A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

0.55 MB·English

by  Julian King

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
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n
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J

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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