JournalofMathematicalBiologymanuscriptNo. (willbeinsertedbytheeditor) A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone Julian King · Karl Unterkofler · GeraldTeschl · SusanneTeschl · HelinKoc · HartmannHinterhuber · AntonAmann 1 1 Received:23March2010/Revised:9November2010 0 2 n a J 7 2 ] M J.King BreathResearchInstituteoftheAustrianAcademyofSciences Q Rathausplatz4,A-6850Dornbirn,Austria E-mail:[email protected] . o K.Unterkofler i b VorarlbergUniversityofAppliedSciencesand BreathResearchUnitoftheAustrianAcademyofSciences - q Hochschulstr.1,A-6850Dornbirn,Austria [ E-mail:karl.unterkofl[email protected] G.Teschl 3 UniversityofVienna,FacultyofMathematics v Nordbergstr.15,A-1090Wien,Austria 5 E-mail:[email protected] 7 4 S.Teschl 4 UniversityofAppliedSciencesTechnikumWien . Ho¨chsta¨dtplatz5,A-1200Wien,Austria 3 E-mail:[email protected] 0 0 H.Koc 1 VorarlbergUniversityofAppliedSciences Hochschulstr.1,A-6850Dornbirn,Austria : v H.Hinterhuber i X InnsbruckMedicalUniversity,DepartmentofPsychiatry Anichstr.35,A-6020Innsbruck,Austria r a A.Amann(correspondingauthor) Univ.-ClinicforAnesthesia,InnsbruckMedicalUniversityand BreathResearchInstituteoftheAustrianAcademyofSciences Anichstr.35,A-6020Innsbruck,Austria E-mail:[email protected],[email protected] 2 Abstract Recommendedstandardizedproceduresfordeterminingexhaledlowerres- piratorynitricoxideandnasalnitricoxide(NO)havebeendevelopedbytaskforces oftheEuropeanRespiratorySocietyandtheAmericanThoracicSociety.Theserec- ommendationshave paved the way for the measurementof nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similarguidelinesforthesamplingofothertracegasesinexhaledbreath,especially volatileorganiccompounds(VOCs)whichmayreflectongoingmetabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath areinfluencedby: – breathingpatternsaffectinggasexchangeintheconductingairways – theconcentrationsinthetracheo-bronchialliningfluid – thealveolarandsystemicconcentrationsofthecompound. TheclassicalFarhiequationtakesonlythealveolarconcentrationsintoaccount.Real- timemeasurementsofacetoneinend-tidalbreathunderanergometerchallengeshow characteristicswhichcannotbeexplainedwithintheFarhisetting.Herewedevelop a compartmentmodelthatreliablycapturestheseprofilesandiscapableofrelating breathtothe systemicconcentrationsof acetone.By comparisonwith experimental data it is inferredthat the major partof variabilityin breath acetoneconcentrations (e.g.,inresponsetomoderateexerciseoralteredbreathingpatterns)canbeattributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations.Moreover,themodelilluminatesthediscrepanciesbetweenobserved andtheoreticallypredictedblood-breathratiosofacetoneduringrestingconditions, i.e.,insteadystate.Particularly,thecurrentformulationincludestheclassicalFarhi andtheScheidseriesinhomogeneitymodelasspeciallimitingcasesandthusisex- pectedtohavegeneralrelevanceforawiderrangeofblood-borneinertgases. Thechiefintentionofthepresentmodelingstudyistoprovidemechanisticrela- tionshipsforfurtherinvestigatingtheexhalationkineticsofacetoneandotherwater- solublespecies.Thisquantitativeapproachisafirststeptowardsnewguidelinesfor breathgasanalysesofvolatileorganiccompounds,similartothosefornitricoxide. Keywords breathgasanalysis·volatileorganiccompounds·acetone·modeling MathematicsSubjectClassification(2000) 92C45·92C35·93C10·93B07 3 1 Introduction Measurement of blood-bornevolatile organic compounds(VOCs) occurring in hu- manexhaledbreathasaresultofnormalmetabolicactivityorpathologicaldisorders has emerged as a promising novel methodology for non-invasive medical