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Ghorbani, R., Schmidt, F M. (2019)Fitting of single-exhalation profiles using a pulmonary gas exchange model: applicationto carbon monoxideJournal of Breath Research, 13(2): 026001https://doi.org/10.1088/1752-7163/aafc91

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J. Breath Res. 13 (2019) 026001 https://doi.org/10.1088/1752-7163/aafc91

PAPER

Fitting of single-exhalation profiles using a pulmonary gas exchangemodel—application to carbonmonoxide

RaminGhorbani and FlorianMSchmidtDepartment of Applied Physics and Electronics, UmeåUniversity, SE-90187Umeå, Sweden

E-mail:florian.schmidt@umu.se

Keywords: real-time breath gas analysis, carbonmonoxide (CO), pulmonary gas exchangemodel, single-exhalation profile, laser absorptionspectroscopy

AbstractReal-time breath gas analysis coupled to gas exchangemodeling is emerging as promising strategy toenhance the information gained frombreath tests. It is shown for exhaled breath carbonmonoxide(eCO), a potential biomarker for oxidative stress and respiratory diseases, that a weighted, nonlinearleast-squaresfit of simulated tomeasured expirograms can be used to extract physiologicalparameters, such as airway and alveolar concentrations and diffusing capacities. Experimental COexhalation profiles are acquiredwith high time-resolution and precision usingmid-infrared tunablediode laser absorption spectroscopy and online breath sampling. A trumpetmodel with axial diffusionis employed to generate eCOprofiles based onmeasured exhalationflow rates and volumes. Theconcept is demonstrated on two healthy non-smokers exhaling at a flow rate of 250ml s−1 duringnormal breathing and at 120ml s−1 after 10 s of breath-holding. The obtained gas exchangeparameters of the two subjects are in a similar range, but clearly distinguishable. Over a series of twentyconsecutive expirograms, the intra-individual variation in the alveolar parameters is less than 6%.After a 2 h exposure to 10±2 ppmCO, end-tidal and alveolar CO concentrations are significantlyincreased (by factors of 2.7 and 4.9 for the two subjects) and the airwayCO concentration is slightlyhigher, while the alveolar diffusing capacity is unchanged compared to before exposure. Usingmodelsimulations, it is found that a three-fold increase inmaximumairwayCOflux and a reduction inalveolar diffusing capacity by 60% lead to clearly distinguishable changes in the exhalation profileshape. This suggests that extended breathCO analysis has clinical relevance in assessing airwayinflammation and chronic obstructive pulmonary disease.Moreover, the novelmethodologycontributes to the standardization of real-time breath gas analysis.

1. Introduction

During the past decade, the advent of novel analyticaltechniques has intensified the interest in real-timedetection of trace species in exhaled breath as alter-native to offline analysis [1, 2]. In the context of thiswork, real-time breath gas analysis refers to controlledonline breath sampling and subsequent quantitativebiomarker detection with sufficient measurementtime-resolution (usually sub-second) and precision toaccurately resolve individual breath cycles. Comparedto offline mixed- or end-tidal breath sampling, theadvantages of theonline approach include fast response,the possibility for continuous (inline) breath monitor-ing over longer time periods, and reduced risk for

sample contamination due to pre-concentration andstorage procedures. An additional benefit of breath-cycle-resolved detection is that single-exhalation pro-files contain spatiotemporal information about the gasexchange in the respiratory tract. Coupled to suitablemathematical models of gas exchange [3], this enablesbiomarker source discrimination and non-invasivedetermination of physiological parameters, which canlead to improved data interpretation, a better under-standing of the origin and biochemical pathways ofbiomarkers and, eventually, to novel breath tests.

The shape of an exhalation profile primarilydepends on the locations of biomarker productionand exchange in the respiratory tract (alveoli, airways,oral/nasal cavities), and the breath sampling

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conditions (e.g. exhalation flow rate and volume,inhaled concentration, body position) [3]. In general,compounds with low water/blood solubility willexchange in the alveolar region, whereas highly water-soluble molecules will exchange in the airways. Forexample, both carbon monoxide (CO) and nitricoxide (NO) have a low water solubility, but exhaledCO originates mainly from the alveoli, leading to highend-tidal values [4], while exhaledNO to a large extentstems from ambient air and nasal/airway production,resulting in a characteristic maximum in the begin-ning of the exhalation [3, 5]. High initial concentra-tions can also be expected for ammonia (NH3), whichmostly originates from the oral cavity, but the excep-tionally high water solubility and the propensity toadsorption hamper quantitative detection and have sofar prevented the reliable measurement of NH3 exha-lation profiles [6].

Real-time breath analysis is routinely performedin clinical practice only for carbon dioxide (CO2)usingminiature capnographs based on non-dispersiveinfrared (NDIR) spectroscopy. Compact optical set-ups can also be used for rapid measurement of theother major breath species, oxygen (O2) and watervapor (H2O) [7]. However, more sophisticated analy-tical techniques are needed for real-time analysis of theless abundant molecules. These methods include soft-ionization mass spectrometry (MS), such as selected-ion flow tube and proton transfer reaction MS [1],electrospray ionization MS [8], non-equilibrium dilu-tion ion mobility spectrometry [5] and laser absorp-tion spectroscopy (LAS) [2, 9].

