Borer, David

Latzin, Philipp

Obrist, Dominik

Rösgen, Thomas

Singer, Florian

Yammine, Sophie

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A COMPUTER MODEL FOR SINGLE-BREATHWASHOUTWITHDOUBLE-TRACER GAS TO HELP UNDERSTANDING VENTILATIONINHOMOGENEITYDavid Borer1, Sophie Yammine2, Florian Singer2, Thomas Rösgen 1, Philipp Latzin2 and Dominik Obrist11Institute of Fluiddynamics, ETH Zürich, Switzerland2Division of Respiratory Medicine, Dept of Paediatrics, University Hospital of Bern, Switzerlanddborer@ifd.mavt.ethz.chAbstract: We present a numerical model for a single-breathwashout of a helium–sulfur hexafluoride–air mixture. Themodel is validated against measured data.Keywords: Single breath washout, double tracer gas, cysticfibrosis, numerical model.IntroductionIn lung disease, tests for ventilation inhomogeneity overseveral breaths (multiple-breath washout) are sensitive butnot established for clinical routine due to long duration. Anew test over one breath (single-breath washout; SBW) hasrecently been invented. This test uses a gas mixture contain-ing 5% sulfur hexafluoride and 26.3% helium and is thuscalled double-tracer gas (DTG) SBW. It is easy to performin children and seems promising for clinical routine due tothe short duration. Children with cystic fibrosis (CF) lungdisease have steeper slopes of the signal during phase III ofthe exhalation (SIII) compared to healthy controls [1].MM mg. mol-16004002000-2000.0 0.1 0.2 0.3 0.4Volume lCO2 %0123456MM mg. mol-16004002000-2000.0 0.1 0.2 0.3 0.4Volume lCO2 %0123456Figure 1: DTG-SBW giving molar mass (MM) samples(dots) and carbon dioxide (CO2) samples (dashes) plottedagainst expired volume in a boy with CF (right panel) anda healthy boy (left panel), both aged nine years. Follow-ing MM correction for the CO2 fraction, MM above zeroreflects greater SF6 than He contribution and, vice versa,MM below zero reflects greater He than SF6 contribution.Investigators fitted the slope (SIII, solid line) according tothe phase III of MM and CO2 between 65% and 95% ofexpired volume. SIII was -591.6 mg/mol/L in CF and -65.8mg/mol/L in healthy control.We have developed a computer model for the DTG-SBWtests which simulates the ventilation of the whole lung withthe different gas species. The predicted composition of theexhaled air can be directly compared to the measured MMsignal from a diagnostic test. Differences between the pre-dicted and the measured signal can be eliminated by themedical practitioner in an iterative process by modifyingthe morphological data of the model lung. These modifi-cations support the diagnosis by localizing the obstructionsin the airway tree and by quantifying the severity of theseobstructions.MethodsThe basis of the SBW model is a one-dimensionaladvection-diffusion equation,∂q∂t= Dˆ∂2q∂x2− uˆ ∂q∂x+ αq, (1)withDˆ =SdDSd + Sa, uˆ =1Sd + Sa[Sdu−D∂Sd∂x], (2)where q ∈ [0, 1] is the concentration of a certain gas species,x is the spatial coordinate along the airway and t is the time.The diffusion coefficient D is a physical property of the gasand kept constant. In addition, Taylor diffusion is integratedinto the model by an analytical approach. Sd and Sa are thecross-section of the duct and the alveolei respectively, basedon data from [2]. The parameter α models the absorptionof a gas into the tissue (e.g. oxygen uptake through alveo-lar membranes). For the inert gas species studied here weassume α = 0.The advection velocity u is calculated on the assumptionof laminar flow in a bifurcating ductal network, the localflow resistance is based on the Poiseuille law. The volumeflow at the mouth is prescribed as a sinusoidal function withgiven breath period and tidal volume.In order to reduce the computational cost for solving theequations, we use a largely symmetric lung model whichallows