The LaryngoscopeVC 2009 The American Laryngological,Rhinological and Otological Society, Inc.

Modeling Flow in a Compromised PediatricAirway Breathing Air and Heliox

Mihai Mihaescu, PhD; Ephraim Gutmark, PhD; Shanmugam Murugappan, PhD;

Ravindhra Elluru, MD, PhD; Aliza Cohen, MA; J. Paul Willging, MD

Objectives/Hypothesis: The aim of this studywas to perform computer simulations of flow withinan accurate model of a pediatric airway with subglot-tic stenosis. It is believed that the airflow characteris-tics in a stenotic airway are strongly related to thesensation of dyspnea.

Methods: Computed tomography images throughthe respiratory tract of an infant with subglotticstenosis were used to construct the three-dimen-sional geometry of the airway. By using computa-tional fluid dynamics (CFD) modeling to capture air-way flow patterns during inspiration and expiration,we obtained information pertaining to flow velocity,static airway wall pressure, pressure drop acrossthe stenosis, and wall shear stress. These simula-tions were performed with both air and heliox (he-lium-oxygen mixture).

Results: Unlike air, heliox maintained laminarflow through the stenosis. The calculated pressuredrop over stenosis was lower for the heliox flow incontrast to the airflow case. This led to an approxi-mately 40% decrease in airway resistance when usingheliox and presumably causes a decrease in the levelof effort required for breathing.

Conclusions: CFD simulations offer a quan-titative method of evaluating airway flow dynamicsin patients with airway abnormalities. CFD modelingillustrated the flow features and quantified flow param-eters within a pediatric airway with subglottic stenosis.Simulations with air and heliox conditions mirrored theknown clinical benefits of heliox compared with air. Weanticipate that computer simulation models will ulti-mately allow a better understanding of changes in flowcaused by specific medical and surgical interventionsin patients with conditions associated with dyspnea.

Key Words: Pediatric airway, subglottic stenosis,computational fluid dynamics, heliox.

Laryngoscope, 119:145–151, 2009

INTRODUCTIONClinical studies have widely demonstrated the ther-

apeutic benefits of helium-oxygen mixtures (i.e., heliox)in treating patients with anatomic abnormalities of theupper respiratory tract.1–3 However, little informationexists regarding the physical principles behind the bene-fits and the detailed effects of such mixtures on theairway flow variables (i.e., velocity, static airway wallpressure, pressure drop, and wall shear stress).

Advances in computer technology over the past fewdecades have facilitated the use of computational fluiddynamics (CFD) for investigating flows in various bio-logic systems.4–6 More recently, numerical simulationshave been increasingly applied to study flow patterns inairways with anatomic abnormalities.7–9 For the mostpart, however, these simulations have utilized idealized(i.e., anatomically inexact) adult airway models.

The main objective of our research was to performcomputer simulations of flow within an accurate, ana-tomically derived, three-dimensional model of a pediatricairway with subglottic stenosis. By using CFD modelingto capture flow features in the airway, we obtainedquantitative and qualitative information on flow velocity,static airway wall pressure, pressure drop across the ste-nosis, and wall shear stress. The three-dimensional flowsimulations were used to illustrate the known clinicalbenefits of heliox on pediatric patients with structuralnarrowing of the airway. These simulations are an initialstep in our long-term goal of developing a noninvasiveapproach to quantifying dyspnea severity in childrenwith respiratory tract anomalies.

MATERIALS AND METHODSCFD technique predicts fluid flow characteristics by solv-

ing the physical laws of fluid mechanics (i.e., Navier-Stokesequations) using numerical methods and algorithms embodiedin the form of a computer code. The solution procedure involvesthe construction of the geometrical model, the generation of thecomputational grid within the volume, the discretization of the

From the Department of Aerospace Engineering and EngineeringMechanics (M.M., E.G.), University of Cincinnati; Department ofOtolaryngology–Head and Neck Surgery (E.G., S.M., R.E., J.P.W.),University of Cincinnati College of Medicine; and the Division ofPediatric Otolaryngology (R.E., A.C., J.P.W.), Cincinnati Children’s HospitalMedical Center, Cincinnati, Ohio, U.S.A.

Editor’s Note: This Manuscript was accepted for publication July1, 2008.

