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doi: 10.1152/japplphysiol.01118.2006103:1082-1092, 2007. First published 14 June 2007;J Appl Physiol

Guilherme J. M. Garcia, Neil Bailie, Drio A. Martins and Julia S. Kimbellnasal cavityAtrophic rhinitis: a CFD study of air conditioning in the

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A body of indirect evidence in the literature supports thisargument. First, genuine AR has never been observed in anarrow nose (49), which is consistent with abnormal flowpatterns playing a role in the pathophysiology of the disease.Second, Girgis (18) demonstrated that if a patient with ARblocks his nostrils with pieces of cotton for 24 h, the nasalmucosa will present an entirely different picture on removal of

the plugs; it becomes moist and less pale, and the crustsbecome loosened. Third, crusts are never observed in theparanasal sinuses, where the drying effect of airflow is lessvigorous than in the nasal cavity (49). Finally, Dutt andKameswarans observation (11) that primary AR seems to havea high prevalence in the arid regions bordering the great desertsof Saudi Arabia suggests that low absolute humidity of the airmay trigger AR in susceptible populations.

Further evidence is provided by cases of unilateral ARrelated to a septal deviation. It has been observed that theair-humidifying capacity of the nose is time dependent becausewhen a continuous air stream is drawn through the nose, airbecomes progressively cooler and drier at the outlet (8). There-fore, we suggest that unilateral AR associated with septaldeviation may be explained as follows: if the cavity on theconcave side of the septum is too large, air will flow mostlythrough this patent side, subjecting it to a permanent water andtemperature gradient. If the water gradient is sufficiently largeor the mucosa unhealthy, the mucous layer may dry in regionsof high water flux, leading to crust formation and predisposingto infection. Because of the lack of a cyclic closure of theaffected side, the continuous airflow is a continuous burden tothe mucosa, which will not heal unless artificial irrigation isinstituted or airflow artificially obtunded. Clinical observationssupport this idea: Bunnag and coworkers (5) noted that in ARpatients with marked septal deviation, crust is found only in thewider side of the nasal cavity; Gupta (20) reported improve-

ment in the symptoms of unilateral AR after the septal devia-tion was corrected surgically. This improvement may be due tothe more uniform division of the humidification task betweenthe cavities after surgery. This reasoning suggests that the nasalcycle may have an important role in allowing each cavity torecover after it has been responsible for warming and humid-ifying the air for a while. This duty of the nasal cycle inproviding a rest period for recovery of the nasal epitheliumfrom any damage caused by the airflow has also been proposedby others (4, 12).

The objective of this research was to investigate airflow,water transport, and heat transfer in the nose of an AR patientwho underwent a surgical procedure to narrow his nasal cavity.We also performed calculations of the air-conditioning process

in the noses of four healthy humans to establish a basis forcomparison. Our aim was to test the hypothesis that thepathophysiology of AR is associated with excessive evapora-tion of the mucous layer, as well as to devise strategies toimprove the outcome of cavity-narrowing procedures in thetreatment of AR.

MATERIALS AND METHODS

A 26-year old Caucasian male was diagnosed with primary AR inthe Santa Casa hospital in Belo Horizonte, Brazil. His symptoms wereaggressive fetor; nasal crusting; mucosal atrophy; rhinorrhea; resorp-tion of the turbinates, resulting in a large nasal cavity; and a paradox-ical sensation of nasal congestion. A marked atrophy of the inferior

and middle turbinates yielded roomy nasal passages, especially in theleft side. Both sides were affected by the disease, but the right cavitywas not as wide as the left because of a septal deviation. The patientreported having symptoms since he was 13 years old and that hissymptoms had not responded to repeated courses of antibiotics.

The patient underwent a nasal cavity-narrowing procedure. Ribcartilage was implanted under the mucosa along the floor of the nose,and a septum spur was removed. At the time of surgery, it wasreasoned that the septal deviation assisted in maintaining the rightcavity narrow; therefore the deviation was not corrected. Cartilagewas implanted mostly in the left side as an effort to narrow the mostpatent side. Computerized tomography (CT) scans of the nasal pas-sages were taken before and 6 wk after surgery. Axial slices withthickness of 1.0 mm and an increment of 0.6 mm were used, resultingin 109 cross sections.

The nasal geometry of the four healthy adult humans used in thisstudy came from coronal cross sections of hexagonal meshes that hadbeen created at The Hamner Institutes for Health Sciences (ResearchTriangle Park, NC) from MRI scans of 3-mm spacing (43). TheseMRI scans were carefully selected from a sample of 17 scans ofhealthy volunteers to represent complete nasal passages and a broadrange of surface area-to-volume ratios (19a). All subjects participating

in this study signed a consent form. The research described in thismanuscript was approved by our institution and by the BiomedicalEngineering committee of Conselho Nacional de Pesquisa e Desen-volvimento (CNPq), Brazil, through Postdoctoral Grant 201248/2004-2.