Mathematical models of pulmonary gas exchangein the respiratory tract were developed early on toenable determination of the fractional airway NOcontribution [10, 11] and to improve the interpreta-tion of CO2 [12] and ethanol [3] exhalation profiles.Physiological modeling was also used to better under-stand short-term changes in exhaled isoprene [13] andacetone [14] concentrations. In most of these modelimplementations, end-tidal biomarker levels werecomputed and compared to experiments. Only a fewattempts have been made to compare or fit simula-tions of entire expirograms to experimental real-timedata [15–19]. In a recent work byMountain et al least-squares fitting of O2, CO2 (and N2 tracer) profiles wasemployed to assess lung inhomogeneity [20].

The interest in exhaled breath CO (eCO) as bio-marker for oxidative stress and respiratory diseasesstems from the fact that the molecule is endogenouslyreleased as a byproduct of heme oxygenase (HO-1)activity [21]. While the main part of CO production isdue to systemic heme degradation, with gas exchangein the alveoli, there are indications that HO-1 activitycan also be induced locally in airway and lung tissue[22, 23]. Some studies reported elevated eCO levelsdue to local airway inflammation [24], infections [25]and chronic obstructive pulmonary disease (COPD)[26], but contradictory results were also obtained [27].

In general, exhaled CO also depends on recent envir-onmental exposure, such air pollution and smoking[28], and on the molecular diffusion properties in therespiratory tract, which may deviate from normal indiseased cohorts. For example, in patients with severeCOPD, the CO diffusing capacity is significantlyreduced [29]. Conventional end-tidal eCO analysiswith electrochemical sensors cannot resolve a poten-tial small airway contribution or assess pulmonary dif-fusion, which hampers the interpretation of eCOconcentrations outside the healthy population range.

To add value to eCO diagnostics, a compact LASsensor for sensitive real-time detection of CO inexhaled breath and ambient air has recently beendeveloped [4, 30]. Moreover, a trumpet model withaxial diffusion (TMAD) has been adapted to, for thefirst time, simulate pulmonary gas exchange dynamicsand single-exhalation profiles of CO during systemicelimination [31]. The exhalation profiles are calcu-lated based on four parameters, namely the CO diffus-ing capacities and maximum fluxes in the airways andthe alveolar region. In that study, simulated and mea-sured exhalation profiles have been visually comparedto roughly estimate the model parameters and predictthe equilibrium CO concentrations in the twocompartments.

In this work, a weighted, nonlinear least-squaresfit of the model solution at the mouth grid point to theexperimental CO exhalation profiles is used to extractthe TMAD parameters. The purpose of applying a fitinstead of a manual comparison, is to enable fast, reli-able and precise extraction of the model parameters,including end-tidal CO, in a consistent way. Suchstrategy is little described in the context of breath gasanalysis, but can greatly contribute to the standardiza-tion of (real-time) breath sampling and data evalua-tion. Precise and systematic profile analysis may alsolead to improved gas exchange models and a betterunderstanding of the biomarker physiology. Normalbreathing and BH expirograms from two healthy non-smokers are analyzed to demonstrate the novelapproach. The inter- and intra-individual variations inthe model parameters, and the influence of acuteexposure to elevated CO levels on the parameters arescrutinized. Furthermore, using simulations, it isshown that a small increase in airway CO flux andchanges in the alveolar diffusing capacity, as may beanticipated in the diseased population, have distincteffects on the shape of exhalation profiles and can beresolved. The clinical relevance of extended CO breathanalysis is discussed.

2.Materials andmethods

2.1. Laser-based carbonmonoxide sensorReal-time detection of CO in breath and ambient airwas achieved using a home-built mid-infrared tunablediode laser absorption spectroscopy (TDLAS) system

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[30]. The spectrometer employed a distributed-feed-back interband cascade laser (ICL, Nanoplus GmbH)in combination with a circular, low-volume multipasscell (MPC, IR Sweep, IRcell-4M) for absorption pathlength enhancement (4m) and 2f-wavelength modula-tion spectroscopy for noise-reduction. Breath sampleswere analyzed in theMPC at a pressure of 100 Torr andat close to room temperature (23 °C). The absorptionspectra were scanned with a frequency of 140Hz andaveraged 10 times. This sensor provided selective,interference-free eCOquantification down to 9 ppb at aprecision of 5 ppb and time-resolution of 0.1 s. Therapid gas exchange in the MPC (<0.1 s) required forreal-time detection was guaranteed by the low MPCvolume (38ml) and the pumping speed (360ml s−1 at100 Torr) of the vacuum pump (Leybold, Divac1.4HV3C). True real-time capability of the system waspreviously confirmed by direct comparison of eCO2

profiles measured by capnography and TDLAS [4]. Themain components of the experimental setup are shownschematically infigure 1.

