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1Biomedical Physics Laboratory, Université Libre de Bruxelles; and 2Chest Department, Erasme University Hospital, Brussels, Belgium
Submitted 27 September 2007 ; accepted in final form 16 January 2008
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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exhaled nitric oxide; alveolar nitric oxide; asthma; modeling
One consequence of the presence of NO backdiffusion is that models assuming two independent compartments lead to an underestimation of actual bronchial NO production (21, 23). Another consequence of NO backdiffusion is that it constitutes an additional NO source for the alveolar compartment and, hence, contributes to an increase of the alveolar NO concentration. Hence, two-compartment models that neglect backdiffusion also overestimate alveolar NO production by attributing measured alveolar NO concentration entirely to in situ production (4, 23).
Recently, Condorelli et al. (4) demonstrated a technique to account for the impact of airway NO production on alveolar concentration and applied this technique in healthy subjects. In the present work, we aimed to establish a relationship between alveolar NO concentration and exhaled NO concentration to estimate which part of alveolar NO concentration is actually due to in situ alveolar NO production in asthma patients perfectly controlled (including no airway obstruction). We also aimed to experimentally demonstrate the link between backdiffusion and alveolar concentration in this population. This was done by first performing simulations with a model incorporating axial diffusion and considering a range of bronchial and alveolar productions relevant to clinical situations. Then the theoretical relationships obtained from the simulations were tested on experimental data obtained from healthy subjects and patients with stable asthma.
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MATERIALS AND METHODS |
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Methods.
A chemoluminescence analyzer (LR 2000, Logan Research, Rochester, UK) was used to measure NO online. The instrument was calibrated daily with two calibration mixtures (103 ppb NO in nitrogen and 20 ppb in helium). Alveolar NO concentration (FANO) and the "maximal airway flux" (JNO) were computed using the method described by Pietropaoli et al. (17), i.e., as, respectively, the y-intercept and the slope of the line fitted on the exhaled NO values as a function of the inverse of the expired flow; and by the method proposed by Tsoukias et al. (22), i.e., as the slope and y-intercept of the line fitted on NO output (exhaled NO values times the expired flow) as a function of the expired flow. The exhaled NO tracings were obtained for flow rates of 50, 175, and 300 ml/s. Exhaled NO at 50 ml/s will be further referred to as the exhaled NO (FENO) according to American Thoracic Society/European Respiratory Society standard (1). Exhaled NO was also measured at 50 ml/s after 2 min equilibration with heliox (FENO,He). The decrease of exhaled NO due to heliox (
FEheliox) was expressed in absolute value (FENO – FENO,He) and as a percentage of the value in air [(FENO – FENO,He)/FENO]. A positive FE value corresponds to a decrease of exhaled NO with heliox compared with air.
Studied populations. We studied 10 healthy nonsmoker subjects (8 men; age 38 ± 14 yr; range 19–56 yr) and 21 nonsmoker patients with asthma diagnosed according to standard criteria (9). Asthma control had been assessed using a French translation of the Asthma Control Questionnaire (ACQ) from Juniper et al. (13). An ACQ score below 0.75 identifies a patient whose asthma is well controlled (12). Table 1 summarizes patient characteristics. Three patients out of 21 declined to perform heliox measurements.
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Model Simulation Study
We used Eq. 1 incorporating convective and diffusive NO transport (6) and NO source terms (23) in geometrical boundaries based on the Weibel's symmetrical model (25)
 | (1) |
(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 cm2/s (14). This model has been accepted as a good tool to provide a realistic description of gas concentration profiles in the lung periphery when anatomic asymmetry is neglected (6).
The last term of Eq. 1 is the NO source term: the difference between NO production (
NO; in pl/s) and NO diffusion into blood (DNO being expressed in pl·s–1·ppb–1) per unit volume. We considered
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awNO(z) and ANO(z) are airway and alveolar NO production, respectively, and DawNO(z) and DANO(z) are airway and alveolar NO transfer factor, respectively.