diagno- sisandtherapeuticmonitoringofdisease,drugtestingandtrackingofphysiological processes[2,3,1,73,57].Apartfromtheobviousimprovementinpatientcompliance and tolerability, major advantages of exhaled breath analysis compared to conven- tionaltestprocedures,e.g.,basedonbloodorurineprobes,includede factounlim- ited availability as well as rapid on-the-spot evaluation or even real-time analysis. Additionally,ithasbeenpointedoutthatthepulmonarycirculationreceivestheen- tirecardiacoutputandthereforethebreathconcentrationsofsuchcompoundsmight provideamorefaithfulestimateofpooledsystemicconcentrationsthansinglesmall- volume blood samples, which will always be affected by local hemodynamicsand blood-tissueinteractions[65]. Despitethishugepotential,theuseofexhaledbreathanalysiswithinaclinicalsetting isstillratherlimited.Thisismainlyduetothefactthatdrawingreproduciblebreath samplesremainsanintricatetaskthathasnotfullybeenstandardizedyet.Moreover, inherenterrorsourcesintroducedbythecomplexmechanismsdrivingpulmonarygas exchangearestillpoorlyunderstood.Thelackofstandardizationamongthedifferent samplingprotocolsproposedin the literaturehas led to the developmentof various sophisticatedsamplingsystems,whichselectivelyextractend-tidalairbydiscarding anatomicaldead space volume [42,28,13]). Even thoughsuch setups present some progress,they are far from being perfect.In particular,these sampling systems can usuallynotaccountforthevariabilitystemmingfromvaryingphysiologicalstates. Incommonmeasurementpracticeitisoftentacitlyassumedthatend-tidalairwill reflectthealveolarconcentrationC ,whichinturnisproportionaltotheconcentra- A tionoftheVOCinmixedvenousbloodC ,withtheassociatedfactordependingon v¯ the substance-specific blood:gaspartition coefficientl (describingthe diffusion b:air equilibriumbetween capillariesand alveoli),alveolarventilationV˙ (governingthe A transportofthecompoundthroughtherespiratorytree)andcardiacoutputQ˙ (con- c trollingtherateatwhichtheVOCisdeliveredtothelungs): C v¯ C =C = . (1) measured A l +V˙A b:air Q˙c This is the familiar equation introducedby Farhi [21], describingsteady state inert gaseliminationfromthelungviewedasasinglealveolarcompartmentwithafixed overall ventilation-perfusion ratio V˙ /Q˙ close to one. Since the pioneering work A c ofFarhi,bothequalitiesintheaboverelationhavebeenchallenged.Firstly,forlow bloodsolubleinertgases,characterizedbyl ≤10,alveolarconcentrationsresult- b:air ingfromanactuallyconstantC caneasilybeseentovarydrasticallyinresponseto v¯ fluctuationsinbloodorrespiratoryflow(seealso[43,41]forsomerecentfindingsin thiscontext).WhilethissensitivityhasbeenexploitedinMIGET(MultipleInertGas Elimination Technique, cf. [93,92]) to assess ventilation-perfusion inhomogeneity 4 throughoutthenormalanddiseasedlung,itisclearlyproblematicinstandardbreath samplingroutinesbasedonfreebreathing,asslightlychangingmeasurementcondi- tions(regarding,e.g.,bodyposture,breathingpatternsorstress)canhavealargeim- pactontheobservedbreathconcentration[19].Thisconstitutesatypicalexampleof aninherenterrorsourceasstatedabove,potentiallyleadingtoahighdegreeofintra- and consequently inter-individual variability among the measurement results [64]. Itishenceimportantto investigatethe influenceofmedicalparameterslikecardiac output,pulse,breathingrateandbreathingvolumeonVOCconcentrationsinexhaled breath.In contrast,while highlysolubleVOCs (l >10)tendto beless affected b:air by changesin ventilationand perfusion,measurementartifacts associated with this class of compoundsresult from the fact that – due to their often hydrophilicprop- erties – a substantialinteraction