Send correspondence to Dr. Mihai Mihaescu, PhD, University ofCincinnati, Department of Aerospace Engineering and EngineeringMechanics, 310 Rhodes Hall, ML 0070, Cincinnati, OH 45221-0070.E-mail: Mihai.Mihaescu@uc.edu

DOI: 10.1002/lary.20015

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governing equations on the grid, and an iterative algorithmthat is applied to these equations with proper initial and bound-ary conditions. The CFD solver used here is part of thecommercial software package Fluent and is based on the Reyn-olds Averaged Navier-Stokes (RANS) approach with standard k-� turbulence model. It was previously applied for investigatingthe flow features in airway models generated using imagingdata from patients with Obstructive Sleep Apnea.10,11

Construction of the Airway ModelComputed tomography (CT) images through the respiratory

tract of an infant with subglottic stenosis were used to accuratelyconstruct the three-dimensional geometry of the airway. Twentycross-sectional CT images of 2.5 mm thickness and with zerospacing between them were acquired at different axial locationsfrom the epiglottis to the carina (Figs. 1A and 1B). The CT scanshad a spatial resolution of 512 � 512 pixels. The sensitivity alongthe x and y axes was equal to 0.31 mm. An Edge Detection Pro-gram10 (EDP) determined the Cartesian coordinates (x, y) ofairway boundaries in each of the 20 images. The computer-gener-ated airway boundaries as identified by the EDP are shown in

Figure 1C. The coordinates of airway boundaries were used asinput to the commercial mesh generator software Gambit (Flu-ent). This program was employed to construct the three-dimensional geometry of the airway lumen (Fig. 1D). The soft-ware then generated the computational grid/mesh within thevolume of the airway as shown in Figure 1E. The constructedmesh comprised approximately 3 � 105 computational cells. Afiner grid density near the wall of the airway is achieved with theaim of a better description of the complex geometrical boundary.

Clinical and Boundary ConditionsAir and heliox flow simulations through the reconstructed air-

way model were conducted for the inhalation and exhalationphases of breathing at the flow rates of 3 L/minute, 5 L/minute, and10 L/minute. As inlet boundary condition, the axial velocity wasspecified at the inlet surface of the computational domain in orderto match the desired volumetric flux. No-slip boundary conditionsfor velocity were set at the airway walls, and a flux conserving zerogradient boundary condition was applied at the outlet surface ofthe computational domain. For the heliox simulations, additionalboundary conditions were required in terms of the mass fraction of

Fig. 1. Steps involved in the construction of the three-dimensional airway model. (A, B) CT data acquisition—sagittal and axial CT images.(C) Airway boundary identification. (D) Reconstruction of airway’s geometry. (E) Computational mesh generation.

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oxygen at the inlet plane in order to impose the desired conditionsfor the heliox system of 70% helium and 30% oxygen. The density ofheliox (70:30) was 0.507 kg/m3, and its molecular viscosity 1.72e-5kg/(m�s). The density of air and its molecular viscosity were 1.23 kg/m3 and 1.75e-5 kg/(m�s), respectively.

Comparisons were made between velocity, static pressure,pressure drop across the stenosis, and wall shear stress distri-butions for all of the clinical conditions.

RESULTS

Airflow CharacteristicsFlow in the upper airways is characterized as lami-

nar (smooth and streamlined), turbulent (chaotic/

irregular), or transitional (changing from a laminar to aturbulent state). Any airway constriction can increasethe complexity of the flow and can change it from lami-nar to turbulent. The Reynolds number is used toidentify the character of the flow field based on its veloc-ity, the radius of the airway, and the physical propertiesof the gas. Above a certain value called the critical Reyn-olds number (Recritical � 2,300), turbulence occurs. Belowthis value, the flow is laminar. A turbulent chaotic flowin the airway results in increased energy loss (frictionalresistance increases) and therefore requires larger driv-ing pressure to maintain constant airflow. Due to thesimilarity of flow behaviors (i.e., the flow exhibits accel-eration and induced pressure drop at the site of the

Fig. 2. Air and heliox flow compari-sons during inspiration at the flowrate of 10 L/minute: (A) Contours ofaxial velocity (m/second) along alongitudinal plane and 20 crossplanes. (B) Contours of static pres-sure (Pascals) on the airway wall.

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stenosis) found at all three flow rates (3 L/minute, 5 L/minute, and 10 L/minute), we report detailed resultsonly for the clinical condition of 10 L/minute.