The nasal geometries were reconstructed in three dimensions usingmedical imaging software (Mimics, Materialise, Ann Arbor, MI) andmeshed with tetrahedral elements (ICEM-CFD, Ansys, Canonsburg,PA). The quality of the tetrahedra was checked using ICEM-CFD toensure that all cells had an aspect ratio larger than 0.3, a value neededto avoid distorted elements and optimize the accuracy of the numer-ical simulations. The nasal cavity was modeled as a rigid structure.

Steady-state inspiratory air, heat, and water transport were simu-lated using Fluent (Fluent, Inc., Lebanon, NH). Pressure-inlet andpressure-outlet boundary conditions were used to mimic the pressure-

driven respiration occurring in real life. A constant pressure drop wasimposed equally on both nostrils of each reconstructed nose andchosen (using the target-mass-flow-rate feature of Fluent) such thatthe total volumetric flow through the nostrils was 250 ml/s, corre-sponding to resting breathing (2). A no-slip (zero velocity) boundarycondition was assumed at the airway walls.

The experimental literature on nasal respiration suggests that air-flow is primarily laminar in healthy adults during resting breathing (7,21, 30). Likewise, most published CFD investigations assume thatnasal airflow is laminar at rest (3, 31, 40, 48, 56). However, there areno experimental data on the airflow patterns in abnormally wide nasalcavities, such as noses affected by AR. Also, the flow rate at whichturbulence effects become important in healthy noses is still uncertainsince some researchers have observed a partially turbulent flow evenat low air velocities (17, 45). For this seminal study, we assumed that

nasal airflow is laminar in normal and abnormal geometries. Forhealthy nasal cavities, this hypothesis has been shown to provideaccurate predictions (31, 48).

Lindemann and coworkers (34) measured mucosa temperatureduring the respiratory cycle in 15 healthy volunteers at room condi-tions of 25 1C and 30 4% relative humidity (RH). They reportedthat during the course of inspiration, temperature decreased from32.5 1.1C to 30.2 1.7C in the nasal valve and from 34.4 1.1C to 33.2 2.3C in the nasopharynx. During expiration, themucosal temperature increased back to original values. Thus weadopted a mean value of 32.6C for the mucosal temperature duringinspiration. Ambient air was set to 20C at the nostrils, and outflowboundary conditions were applied to the outlet (see APPENDIX fordetails). To account for the cooling effect of water evaporation, our

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heat flux calculation included a term of water flux times the latent heatof evaporation, as proposed by Naftali et al. (40) (APPENDIX).

The respiratory epithelium is coated with mucus, and thus air wasassumed to be at 100% RH at the air-tissue boundary of the main nasalcavity. However, the nasal vestibule is lined with squamous epithe-lium, and therefore water flux was set to zero in this region. To definethe vestibule, we created a curve on the nasal surface by intersectingthe nasal geometry with a cylinder (diameter 20 mm) whose axis is

perpendicular to the septum. This curve was a good first approxima-tion of the limen nasi, the anatomic ridge marking the boundarybetween the nasal cavity proper and the vestibule (33). The curve wasthen used to split the nasal surface, defining a region covered withsquamous epithelium (nasal vestibule) and a region covered withrespiratory epithelium (proper nasal cavity), where the above-men-tioned boundary conditions were defined. Ambient air was consideredto be at 50% RH, while outflow boundary conditions were applied tothe outlet (see APPENDIX).

Nasal resistance (Rnose), defined as Rnose p/Q, where p is thepressure drop in pascals (Pa) and Q is the flow rate in milliliters persecond (ml/s), was computed from the simulation results and com-pared with literature data obtained by rhinomanometry (38). Meshdensity tests were conducted to ensure grid independence of allresults, and the data reported here were obtained in meshes of

900,0001,300,000 tetra cells. More details on the differential equa-tions solved in Fluent, computational algorithms employed, andboundary conditions and physical properties utilized can be found inAPPENDIX.

RESULTS

To characterize the geometry of the atrophic nose andcompare it with healthy cavities, cross-sectional areas of coro-nal sections from the nostrils to the beginning of the nasophar-ynx were calculated (Fig. 1). The cross-sectional areas of thehealthy nasal airways were at a minimum 15 mm posterior tothe nostrils. This region, known as the nasal valve, correspondsto the level prior to and including the anterior end of theinferior turbinate, and it is responsible for most of the resis-tance to airflow (22, 25, 42). Posterior to the valve, thecross-sectional area increased rapidly to a plateau value thatwas maintained through most of the turbinate region. Ap-proaching the choanae, the turbinates receded, the cross sec-tions gradually became two oval empty spaces, and the cross-sectional areas increased rapidly.