between the exhalateand the mucosa layerslining the conductingairways can be anticipated [6]. In other words, for these substances C 6=C , with the exact quantitative relationship being unknown. Examples measured A ofendogenouscompoundsthatarereleasedintothegasphasenotonlythroughthe blood-alveolarinterface,butalsothroughthebronchialliningfluidare,e.g.,acetone andethanol[7,89]. Acetone(2-propanone;CAS number67–64–1;molar mass 58.08g/mol) is one ofthemostabundantVOCsfoundinhumanbreathandhasreceivedwideattention inthebiomedicalliterature.Beinganaturalmetabolicintermediateoflipolysis[38], endogenousacetone has been consideredas a biomarkerfor monitoringthe ketotic stateofdiabeticandfastingindividuals[86,68,72,78],estimatingglucoselevels[22] orassessingfatloss[49].Nominallevelsinbreathandbloodhavebeenestablished in[94,77],andbioaccumulationhasbeenstudiedintheframeworkofexposurestud- iesandpharmacokineticmodeling[98,47,59]. Despite this relativelylarge body of experimentalevidence,the crucial link be- tweenacetonelevelsinbreathandbloodisstillobscure,thushinderingthedevelop- mentof validatedbreath tests for diagnosticpurposes. For perspective,multiplying theproposedpopulationmeanofapproximately1m g/l[77]inend-tidalbreathbythe partitioncoefficientl =340[7]atbodytemperatureappearstogrosslyunderes- b:air timateobserved(arterial)bloodlevelsspreadingaround1mg/l[94,98,40].Further- more,breathprofilesofacetone(andotherhighlysolublevolatilecompoundssuchas 2-pentanoneormethylacetate) associatedwith moderateworkloadergometerchal- lenges of normalhealthy volunteers drastically depart from the trend suggested by Equation(1)[42,43].Inparticular,thephysiologicalmeaningofthesediscrepancies hasnotbeenestablishedinsufficientdepth. Withthebackgroundmaterialofthepreviousparagraphsinmind,weviewace- toneasaparadigmaticexamplefortheanalysisofhighlysoluble,blood-borneVOCs, eventhoughitcannotcoverthewholespectrumofdifferentphysico-chemicalchar- acteristics. The emphasis of this paper is on developing a mechanistic description of end-tidal acetone behavior during different physiological states (e.g., rest, exer- cise, sleep and exposurescenarios).Such a quantitativeapproachwill contributeto a better understanding regarding the relevance of observable breath concentrations ofhighlysolubletracegaseswithrespecttotheunderlyingendogenoussituationand henceconstitutesanindispensableprerequisiteforguidingtheinterpretationoffuture 5 breathtestresults.Moreover,itwillallowfora standardizedexaminationofthein- formationcontentandpredictivepowerofvariousbreathsamplingregimesproposed intheliterature.Specifically,ourworkalsoaimsatcomplementingpreviousstudies centeredonsinglebreathdynamicsduringrestingconditions[89,35,5,7,47]. Byadoptingtheusualcompartmentalapproach[46,17,59,71]ourformulationis simpleinthesensethatnodetailedanatomicalfeaturesoftherespiratorytractmust betakenintoaccount.Althoughmodelsofthistypehavebeencriticizedfortheirun- derlyingassumptions[24](e.g.,regardingthecyclicnatureofbreathing),theyprove asvaluabletoolsforcapturingbothshort-termbehaviorasindicatedaboveandphe- nomenathatarecharacteristicforsamplingscenariosextendingoverminutesoreven hours. Consequently, while the physical derivation to be presented here is clearly drivenbythewell-establishedtheorycoveringsolublegasexchangeinasingleexha- lationframework,itextendstheseideastoamacroscopiclevel,thusyieldingamodel thatcanserveasatemplateforstudyingthemid-tolong-termkineticsofacetoneand similarvolatileorganiccompoundsinbreathandvariouspartsofthehumanbody 2 Experimentalbasics Hereweshallbrieflydiscusstheexperimentalbackgroundpertinenttoourownphe- nomenological