In the present study, the baseline overall source terms values are 3,083 and 3,167 pl/s for awNO and ANO, respectively, and 5.07 and 1,558 pl·s–1·ppb–1 for DawNO and DANO, respectively. DawNO, DANO, and ANO values were taken from Pietropaoli et al. (17), and awNO value was adjusted by trial and error to mimic the mean experimental FENO in our healthy subjects group. The distribution of the NO sources as a function of z and details about numerical computation of Eq. 1 solutions are described elsewhere (23). The boundary conditions are F = 0 at the model entry (no NO inspired), and dF/dz = 0 at the model end (15).
Simulations considered bronchial and alveolar productions ranging from this baseline value to a fivefold increase. The limit case corresponding to a nil alveolar production was also considered.
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. Before the maneuver, a steady concentration profile inside the model had been established by simulating 25 breath cycles (1-s inspiration and 1-s expiration at 500 ml/s).
The primary outcomes of the simulations were 1) the expired NO concentration (FENO) at the end of the maneuver and 2) the alveolar NO concentration (FANO) present in the model in the last lung generation before the maneuver. It is to be noted the simulated FANO was directly available as model outcome and not computed like experimental FANO. FENO,He was also simulated using a diffusion coefficient of 0.6 instead of 0.22 cm2/s (14). Finally, the hypothetical case D = 0 (no axial diffusion) was also considered.
Statistical methods. Paired and unpaired t-tests and regression analysis were used. The level of significance was taken as P < 0.05.
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RESULTS |
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No difference appeared between FANO values computed by the method of Pietropaoli et al. (17) and by the method of Tsoukias et al. (22) for healthy subjects (3.4 ± 1.3 and 3.1 ± 1.5 ppb, respectively; P = 0.31) and for asthma patients (5.1 ± 2.9 and 4.8 ± 3.1 ppb, respectively; P = 0.74). In the following figures, only FANO computed by the method of Pietropaoli et al. (17) will be displayed.
Similarly, no difference appeared between methods in JNO computation for healthy subjects (669 ± 274 and 745 ± 311 pl/s, respectively; P = 0.15) and for asthma patients (2,067 ± 1,009 and 2,254 ± 1,150 pl/s, respectively; P = 0.69).
A regression analysis on all subjects between JNO [determined by the method of Pietropaoli et al. (17)] and FENO showed a nearly perfect fitting:
 | (2) |
JNO computed by the method of Tsoukias et al. (22) is linked to FENO by a 0.020 factor (r2 = 0.984). The r2 value in Eq. 2 means that JNO and FENO give the same information. Therefore, the latter was only considered.
A simulation with baseline values gives FENO and FANO values equal to 17.1 ppb (vs. 16.7 ± 5.1 ppb in our healthy subjects group) and 3.1 ppb (vs. 3.4 ± 1.3 ppb in our healthy subjects group), respectively.
Figure 1 presents the simulated NO concentration profiles at the end of expiration as a function of the distance from alveolar end for the baseline bronchial production (curve 1) and for two different bronchial productions. A substantial NO concentration gradient is present at the level of the acinus entrance between the airways and the alveoli. This gradient increases with bronchial NO production resulting in increasing alveolar concentration.
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FEheliox) between heliox-filled and air-filled FENO. The mean value was equal to 35.6 ± 8.6% for healthy subjects (open circles) and to 30.3 ± 6.3% for well-controlled asthma patients (closed circles). There was no statistical difference between the two groups (P = 0.101). Pooling healthy subjects and asthma patients, the mean FEheliox was equal to 31.9 ± 7.3%. The dashed lines are the upper and lower limits of FE simulated over the entire range of bronchial and alveolar productions here considered.
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 | (3) |
Conversely, Eq. 3 also enables us to derive FANO,prod, i.e., the alveolar concentration actually due to alveolar production, from experimentally accessible indexes, which are FENO and FANO, by a very simple equation:
 | (4) |
Regression line obtained from the entire population on Fig. 4B (with its 95% confidence interval) is presented alongside the simulations that consider nil (dashed line) and baseline alveolar production (dotted line).
