency,theimpedanceispredictedbythetwopointformulaZ!k=2Z!k)]TJ/F20 7.97 Tf 6.448 0 Td[(1)]TJ/F53 11.955 Tf 12.534 0 Td[(Z!k)]TJ/F20 7.97 Tf 6.448 0 Td[(2+Olog!k !k)]TJ/F20 7.97 Tf 6.448 0 Td[(12B-3Fortheremainderoftheimpedancescan,theimpedanceispredictedbyZ!k=3Z!k)]TJ/F20 7.97 Tf 6.448 0 Td[(1)]TJ/F20 11.955 Tf 11.996 0 Td[(3Z!k)]TJ/F20 7.97 Tf 6.447 0 Td[(2+Z!k)]TJ/F20 7.97 Tf 6.448 0 Td[(3+Olog!k !k)]TJ/F20 7.97 Tf 6.448 0 Td[(12B-4Anessentialfeatureofthevariableamplitudemodulationtechniqueisthatdy-namicadjustmentofthecurrentmeasuringresistorisrequiredtoachieveaccept-ablesignal-to-noiseratios.AppropriatemeasuringresistorselectionwasachievedinthisworkusingacustomsoftwarecontrolinterfacewritteninLabVIEWGrforWindows.Theapplicationofvariable-amplitudegalvanostaticmodulationwasshowntobelessinvasivethantraditionalconstantamplitudegalvanostaticcontrol. 263 Thevariableamplitudegalvanostaticmodulationtechniquehasbeenappliedtocorrosionstudiesofcopperandsteel. 264 B.2ErrorAnalysisofVAGModulationSchemeAstudywasperformedinthisworktoassesstheaccuracyofthepredictivealgorithmfortheskinsystem.Atypicalskinimpedancespectrumwasusedtocomparethealgorithmpredictionsforimpedancetothemeasuredvaluesatat

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249 eachfrequency.ThepercentrelativeerrorwascalculatedaccordingtoErelative=jZ!jestimated)-185(jZ!jdata jZ!jdata100%B-5wherejZ!jestimatedandjZ!jdataaretheimpedancequantitiesfromthealgorithmandmeasurement,respectively.Thepercentrelativeerrorasafunctionoffre-quencyispresentedinFigure B-1 .Predictionsbasedontheimpedancedataareshownbythelledtriangles.Theerrorsappeartoberandomlydistributedwithameanof3.03x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2%andstandarddeviationof1.18%.Theerrorscontaincontri-butionsfromthepredictivealgorithmandtheexperimentalapparatusaccordingtoEtotal=Ealgorithm)]TJ/F53 11.955 Tf 12.534 0 Td[(EinstrumentB-6whereEalgorithmrepresentstheerrorassociatedwithTaylorseriespredictionoftheimpedanceandEinstrumentistheerrorcontributionfromtheexperimentalappara-tus.Althoughtherelativeerrorforthepredictionoftheimpedancewasaslargeas2.2%theinuenceoftheerrorontheexperimentisexpectedtobeminimal.Aslongastheinstrumentprovidesanacceptablesignal-to-noiseratioandlinearityismaintainedinthesystem,accurateimpedancemeasurementsshouldbeobtained.Thenumericalaccuracyofthepredictivealgorithmwasestimatedfromsim-ulationsofanidealcircuitnetworkconsistingofaresistorinserieswithaRCelementsee,forexampleFigure, 3-3 andasecondcircuitnetworkconsistingofaresistorinserieswithaparallelcombinationofaresistorandaconstantphaseelementsee,forexample,Figure 3-6 .Theconstantphaseelementnetworkwasincludedinthesimulationsbecauseitprovidesanimpedanceresponsewhichissimilartothatofskin.Forbothnetworksthepolarizationimpedanceandcharac-