The before-surgery nasal geometry of the AR subject wasremarkably different. The cross-sectional area increasedsteadily from the nostrils to the end-turbinate region (except for

a small decline at the nasal valve), being at least twice thenormal value throughout most of the turbinate region (Fig. 1).After implantation of rib cartilage under the mucosa on thefloor of the nose, the cross-sectional areas of the anteriorportion became similar to normal. The posterior part, however,was not modified during surgery and, therefore, remainedwide. An expansion of both inferior turbinates was observed

throughout the nasal cavity after surgery (Fig. 2).Volumes and surface areas of the models were calculated for

each nasal cavity from the nostrils to the end of the septum(Table 1). The atrophic nose had a smaller surface area and alarger volume than the normal subjects. Surgery decreased thevolume but did not increase the surface area. A useful mea-surement to determine whether a nasal cavity is narrow or wideis the surface area-to-volume ratio (SAVR). The narrower thecavity is, the larger is the SAVR, and vice versa. Our sampleof four healthy humans had a mean SAVR of 0.97 0.14mm1 for the left and right cavities combined. This value is ingood agreement with a recent study by Yokley (53), who usedCT scans to calculate SAVRs in a much larger sample (40

European Americans and 9 African Americans) of healthyvolunteers. He found SAVR 1.05 0.23 mm1 in Europeandescendents and SAVR 1.03 0.29 mm1 in African ones.In contrast, before surgery the atrophic nose had a SAVR of0.39 mm1, which increased to 0.50 mm1 after surgery.

Several investigators have reported that in a normal nose, airflows mainly near the septum, especially along the floor of thenose and between the septum and the middle meatus (30, 42,48, 52). A small percentage of air flows through the meatusesand the olfactory slit. The turbinates have been reported tohave a streamlining effect, directing the flow to the nasophar-ynx, leaving the airflow distribution almost unchanged as flowrate increases (21, 31, 42, 48). In contrast, our simulationsdisplayed a very different pattern in the atrophic nasal cavity.We predicted that in an empty nose, the air flows mainlythrough the upper half of the cavity, while a low-velocity eddywas observed in the inferior portion (Fig. 2).

Our simulations predicted that the atrophic nose did notwarm or humidify the air as effectively as the healthy nasalairways studied (Table 2). Simulated air temperature wasalready within 1.5C of the mucosal temperature at the mid-turbinate region for the normal subjects (4050 mm after thenostrils; Fig. 3A). Meanwhile, at the same location, the tem-

Fig. 1. Cross-sectional areas of coronal sections of the humannose (left and right cavities combined). The distance along thenose is measured from the first coronal section after the nostrils.The curve representing a normal nose is an average of the 4healthy subjects included in this study; the bars show the rangeof variation in these data. Atrophic pre-op and atrophic post-oprefer, respectively, to the atrophic nose before and after surgery.

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perature was still 2728C in the before-surgery atrophic nose,which is 4.65.6C below the mucosal temperature. Aftersurgery, the airflow simulations predicted the nose had par-tially recovered its capacity to warm the inspired air (Fig. 3A;

Table 2). A similar behavior was predicted for air humidifica-tion (Fig. 3B; Table 2).

To provide a partial test of our hypothesis that AR is relatedto exaggerated evaporation of the mucous layer, we computedwater fluxes per unit area throughout the nasal mucosa(Figs. 46; Table 3). In the normal noses studied, inspired airwas warmed and humidified mainly in the anterior-inferiorportion of the cavity (Fig. 3), in agreement with previousreports (28, 40), and thus this was the region with the largestheat and water fluxes (Figs. 5 and 6). In contrast, the disturbedflow pattern and smaller surface area of the atrophic nosepredicted a very different scenario. Here, large water fluxeswere spread throughout most of the nasal cavity (Figs. 5 and 6),with hot spots along the superior part of the cavity and on themiddle turbinate (Fig. 4). Past the nasal valve, heat and waterfluxes were higher in the atrophic geometries than in thenormal subjects (Fig. 5). In particular, the AR nose had muchhigher heat and water fluxes in the nasopharynx compared withthe normal noses (Table 3).