2.2.Online breath sampling systemPulmonary gas exchange and exhaled biomarkerconcentrations strongly depend on the breath sam-pling conditions, including hyperventilation, bodyposition and inhaled biomarker concentrations [32].Tominimize these effects and ensure repeatability, thesampling process was standardized using an advancedbreath sampling system that controlled the breathingfrequency and the inhalation and exhalation flow rates(IFR and EFR, respectively).

The online breath sampler (figure 1) comprised aflow meter (Phillips Respironics, FloTrak Elite Mod-ule), a mainstream capnograph (Phillips Respironics,Capnostat 5) and a Teflon buffer tube of length 15 cmand volume 30 ml. A mouthpiece made of Teflon anda disposable anti-bacterial filter (GVS, Eco Maxi Elec-trostatic Filter, 4222/701) were mounted at the inlet.The flowmeter was a fixed orifice differential pressuretype, which potentially can evaluate more than 60respiratory parameters on a breath by breath basis

including the flow rate (range−5000 to+5000 ml s−1,resolution 0.2 ml s−1), volume (range −1000 to+4000ml, resolution 1ml) and airway pressure (range−150 to +150 cmH2O, resolution 0.05 cmH2O). Thecapnograph was a NDIR single beam optical devicewith a CO2 measurement range of 0%–19.7% and aresolution of 0.1%.

A two-way non-rebreathing valve (Rudolph Inc.)was connected to the outlet of the buffer tube to sepa-rate the inspiration and expiration routes, as subjectsperformed both inhalation and exhalation through thebreath sampler. In order to restrict IFR and EFR closeto desired values, suitable orifices of different dia-meters were installed at the inlet and outlet ports of thetwo-way valve. A LabVIEW computer interface withaudiovisual indicators helped the subjects to maintainthe intended IFR/EFR and breathing frequency(6 or 3 breaths/min for normal breathing and breath-holding, respectively) according to the protocol speci-fied in section 2.6. A portion of the inhaled andexhaled breath was continuously extracted from thebuffer tube and led to theMPC of the TDLAS sensor ata flow rate of 50 ml s−1 (set by the vacuum pumpspeed).

Figure 2 shows typical respiratory data sets recordedover a single breath-cycle during normal breathing forthe two healthy, non-smoking subjects. For a breathingfrequency of 6 breaths/min and an IFR/EFR of around250ml s−1 (average indicated by a dashed line), theinhaled/exhaled volumes were close to 1250ml. A clearinter-individual difference in airway pressure and end-tidal CO2 concentration can be observed. In all experi-ments, the respiratory data and ambient air CO (Camb)were continuously recorded during the breath cyclesand later used as input parameters to the mathematicalmodel of pulmonaryCOgas exchange dynamics.

2.3. Pulmonary gas exchangemodelThe TMAD is based on a one-dimensional, trumpet-shaped representation of the respiratory tract follow-ing Weibel’s symmetrically bifurcating lung structure[33, 34] rescaled for a total airspace volume of 3700 ml

Figure 1. Schematic drawing of the breath sampler consisting of a teflonmouth piece (TMP), an anti-bacterial filter (ABF), an inlinecapnograph (CPN) andflowmeter (FM), a 15 cm long buffer tubemade of Teflon, and a two-way non-rebreathing valve (2WV)withorifice of variable size. Respiratory datawere evaluated by the FloTrak EliteModule (FLTK), and breath samples were analyzed foreCOusing tunable diode laser absorption spectroscopy (TDLAS sensor).

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[35] and using the latest anatomical data [31]. Figure 3shows a schematic drawing of the TMAD with themainmodel parameters indicated.

The governing equation, which accounts for theaxial gas transport and radial sources and sinks as afunction of time and axial distance z along the trum-pet, can generally bewritten as

+

=+ ¢ ¢ ¢ ¢

⎧⎨⎩⎡⎣⎢

⎤⎦⎥

⎫⎬⎭( ) ( )

( )( ) ( )

A zN z

NA

t

T V D z

S J D J D z

dC

d

, ,

, , , , , 1

c,awalv

tc,A

CO

CO,air

awCO awCO ACO ACO

where Ac,aw is the airway cross-sectional area (cm2),which follows a power-law relation (∼1/z2) towardsthe lower airway generations (towards the mouth),Ac,A is the total cross-sectional area of the alveolarcompartment (cm2), the function T describes theconvective bulk flow and axial diffusion, and thefunction S represents the flux to and diffusion from

the airway and alveolar regions per unit axial distance.The functionT is given by

= -

+

⎡⎣⎢

⎤⎦⎥

( )

( ) ( )

T V D VC

z

Dz

A zC

z

,d

dd

d

d

d, 2

CO,airCO

CO,air c,awCO

where V is the volumetric (inhalation and exhalation)flow rate (ml s−1), DCO,air the molecular diffusivity ofCO in air (cm2 s−1). The function Shas the form

¢ ¢ ¢ ¢

= ¢ - ¢ -

+ ¢ - ¢

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

( )

( ) ( )

( ) ( ) ( )

S J D J D

J D CN z

N

J D CN z

N

, , ,

1

, 3

awCO awCO ACO ACO

awCO awCO COalv

max

ACO ACO COalv

t

where J′awCO and J′ACO are the maximum fluxes perunit axial distance (pl s−1 cm−1) and D′awCO and

Figure 2.Typical respiratory data obtainedwith the breath sampler for one breath cycle (normal breathing) of (a) subject 1 and (b)subject 2. Inhalation/exhalation flow rate (IFR/EFR) and volume, airway pressure and exhaled carbon dioxide (eCO2) are shown. Thedashed lines indicate themean IFRs and EFRs.