Flow VariablesFigure 2A shows the color contours of the main ve-

locity component (i.e., axial velocity) during theinspiration phase along the longitudinal plane of 20cross-sectional planes for air and heliox conditions. Com-puted axial velocities for both conditions are similar,with the flow accelerating at the minimum cross-sec-tional area (i.e., site of stenosis). The Reynolds numberof the airflow calculated at the site of the stenosis was5,200, indicating that the flow was turbulent. The Reyn-olds number corresponding to heliox (lower-densityfluid) was 2,170, typical of laminar flow. Downstream ofthe stenosis, flow separation occurs and retrograde flowdevelops along the posterior airway wall as shown in theclose-up caption in Figure 2A.

The static pressure distributions along the airwaywall during inspiration are presented in Figure 2B forair and heliox conditions. A substantial negative staticpressure was found for airflow at the site of stenosis(�845 Pa), which may imply the potential for airway col-lapse at this site. The minimum wall static pressurevalue calculated for heliox (�366 Pa) was approximately40% of the calculated value for air at the same flow rate.

Figure 3 shows the shear stress values on the air-way wall during inspiration for air and heliox.Approximately a 16% reduction in the shear stress val-ues on the wall of the airway at the site of stenosis wasfound when using heliox (8.9 Pa) as compared with air(10.6 Pa).

The contours of axial velocity and static pressureduring exhalation are depicted in Figures 4A and 4B forair and heliox. Larger recirculation regions were founddownstream of the stenotic area (toward the proximal

airway) during exhalation (Fig. 4A) as compared with in-halation that was presented in Figures 2 and 3. Theminimum wall static pressure values for air and helioxduring exhalation at the site of the stenosis wereslightly lower relative to these values during inhalation.

The dependence of static pressure and wall shearstress values on flow rate is shown for air and helioxconditions in Figures 5A and 5B. These values were cal-culated on the airway wall at the stenosed region for theflow rates of 3, 5, and 10 L/minute for both inspirationand expiration flows. The static pressure at the site ofminimum cross-sectional area decreased substantiallywith increasing flow rate. The minimum wall static pres-sure value for heliox was equal to approximately 40% ofthe value for air at all three flow rates. Additionally,approximately 16% lower wall shear stress values werecalculated for heliox relative to air (Fig. 5B). The wallshear stress values at the stenosis site were found to bethe same as comparing the inspiration and exhalationphases.

Figure 6A presents the calculated pressure dropsbetween the proximal and distal regions (DP ¼ Pinlet �Poutlet) of the airway model for air and heliox flows at allconsidered clinical conditions. Increased pressure dropvalues were found as the flow rate increases from 3 L/minute to 5 L/minute to 10 L/minute. For expiration,larger pressure drop values were predicted as comparedwith inspiration. This observation is consistent with thefact that during the expiration the recirculation regionsgenerated downstream of the stenosis are longer andstronger as shown by comparing Figures 2A and 4A.Approximately a 40% reduction in the pressure drop val-ues was found for the heliox compared with air for thesame clinical condition. In addition to the CFD results,the induced pressure drops between the proximal anddistal region were estimated based on a formula derivedusing the theoretical fluid dynamics analysis of a sym-metric pipelike geometry with an obstruction.12 The

Fig. 3. Air and heliox flow compari-sons during inspiration at the flowrate of 10 L/minute: contours ofshear stress distribution (Pascals) onthe airway wall.

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theoretical results are plotted in Figure 6A for bothheliox and air additional to the CFD predictions. Consid-ering that the analytical formula was derived for asymmetric pipelike geometry where it was assumed thatthe pressure-flow relation is dominated by the restric-tion and not by the details of the geometry, there is anoverall good match between the CFD results and thetheoretical ones.

The dependency on the flow rate of pressure dropbetween the proximal and stenotic region (DPmax ¼Pinlet � Pstenosis) is depicted in Figure 6B. It was foundthat the ratio between the heliox and air pressure dropsat the same flow rate is roughly 0.4, consistent with the

fact that the ratio between the heliox and air densitiesis 0.4.

DISCUSSIONPrior reports have shown the potential of utilizing

the CFD modeling technique in analyzing flows throughupper respiratory airway models of adults with or with-out obstructions.6–9 Most of the studies that involvedairway obstructions used simplified (anatomically incor-rect) airway models or neglected the importance of wallshear stress distribution that shows the locations wherethe flow interacts most with the airway walls.7,9

Fig. 4. Air and heliox flow compari-sons during expiration at the flowrate of 10 L/minute. (A) Contours ofaxial velocity (m/second) along alongitudinal plane and 20 crossplanes. (B) Contours of static pres-sure (Pascals) on the airway wall.