us to resolve only on the order ofN different airwaysrather than all 2N airways in a lung (whereN is the numberof airway generations).The model described so far is closely related to a symmet-ric trumpet model. In an extension, we include asymmetricbranches to determine inhomogeneous gas transport in thelung, based on localised ventilation differences in the hier-archical bifurcating duct flow. This is realised by adjustingthe resistance at the branches and therefore the ventilationinto the distal airways and acini. Changes are applied byassigning a transmissibility factor to the airway resistance,the lower the factor the higher the resistance.Biomed Tech 2013; 58 (Suppl. 1) © 2013 by Walter de Gruyter · Berlin · Boston. DOI 10.1515/bmt-2013-4327The simulation is programmed in Matlab, with a GUI asfront end. Input parameters include the tidal volume (TV),functional residual capacity (FRC) and breath period. Themain usage of the GUI is to define the asymmetric structureof the lung and introduce restrictions. Figure 2 shows theGUI for a example case, where we introduced variationsafter generation 8.0 5 10 15 20 25Figure 2: GUI of computer model.In Figure 3 the resulting morphology is shown. Each branchsplits into 20% and 80% of total sub–volume with one re-stricted daughter branch.Volume fractionsTransmissibilityfactors0.11Figure 3: Visualization of the modelled lung morphology,the thickness of the bar depicts the fraction of the wholelung at that generation. The transmissibility factors arecolour coded.ResultsAs an example we present model results (figure 4) for aDTG-SBW test on the lung morphology shown in figure3. The predicted MM signal (figure 5) can be compared tomeasured data (e.g. figure 1). In particular, the followingcharacteristic values are compared:MMmax : Maximum molar mass during exhalationVmax : Expired volume at maximum molar massSIII : Slope of MM signal (figures 1 and 5) duringphase IIIFigure 5 illustrates how SIII depends on the severity of theobstructions in the fractal lung model of figure 3.0 10 20 2600.050.10.150.2Relative concentrationGeneration zConcentration in lung  HeSF6Figure 4: Simulated gas distribution for obstructed path-ways.0 100 200 300 400−101234SIII=−72, MMmax=3.2, Vmax=57.8Exhaled volume [ml]MM [g/mol]0 100 200 300 400−101234SIII=−418, MMmax=2.9, Vmax=57.8Exhaled volume [ml]MM [g/mol]Figure 5: Concentration profile at mouth. Left: symmet-ric lung, SIII = −72mg/mol/L. Right: obstructed lung,SIII = −418mg/mol/L.DiscussionIn CF lung disease, steep SIII reflects ventilation inho-mogeneity near the acinus entrance. The present DTG-SBW is a promising test to assess ventilation inhomogene-ity in an easy and fast way and has great potential forwidespread clinical use. The integration of the computermodel into available software will help understanding un-derlying pathophysiological processes. Before this can bedone on a routine basis, further studies of the exact effect ofdifferent morphological asymmetries are required.AcknowledgementThis study was supported by an unrestricted grant no.14435.1 PFLS-LS of the Federal Department of EconomicAffairs Switzerland, Commission for Technology and Inno-vation (CTI), Innovation Promotion Agency.Bibliography[1] F. Singer, G. Stern, C. Thamrin, C. Abbas, C. Casaulta,U. Frey, and P. Latzin, “A new double-tracer gas single-breath washout to assess early cystic fibrosis lung dis-ease,” European Respiratory Journal, vol. 41, no. 2,pp. 339–345, 2013.[2] D. P. J. Six, W. R. De Vries, and S. C. M. Luijendijk,“Alveolar sacs and the expirograms of He and SF6: amodel study,” Comput. Biomed. Res., vol. 24, pp. 321–331, July 1991.

A Computer Model for Single-Breath Washout with Double-Tracer Gas to Help Understanding Ventilation Inhomogeneity

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