## Abstract

Model simulations of nitric oxide (NO) transport considering molecular diffusion showed that the total bronchial NO production needed to reproduce a given exhaled value is deeply influenced by its axial distribution. Experimental data obtained by fibroscopy were available about proximal airway contribution (Silkoff PE, McClean PA, Caramori M, Slutsky AS. Zamel N. *Respir Physiol* 113: 33–38, 1998), and recent experiments using heliox instead of air gave insight on the peripheral airway production (Shin HW, Condorelli P, Rose-Gottron CM, Cooper DM, George SC. *J Appl Physiol* 97: 874–882, 2004; Kerckx Y, Michils A, Van Muylem A. *J Appl Physiol* 104: 918–924, 2008). This theoretical work aimed at obtaining a realistic distribution of NO production in healthy adults by meeting both proximal and peripheral experimental constraints. To achieve this, a model considering axial diffusion with geometrical boundaries derived from Weibel's morphometrical data was divided into serial compartments, each characterized by its axial boundaries and its part of bronchial NO production. A four-compartment model was able to meet both criteria. Two compartments were found to share all the NO production: one proximal (*generations 0* and *1*; 15–25% of the NO production) and one inside the acinus (proximal limit, *generations 14–16*; distal limit, *generations 16* and *17*; 75–85% of the NO production). Remarkably, this finding implies a quasi nil production in the main part of the conducting airways and in the acinar airways distal to *generation 17*. Given the chosen experimental outcomes and reliant on their accuracy, this very inhomogeneous distribution is likely the more realistic one that may be achieved with a “one-trumpet”-shaped model. Refinement should come from a more realistic description of the acinus structure.

- exhaled nitric oxide
- nitric oxide bronchial production
- modeling

although perfectly mixed compartment models have constituted a major advance in the understanding of exhaled nitric oxide (NO) features (10, 16, 25), models incorporating axial diffusion and convection in realistic boundaries (20, 26) have shown the limitations of compartment models and their fallacy in the estimation of NO bronchial production. Indeed, an axial diffusion flux from airways toward alveoli at the onset of the acinus impacts the magnitude of exhaled NO concentration by retrieving NO molecules from the expired flow (20, 26). Moreover, as a consequence of this “back diffusion,” the way NO production is axially distributed on the airways affects the total NO production needed to reach a given exhaled concentration (26). A recent study (23) addressing the issues of ventilation distribution and NO production distribution confirmed that the latter is the most important factor affecting exhaled concentration.

Several experiments have addressed the issue of very proximal airway production by direct fibroscopic measurements in healthy adults (3, 6, 7, 12, 21). Among them, the study of Silkoff et al. (21) provides the most interpretable and useful information.

On the other hand, although an axial diffusion phenomenon seems like it would confuse the issue of exhaled NO interpretation, it is essentially an opportunity to experimentally approach very peripheral NO behavior. Experiments using heliox instead of air, hence amplifying the back diffusion, led to very consistent results in healthy adults (11, 19).

The two preceding experimental facts constitute constraints for simulated outcomes. This work aimed at using these constraints to quantitatively assess a realistic NO production distribution along the bronchial tree in healthy adults. To achieve this, a model considering axial diffusion with geometrical boundaries derived from Weibel's morphometrical data was divided into serial compartments, each characterized by its axial boundaries and a given percentage of the total bronchial NO production.

## MATERIAL AND METHODS

### Experimental Criteria

#### Proximal criterion.

In normal subjects, Silkoff et al. (21) found that during a 50 ml/s expiration, the NO concentration measured at 45 cm from the lips was, on average, 56% of the value measured at the glottis. We defined (1) where Fe_{NO} and Fno_{tip} are NO concentrations measured at the glottis and at the tip of the catheter, respectively. The experimental value for this criterion is 0.56 with a standard deviation equal to 10.8. (21).