findings presented throughout the paper. In particular, these results were obtained with the necessary approvals by the Ethics Committee of the Inns- bruckMedicalUniversity.Allvolunteersgavewritteninformedconsent. Breath acetone concentrations are assessed by means of a real-time setup de- signedforsynchronizedmeasurementsofexhaledbreathVOCsaswellasavariety of respiratoryandhemodynamicparameters,see Fig. 1. Extensivedetailsare given in[42]. Thebreath-relatedpartofthementionedsetupconsistsofaheadmaskspirometer system allowing for the standardized extraction of predefined exhalation segments which–viaaheatedandgastightTeflontransferline–arethendirectlydrawninto a Proton-Transfer-Reactionmass spectrometer (PTR-MS, IoniconAnalytik GmbH, Innsbruck, Austria) for online analysis. This analytical technique has proven to be a sensitive method for quantification of volatile molecular species M down to the ppb(partsperbillion)rangeonthebasisof“soft”chemicalionizationwithinadrift chamber,i.e.,bytakingadvantageoftheprotontransfer H O++M→MH++H O 3 2 fromprimaryhydroniumprecursorionsoriginatinginanadjointhollowcathode[52, 53].NotethatthisreactionschemeisselectivetoVOCswithprotonaffinitieshigher thanwater(166.5kcal/mol),therebyprecludingtheionizationofthebulkcomposi- tionexhaledair,N ,O andCO .CountratesoftheresultingproductionsMH+ or 2 2 2 fragmentsthereofappearingatspecifiedmass-to-chargeratiosm/zcansubsequently be convertedto absolute concentrationsof the protonatedcompounds(see [76] for further details on the quantification of acetone as well as [42] for the underlying PTR-MS settings used). The carbon dioxide concentrationC of the gas sample CO2 6 is determined by a separate sensor (AirSense Model 400, Digital Control Systems, Portland,USA). MATLAB TCP/IP Algorithms Dataanalysis T = 5s alveolar ventilation, T ECG, cardiac output, tidal volume CP blood pressure /IP oar MedikrSpiroSt VOCco /n ccaernbtorant idoinosxide flow-triggered valve heatedTeflonline(~40°C) IoniconAnalytik PTR-MS CNSystems TaskForceMonitor Fig.1 ExperimentalsetupusedforobtainingVOCprofilesandmedicalparameters[42].Itemsinitalic correspondtomeasurablevariables. Theselective analysisofpredefinedbreathsegmentsisensuredby flow-triggeredsampleextraction. Inadditiontothebreathconcentrationprofilesofacetone,itwillbeofimportance forustohaveathandacontinuousestimateofthecorrespondingsamplewatervapor contentC .Ashasbeenputforwardintheliterature,thewaterdimer(H O+)H O water 3 2 canbeusedforthispurpose[96,4].Morespecifically,thecorrespondingpseudocon- centration signal at m/z=37 calculated according to Equation (1) in [76] using a standard reaction rate constant of 2.0×10−9 cm3/s yields a quantity roughly pro- portionaltosamplehumidity.Slightvariationsduetofluctuationsofthe(unknown) amount of water clusters forming in the ion source are assumed to be negligible. Absolute quantification can be achieved by comparison with standards containing predefinedhumiditylevels.SuchstandardswithC andC varyingovertheex- CO2 water perimental physiologicalrange of 2 – 8% and 2 – 6%, respectively, were prepared usingacommercialgasmixingunit(Gaslab,BreitfussMesstechnikGmbH,Harpst- edt,Germany),resultinginameancalibrationfactorof2.1×10−4andR2≥0.98for allregressions.Ithasbeenarguedin[39]thattheaforementionedpseudoconcentra- tioncandrasticallybeaffectedbythecarbondioxideconcentration,which,however, could not be confirmed with our PTR-MS settings. Although the computed water contentis slightly overestimatedwith increasingC , the sensitivity was foundto CO2 staywithin10%ofthemeanvaluegivenabove.Nevertheless,werecognizethatthis approximatemethodfordeterminingwatervaporlevelscanonlyserveasafirstsur- rogateformoreexacthygrometermeasurements. 