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In the present study, CFD simulations that describeair and heliox flow patterns in the respiratory tract of apediatric patient with subglottic stenosis are presented.The airway model was accurately constructed usingcross-sectional CT images of the patient’s airway. Ourresults demonstrated that the presence of the stenosis inthe airway changed the flow of air from laminar to tur-bulent at flow rates at or above 5 L/minute, with theReynolds number at 5 L/minute being 2,600. In contrast,the flow characteristics of heliox remained laminarthrough the site of stenosis, with Reynolds numbers lessthan 2,170 for all three flow rates. In a clinical context,the work of breathing air becomes increasingly laboredto overcome the increased driving pressures required.With heliox, due to its low density, the Reynolds numberof the flow decreases, minimizing the overall work ofbreathing. Additionally, heliox diminishes the effect ofairway obstruction, minimizing the pressure differential

across the stenosis. It is known that at a high enoughReynolds number turbulence occurs and such flows inconfined geometries are characterized by higher fric-tional losses, and therefore require larger drivingpressure compared with laminar flows.13 Nevertheless,the advantages of heliox are maintained under fully tur-bulent conditions because the low-density mixture flowsfaster than air.12

Static wall pressures calculated at the site of thestenosis for air in our static model showed significantnegative forces on the airway wall. The static wall pres-sure value calculated for heliox was equal toapproximately 40% of its value for air. When the site ofnarrowing is malacic in a dynamic airway, further col-lapse at the stenotic site would occur. The increase ofnegative static pressure on the airway wall towards zerowould lessen the degree of collapse of the malacic seg-ment, thus improving flow and reducing the driving

Fig. 5. Static pressure (A) and wall shear stress (B) dependency on the flow rate for air and heliox flows. These flow variables are computedon the airway wall at the site of stenosis.

Fig. 6. Pressure drop dependency on the flow rate for air and heliox flows. (A) Pressure drops calculated between model inlet and outlet.(B) Pressure drops calculated between model inlet and stenosis region.

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pressure required for respiration. This clinical scenariois consistent with the observed effects of heliox adminis-tered to children with airway obstruction.

The comparisons of the pressure drops across steno-sis predicted by CFD to those obtained using atheoretical formula derived for a symmetric pipelike ge-ometry with obstruction12 show an overall goodagreement (Fig. 6A). The 40% reduction in the pressuredrop values found for heliox compared with air corre-lates with other CFD results obtained on not-exactairway models with artificially inserted stenoses.7

The resistance (R) of the airway can be estimated(R � DP/U2) using the knowledge of the pressure drop(DP) and of the flow rate (U). Considering the presentdata, the resistance of the airway was reduced by 40%by using heliox compared with air for the same volumet-ric flow rate.

For both air and heliox simulations, recirculationregions (reversed flow) developed downstream of the ste-nosis. The flow stream separated, with isolated areasdeveloping flow patterns distinct from that of the pri-mary stream (Figs. 2A and 4A). Regions were seenwhere flow direction was opposite to that of the primarystream. This necessitated an increase in the pressurerequired to maintain the same flow rate distal to the ste-nosis; however, these pressure changes were less forheliox. The size and configuration of these regions weredependent upon flow rates and respiratory phase. Froma clinical perspective, these rotational flow structurescontribute to the overall pressure differential and hencethe work of breathing.

Shear stress represents a measure of the forcesexerted tangential to the luminal surface of the airway.Laminar flow exerts the minimum force on the airwaywall interface by developing a stable boundary layerbetween the primary stream of flow and the airwaywall. Turbulent flow disrupts this boundary layer, gener-ating greater shear stress values. By preserving laminarflow, heliox reduced shear wall stress by 16% (Figs. 3and 5B). In a patient with a stenotic airway, turbulentflow within the airway could cause trauma to the airwaymucosa, thus inducing an inflammatory response thatmay play a role in the progression of a stenosis.

The next phase in our application of CFD modelingto pediatric airway pathology is to create a precise phys-ical model from which measurements of flow velocity,static wall pressure, pressure changes, and wall shearstress can be obtained to validate our findings.

CONCLUSIONSCFD simulations offer a quantitative method of

evaluating in a noninvasive way the airway dynamics in

patients with airway abnormalities. In our study, CFDmodeling illustrated the flow features and quantified theflow variables (velocity, static airway wall pressure,pressure drop across the stenosis, and wall shear stressvalues) within a pediatric airway with subglottic steno-sis. Simulations with air and heliox conditions mirroredthe known clinical benefits of heliox compared with air.We anticipate that computer-simulation models will ulti-mately allow a better understanding of changes in flowcaused by specific medical and surgical interventions inpatients with conditions associated with dyspnea.

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