Figure 3. Schematic drawing of the trumpetmodel of the lung. JawCO—totalmaximumvolumetric flux of CO from the airways;DawCO—total diffusing capacity of CO in the airway; JACO—totalmaximumvolumetric flux of CO from the alveoli;DACO—totaldiffusing capacity of CO in the alveolar region;CCO—momentary concentration of gaseousCO in the respiratory tract;CawCO—airway tissue COconcentration at equilibrium;CACO—alveolar CO concentration at equilibrium; z—axial position in thelung.

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D′ACO the diffusing capacities per unit axial distance(pl s−1 ppb−1 cm−1) in the conducting airways and thealveolar region, respectively, Nalv is the number ofalveoli per unit axial distance, Nmax the maximumnumber of alveoli at any axial position, and Nt is thetotal number of alveoli.

The mass balance equation, equation (1), is solvednumerically using the method of lines, and providesthe distribution of CO in the respiratory tract duringinhalation, exhalation and breath-holding with spatialand temporal resolutions of 1 mm and 0.01 s, respec-tively. Single-exhalation profiles are extracted fromthe first simulated grid point (z=0) representing themouth. Details on the model parameters, the bound-ary conditions and the numerical solution can befound in [31].

2.4. Nonlinear least-squaresfitting implementationThe solution of the TMAD at the mouth grid point isfitted to the experimental eCO profiles using aweighted, nonlinear least-squares algorithm imple-mented in MATLAB. There are four open parametersrepresenting the sinks and sources in the airway andthe alveolar regions, namely JawCO, DawCO, JACO andDACO, which denote the total J′awCO, D′awCO, J′ACOand D′ACO in units of pl s−1. and pl s−1 ppb−1,respectively. These four parameters affect the exhala-tion profile shape in different ways (no mutualdependencies) and are uniquely determined in thefitting process. Starting values for the open TMADparameters have previously been estimated [31]. Asmentioned above, other input data to the model werethe actual IFRs and EFRs, inhaled/exhaled volumesand the inhaled COconcentration.

Due to the steep eCO increase in exhalation phase II,which represents the transition between the conductingairways and the alveolar region, this phase is particularlysensitive to discrepancies between the anatomical dataassumed in the TMAD and the actual lung structure ofthe subject providing the sample. Therefore, a good fitcannot be expected in this region and more weight wasput on the data points in phases I and III, which are thedominant regions for evaluation of the gas exchange inconducting airways and alveoli, respectively. The first4% of the expirogram data points (corresponding tophase I) were weighted 20 time more and the last 74%(corresponding to phase III) 60 timesmore than the restof the profile (phase II). Since the data acquisitionrate and exhaled volumewere kept constant, the relativeamount of data points in each exhalation phase wasthe same regardless of exhalation flow rate and time.The TMAD fitting parameters, JawCO, DawCO, JACO andDACO, were free to vary in the range of 100–500 pl s−1,1.0–1.6 pl s−1 ppb−1, 5×105–2×108 pl s−1, and300–5×105 pl s−1 ppb−1, respectively.

For healthy, non-smoking subjects, the airway COcontribution is usually very small and the airwayTMAD parameters (JawCO and DawCO) cannot be

accurately determined from normal breathing pro-files. During a BH maneuver, however, there is moretime for airway tissue CO to diffuse into the gasstream, which increases the sensitivity to the airwayparameters. Thus, in this work, JawCO andDawCO werefirst determined from an expirogram recorded after10 s BH, and then fixed in the fits to the normalbreathing exhalation profiles. The alveolar and airway(tissue) CO concentrations predicted for equilibriumconditions, CACO and CawCO, were obtained from theratios JACO/DACO and JawCO/DawCO, respectively. Thecomputational time forfitting a typical normal breath-ing eCO profile recorded at an EFR of 250 ml s−1 andan exhalation volume of 1250 ml was around 45 s on astandard office PC. For a 10 s BH profile, the time was4–5 min As expected, the computational time increa-ses with decreasing IFR and EFR, and increasingBH time.

2.5. Controlled human exposure to carbonmonoxideThe effect of CO exposure on the eCO profiles andTMAD parameters was investigated in a humanexposure study including intermittent exercise. Thesubjects stayed in a controlled environment exposurechamber (18 m3) [36] for 2 h, breathing a mixture of10±2 ppmCO in air derived from a 300 ppmCO gasstandard (AGA Gas AB) by dilution with air. Theexpected increase in blood carboxyhemoglobin(COHb) concentration due to the CO exposure wascalculated using the differential Coburn–Forster–Kane (CFK) equation [37] and healthy non-smokerblood and lung properties. An increase in COHb levelof around 60% compared to normal (up to 1.3%saturation from an initial value of 0.8%)was predictedfor the 2 h exposure assuming an alveolar ventilationrate of 30 l min−1. The COHb level can also becalculated from the measured alveolar CO concentra-tion (CACO) using an empirical relationship givenby [38]

= + ( )CCOHb 0.63 0.16 , 4ACO

where CACO is in ppm, and COHb is obtained in unitsof% saturation.