7 Despite the fact that molecular oxygen is not protonated, the breath oxygen con- centrationC – relative to an assumed steady state value of about 100 mmHg in O2 end-tidal (alveolar) air during rest [54] – within one single experimentcan still be assessedbymonitoringtheparasiticprecursorionO+ atm/z=32.Thisionresults 2 fromasmallamountofsamplegasenteringtheionsourcewithsubsequentionization of O underelectron impact[65]. For normalizationpurposes,the respective count 2 ratesareagainconvertedtopseudoconcentrations.Table1summarizesthemeasured quantitiesrelevantforthispaper.Ingeneral,breathconcentrationswillalwaysrefer toend-tidallevels,exceptwhereexplicitlynoted.Moreover,atypicalsamplinginter- valof5sisassumedforeachvariable(correspondingtobreath-by-breathextraction ofend-tidalVOClevelsatanormalbreathingrateof12tides/min). Table1 Summaryofmeasuredparameterstogetherwithsomenominalvaluesduringrestandassuming ambientconditions.Breathconcentrationsrefertoend-tidallevels. Variable Symbol Nominalvalue(units) Cardiacoutput Q˙c 6(l/min)[58] Alveolarventilation V˙A 5.2(l/min)[97] Tidalvolume VT 0.5(l)[97] Acetoneconcentration Cmeasured 1(m g/l)[77] CO2content CCO2 5.6(%)[54] Watercontent Cwater 4.7(%)[26] O2content CO2 13.7(%)[54] 3 Acetonemodeling 3.1 Preliminariesandassumptions Classicalpulmonaryinertgaseliminationtheory[21]postulatesthatuptakeandre- movalofVOCstakesplaceexclusivelyinthealveolarregion.Whilethisisareason- ableassumptionforlowsolublesubstances,ithasbeenshownbyseveralauthorsthat exhalationkineticsof VOCs with highaffinityfor bloodand water such as acetone areheavilyinfluencedbyrelativelyquickabsorptionandreleasemechanismsoccur- ringintheconductiveairways(see,e.g.,[5]foragoodoverviewofthistopic).More specifically,duetotheirpronouncedhydrophiliccharacteristicssuchcompoundstend tointeractwiththewater-likemucusmembraneliningthispartoftherespiratorytree, thereby leading to pre- and post-alveolar gas exchange often referred to as wash- in/wash-outbehavior.Thepresentmodelaimsattakingintoconsiderationtwomajor aspectsinthisframework. 3.1.1 Bronchialexchange It is now an accepted fact that the bronchialtree plays an importantrole in overall pulmonarygasexchangeofhighly(water)solubletracegases,affectingbothendoge- nousclearanceaswellasexogenousuptake.Forperspective,Andersonetal.[7]in- 8 ferredthatwhilefreshairisbeinginhaled,itbecomesenrichedwithacetonestoredin theairwaysurfacewallsoftheperipheralbronchialtract,thusleadingtoadecrease of the acetone pressure/tension gradient between gas phase and capillary blood in the alveolar space. This causes an effective reduction of the driving force for gas exchangein the alveoliand minimizesthe unloadingof the capillaryacetonelevel. Correspondingly,duringexhalationtheaforementioneddiffusionprocessisreversed, withacertainamountofacetonebeingstrippedfromtheairstreamandredepositing ontothepreviouslydepletedmucuslayer.Asaphenomenologicalconsequence,ex- haledbreathconcentrationsofacetoneandotherhighlywatersolublesubstancestend tobediminishedontheirwayupfromthedeeperrespiratorytracttotheairwayopen- ing,therebydecreasingoveralleliminationascomparedtopurelyalveolarextraction. Similarly,expositionstudiessuggestapre-alveolarabsorptionofexogenousacetone duringinhalationandapost-alveolarrevaporizationduringexpiration,resultingina lowersystemicuptakecomparedtowhatwouldbeexpectediftheexchangeoccurred completelyinthealveoli[98,47,87]. From the above, quantitative