#### Heliox criterion.

At 50 ml/s of expiratory flow, Fe_{NO} was shown to systematically decrease when heliox (21% oxygen, 79% helium) was substituted for air in normal subject lungs (11, 19). We defined (2) where Fe_{NO} and Fe_{NO,He} are the exhaled NO concentrations measured in air and heliox, respectively. In healthy adults, Shin et al. (19) and Kerckx et al. (11) reported Fno_{He} values equal to 0.67 (±0.15) and 0.63 (±0.09), respectively. These values are not significantly different (unpaired Student's *t*-test, *P* = 0.54). Therefore, by combining these results, the Fno_{He} target value is equal to 0.65 with a standard deviation equal to 0.12.

### Model Simulation Study

#### Model principles.

We used *Eq. 3*, incorporating convective and diffusive NO transport and NO source terms (26) in geometrical boundaries based on Weibel's symmetrical model (28): (3) where *t* is time, *z* is the distance from the alveolar end, F(*z*,*t*) is the NO concentration, and D is the molecular diffusion coefficient. *S*(*z*,*t*), *s*(*z*,*t*), V(*t*), and *Q̇*(*z*,*t*) are total cross-sectional area (airways + alveoli), airway total cross-sectional area, volume, and axial flow, respectively. D was taken to equal 0.22 and 0.6 cm^{2}/s to simulate experiments in air and in heliox, respectively. This model has been accepted as a good tool to provide a realistic description of gas concentration profiles in the lung periphery when anatomical asymmetry is neglected (14).

The last term of *Eq. 3* is the NO source term: the difference between NO production (V̇no; in pl/s) and NO diffusion into blood (Dno; in pl·s^{−1}·ppb^{−1}) per unit volume. We considered and where V̇aw_{NO}(*z*) and V̇a_{NO}(*z*) are airway and alveolar NO production, respectively, and Daw_{NO}(*z*) and Da_{NO}(*z*) are airway and alveolar NO transfer factor, respectively.

Details about numerical computation of *Eq. 3* solutions are described elsewhere (26). The boundary conditions are F = 0 at the model entry (no NO inspired) and dF/d*z* = 0 at the model end (14).

#### Simulation conditions.

In the present study, the values of the overall alveolar source term (V̇a_{NO}) and the alveolar (Da_{NO}) and airway (Daw_{NO}) transfer terms were equal to 3,167 pl/s, 1,558 pl·s^{−1}·ppb^{−1}, and 5.07 pl·s^{−1}·ppb^{−1}, respectively (16). The V̇aw_{NO} value was adjusted to obtain Fe_{NO} = 10, 15.5, 20, and 50 ppb. The latter values cover the range of recently published reference values for normal subjects (24).

Before any simulated maneuver, a steady concentration profile inside the model [F(*z*,*0*)] was established by simulating 25 breath cycles (1-s inspiration and 1-s expiration at 500 ml/s). The simulated maneuver always consisted of a 2-s inspiration at 500 ml/s from a preinspiratory volume of 3,700 ml, followed by a 20-s expiration at 50 ml/s.

#### Simulation outcomes.

The outcomes of the simulations were *1*) the expired NO concentration (Fe_{NO}); i.e., the concentration at the model entry that anatomically corresponds to the glottis; *2*) the NO concentration at the tip of a 45-cm catheter (Fno_{tip}); because of the uncertainty about this exact location, we considered the NO concentrations at the onset of either *generation 2* or *3* (Fno_{2gen} or Fno_{3gen}, respectively) and computed the simulated values of Fno_{prox} using *Eq. 1* with either Fno_{tip} = Fno_{2gen} or Fno_{tip} = Fno_{3gen}; and *3*) the expired NO concentration with D = 0.6 cm^{2}/s (Fe_{NO,He}); the simulated values of Fno_{He} were computed using *Eq. 2*.

All concentrations were measured at the end of the 20-s expiration.

In addition, we defined a function R as (4) assessing the closeness of simulated values to average experimental target values.