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250 FigureB-1:PercentrelativeerrorforpredictionofimpedancefromVAGalgo-rithm.OpendiamondsrepresenterrorforidealcircuitconsistingofaresistorinserieswithasingleRCelement.Thelledcirclesaretheerrorsfromtheconstantphaseelementcircuit.Thesolidtrianglesrepresenttheerrorforpredictedimped-ancevaluesobtainedfromatypicalimpedancespectraofskin. teristicfrequencywerethesame.Thedifferenceintheimpedancevaluesobtainedfromcircuitmodelparametersandthealgorithmpredictionsprovidedforesti-matesofEalgorithm.TherelativeerrorsfromthesimulationwiththeRCnetworkarepresentedbytheopendiamondsinFigure B-1 .Theabsolutevalueoftheerrorswaslessthan0.6%.Theerrorsshowedsignicanttrendingasafunctionoffrequencywithameanof1.20x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1%andstandarddeviationof2.76x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1%.Similarly,theabsolutevalueoftherelativepercenterrorsfromthesimulationwiththeconstantphaseelementnetworkarepresentedasopencirclesinFigure B-1 .Theabsolutevalueoftherelativeerrorsforthissystemwaslessthan0.2%oftheimpedancemagni-tude.Themeanandstandarddeviationofthepercenterrorswas1.97x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2%and7.24x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2%,respectively.Trendingoftheerrorsasafunctionoffrequencywasobserved.Forbothsystemstheerrorsweregreatestclosetothecharacteristicfre-

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251 quency,althoughthespreadofthedatawassignicantlysmallerfortheconstantphaseelementnetwork.ThelargerpredictionerrorsassociatedwiththeRCelementnetworkwerelikelycoupledtotherelativelylargerslopeoftheimpedanceasafunctionoffre-quency.Theequationsforthepredictivealgorithmarederivedfromarst-orderTaylor'sseriesexpansionoftheimpedance.Theexpansionprovidesestimatesfortheimpedanceatthenextmeasuringfrequencybymultiplyingtheslopeoftheimpedancebythefrequencyinterval.SincetheslopeoftheRCelementnet-workisgreaterthantheconstantphaseelementnetwork,especiallyatfrequenciesnearthecharacteristicfrequency,errorsinthepredictionoftheimpedancewillbegreater.Ingeneral,thepredictivealgorithmwillbemoreaccurateforsystemssuchasskinwheretheimpedancechangeslessdramaticallyasafunctionoffrequencyascomparedtoaRCelementnetworkwiththesamepolarizationimpedanceandcharacteristicfrequency.

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APPENDIXCSTATISTICALOUTPUTTheresultspresentedinthisappendixweregeneratedinthepreliminaryanal-ysisofvarianceintheskinimpedancedatasets.Statisticalparametersdescribingthedistributioncharacteristicsoftheimpedancedataarepresentedintherstsec-tion.Skinpolarizationresistanceandcriticalfrequencywereselectedascharac-teristicparametersfortheimpedancespectra.Thedataweregroupedaccordingtoelectrolytetypetoevaluatetheinuenceofcationchargeonthevariationinskinimpedance.TheresultsfromregressionsoftheGeneralizedLinearModeltovarioustransformationsoftheskinimpedancedataarepresentedinSection C.2 andhistogramsoftheskindataarepresentedinSection C.3 .C.1DistributionStatisticsfromEISMeasurementsofSkinHydrationAtthestartofallexperimentsdescribedinthistextmultipleelectrochemicalimpedancespectrawerecollectedtomonitorskinhydration.Theheat-separatedepidermalmembraneswereimmersedininorganicchloridesaltsolutionsofmono-valentordivalentcations.Asalargedatabaseofmeasurementswascollectedthepolarizationresistanceandcriticalfrequencywereselectedasrepresentativepa-rametersforskintransportproperties.Thepolarizationresistanceandcriticalfre-quencyassociatedwiththeimpedancespectraofskinhydrationwereseparatedaccordingtoelectrolytetype.Student'st)]TJ/F20 11.955 Tf 9.671 0 Td[(testsandF-testswereperformedonthedatasetstodeterminewhetherthepopulationmeansandpopulationvarianceswereequalfortheexper-imentsconductedinmonovalentanddivalentcations.Furthermore,thegrouping 252