After surgery the atrophic nose had a significant imbalancein the partitioning of airflow (Table 4). While 64% of the airflowed through the left cavity before surgery, this fractionincreased to 91% postoperatively. Consequently, the left cavitycarried out most of the air conditioning, leading to much higherheat and water fluxes in this side than in the right side andpreventing a desired reduction in water flux levels on the leftside postoperatively (Table 3). This imbalance in airflow dis-tribution was partially due to a postsurgery constriction in theright side caused by excess implantation of cartilage at thenasal valve area (more details below).

Postoperative CT scans depicted the atrophic nose 6 wk afterthe procedure. At this stage, the patient reported nasal obstruc-

Fig. 2. Airflow patterns in the atrophic nose compared with ahealthy nasal cavity colored by air speed magnitudes. Left:streamlines of massless particles released from the left nostril.

Right: airflow distribution at coronal cross-sections at 15 mm(a), 35 mm (b), and 55 mm (c) after the nostrils.

Table 1. Geometrical features of our 6 human meshes

Subject/Region Surface Area, mm2 Volume, ml SAVR, mm1

Healthy nose 1Left cavity 9,900 9.2 1.07Right cavity 10,190 8.7 1.17Both cavities 20,090 18.0 1.12




Atrophic preopLeft cavity 7,130 24.0 0.30Right cavity 6,220 10.5 0.59Both cavities 13,350 34.5 0.39

Atrophic postopLeft cavity 6,270 13.7 0.46Right cavity 5,860 10.6 0.55Both cavities 12,130 24.3 0.50

Atrophic preop and atrophic postop refer, respectively, to the pre- andpostoperative geometries of the atrophic nose. SAVR is the surface area-to-volume ratio of the nasal cavity from the nostrils to the end of the septum.




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tion and anosmia, but no crusting, rhinorrhea, or fetor. Sixmonths after surgery, partial resorption of the implant wasnoted. The patient was satisfied with the absence of stench, butendoscopy revealed crust formation on the posterior portion ofthe septum, between the septum and the superior turbinate, andalong the medial aspect of the middle and inferior turbinates onthe left side. There were fewer crusts in the right cavity, andthese were located on the proximal aspect of the middleturbinate and in the upper posterior region. The larger amountof crusts on the left side correlated with the higher left-sideflow rate and water flux levels (Tables 3 and 4). The postop-erative total amount of crusts seemed to be smaller than the

preoperative, which might be related to the improvement of thefetor 6 mo after the operation. Anosmia and nasal obstructionwere persistent symptoms.

Despite the patients preoperative complaint of nasal con-gestion, the calculated nasal resistance of the AR nose wassmaller than the values predicted for the four healthy nosesbefore surgery (Table 2; Fig. 7). On the other hand, thepostoperative nasal resistance was predicted to be twice aslarge as the average for our four healthy noses. This higherpostoperative resistance was partially due to the cavity-narrow-ing procedure and partially due to the different positions of thesoft palate in the before and after CT scans, which led to a

Table 2. Air temperature, relative humidity, and water content at the nasopharynx, and nasal resistance for inspiratoryairflow of 250 ml/s through left and right cavities combined

Subject Temperature, oC RH, % Water Content, kg/m3 Rnose, Pa/(ml/s)

Healthy nose 1 32.4 100.0 0.0366 0.070Healthy nose 2 32.3 100.0 0.0362 0.082Healthy nose 3 32.3 100.0 0.0363 0.039

Healthy nose 4 32.0 99.8 0.0356 0.046Atrophic preop 29.7 95.7 0.0297 0.028Atrophic postop 30.9 98.2 0.0330 0.119

Atrophic preop and atrophic postop refer, respectively, to the pre- and postoperative geometries of the atrophic nose. Mucosal temperature and relativehumidity (RH) were assumed to be 32.6C and 100%, respectively. Rnose, nasal resistance.

Fig. 3. Temperature (A) and water content (B) of the air streamaveraged over coronal cross sections along the human nose. SeeFig. 1 legend for more information on symbols.




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narrower nasopharynx in the postsurgery geometry. The rise innasal resistance a month and a half postoperatively was ex-pected: the surgeon had anticipated that partial resorption ofthe implants would occur and implanted excess cartilage.Because of the implant resorption, nasal resistance most likelydiminished since the CT scans were taken, but no quantitativeassessment could be made because of the lack of a rhinoma-nometer in our Brazilian clinic. Thus our data suggest that thepreoperative complaint of nasal congestion was due to loss ofsensory receptors, in agreement with rhinomanometry datacollected by Moore and Kern (38) for 135 AR patients, whilethe postoperative nasal congestion may be associated with theincreased nasal resistance.