2.6.Human subjects and study protocolTwo healthy, male non-smokers (subjects 1 and 2, aged42 and 37 years, respectively) participated in the pilot-study. No diary restrictions were imposed on thesubjects, but they were asked not to exercise for 3 h priorto the test. All eCO measurements were conductedbetween 1 pm and 3 pm on weekdays in late October inUmeå, Sweden. Twodifferent breathingmaneuverswereconsidered. The first maneuver, here referred to as‘normal breathing’, comprised 5 s inhalation of ambientair at 250ml s−1 IFR, followed by 5 s exhalation at250ml s−1 EFR. This resulted in inhalation/exhalationvolumes of about 1250ml, depending on how well the

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subjects followed the audiovisual indicators. The secondmaneuver consisted of 10 s inhalation at 120ml s−1 IFR,followed by 10 s breath-holding and 10 s of exhalation at120ml s−1 EFR. These two breathing maneuvers werealso performed 7min after the end of the 2 h exposure to10 ppm CO. During the exposure in the chamber, thesubjects alternated between 15min of moderate cyclingand 15min of rest. The sequence of breath cycles wasrecorded by performing twenty successive normalbreathing maneuvers. All breath samples were giventhrough the mouth, while subjects were sitting upright.The study protocol was approved by the Regional EthicalReview Board at Umeå University (2017/306-31 and2018-35-23M).

3. Results

3.1. Least-squaresfitting of single-exhalationprofilesFigure 4 presents measured, normal breathing COexhalation profiles (red markers, every 2nd data point

shown) from subjects 1 and 2, together with weightedTMAD curve fits (blue lines) and fit residuals (lowerpanels). The corresponding breath sampling data forthese expirograms is shown in figure 2. Time zeroindicates the start of the exhalation. The prevailingambient air CO concentration was continuouslysampled during inhalation. In figure 4(a), the threeexhalation phases are indicated with Roman numerals.Phase I represents the air from anatomical dead-spaceand the conducting airways, phase III represents the airfrom the alveoli, and phase II denotes the transitionbetween phases I and III. The airway TMAD parameters(JawCO and DawCO) used in the fits to the normalbreathing eCO profiles were fixed to those determinedfrom the BH profiles shown in figure 5, which depictssingle-exhalation profiles recorded after 10 s BH (redmarkers, every 2nd data point shown) with curve fits(blue lines) and the fit residuals (lower panels). Indepen-dent of the starting values and allowed optimizationranges, the TMAD parameters converged to the valuessummarized in table 1.

Figure 4.Weighted, nonlinear least-squares TMAD fits (solid lines) tomeasured normal breathing eCOprofiles (markers) fromhealthy non-smoker subjects 1 and 2. The average EFRs are indicated. The lower panels show the residuals of the fits. For clarity, onlyevery 2nd experimental data point is shown in the region of thefit. In panel (a), the three exhalation phases are indicated by Romannumerals.Camb—ambient air CO.

Figure 5.Weighted, nonlinear least-squares TMAD fits (solid lines) tomeasured 10 s breath-holding eCOprofiles (markers) fromhealthy non-smoker subjects 1 and 2. The average EFRs are indicated. The lower panels show the residuals of the fits. For clarity, onlyevery 2nd experimental data point is shown in the region of thefit.

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3.2. Intra-individual variations in the TMADparametersThe repeatability of the breath sampling procedureand robustness of the TMAD fitting routine werestudied by looking at the intra-individual variations ofthe model parameters under normal breathingconditions.

As presented in figure 6, sequences of twenty con-secutive breath-cycles were measured for both sub-jects (left panels) and analyzed using TMAD fits. Theright panels in figure 6 show the TMAD fits (blue lines)to five of the measured eCO profiles (red markers).The TMAD parameter mean values and coefficients ofvariation (CV) extracted from fits to all twenty profilesare given in table 2. The mean IFR and EFR were242 ml s−1 and 243 ml s−1 for subject 1, and263 ml s−1 and 258 ml s−1 for subject 2, respectively.The mean ambient air CO concentrations were 115ppb and 149 ppb, respectively. The intra-individualCV of JACO and DACO were less than 6% for subject 1and less than 5% for subject 2. Inter-individually, themean value of JACO for subject 1 is almost twice that ofsubject 2, whereas there is less than 9% difference inthemeanDACO.