#### Axial distribution of bronchial NO production.

We considered three modes of axial distribution of bronchial NO production: a proportional distribution model, where NO production is considered distributed proportionally to the epithelial surface (26) or the airway volume (20), and weighted distribution models, where the “trumpet”-shaped model was divided in serial compartments, each characterized by its distal generation and by a given percentage of V̇aw_{NO}. Figure 1 schematically shows the features of this model. A two- and a four-compartment model were considered. It has to be stressed that the term “compartment” in this context does not refer to a perfectly mixed unit; *Eq. 3* governs NO transport along the entire model.

##### TWO-COMPARTMENT MODEL.

The more proximal compartment (Comp1) begins at the onset of *generation 0* (model entry) and ends at the end of *generation n*. Comp2 constitutes the remaining part of the bronchial airways (Fig. 1). Comp1 and Comp2 produce α and (1 − α)% (0 < α ≤ 100) of the total bronchial NO (V̇aw_{NO}), respectively. Inside each compartment, the production is proportional to the epithelial surface or to the airway volume.

Simulation outcomes were obtained by considering the combinations of 6 values of Comp1 distal limit (*generations 0*, *1*, *2*, *3*, *4*, and *5*) and 20 values of α (from 0.05 to 1 with 0.05 step). For each set of parameters (*n*,α), the function R was computed (*Eq. 4*). The optimal parameter set corresponds to the minimal R value.

##### FOUR-COMPARTMENT MODEL.

The model was divided into four serial compartments: Comp1 (the more proximal starting at *generation 0*), Comp2, Comp3, and Comp4 (the more distal ending at *generation 23*) (Fig. 1). Each compartment is characterized by its distal generations (*n1*, *n2*, *n3*, and *23*, respectively) and by the percentage of the total NO it produces (α*n*, *n* = 1, 2, 3, and 4, respectively; α*1* + α*2* + α*3* + α*4* = 100). Inside each compartment, the production is proportional to the epithelial surface, or to the airway volume.

Simulation outcomes were obtained by considering combinations of 19 values of α*1* (from 5 to 95% with a step of 5%), 5 values of α*2* and α*4* (10, 1, 10^{−1}, 10^{−3}, and 10^{−5}%), 7 values of *n1* (*generations 0*, *1*, *2*, *3*, *4*, *5*, and *6*), 8 values of *n2* (*generations 9*, *10*, *11*, *12*, *13*, *14*, and *15*), and 4 values of *n3* (*generations 15*, *16*, *17*, and *23*). It is to be noted that the case *n3* = 23 corresponds to three compartments in series.

For each set of parameters (*n1*, *n2*, *n3*, α*1*, α*2*, α*4*) (α*3* being computed as 100 − α*1* − α*2* − α*4*), the function R was computed (*Eq. 4*). We considered the parameter sets corresponding to the minimal R value and/or leading to Fno_{prox} and Fno_{He} simultaneously falling into their experimental intervals [mean − SD, mean + SD].

In both compartmental models and for each set of parameters, the R function value was computed with either Fno_{prox} = Fno_{2gen}/Fe_{NO} or Fno_{prox} = Fno_{3gen}/Fe_{NO}. In all models, Daw_{NO} is spread the same way (surface or volume proportionality) as NO production. Alveolar production (V̇a_{NO}) and transfer factor (Da_{NO}) were considered proportional to alveolar surface.

#### Comparison with breath-hold experiments.

The amount of NO exhaled during the initial peak after breath hold was simulated with the proportional model and with the four-compartment model. For the latter model, the set of parameters minimizing the R function was considered. In both models, a Fe_{NO} value of 15.5 ppb was adjusted. The simulation conditions were a 2-s inspiration at 500 ml/s from a preinspiratory volume of 3,700 ml, a breath hold, and a 1.5-s expiration at 300 ml/s. Breath-hold times were 5, 10, 20, and 30 s. The NO amount under the peak was computed according to the study by Shin et al. (18).