assessments examining the relationships between the measured breath concentrationsand the underlyingalveolar levels are complex andneedtotakeintoaccountavarietyoffactors,suchasairwaytemperatureprofiles andairwayperfusionaswellasbreathingpatterns[5,6]. Inaccordancewithpreviousmodelingapproaches,weconsiderabronchialcom- partment separated into a gas phase and a mucus membrane, which is assumed to inherit the physical propertiesof water and acts as a reservoir for acetone [47,59]. Partoftheacetonedissolvedinthislayeristransferredtothebronchialcirculation, wherebythemajorfractionoftheassociatedvenousdrainageispostulatedtojointhe pulmonaryveinsviathepostcapillaryanastomoses[54].AstudybyMorrisetal.[61] on airway perfusionduringmoderateexercisein humansindicatesthatthe fraction q ∈[0,1)ofcardiacoutputQ˙ contributingtothispartofbronchialperfusionwill bro c slightlydecreasewithincreasingpulmonarybloodflow.AccordingtoFigure3from theirpaperandassumingthatQ˙rest=6l/minwecanderivetheheuristiclinearmodel c q (Q˙ ):=max{0,qrest(1−0.06(Q˙ −Q˙rest))}. (2) bro c bro c c TheconstantqrestwillbeestimatedinSection4.Asaroughupperboundwepropose bro theinitialguessqrest=0.01[54].Westressthefactthatthebronchialcompartment bro justintroducedhastobeinterpretedasanabstractcontrolvolumelumpingtogether thedecisivesitesofairwaygasexchangeinonehomogeneousfunctionalunit.These locationscanbeexpectedtovarywidelywiththesolubilityoftheVOCunderscrutiny aswellaswithphysiologicalboundaryconditions[5]. 3.1.2 Temperaturedependence There is strong experimental evidence that airway temperature constitutes a major determinantforthepulmonaryexchangeofhighlysolubleVOCs,cf.[36].Inparticu- lar,changesinairwaytemperaturecanbeexpectedtoaffectthesolubilityofacetone andsimilarcompoundsinthemucussurfaceoftherespiratorytree.Itwillhencebe 9 importanttospecifyatentativerelationshipcapturingsuchinfluencesontheobserv- ablebreathlevels.Aswillberationalizedbelow,thismaybeachievedbytakinginto accounttheabsolutehumidityoftheextractedbreathsamples. Passing through the conditioning regions of the upper airways, inhaled air is warmedtoameanbodycoretemperatureofapproximately37◦Candfullysaturated withwatervapor,thusleadingtoanabsolutehumidityofalveolarairofabout6.2% atambientpressure.Duringexhalation,dependingontheaxialtemperaturegradient betweenthelowerrespiratorytractandtheairwayopening,acertainamountofwater vaporwillcondenseoutandreducethewatercontentC intheexhalateaccording water to the saturation water vapor pressure P (in mbar) determined by local airway water temperatureT (in◦C)[56,27].Therelationshipbetweenthesetwoquantitiescanbe approximatedbythewell-knownMagnusformula[80] 17.62T P (T)=6.112exp , (3) water (cid:18)243.12+T(cid:19) validforatemperaturerange−45◦C≤T ≤60◦C.Fornormalphysiologicalvaluesof T,theresultingpressureissufficientlysmalltotreatwatervaporasanidealgas[70] andhencebyapplyingDalton’slawweconcludethatabsolutehumidityC (in%) water oftheexhalatevariesaccordingto P (T) water C (T)=100 , (4) water P ambient whereP istheambientpressure.Invertingtheaboveformula,theminimumair- ambient way temperatureT =T (C ) duringexhalationbecomesa functionof mea- min min water suredwatercontentinexhaledbreath.Fromthis,ameanairwayandmucustempera- turecharacterizingthehomogeneousbronchialcompartmentoftheprevioussection willbedefinedas T (C )+37 T¯(C ):= min water , (5) water 2 corresponding to a hypothesized linear increase of temperature along the airways. Note that this assumption is somehow arbitrary in the sense that the characteristic temperatureof the airwaysshouldbe matchedto the primary(time-and