Figure 5 shows individual FANO and FANO,prod for healthy subjects, asthma patients with FENO 
50 ppb (n = 12), and asthma patients with FENO >50 ppb (n = 9). Table 2 shows, in the three groups, the average values (±SD) of FENO, FANO, and FANO,prod. Cases a and b correspond to FANO computed according to the method of Pietropaoli et al. (17), and FANO,prod computed by Eq. 4, respectively. Cases c and d correspond to FANO computed according to the method of Tsoukias et al. (22) and FANO,prod computed from the correction formula of Condorelli et al. (4), respectively. The latter correction formula uses JNO computed by the method of Tsoukias et al. (22). The two approaches give quantitatively and statistically similar results, i.e., FANO,prod identical in the three groups after correction.
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FEheliox (in ppb) for a range of bronchial production and alveolar production. For a given alveolar production, FANO is linearly linked to FEheliox when bronchial production varies. An increase of alveolar production results in an upward translation of the linear relationship between FANO and FEheliox. In Fig. 6B, this relationship between FANO and FEheliox is assessed experimentally, using data from healthy subjects (open squares) and well-controlled asthma patients (closed squares). As in Fig. 4B, the regression line (with its 95% confidence interval) obtained from the entire study population (solid line) is plotted alongside the simulations that consider a nil alveolar production (dashed line) and a baseline alveolar production (dotted line).
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DISCUSSION |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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We computed FANO (and JNO) by including exhaled NO measured at 50 ml/s. Pietropaoli et al. (17) demonstrated a linear relationship between the inverse of the flow and exhaled NO for flows greater than 70 ml/s. However, huge nonlinearity only arises for very low flows (<20 ml/s). In the present study, an r2 value greater than 0.98, in individual adjustments as well as in adjustment on pooled data (18), strongly suggests an acceptable linearity.
In a recent work addressing treated asthma, Gelb et al. (8) showed that alveolar NO may still be reduced by systemic treatment after inhaled treatment. The authors raised the issue of the alveolar spaces contamination by NO coming from airways. Indeed, they found a weak but significant correlation between NO bronchial flux and alveolar concentration. However, in addition to a slightly different FANO determination method, the asthma control status of their patients was not defined as in the present study, and most of them, although stable, presented a certain degree of airways obstruction. The stronger relationship seen in the present work (Fig. 4B) is likely due to the fact that well-controlled asthma was specifically addressed, implying an absence of obstruction (mean FEV1: 98%predicted). This allowed isolating the effect of increased bronchial NO production, avoiding the confounding effect of airway caliber reduction. The latter has been shown, for not yet elucidated reasons, to decrease exhaled NO during bronchoprovocation challenge (5, 10). Our asthma group is free of airway obstruction and presents a broad range of exhaled NO, which enables us to specifically assess the contribution of bronchial production to alveolar concentration.
Classical compartment models consider a positive (NO production) and a negative (NO uptake by blood) source both in alveolar and in bronchial compartment. However, theoretical works (21, 23) with models incorporating convection and axial diffusion transport emphasized the crucial role of the latter and highlighted a backdiffusion flux (i.e., against expired flow) from small bronchi toward alveoli due to the gradient between bronchial and alveolar concentrations (Fig. 1). This flux constitutes an additional negative source for the bronchial compartment (tending to lower NO expired concentration) and a positive source for the alveolar compartment (tending to increase NO alveolar concentration). The simulations of FENO and FANO depicted in Fig. 2 illustrate these effects. Figure 2A shows that, at any level of bronchial production, molecular diffusion dramatically affects expired NO concentration. Indeed, backdiffusion precludes some NO molecules produced in bronchial wall from being expired. An increase of NO diffusivity (from D = 0.22 to 0.6 cm2/s) amplifies this phenomenon (19, 20). In the present study, measurements performed after equilibration with heliox show a 30% FENO decrease from value in air (Fig. 3). This reduction, which is in quantitative agreement with values observed by Shin et al. (20) in healthy subjects, is similar in patients with stable asthma and in healthy subjects. In addition, the mean experimental FEheliox is adequately predicted by simulations in the considered range of NO alveolar and bronchial productions (Fig. 3, dashed lines). However, the scattering of experimental values is not reproduced by the simulations, suggesting that factors other than NO production affect FEheliox.