## RESULTS

Table 1 shows, for each distribution mode of NO bronchial production, the set of parameter values that minimize the function R. The total airway production required to achieve a Fe_{NO} value equal to 15.5 ppb also is given. The optimal set of parameters for the two- and four-compartment models are similar, considering NO production proportional to either epithelial surface or airway volume inside each compartment. The associated values of the R function also are very close. Consequently, from now on, results will refer to NO production proportional to epithelial surface.

It is noteworthy that considering either Fno_{2gen} or Fno_{3gen} as the catheter tip concentration only changed the minimal value of the R function by 0.7 and <0.01% in the two-and 4-compartment models, respectively. Consequently, from now on, only F̅n̅o̅_{p̅r̅o̅x̅} = Fno_{2gen}/Fe_{NO} will be considered. From the proportional model to the four-compartment model, a 93% decrease of the minimal R value was observed.

Figure 2 presents the NO axial production as a percentage of the total production in each generation for the proportional model (*A*), the two-compartment model (*B*), and the four-compartment model (*C*). For the same respective distributions, Fig. 3, *A–C*, presents NO concentration profiles as a function of the axial distance and the generation number. Concentrations are indicated at the onset of *generations 2* (Fno_{2gen}), *3* (Fno_{3gen}), and *0* (Fe_{NO}).

To visually assess the accuracy of the considered NO production distribution, we have presented the main results in a F̅n̅o̅_{H̅e̅}-F̅n̅o̅_{p̅r̅o̅x̅} plot (Fig. 4). The open diamonds correspond to the mean experimental values, and the open rectangles indicate the experimental area (mean ± SD).

### Two-Compartment Model

In Fig. 4*A*, each line corresponds to one Comp1 distal generation value (*n* = 0, 2, 4, and 5), and each point on a given line corresponds to a Comp1 production weighting (from *right* to *left*, α = 5 to 95%). The open circle indicates the (*n*,α) combination leading to the minimal R function. The open square corresponds to the proportional model. It appears that, although closer to the experimental area than the proportional case, this model is unable to simultaneously fulfill the two criteria for any (*n*,α) combination.

Figure 5, *A* and *B*, allows assessment of the R function sensitivity to each individual parameter (α or *n*) of the two-compartment model. The nonvarying parameter value was taken from Table 1.

### Four-Compartment Model

In Fig. 4*B*, each line corresponds to one Comp3 distal generation value (*n3* = 16, 17, and 23), and each point on a given line corresponds to a Comp1 production weighting (from *right* to *left*, *α1* = 5 to 95%). The other parameters were taken as *n1* = 1, *n2* = 15, and α*2* = α*4* = 0.001%. It is noteworthy that only the four-compartment model provides outcomes compatible with experiments. A three-compartment model (*n3* = 23) is always outside the experimental area.

Figure 5, *A–D*, allows assessment of the R function sensitivity to each individual parameter (α*1*, *n1*, *n2*, or *n3*) of the four-compartment model. The nonvarying parameter value was taken from Table 1. The R function was found to be minimal for any values of α*2* and α*4* less than 1% (not represented). Given this, α*3* may be considered as the complement to 100 of α*1*.

Table 1 parameter values correspond to the minimal R function. However, other combinations led to Fno_{prox} and Fno_{He} inside the experimental area. These combinations are described in Table 2. The distal limit of Comp1 has to be more proximal than *generation 2*; the proximal limit of Comp3 lies in the interval of *generations 13–15* and its distal limit in the interval of *generations 16* and *17*. The NO production weighting is between 15 and 25% for Comp1 and, hence, between 75 and 85% on Comp3, given that the weightings of Comp2 and Comp4 are negligible.