3.3. Exposure to carbonmonoxideExposure to exogenous CO gives rise to an increase inblood COHb, which, in turn, results in elevated eCOconcentrations during elimination [28, 37]. Wehypothesize that, for healthy non-smokers, exposurewill mainly affect the maximum CO flux, but not thelung diffusion properties. Figure 7 shows measuredsingle-exhalation eCO profiles (markers) for the twosubjects before and 7 min after the 2 h exposure to10±2 ppm CO, together with least-squares fits(lines) to the experimental data. In each case, theairway TMAD parameters (JawCO and DawCO) havefirst been determined from fits to the correspondingBH curves (not shown). The extracted parameters arepresented in table 3.

Compared to the control values, JACO was sub-stantially increased after exposure (by factors of 2.7and 4.9 for subjects 1 and 2, respectively), which sug-gests elevated COHb levels. Indeed, the COHb valuescalculated from CACO using equation (4) wereincreased accordingly and similar to those predictedwith the CFK model (section 2.5) considering ventila-tion rates of 26 l min−1 and 36 l min−1 for subjects 1and 2, respectively. For both study participants, aslightly elevated equilibrium airway (tissue) CO con-centration was found after exposure. The alveolar dif-fusing capacities, on the other hand, did not changesignificantly for subject 1 (6% increase), and not at allfor subject 2.

3.4. Simulation of respiratory disease conditionsThe potential of the novel methodology to assesshealth conditions connected to respiratory diseases

was investigated by simulating eCO profiles that couldbe expected from subjects with airway inflammation(increased JawCO) and an obstructive lung disease(decreased DACO). We hypothesize that a curve fit tohighly precise and time-resolved TDLAS data, aspresented in this study, can be used to extractparameters that reflect changes in the exhalationprofile shape associatedwith the diseases.

Figure 8(a) presents eCO profiles (10 s BH,240 ml s−1 IFR/EFR) for a healthy subject (blue solidlines) and for a subject with three-fold increased max-imum airway flux (red dashed line). Figure 8(b) showsa comparison between CO expirograms (normalbreathing, 240 ml s−1 IFR/EFR) for a healthy subject(blue solid line) and for a subject with an alveolar COdiffusing capacity reduced to 40% of normal with (reddashed line) and without (green dashed-dotted line)simultaneously increased COHb level (controlled bymeans of JACO). COHb is believed to be elevated inCOPD [39], but this may not always be the case. Theinitial TMAD parameters representing a healthy sub-ject were taken from the average data of subject 1 givenin table 2. Ambient air CO concentrations and meaninhaled/exhaled volumes were assumed to be 100 ppband 1200 ml, respectively. For all cases, the TMADparameters used for the simulated CO expirogramsare provided in table 4.

4.Discussion

The TMAD is a rather complex 1D model of pulmon-ary gas exchange with a reasonably realistic anatomicalstructure and inclusion of axial diffusion. It is shownfor CO, two healthy non-smokers and differentbreathing patterns that the numerical solution of suchmodel for the gas concentration at the mouth can befitted to experimental real-time breath data withexcellent results (figures 4–7). Compared to a merecomparison as reported in [31], curve fitting enablesrapid and more precise determination of the uniqueTMAD parameters. In combination with a highlyprecise analytical method, such as LAS, this providesthe possibility to resolve small inter- and intra-individual variations in eCO due to health or samplingconditions. TheTMADcanbe adapted to suit differentbiomarkers by considering their physical and physio-logical properties and corresponding initial estimatesof themodel parameters.

In principle, all four TMAD parameters can beextracted from a fit to a single-exhalation profile mea-sured during systemic CO elimination at close-to nor-moventilation and fixed EFR. For healthy subjects,however, the airway contribution is small and the sen-sitivity to the airway TMAD parameters (JawCO andDawCO) accordingly low for normal breathing profiles.By analyzing BH profiles, on the other hand, the air-way parameters can be obtained with reasonable pre-cision and used to determine the alveolar TMAD

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Table 1.Gas exchange parameters extracted from the TMAD fits to the experimental data in figures 4 and 5, and corresponding respiratory data. ETCO—end-tidal CO concentration,V—average of inhaled/exhaled volume,ETCO2—end-tidal CO2 concentration.

Respiratory dataa

Figures JawCO DawCO JACO DACO ETCOa CACO CawCO VI VE V ETCO2 Camb

pl s−1 pl s−1 ppb−1 pl s−1 pl s−1 ppb−1 ppb ppb ppb ml s−1 ml s−1 ml % ppb

4(a) 192 1.6 2.21×107 10 461 1969 2113 120 242 246 1201 6.4 120

4(b) 291 1.6 1.23×107 10 867 1050 1136 182 255 257 1289 5.8 154

5(a) 192 1.6 1.35×107 6361 2062 2118 120 115 119 1121 7.7 90

5(b) 291 1.6 8.37×106 6434 1248 1301 182 130 128 1177 6.1 127

a Directlymeasured; all other parameters are derived from themodel fits.

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values for normal breathing. As a consequence of theweighted fitting strategy, a good overall fit is achieved,but a small discrepancy in exhalation phase II remains

(figures 4–7). Possible reasons for this discrepancy aredifferences between assumed and actual morphologicdata (number and distribution of alveoli, airway and

Figure 6. Sequences of twenty consecutive normal breathing eCOprofiles (left panels) and corresponding nonlinear least-squares fits(left panel, lines) to five of the profiles (markers) from (a) subject 1 at average EFRof 243 ml s−1, and (b) subject 2 at average EFRof258 ml s−1.While only 5 curvefits are shown for clarity, the statistics in table 2 is based on fits to 20 profiles.