DISCUSSION

The human nose is responsible for warming, humidifying,and cleaning inspired air. To accomplish this task, the nasalmucosa is coated with a thin layer of mucus, which trapsair-borne particles as well as moistens the air by evaporation.AR is a chronic disease of the nasal mucosa, and its etiology isstill unknown. The disease is characterized by progressiveatrophy, nasal crusting, dryness, fetor, enlargement of the nasal

space, and a paradoxical sensation of nasal congestion. Twocomprehensive reviews of AR have recently been published,and the readers are referred to them as detailed descriptions ofthis disease (11, 38).

Fig. 4. Regions of the nasal mucosa were thewater flux per unit area exceeds 2 104

kg/(s m2). Only the left cavity and the naso-pharynx are shown. (Nostrils are to the left;nasopharynx to the right.) Note that the wa-ter flux was set to be zero at the nasalvestibule. Atrophic pre-op and atrophicpost-op refer, respectively, to the pre- andpostoperative geometries of the atrophicnose.

Fig. 5. Circumferential averages of heat flux (A) and water flux(B) through the nasal wall as a function of the distance from thenostrils. For each subject, the data represent the nasal cavitywith the higher air flow rate (Table 4). See Fig. 1 legend formore information on symbols.




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We simulated the airflow and transport processes that occurin the nasal cavities of four healthy humans and one ARpatient. We found that, while air humidification occurredmainly in the anterior-inferior portion of the cavity in thehealthy noses studied (Figs. 5 and 6), high water fluxes weremore spread out in the AR nose, with hot spots at the superiornasal cavity and on the proximal aspect of the middle turbinate(Fig. 4). These hot spots correlated with the regions wherecrusting is more frequently observed in AR patients in ourBrazilian clinic. Other investigators have also reported that themiddle turbinate is more frequently affected than the inferiorturbinate (23, 47). Ssali (47) stated that in the early stage of thedisease crusts may be confined to the middle and superior

turbinates, but one hardly ever finds crusts confined to theinferior turbinate without involvement of the middle one.These findings suggest that the superior air current that waspredicted in our simulations (Fig. 2) may be a prevailingfeature of AR, leading to crust formation mainly in the upperhalf of the cavity. Our simulations also predicted an above-normal mucus evaporation past the nasal valve in the AR nose(Fig. 5). In particular, water fluxes were substantially higher atthe nasopharynx of the atrophic nose compared with thenormal noses (Table 3). This may explain why AR is oftenaccompanied by pharyngitis sicca, a disease characterized byatrophy of the mucous glands and absence of their secretion(11, 44).

Fig. 6. Circumferential averages of heat flux (A) and water flux(B) through the nasal wall as a function of the height from thenasal floor. For each subject, the data represent the nasal cavitywith the higher air flow rate (Table 4). See Fig. 1 legend formore information on symbols.

Table 3. Total heat and water fluxes per unit area in each region of the nasal cavity

Subject

Heat Flux, 103 W/m2 Water Flux, 104 kg/(s m2)

Leftcavity

Rightcavity Nasopharynx

Leftcavity

Rightcavity Nasopharynx

Healthy nose 1 1.12 0.93 0.03 3.99 3.30 0.11Healthy nose 2 1.17 1.24 0.05 4.17 4.43 0.17Healthy nose 3 0.66 1.05 0.11 2.35 3.72 0.37Healthy nose 4 1.01 0.80 0.28 3.61 2.88 0.98Atrophic preop 1.17 0.78 0.86 4.12 2.80 3.02Atrophic postop 2.18 0.26 0.72 7.92 0.99 2.58

Atrophic preop and atrophic postop refer, respectively, to the pre- and postoperative geometries of the atrophic nose.




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These results are consistent with the hypothesis that abnor-mal patterns of mucus evaporation may play a key role in thepathophysiology of AR. The wide nasal cavity of the ARpatient (demonstrated by below-normal surface area-to-volumeratio) generated an abnormal flow pattern. This abnormaldistribution of airflow, in turn, led to an increase in the water

fluxes in regions that normally would not be subject to highlevels of mucus evaporation, namely the upper half of the nasalcavity (Fig. 6B). The drying effect of the airflow would beexpected to increase the viscosity of the mucus, fostering theformation of crusts. These crusts may in turn impair thedelicate ciliary apparatus, causing stasis of the secretion, per-haps leading to more crust formation. The lack of nasalclearance facilitates infection by opportunistic pathogens; andthe fetor that characterizes the disease may come from thesehighly infected crusts. This reasoning was also proposed byWachsberger (49).