### Influence of Fe_{NO} Value

To achieve a Fe_{NO} value of 10, 15.5, 20, and 50 ppb with the four-compartment model, the overall airway production was adjusted to 815, 1,420, 1,890, and 5,051 pl/s, respectively. The optimal set of parameters was found to be Fe_{NO} independent, but the optimal R function decreased when Fe_{NO} increased (R = 0.021, 0.013, 0.010, and 0.005, respectively). This comes from a better achievement of the “heliox criterion” when Fe_{NO} increases (F̅n̅o̅_{H̅e̅} = 0.78, 0.73, 0.72, and 0.71, respectively, for a target value of 0.65).

## DISCUSSION

The main finding of this study is that, in normal subjects, the best simultaneous achievement of proximal and distal constraints requires a very heterogeneous axial distribution of bronchial NO production. All the production is concentrated on the very first generations and on a narrow zone of the peripheral airways of the bronchial tree (Fig. 2*C*). This result is compatible with the study by Condorelli et al. (2), which also deduced some bimodal distribution of production, with overweighted trachea and oropharynx compartments. In the present study, a noteworthy finding is a gap of NO production between *generations 2* and *14*.

Although a lot of experimental data are available in the field of exhaled NO in normal subjects, we purposely considered experimental constraints giving insights on very different parts of the bronchial tree to challenge our simulations. Several groups have addressed the issue of the proximal airway contribution to exhaled NO, either directly, by fibroscopic measurement of exhaled NO distal to the very first generations (3, 6, 7, 12, 21), or indirectly, by measurement of NO samples at the mouth after breath hold (4). Data from Dillon et al. (3) and Dweik et al. (6) are difficult to interpret, because these studies were performed in tidal breathing. Silkoff et al. (21) performed NO samplings during expiration at 50 ml/s at the mouth, at the glottis, and at the level of the second generation (or the onset of the third), .i.e., at the tip of a 45-cm-long catheter. The authors demonstrated that the concentration at this location was, on average, 56% of the concentration at the glottis (which corresponds to our model entry), evidencing a great NO production in the very first generations. On the contrary, in the study by Gabbay et al. (7), only a small difference was found between the mouth and the bronchi when NO was sampled at 250 ml/s. However, preliminary simulations showed that even with an overweighted NO production in the first generations, this relatively high expired flow smoothes out any concentration difference (data not shown). Dubois et al. (4) proposed an elegant method to estimate equilibrium NO values from the trachea down to respiratory bronchioles. Unfortunately, experimental expired flows were not described. Despite the stimulating input of this study, this precludes a reliable use of these data. Overall, the data from Silkoff et al. (21) were chosen as the first experimental constraint (“proximal criterion”), because it is directly measured and constitutes a direct insight into the NO production in the first generations.

The second experimental constraint, although resulting from a direct measurement, needs to be presented in the light of theoretical considerations. A bronchoalveolar NO concentration gradient in the acinar zone produces a back-diffusion NO flux toward alveoli. As a result, fewer NO molecules are available in the expiration flux, and the exhaled NO concentration is lowered.

Experimental evidence of this phenomenon was obtained by replacing air with heliox in normal subjects (11, 19) and asthmatic lungs (11). Because helium is more diffusive than air, one expects the back-diffusion NO flux to be amplified and, hence, the expired concentration to be decreased, compared with air experiments. Indeed, a 35% decrease was consistently found in normal subjects (11, 19). This experimental result (“heliox criterion”) constitutes an insight into the NO production in the preacinar and acinar generations. The importance of back diffusion also explains why the experiments of Dubois et al. (4) were not considered as a constraint. Indeed, any peripheral rise of concentration during breath hold will be “swallowed” by the alveolar compartment (26). Consequently, the simulations of this experiment show little sensitivity to the magnitude of any peripheral NO production.

### Proportional Model

When NO production is spread proportionally to the epithelial surface, the heliox criterion is well met (Fig. 4*A*). This type of distribution implies that a great part of the total NO production comes from the acinar bronchioles, since they constitute the main part of the epithelial surface. Nevertheless, it also implies a very low production in the three first generations (∼1% of total production). Therefore, the proximal criterion is far from being fulfilled.