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253 schemeprovidedforproperassessmentofthecontributionstotheoverallvaria-tioninskinproperties.Forexample,theskinspecimenswereobtainedmultiplecadavers,therefore,thevariationinskinpropertiescouldbecausedbydifferencesbetweenthecadaversorbyregionalvariationswithinagivendonorsample.AdetaileddescriptionofthestatisticalanalysisprocedureisprovidedinChapter 7 .Theanalysisofvariancemethodologyrequiresthatthepopulationbenor-mallydistributed.Logarithmicandsquareroottransformationsofthepolariza-tionresistanceandcriticalfrequencydatawereappliedtodeterminethemostap-propriaterepresentationforthemeasurements.Keystatisticalparameters,suchasmean,kurtosiscoefcient,andskewness,fromthepopulationofimpedancemeasurementsandtransformeddatasetsareprovidedinTables C-1 C-3 .Theparameterswereusedtoguidethestatisticalanalysis. TableC-1:Distributionstatisticsforskinpolarizationresistanceandcriticalfre-quencyasafunctionelectrolytetype PolarizationResistance CriticalFrequency Statistic Monovalent Divalent Monovalent Divalent Mean 6.22x104 9.31x104 715.66 435.33 StandardError 4.41x103 9.58x103 77.57 93.54 Median 3.09x104 7.00x104 169.66 78.75 Mode 1.14x104 3.07x104 954.10 53.65 StandardDeviation 8.81x104 1.04x105 1.55x103 1.02x102 SampleVariance 7.76x109 1.09x1010 2.39x106 1.04x106 Kurtosis 12.43 7.85 20.79 14.04 Skewness 3.08 2.67 4.35 3.67 Minimum 1.28x103 1.72x103 3.66 11.56 Maximum 6.39x105 5.22x105 1.16x104 5.37x103 Sum 2.48x107 1.11x107 2.85x105 5.18x104 Count 398 119 398 119 CondenceLevel.0% 8.67x103 1.90x104 152.50 185.24 C.2AnalysisofVarianceforEISMeasurementsofSkinHydrationTheresultsfromtheanalysisofvariancefortheGeneralizedLinearModelrep-resentationofthepolarizationimpedanceandcriticalfrequencyofskinsamples

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254 TableC-2:Distributionstatisticsforlog10ofskinpolarizationresistanceandcriti-calfrequencyasafunctionelectrolyte PolarizationResistance CriticalFrequency Statistic Monovalent Divalent Monovalent Divalent Mean 4.456 4.727 2.30 2.03 StandardError 0.028 0.049 3.72x10)]TJ/F20 7.97 Tf 6.447 0 Td[(2 6.01x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 Median 4.498 4.845 2.23 1.90 Mode 4.058 4.487 2.98 1.73 StandardDeviation 0.550 0.529 7.33x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 6.55x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 SampleVariance 0.302 0.280 5.38x10)]TJ/F20 7.97 Tf 6.447 0 Td[(1 4.30x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Kurtosis -0.568 1.090 -4.82x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 1.55x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Skewness 4.77x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 -0.930 -6.13x10)]TJ/F20 7.97 Tf 6.448 0 Td[(3 8.53x10)]TJ/F20 7.97 Tf 6.448 0 Td[(1 Minimum 3.107 3.235 0.563 1.06 Maximum 5.806 5.717 4.06 3.73 Sum 1729.046 562.53 891.90 241.90 Count 388 119 388 119 CondenceLevel.0% 5.49x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 9.61x10)]TJ/F20 7.97 Tf 6.447 0 Td[(2 7.32x10)]TJ/F20 7.97 Tf 6.448 0 Td[(2 0.119 immersedinmonovalentanddivalentelectrolytesolutionsarepresentedinSec-tions C.2.1 and C.2.2 .C.2.1RegressiontoPolarizationResistanceTheresultsfromtheanalysisofvariancefortheGeneralizedLinearModelrep-resentationofthepolarizationimpedanceofskinsamplesimmersedinmonova-lentanddivalentelectrolytesolutionsispresentedinTables C-4 and C-5 .TheF-testparameterandprobabilityvaluesforacceptanceofthenullhypoth-esisfortheeffectofthedonorfromwhichapieceofskinwasextractedonthepolarizationresistanceofthespecimensimmersedinmonovalentelectrolytewere1.57and9.84%,respectively.TheF-testparameterandprobabilityvaluesforef-fectoflocationfromwhichapieceofskinwasobtainedwere152.88andlessthan0.01%.ThenullhypothesiswasrejectedforbotheffectsasF-testprobabilitiesforacceptanceofthenullhypothesisweresosmall.Theresultsimpliedthattherewasasignicanteffectonpolarizationimpedanceforskinimmersedinmonova-lentelectrolyteduetothedonorsampleandthelocationfromwhichthespecimen