Mygind et al. (39) explain how the normal nasal epitheliumgradually changes from squamous epithelium to pseudostrati-fied columnar epithelium with abundant ciliated cells moving

from the vestibule toward the turbinates. The ciliated cells donot appear suddenly, but rather their density increases gradu-ally going deeper into the nose. The prediction of high waterflux in the anterior portion of the healthy nose (Figs. 4 and 5)suggests that ciliated cells are more predominant in regions oflow water flux. Since in the atrophic nose large water fluxeswere not restricted to the anterior portion of the cavity, wepropose that the abnormal patterns of water fluxes in the

atrophic nose may lead to replacement of ciliated cells by someother type in the respiratory epithelium. The characteristicfinding of patches of squamous epithelium in the respiratorymucosa of AR patients is in agreement with this reasoning (1,5, 11, 19). It is recognized that exposure to irritants in generalcan cause squamous metaplasia. Thus squamous metaplasiamay occur in AR patients because of the drying effects of

airflow, rather than being the root cause for the lack of mucouslayer. Once the epithelium has been replaced, the patches ofsquamous epithelium may be expected to contribute to theshortage of mucus, stasis, and progress of the disease. Morestudies are needed, however, to establish a causal associationbetween regions of high mucus evaporation and squamousmetaplasia.

AR is not permanently cured by antibiotics (38). One way tocontrol the disease is to irrigate the nose artificially, but thesymptoms return whenever the irrigation is ceased. Our hy-pothesis may explain this relentless nature of the diseasebecause the disease would not be expected to recede whileexcessive evaporation of the mucus continued. The hypothesisalso suggests that closure of the nostrils (Youngs procedure)stops the disease because suturing the nostrils releases the nosefrom its humidification task.

The anosmia in AR patients has been proven to be a sensoryproblem, since electron microscopic studies have shown thatthese patients have atrophy of the olfactory epithelium recep-tors (38). Our simulations suggest that loss of these receptorsmay be due to the high water flux predicted at the olfactoryregion (Figs. 4 and 6B). In a healthy nose, air flows mainlyalong the floor and between the septum and the middle meatus(16, 48, 52). Only 1015% of the air passes through theolfactory slit. In contrast, in the atrophic nose, most of the airflowed along the upper half of the nose (Fig. 2). Comparedwith the healthy nose, this abnormal airflow distribution sub-

jects the olfactory epithelium to increased water and heat fluxesthat may damage the olfactory cells by drying the epithelium.

The sensation of nasal congestion in AR has been proposedto be due to the loss of receptors for pain and temperature (38).However, this hypothesis is still unproven (38). The calculatednasal resistance for the before-surgery atrophic nose, 0.028Pa/(ml/s), is below the range of resistances we computed forthe four normal cavities, namely 0.0390.082 Pa/(ml/s). This

Table 4. Flow partitioning between left and right nasalpassages in the 6 human nasal geometries studied

Subject

Flow Partitioning

Left Cavity Right Cavity

Healthy nose 1 54.7% 45.3%Healthy nose 2 48.1% 51.9%

Healthy nose 3 37.5% 62.5%Healthy nose 4 57.6% 42.4%Atrophic preop 63.8% 36.2%Atrophic postop 90.8% 9.2%

Atrophic preop and atrophic postop refer, respectively, to the pre- andpostoperative geometries of the atrophic nose.

Fig. 7. Pressure averaged over coronal cross sections versusdistance from nostrils in the atrophic and normal noses studied.See Fig. 1 legend for more information on symbols.




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finding substantiates the nomenclature paradoxical for thecomplaints of nasal congestion associated with AR and is inagreement with rhinomanometry data collected by Moore andKern (38) in 135 AR patients. The mean total nasal resistancein their patients was 0.12 Pa/(ml/s), while literature reports forhealthy subjects are on the order of 0.150.30 Pa/(ml/s) (38).The resistance figures calculated by CFD are somewhat lower

than the ones obtained through rhinomanometry, as also foundin other CFD studies (50). However, it should be borne in mindthat by convention, rhinomanometry calculates nasal resistanceat a transnasal pressure drop of 150 Pa (6). The simulationspresented in this study were based on resting airflow rates,where the transnasal pressure drop is considerably lower. Thenonlinear shape of the pressure-flow curve for nasal airflowmeans that the resistance figures calculated in this work are notdirectly comparable to rhinomanometry. Nevertheless, bothmethods are consistent in predicting reduced nasal resistancesfor AR patients.