### Two-Compartment Model

A logical step forward was to consider two serial compartments with adjusted NO production weightings. Table 1 shows a spectacular improvement of the overall accuracy of the model (R function), with the first generation yielding 15% of the total NO. However, with this optimal parameter adjustment, the proximal criterion is achieved but the heliox criterion is out of reach for any combination of Comp1 extent and production (Fig. 4*A*). Indeed, weighting the proximal airways lowers the peripheral gradient between bronchial and alveolar areas, which is responsible for the loss of exhaled NO in heliox (Fig. 3*B*). Despite the concentration difference created between the very first airways and the more distal ones, the diffusion flux is by far too low to be emphasized by heliox use because of the small airway cross section in this zone.

### Four-Compartment Model

The optimal way to maintain a peripheral gradient without lowering the proximal airway weighting was to consider two zones sharing all the NO production: one at the entry of the bronchial tree (Comp1), producing 15–25% of the total NO, and one covering the onset of the acinus (Comp3, from *generations 13–15* to *generations 16* and *17*; Table 2 and Fig. 2*C*), producing the remaining part of NO. Therefore, the NO production is quasi nil in the airways distal to *generation 17* (Comp4) or lying between *generations 2* and *13* (Comp2). This configuration allows a preserved production on Comp1, a maximized production on Comp3, and a sharp peripheral gradient (Figs. 2*C* and 3*C*). As a consequence, the heliox and the Silkoff criteria may be simultaneously satisfied (Fig. 4*B*). Noteworthy, the end-expiratory NO concentration reaches a plateau between *generations 2* and *13* (Fig. 3, *B* and *C*). This explains why the exact location of the catheter tip (2nd or 3rd generation) does not affect our optimal sets of parameters.

Figure 5, *A* and *B*, presents the sensitivity of the R function (assessing the accuracy of the 2 criteria fulfillment) to the extent (*B*) and the production weighting (*A*) of the proximal compartment (Comp1). Remarkably, the shapes of these sensitivity curves are similar for the two-compartment and the four-compartment models. The parallel shift toward lower R values for the four-compartment model only results from the gathering on a very narrow zone of the remaining NO production (Comp3), whereas it is spread on the entire remaining part of the bronchial tree in the two-compartment model. The gap of NO production in most of the conducting airways and in the acinar airways distal to *generation 17* is thus mandatory to approach the heliox criterion. It should be noted that Comp3, even spread on few generations, represents 35% of the total epithelial surface.

Compartment models yield the same optimal set of parameters and similar corresponding R function values with the four-compartment model, considering NO production proportional either to epithelium surface (26) or to airway volume (20). This means that to meet both criteria, the weights of each compartment have to be such that the way the production is spread inside the compartments becomes of secondary importance.

The last column of Table 1 illustrates how the way that NO production is distributed along the bronchial tree affects the total airway production needed to achieve an exhaled value of 15.5 ppb. It confirms the influence on exhaled NO of the production distribution (26). Suresh et al. (23) recently emphasized that to achieve a given exhaled concentration, overall NO production has to be increased when production is locally increased in a peripheral compartment and decreased when the production is locally increased in a proximal compartment. This is consistent with our findings that production has to be higher when the periphery yields the major part of NO, as in the proportional model.

### Influence of Fe_{NO} Value and NO Parameters

Of note, the optimal set of parameters in the four-compartment model is not affected by the achieved Fe_{NO} values. However, the minimal value of the R function is decreasing with increasing Fe_{NO} (thus increasing V̇aw_{NO}) due to a better achievement of the heliox criterion. This is due to an increasing back-diffusion gradient when overall airway production increases. When for a given Fe_{NO} this gradient decreases due to alveolar concentration increase, either because Da_{NO} decreases or V̇a_{NO} increases, the R function value increases (data not shown). However, this effect is small, since even doubling alveolar concentration has little affect on the gradient. As already shown in Ref. 26, Daw_{NO} has little impact on any model outcome.