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255 TableC-3:Distributionstatisticsforsquarerootofskinpolarizationresistanceandcriticalfrequencyasafunctionelectrolyte PolarizationResistance CriticalFrequency Statistic Monovalent Divalent Monovalent Divalent Mean 206.06 270.01 19.93 14.52 StandardError 6.89 13.07 0.92 1.38 Median 177.53 264.51 13.03 8.87 Mode 106.94 175.14 30.89 7.32 StandardDeviation 135.76 142.62 18.20 15.04 SampleVariance 1.84x104 2.03x104 331.28 226.27 Kurtosis 2.38 2.01 6.02 5.77 Skewness 1.43 1.10 2.21 2.42 Minimum 35.79 41.43 1.91 3.40 Maximum 799.65 722.22 107.51 73.25 Sum 8.00x104 3.21x104 7733.55 1728.41 Count 388 119 388 119 CondenceLevel.0% 13.55 25.89 1.82 2.73 TableC-4:CalculatedcontributionstovariancefromregressionofGLMmodeltoskinpolarizationresistancedataforpiecesimmersedinmonovalentelectrolyte Variable DOF MeanSq. Fvalue Probability Donortype 16 3.72x1010 1.57 0.0984 LocationDonor 79 2.57x1010 152.88 <0.0001 wasextracted.Similarresultswereobtainedfromtheregressionofthestatisticalmodeltothedatasetforskinimmersedindivalentelectrolyte,however,theeffectofdonorsampleonthepolarizationimpedancewasevengreaterasbothproba-bilitiesforacceptanceofthenullhypothesiswerelessthan0.01%.C.2.2RegressiontoCriticalFrequencyTheresultsfromtheanalysisofvarianceforerrortermsfortheGeneralizedLinearModeltothecriticalfrequenciesofskinsamplesimmersedinmonovalentanddivalentelectrolytesolutionsispresentedinTables C-6 and C-7 .TheF-test TableC-5:CalculatedcontributionstovariancefromregressionofGLMmodeltoskinpolarizationresistancedataforpiecesimmersedindivalentelectrolyte Variable DOF MeanSq. Fvalue Probability Donortype 11 1.03x1011 12.07 <0.0001 LocationDonor 20 7.77x109 87.32 <0.0001