Backdiffusion also constitutes a positive source for the alveolar compartment, being expected to increase the steady-state alveolar concentration independently from in situ production. Simulations of Fig. 2B show that, for a constant alveolar production, an increase of bronchial production hugely affects alveolar concentration when axial diffusion is considered (D = 0.22 or D = 0.6 cm2/s). When D = 0, a fivefold increase of bronchial production does not affect FANO. A greater diffusivity (D = 0.6 cm2/s), as it decreases FENO, increases FANO by increasing the backdiffusion flux.
The link between FENO and FANO, via backdiffusion, is addressed in Fig. 4. Despite the simultaneous involvements of convection and diffusion transports in a relatively complex geometrical structure, simulations of Fig. 4A predict a linear relationship between FANO and FENO. Indeed, in steady-state conditions, fast arising during expiration (23), the backdiffusion flux, i.e., the airway source of alveolar NO, is governed by the Fick's law of the first order, i.e., directly proportional to the gradient between airways and alveolar concentrations. This leads to a first-order relationship between alveolar and airway concentration. The last term of Eq. 3 indicates that 8% of FENO contributes to alveolar concentration. Instead of numerically solving a time-dependent transport equation (Eq. 1), Condorelli et al. (4) found an equivalent formula (based on bronchial production instead of FENO) by analytically solving a steady-state equation incorporating axial diffusion in Weibel morphometrical data. This formula, combined with Eq. 2, predicts 6% contribution of FENO to alveolar concentration. This smallest impact of airway production in the equation of Condorelli et al. (4) likely comes from a relatively smaller NO production at the onset of the acinus in their governing equation, slightly reducing the impact of backdiffusion. It is to be noted that the nearly perfect link between JNO and FENO was already pointed out by Paraskakis et al. (16). The predictions of our simulations are confirmed by experimental values of alveolar and exhaled concentrations (Fig. 4B). The regression line has a slope of 0.075, nearly identical to the simulations. Importantly, the regression line is nearly superimposed to the simulation line considering baseline alveolar production (dotted line), which gives simulated alveolar concentration very close to the average experimental value in normal subjects. Moreover, the 95% confidence interval is above the simulation line considering nil production (dashed line). This suggests that an in situ production actually occurs, even if some individual FANO of asthma patients as well as of healthy subjects may be compatible with a very low NO production in the alveoli, as concluded by Condorelli et al. (4) for healthy subjects. Conversely, some patients, especially with high FENO, present an elevated alveolar concentration, even after correction, as illustrated on Fig. 5. Nonetheless, FANO values are significantly different in asthma patients with FENO >50 ppb and in healthy controls, whereas FANO,prod are, in average, equivalent. Computations made according to the findings of Condorelli et al. (4) leads to the same conclusions (Table 2).
Finally, the impact of backdiffusion on FANO may be assessed by the link between FANO and the absolute difference between exhaled NO in air and in heliox (FEheliox in ppb), the latter being the only marker of backdiffusion amplitude that is experimentally accessible. Results are presented on Fig. 6. Simulations predict a linear relationship between FANO and FEheliox for a given alveolar production (Fig. 6A). Measured values of FANO and FEheliox (Fig. 6B) confirm these predictions. Their good correlation (r = 0.68; P < 0.001) attests that backdiffusion is an important determinant of the alveolar concentration. Moreover, in accordance with Fig. 4B, the regression line is close to the simulation with the baseline alveolar production (dotted line).
In conclusion, the present study brings experimental evidence that backdiffusion is a link between alveolar concentration and bronchial production in healthy subjects and in stable asthma patients. A very simple relationship between alveolar concentration and exhaled NO measured at 50 ml/s expired flow allows estimation of the part of alveolar concentration actually due to in situ production (Eq. 4). Importantly, comparisons between simulations and experiments allow concluding that patients with stable and unobstructed asthma have the same alveolar NO production as healthy subjects.
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GRANTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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