### Comparison With Breath-Hold Experiments

Simulations of experimental NO amounts under exhaled peak after breath hold obviously show that the four-compartment model reproduces experimental data (18) much better than the proportional model. Amounts of NO were chosen instead of peak values because the former is much less sensitive to experimental device (and bronchial tree) transfer function. These results confirm that a great proportion of NO production must be concentrated in proximal airways and that peripheral production has little influence on the initial NO peak. Indeed, considering the proportional model, in the absence of substantial proximal production and despite an overall greater NO production (Table 1), NO peak is swallowed by the alveolar compartment (26), and exhaled NO amount is far from experimental values.

### Qualitative Evidence of NO Production Areas

A recent study (22) showed that in normal human tracheal epithelial cultured cells, NO gas phase release was one order of magnitude greater at baseline than in small conducting airway epithelial cells (9). On the other hand, Shaul et al. (17) showed that endothelial NO synthase (eNOS) is expressed in cultured cells of the same lineage as Clara cells (NCI-H441 human bronchiolar epithelial cells). In 1999, Boers et al. (1) found, in normal human lungs, a virtual absence of Clara cells in the proximal airway epithelium but an increasing number of them from terminal to respiratory bronchioles. Our predictions are in line with these results: a huge production in a very proximal (22) and a very distal compartment (1, 17) with very low, if any, production in the intermediary airways (1, 9). The most recent study (9) also showed an upregulation of NO release after exposure to cytokines, giving some clue as to the distribution of NO production in diseased states.

### Experimental and Model Limitations

The study by Silkoff et al. (21) was performed on few subjects, and the authors acknowledged an effect of lidocaine on the exhaled NO value, possibly by a direct effect on NOS (13). This may constitute an uncertainty about F̅n̅o̅_{p̅r̅o̅x̅}, which was chosen, in this study, as the most likely.

Although heliox experiments constitute a unique opportunity to gain an insight into the lung periphery, and although only models incorporating both axial diffusion and realistic geometrical boundaries are able to take advantage of this information, Fig. 6 shows that the model outcomes, although compatible with the experimental constraints, remain relatively far from the “ideal” point. From Fig. 4, it appears that the heliox constraint is impossible to meet for the two-compartment model and is not fully met with the four-compartment and even the proportional model. On the basis of existing experimental knowledge and modeling expertise, the axial production distribution represented in Fig. 2*C* is most likely. However, the model needs to be refined by introducing new features. Recent works are tending to suggest that ventilation distribution has little affect on exhaled NO concentration in healthy subjects where regional production is not heterogeneous (23, 27). Nevertheless, this conclusion was based on macroscopic units for which ventilation inhomogeneities were convection driven. It is known that intra-acinar inhomogeneities are created by diffusion-convection interaction in relation with the intrinsic asymmetry of the acinus (8, 15). These inhomogeneities may affect the simulated gas profile in the lung periphery in a way impossible to reproduce by a symmetrical trumpet-shaped model. Hence, further model developments should incorporate realistic acinar asymmetry (5).

In conclusion, to simultaneously approach experimental outcomes focusing on the proximal and the very distal airways of healthy adults, a very inhomogeneous axial distribution of NO production is required. Keeping in mind that this result relies on the accuracy of experimental outcomes; it implies huge peaks of production in the very first generations and inside the acinus and, consequently, a quasi-nil production in most of the conducting airways. This study reaffirms the need for a model of NO transport incorporating axial diffusion but also emphasizes the need for more realistic geometrical boundaries.

## GRANTS

This study was funded by a European Space Agency Microgravity Application Programme (Airway NO in Microgravity). AstraZeneca provided a grant for the exhaled biomarker laboratory.

- Copyright © 2009 the American Physiological Society