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256 TableC-6:CalculatedcontributionstothetotalvariancefromregressionofGLMmodeltothecriticalfrequencyofskinimmersedinmonovalentelectrolyte Variable DOF MeanSq. Fvalue Probability Donortype 16 9.84x106 1.14 0.332 LocationDonor 79 9.31x106 294.96 <0.0001 TableC-7:CalculatedcontributionstothetotalvariancefromregressionofGLMmodeltothecriticalfrequencyofskinimmersedindivalentelectrolyte Variable DOF MeanSq. Fvalue Probability Donortype 11 3.75x106 0.85 0.6005 LocationDonor 20 4.05x106 396.28 <0.0001 parameterandprobabilityvaluesforacceptanceofthenullhypothesisi.e.,thattherewasnosignicantvarianceincriticalfrequencyforskinimmersedinmono-valentelectrolyteduetothedonorsamplefromwhichthepiecewasobtainedwere1.14and33.2%.Similarly,theF-testparameterandprobabilityvaluesforeffectoflocationfromwhichapieceofskinwasobtainedwere396.28and60.05%.Thenullhypothesisfortheeffectofdonorsampleonthecriticalfrequencyforskinimmersedinmonovalentelectrolytecouldnotberejected,astherewasa33.2%chanceofselectingtwopiecesofskinwithsimilarcriticalfrequenciesfromdifferentdonors.Alternativelystated,therewasasmallvariationincriticalfre-quencyduetodifferencesinskinfromthedonorpopulation.SincetheF-testprob-abilityvaluefortheeffectofextractionsiteofskinimmersedindivalentelectrolytewas60.05%,thenullhypothesiswasnotrejected.TherelativelyhighF-testvalueindicatedthesite-to-sitevariationofcriticalfrequencywasinsignicant.Thisim-pliedtheeffectofextractionlocationoncriticalfrequencyforskinimmersedindivalentelectrolytewasnotaspronouncedasfortheskinsamplesimmersedinmonovalentelectrolyte.Theanalysisofvariancestudyindicatedthatthepolarizationimpedancesandcriticalfrequenciesforpiecesofskinobtainedfromthesamedonorsamplewerenotcorrelated.Inotherwords,theintra-individualvariationofskinproperties

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257 wasgreaterthantheinter-individualvariation.Theresultssuggestthatimped-anceresponseofskinsamplesextractedfromthesamedonorcannotbeconsid-eredasidenticalspecimens.C.3HistogramsofSelectedSkinPropertiesDuringHydrationThehistogramscorrespondingtomeasuredvaluesandtransformedvaluesofselectedskinpropertiesarepresentedhere.Theguresaregroupedaccordingtoelectrolyte.Histogramsofthepolarizationresistanceandcriticalfrequencyarepresentedseparately.

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258 a bFigureC-1:Histogramsofthepolarizationresistanceofskinimmersedinmono-valentelectrolyte.aMeasuredvalues.bDatatransformedbythebase10loga-rithm.

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259 a bFigureC-2:Histogramsofpolarizationresistanceofskinimmersedindivalentelectrolyte.aDistributionofmeasuredvalues.bDatatransformedbythebase10logarithm.

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260 a bFigureC-3:Histogramsofskincriticalfrequencyforpiecesimmersedinmonova-lentelectrolyte.aMeasuredvalues.bDatatransformedbythebase10loga-rithm.

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261 a bFigureC-4:Histogramsofthecriticalfrequencyofskinimmersedindivalentelec-trolyte.aDistributionofmeasuredvalues.bDatatransformedbythebase10logarithm.

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BIOGRAPHICALSKETCHMichaelA.Membrinoreceivedabachelorofsciencedegreeinchemicalen-gineeringfromWorcesterPolytechnicInstituteinMay1992.HethenacceptedaNationalScienceFoundationMEDIfellowshipandbeganhisgraduatestudiesattheUniversityofFloridainJanuary1993.AfterhisarrivalinFloridahejoinedProfessorMarkOrazem'selectrochemicalengineeringresearchgrouptopursueadoctorateofphilosophydegree.UponcompletionofdegreerequirementsinMay2002,Mikeplanstosecureapositionfortheapplicationofelectrochemicalengineeringprinciplestoindustrialresearchanddevelopment. 283