Table 2.Mean values and coefficients of variation (CV (%)=Standard deviation/Mean×100) of the TMADand respiratory parametersderived from the 20 breath-cycles shown infigure 6 for subjects 1 (S1) and 2 (S2). ETCO—end-tidal CO concentration,V—average ofinhaled/exhaled volume.

Respiratory dataa

JawCO DawCO JACO DACO ETCOa CACO VI VE V ETCO2 Camb

pl s−1 pl s−1 ppb−1 pl s−1 pl s−1 ppb−1 ppb ppb ml s ml s−1 ml % ppb

Subject 1

S1 192 1.6 2.04×107 9652 1943 2120 242 243 1196 6.5 115

CV — — 5.1 5.8 2.1 2.2 2 2 3.4 1.5 5

Subject 2

S2 291 1.6 1.20×107 10 515 1063 1139 263 258 1301 5.8 149

CV — — 4.7 4.9 1.5 1.5 3 4 3.7 1.1 6

a Directlymeasured; all other parameters are derived from themodel fits.

Figure 7.Nonlinear least-squaresfits (lines) tomeasured normal breathing eCOprofiles before exposure (BE, black diamondmarkers) and 7 min after exposure (AE, red circularmarkers) to 10±2 ppmpure COgas for (a) subject 1 and (b) subject 2. Forclarity, only every 2nd experimental data point is shown.

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lung cross sectional areas, lung symmetry, dead space),and that not all gasmixingmechanisms, as well as ven-tilation heterogeneity, are accounted for in the one-dimensional model. Moreover, in reality, lung volumeand breath gas flow rate are not constant during inha-lation and exhalation. A potential, slight instrumentaldelay during the rapid CO increase in phase II mayalso contribute to the deviation [4].

The observed eCO and TMAD parameters(tables 1–3) are in good agreement with the establishedend-tidal CO range for healthy non-smokers (1–3 ppm)

[21], and the recently reported theoretical estimates andexperimental TMAD parameter values. In general, dueto the diffusion limited CO gas exchange, end-tidal COis always lower than the predicted alveolar equilibriumCO concentrations, and JACO and DACO are sig-nificantly lower after BH than for normal breathing.The absolute values obtained for the alveolar COdiffus-ing capacity are larger than those obtained in the clinicalstandard DLCO test, mainly due to the significantly dif-ferent experimental approach (average over exhalationduring systemic elimination versus inhalation of high

Table 3.Physiological parameters of subjects 1 and 2 determinedwith extended eCOanalysis before and 7 min after a 2 h exposure to10±2 ppmCO in air.

JawCO DawCO JACO DACO ETCOa CACO CawCO ETCO2a COHbb

pl s−1 pl s−1 ppb−1 pl s−1 pl s−1 ppb−1 ppb ppb ppb % %

Subject 1

Before exposure 265 1.6 2.08×107 9837 1965 2115 166 5.8 0.97

After exposure 350 1.6 5.71×107 10 383 5106 5495 219 5.6 1.51

Subject 2

Before exposure 270 1.6 1.30×107 11 575 1054 1123 169 6.0 0.81

After exposure 320 1.6 6.41×107 11 584 5133 5534 200 5.8 1.52

a Directlymeasured parameters.b Obtained from the empirical formula in equation (4). All other parameters are derived from the TMAD fits.

Figure 8. Simulated eCOprofiles for (a) a three-fold increasedmaximumairwayflux (airway inflammation) and 10 s BH, and (b) analveolar diffusing capacity reduced to 40%of normal (severe COPD)with/without increasedCOHb andnormal breathing. Forcomparison, the solid blue lines display simulated eCOprofiles for a healthy subject (based on average subject 1 data in table 2).

Table 4.TMADparameters (based on table 2, subject 1) used to generate the synthetic eCOprofiles shown infigure 8.

JawCO DawCO JACO DACO ETCO CACO CawCO COHba

pl s−1 pl s−1 ppb−1 pl s−1 pl s−1 ppb−1 ppb ppb ppb %

Increasedmaximumairway CO flux (three-fold)

600 1.6 2.00×107 10 000 1976 2000 375 0.95

Case 1: Decreased alveolar diffusing capacity (40% of normal); constant alveolar J—increased COHb

200 1.6 2.00×107 4000 3315 5000 125 1.43

Case 2: Decreased alveolar diffusing capacity and alveolar J (both 40%of normal)—constant COHb

200 1.6 8.00×106 4000 1327 2000 125 0.95

a Obtained from the empirical formula in equation (4).

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CO concentration and constant uptake during BH),and because morphological models tend to over-estimate the diffusing capacity [40]. As expected forhealthy subjects, and given the low water-solubility ofCO, the contribution from and gas exchange with theairways is negligible, and the equilibrium airway (tissue)CO concentrations are close to (slightly higher than)ambient airCO.