solubility- dependent)location ofairway gasexchangeas mentionedabove.Equation(5) thus shouldonlybeseenasasimpleadhoccompromiseincorporatingthisvariability. The decrease of acetone solubility in the mucosa – expressed as the water:air partition coefficient l – with increasing temperature can be described in the muc:air ambienttemperaturerangebyavan’tHoff-typeequation[82] B log l (T)=−A+ , (6) 10 muc:air T+273.15 whereA=3.742andB=1965Kelvinareproportionaltotheentropyandenthalpy of volatilization,respectively.Hence, in a hypotheticalsituationwherethe absolute samplehumidityatthemouthis4.7%(correspondingtoatemperatureofT ≈32◦C andambientpressureatsealevel,cf.[56,26]),localsolubilityofacetoneinthemucus 10 layerincreasesfroml (37◦C)=392inthelowerrespiratorytract(cf.[46])to muc:air l (32◦C)=498atthemouth,therebypredictingadrasticreductionofairstream muc:air acetoneconcentrationsalongtheairways.Theaboveformulationsallowonetoassess thisreductionbytakinginto accountsamplewater vaporasa metaparameter.This meta parameter reflects various influential factors on the mucus solubility l muc:air which would otherwise be intricate to handle due to a lack of information,such as localairwayperfusion,breathingpatterns,mucosalhydrationandthermoregulatory eventswhich in turn will affectaxialtemperatureprofiles. In particular,l for muc:air theentirebronchialcompartmentwillbeestimatedviathemeanairwaytemperature T¯ inEquation(5)as l (T¯)=l (T¯(C )). (7) muc:air muc:air water The strong coupling between sample humidity and exhaled breath concentrations predicted by the two relationships (3) and (6) is expected to be a common factor forallhighlywatersolubleVOCs.Intheframeworkofbreathalcoholmeasurements Lindbergetal.[51]indeedshowedapositivecorrelationbetweenthesetwoquantities along the course of exhalation, which can also be observed in the case of acetone, cf.Fig.2. Variationsoftheacetoneblood:airpartitioncoefficientl =340[7,20]–dom- b:air inatingalveolargasexchange–inresponsetochangesinmixedvenousbloodtem- perature,e.g.,duetoexercise,areignoredassuchchangesarenecessarilysmall[16]. Hence, l will always refer to 37◦C. Similarly, the partition coefficient between b:air mucosaandbloodistreatedasaconstantdefinedby l :=l (37◦C)/l , (8) muc:b muc:air b:air resulting in a value of 1.15. Note, that if the airway temperatureis below 37◦C we alwayshavethat l /l ≥l , (9) muc:air muc:b b:air asl ismonotonicallydecreasingwithincreasingtemperature,seeEquation(6). muc:air 3.1.3 Bronchio-alveolarinteractions Inaseriesofmodelingstudies[89,5],thelocationofgasexchangehasbeendemon- strated to shift between bronchialand alveolar regions depending on the solubility ofthecompoundunderinvestigation.Duringtidalbreathingexchangeforsubstances with blood:airpartition coefficientl ≤10 takes place almost exclusivelyin the b:air alveoli, while it appears to be strictly limited to the bronchial tract in the case of l ≥100.TransportforVOCslyingwithinthesetwoextremesdistributesbetween b:air both spaces. Likewise, for fixed l , the location of gas exchange is expected to b:air varywithbreathingpatterns.AshasbeenconcludedbyAndersonetal.[7],airway contribution to overall pulmonary exchange of endogenous acetone is about 96% during tidal breathing, but only 73% when inhaling to total lung capacity. The ra- tionaleforthisreductionisthatwhilemoreproximalpartsofthemucosaliningare being depleted earlier in the course of inhalation by losing acetone to the inhalate, saturationoftheairstreamwithacetoneiscontinuouslyshiftedtowardsthealveolar region.Furthermore,itcanbearguedthatthemagnitudeofthisshiftincreaseswith