The high efficiency of a healthy nasal cavity for warmingand humidifying the inspired air is well recognized (8, 28, 29,36, 40). The simulations presented in this study predicted thatat rest inspired air was already within 1.5C of the mucosatemperature (Tmucosa 32.6C) at the middle of the normalturbinate region (Fig. 3A). Due to the abnormal patency of theatrophic nose, however, air was still 4.65.6C colder thanTmucosa (27C Tair 28C) when it reached the samelocation before surgery. While in the normal noses air exitedthe nasopharynx at Tair Tmucosa and with 36 g water/m

3 ofair, in the before-surgery atrophic nose air was still 3Cbelow Tmucosa and the water content was still 30 g/m

3 of air(Table 2). These predictions are consistent with experimentalmeasurements by Drettner et al. (10), who measured theair-conditioning capacity of normal and pathological noses andfound that atrophic noses do not condition the air as effectively

as normal ones. Also in agreement with our simulations,Lindemann et al. (35) found a decreased capacity to warminspired air in cavities widened through aggressive sinus sur-gery with resection of the turbinates. Interestingly, dryness andcrusting are also frequent complaints of these patients (35).

Our simulations predicted that the cavity-narrowing proce-dure improved the air-conditioning properties of the atrophicnose. At the nasopharynx level, air was 1.2C warmer and2.5% more humid postoperatively (Table 2). The surgery,however, failed to restore the normal airflow and water fluxpatterns (Figs. 2 and 4). Our analysis of the water transport 6wk after surgery suggests that mucus evaporation increasedpostoperatively in the left cavity (Figs. 5 and 6; Table 3). Thisincrease was partially due to the great imbalance in airflow

partitioning between the two cavities after surgery (Table 4).Six months after surgery, crusts were observed mostly in theleft side, in agreement with the higher airflow and higher waterflux calculated for this side of the nose. At that time it wasobserved that resorption of the implant widened an anteriorconstriction that had occurred on the right cavity due to theimplant, partially reducing the imbalance in airflow distribu-tion between the two cavities. However, it is unlikely that thisredistribution has been sufficient to bring the water flux levelsback to their normal values. Therefore, our analysis suggeststhat the surgery was not a final cure for this patient becausewater flux through the mucosa remained abnormally high andabnormally distributed. At the present time, the patient reports

being satisfied with the surgical outcome because his maincomplaint (the fetor) has resolved, although crusts are stillpresent.

At first sight, there seems to be a contradiction between thehigher magnitude of heat and water fluxes in the atrophic noseand incomplete air conditioning compared with the normalsubjects (Table 2, Fig. 5). This apparent discrepancy is ex-

plained by the reduced surface area available for heat and waterexchange in the atrophic nose. This effectively means that,despite the increased levels of heat and water fluxes (per unitarea), the overall rate of heat and moisture transfer from tissueto air in the atrophic geometries is lower than normal, leadingto incomplete conditioning of inspired air. This finding sug-gests that reconstructive nasal surgeries in AR should target toaugment the nasal surface area to avoid excessive mucusevaporation and drying.

Finally, we would like to discuss some limitations of thisseminal investigation. First, simulations were conducted onlyfor the inhalation part of the respiratory cycle. It is known thatapproximately 1/3 of the heat and humidity transferred frommucosa to inspired air is recovered during exhalation (52).Therefore, humidity recovery during expiration needs to beincluded in future studies to confirm that the patterns ofincreased mucus evaporation in AR noses observed here arenot affected. Second, the cyclic changes of flow direction andmucosal temperature during respiration were approximated byan average, steady-state process. Theoretical arguments sup-port this approach with regard to the airflow patterns (31), butthe dependence of mucosal temperature on airflow patterns isstill unclear. Recent advances in computation capacity are justbeginning to allow the study of time-dependent nasal airflow(26, 37), so that this hypothesis may be tested soon.

Third, we assumed that nasal airflow is laminar in AR andnormal noses. There is evidence that the airflow is indeed

laminar for resting flow rates in healthy noses (7, 21, 30, 31,48), but it is possible that the flow is more turbulent in the widecavities of AR patients. To clarify this issue, the airflowpatterns in a physical replica of the AR nose remain to beinvestigated experimentally. The general conclusions drawn inthis paper, however, would not change if airflow were found tobe turbulent in the atrophic nose, since turbulence wouldincrease the drying effect of the airflow, reinforcing the hy-pothesis that excessive evaporation of the mucous layer playsa key role in the pathophysiology of AR.

In conclusion, the airflow and water vapor transport simu-lations presented in this article support the hypothesis that ARis related to excessive evaporation of the mucous lining. Wesuggest that three main factors contribute to increased water

flux in the mucosa of these patients. First, we found that thelack of turbinates led to an abnormal airflow distribution. Airflowed mainly along the top half of the nose, substantiallyincreasing the humidification burden on this region. Second,we found that the atrophy process reduced the surface areaavailable for water transfer, increasing flux per unit area. Third,we found that a unilateral obstruction concentrates air humid-ification in the most patent side and thus contributes to in-creased water flux in this side. Therefore, our results suggestthat the main goals of a surgery to treat AR should be 1) torestore the original surface area of the nose, 2) to restore thephysiological airflow distribution, and 3) to create symmetriccavities. These three strategies would have the overall effect of




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minimizing the water fluxes per unit area and reestablishing thephysiological pattern of restricting high water fluxes to theanterior-inferior portion of the nose. A procedure that seems tofit these criteria is the reconstruction of the inferior and middleturbinates (41).