The presented breath sampling procedure androbust fitting routine results in a good overall repeat-ability in the CO exhalation profile shape and TMADparameters (figure 6 and table 2). This is confirmed bythe low intra-individual variation (standard deviation)observed for both subjects in the data derived from thebreath-cycle sequences. Inter-individually, the largestand most significant difference is found for JACO, aswell as ETCO and CACO, which points to a differencein systemic COHb production between the two sub-jects. In contrast, the difference in alveolar diffusingcapacity is not equally distinct. In general, the slightvariations in TMAD parameters between the differentexperiments, observed for both subjects, could origi-nate from a daily variation in physiological parametersand/or the overall experimental uncertainty, in part-icular due to breath sampling. Interestingly, the pre-dicted alveolar CO concentrations are fairly consistentthroughout all data.

During the 2 h exposure to 10 ppmCO in inspiredair, CO was taken up by the body, which presumablyresulted in elevated blood COHb values and, subse-quently, in increased end-tidal and alveolar CO levelscompared to the control values before exposure(figure 7 and table 3). In terms of the TMAD para-meters, this appears as an increase in maximumalveolar CO flux. The considerably larger increase inend-tidal CO for subject 2 than for subject 1 (by factorsof 4.9 and 2.7, respectively) may be explained by thefact that the rise in COHbdepends on the alveolar ven-tilation rate during exposure, i.e. COHb increasesmore rapidly, when subjects breath faster. A corresp-onding difference in ventilation rate between the sub-jects was observed (but not explicitly measured) in theexposure experiments. Starting from typical healthypopulation COHb levels, and assuming alveolar venti-lation rates of 26 l min−1 and 36 l min−1 for subjects 1and 2, respectively, the CFK model predicts COHbvalues comparable to those calculated from alveolarCO using equation (4). Importantly, it is shown herefor the first time that also the maximum airway COflux is increased (if only slightly) after exposure. Fur-thermore, the results indicate that the alveolar diffus-ing capacity is not affected by the exposure.

A reduction in alveolar diffusing capacity on theorder of what might be expected in COPD patientsseems to clearly affect the shape of a normal breathingexpirogram, in particular the slope of exhalation phaseIII (alveolar slope), but also the absolute eCO level

(figure 8(b)). Any additional change in blood COHbleads to further alterations of the profile shape. Aminor increase in maximum airway flux only affectsthe eCO profile (exhalation phase I) if a breath-hold-ing maneuver is conducted (figure 8(a)). Clinicallyrelevant changes in airway and alveolar parameterscan be resolved using the fitting methodology. TheCOHb levels calculated from alveolar CO for Case 1,again using equation (4), conform with the COHbvalues previously determined inCOPDpatients [39].

Exhaled breath CO levels outside the normal rangemay originate from variations in endogenous produc-tion (systemic or locally induced HO-1 activity),recent exposure to exogenous CO sources, or can becaused by changes in pulmonary conditions. Theextended breath CO analysis approach proposed hereconstitutes a first step towards being able to locate COsources in parts of the respiratory system other thanthe alveoli, and to distinguish whether eCO reflectsblood-borne CO (COHb, including exogenous sour-ces) or lung diffusion properties. Accurate determina-tion of eCO parameters is of importance inapplications such as non-invasive assessment ofCOHb and red blood cell lifespan [41], oxidative stressmonitoring, and early diagnosis of respiratory dis-eases. Advances in non-invasive physiological mon-itoring can help to elucidate the role of CO as cellularsignalingmolecule and therapeutic agent, and lead to abetter understanding of the CO physiology. However,prior to applying themethodology inmedical researchand clinical applications, the healthy population base-line of the TMAD parameters needs to be establishedin larger cohort studies.

5. Conclusions

Anovel approach to evaluate real-time breath data wasintroduced that involves least-squares fitting of com-plete expirograms using a trumpet-shaped lungmodelwith axial diffusion to simulate the dynamics ofpulmonary gas exchange. It was demonstrated forcarbon monoxide that, in addition to end-tidal CO,maximum CO fluxes, diffusing capacities andexpected equilibrium concentrations in airwaysand alveolar region can be extracted from single-exhalation profiles measured at normoventilationduring systemic CO elimination. LAS and well-controlled online breath-sampling were employed forprecise and accurate real-time detection of CO inbreath and ambient air. In a pilot-study with twohealthy non-smokers, fractional CO contributionsfrom airways and alveoli were distinguished for thefirst time. The expirogram shape and model para-meters showed good repeatability with low intra- andinter-individual variation. Acute exposure to elevatedCO levels only affected the maximum CO fluxes, but

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not the diffusing capacities, in the respiratory tract.Simulations indicated that extended breath CO analy-sis has the potential to assess health conditions relatedto inflammatory and obstructive lung diseases.

Acknowledgments

The authors gratefully acknowledge financial supportfrom the Swedish Research Council (2013-6031) andtheKempe Foundations (SMK-1446).

ORCID iDs

RaminGhorbani https://orcid.org/0000-0002-7272-533XFlorianMSchmidt https://orcid.org/0000-0002-5065-7786

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