APPENDIX

Description of the Computational Method

The conservation of mass and momentum for laminar, in-compressible flow are described, respectively, by the equations

u 0

u

t (u )u p 2u

where u u(x,y,z,t) is the velocity vector, t is time, is fluiddensity, and is dynamic viscosity (13, 51). In our simula-tions, we adopted 1.20 kg/m3 and 1.9 105 kg/ms(24, 40).

Heat transfer is governed by the equation of energy conser-vation

T

t (u )T

k

cp

2T

where T T(x,y,z,t) is temperature, cp 1,005.9 J/(kg K) isthe specific heat, and k 0.0268 W/(mK) is the thermalconductivity of air (40). The transport of moisture from themucosa to air is governed by the convection-diffusion equation

tcH2O (u )cH2O DH2O

2cH2O

where cH2O cH2O (x,y,z,t) is the water vapor concentration

in air and DH2O 2.6 105

m2

/s is the mass diffusivityof water vapor in air (24, 40).

Steady-state versions of these equations were solved on adual-processor workstation (Dell Precision, Intel Xeon 3.60GHz, 3.93 GB of RAM) using Fluent 6.2.16 (Fluent, Lebanon,NH). Fluent uses the finite volume method to solve the differ-ential equations numerically. The segregated solver withSIMPLEC pressure-velocity coupling and second-order, up-wind discretization were utilized for solution of the aboveequations (14). Since the physical properties of the air-watervapor mixture were assumed constant, an uncoupled solutionstrategy was employed; namely, the flow field was obtainedfirst and then the energy conservation and convection-diffusionequations were solved.

For the healthy-nose meshes (106 tetrahedral cells), Fluenttook2 h to solve the flow field (450 iterations) and 7 minto solve the heat/water transport equations (25 iterations).The atrophic-nose meshes required typically twice as manyiterations/CPU time to converge, despite having approximatelythe same number of cells. Convergence was confirmed bysmall residuals (continuity: 103; velocities: 5 105;energy equation: 3 107; convection diffusion equation:7 106) and by monitoring the flow rate, temperature, andRH at the outlet surface for stabilization.

RH is the ratio of the partial pressure of water vapor actuallypresent in the mixture (pH2O) to the water vapor pressure ofsaturated air at the same temperature (pH2O,s). The latter is

calculated in Fluent from experimental data, while the formeris obtained in Fluent from the water concentration in air(cH2O) using the ideal-gas law pH2O RTcH2O/MMH2O, whereR 8.31 Pa m3/(mol K) is the universal gas constant andMMH2O 0.018 kg/mol is the molecular mass of water. Ourboundary condition of 100% RH at the walls (at 32.6C) wasdefined as cH2O Wall 0.03694 kg/m

3. For the inlet, 50% RH (at

20C) corresponds to cH2O Inlet 0.00869 kg/m3

. The out-flow boundary condition in Fluent imposes ( Tn) 0 and( cH2O n) 0 at the outlet, where n is a unit vector normal tothe surface. Any backflow at the outlet was assumed to be at32.6C and 100% RH.

Fluent 6.2 does not provide the option of plotting species flux[fluxH2O DH2O (n cH2O)Wall] through the domain walls.Therefore, a user-defined function was written in Fluent tomake the water flux data available as a user-defined memoryvariable. To take into account that water evaporation increasesthe heat lost by the nasal mucosa, heat flux (fluxheat) wascomputed from

fluxheat k T fluxH2OH

where H 2.411 106

J/kg is the latent heat of evaporationof water at nasal-tissue temperature (40).

ACKNOWLEDGMENTS

We thank Jeffry Schroeter, Kambiz Nazridoust, Mel Andersen, DarinKalisak, Rebecca Segal, David Wexler, Maurlio N. Vieira, and RonaldDickman for contributions to this research. We are also grateful to Dr. UedsonTazinaffo and to the Hospital Madre Teresa (Belo Horizonte, Brazil) for kindlyproviding the CT scans used in this study.

GRANTS

This work was made possible by a postdoctoral grant from CNPq, Brazil,and the financial support of the American Chemistry Council to The HamnerInstitutes for Health Sciences (previously CIIT Centers for Health Research).

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