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Departments of 1Biomedical Engineering, 2Chemical Engineering and Materials Science, and 3Pediatrics, and 4The General Clinical Research Center, University of California, Irvine, California 92697
Submitted 3 December 2003 ; accepted in final form 22 April 2004
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ABSTRACT |
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 TOP ABSTRACT GlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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gas exchange; model; exhaled breath
Recently, our laboratory (17) and others (31) separately demonstrated theoretically that axial diffusion may play an important role in NO transport. During exhalation, the concentration of NO is higher in the airways compared with the alveoli, creating a gradient for diffusion of NO from the airways to the alveolar region (the opposite direction of convection). Thus the alveolar region may serve as a sink for NO produced in the airways, and neglecting axial diffusion may introduce significant error in the estimation of the flow-independent NO parameters such as J'awNO and CANO. On the basis of our earlier theoretical result (17), we hypothesize that axial diffusion of NO in the gas phase significantly reduces exhaled NO concentration by "backdiffusion" of NO from the airways to the alveolar region. The backdiffusion of NO may falsely lower the estimate of airway flux (i.e., J'awNO) and elevate the steady-state alveolar concentration (i.e., CANO).
To probe the impact of axial diffusion experimentally, the present study utilized heliox as the insufflating gas during a single-breath maneuver. Heliox is a mixture of 80% helium and 20% oxygen that increases the molecular diffusivity of NO 2.3-fold in the gas phase relative to air while introducing only a minimal impact on upper airway gas mixing because of a lower density (See METHODS and DISCUSSION for details). We found that heliox decreased the concentration of NO in the exhaled breath during all three phases of the exhalation profile. Analysis of the data by a single-path trumpet model that considers axial diffusion suggests that backdiffusion of NO from the airways to the alveolar region significantly impacts the partitioning of exhaled NO into airway and alveolar contributions.
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Glossary |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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EE (ppb)
ENO
ANO
'awNO
'ANO
E during expiration (ml/s)
I during inspiration (ml/s)
NO
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METHODS |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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Subjects. Nine healthy adults (five women) participated in this study, and their characteristics are presented in Table 1. All subjects had an forced expiratory volume in 1 s (FEV1) to forced vital capacity (FVC) ratio > 0.80, and those with a history of smoking at any time, cardiovascular, pulmonary, or neurological diseases were excluded. The Institutional Review Board at the University of California, Irvine approved the protocol, and written, informed consent was obtained from all subjects.
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2.3-fold (i.e., DNO,heliox 
2.3 DNO,air) (14), and gas density decreases by approximately threefold (12). The former enhances gas-phase diffusion of NO (the impact is primarily in the small airways and is the desired effect for this study), whereas the latter reduces mixing and axial dispersion of NO primarily in the larger airways, which has a negligible impact on this study (see DISCUSSION for details).
The first maneuver was three repetitions of a single-breath maneuver that included a preexpiratory 20-s breath hold followed by a decreasing flow rate (from 6 to 1% of vital capacity per second) (29) to measure CNOpeak, W50, VI,II, and AI,II, and to estimate several flow-independent NO-exchange parameters. A positive pressure of >5 cmH2O was maintained to prevent nasal contamination during the breath hold (1). A Starling resistor (Hans Rudolph, Kansas City, MO) with a variable resistance was used to progressively decrease the flow rate during the exhalation. A schematic of the experimental apparatus has been previously presented (29). The second maneuver was a vital capacity maneuver performed in triplicate to collect plateau NO concentration on the basis of the American Thoracic Society guidelines (1) in which the exhalation flow rate was maintained at a target of 50 ml/s.
Before performing the breathing maneuvers in heliox, each subject inhaled heliox during quiet tidal breathing for 2 min to washout nitrogen in the functional residual capacity. To determine the potential impact of nitrogen in the residual volume, each subject also performed the preexpiratory breath hold maneuver with a 20-s breath hold in the presence of heliox without tidal breathing heliox before the maneuver. After measurement of the indexes of NO-exchange dynamics (4, 5, 25), general spirometry such as FVC, FEV1, and FEV1 by FVC were measured in all subjects (Vmax229; Sensormedics, Yorba Linda, CA) by using the best performance (see Table 1) from three consecutive maneuvers.
Airstream analysis. A chemiluminescence NO analyzer (NOA280, Sievers, Boulder, CO) was used to measure the exhaled NO concentration. The instrument was calibrated on a daily basis by using a certified NO gas (45 ppm NO in 100% N2 for air calibration and 45 ppm NO in 100% He for heliox calibration; Sievers). The zero-point calibration was performed with a NO filter (Sievers) immediately before the collection of a profile. Calibration with 80% of carrier gas (either nitrogen or helium as in the case of air or heliox, respectively) balanced with oxygen resulted in a negligible change in the response of the instrument (<2% for helium). The flow rate and pressure signals were measured via a pneumotachometer (RSS100, Hans Rudolph). The pneumotachometer was calibrated daily, set to provide the flow in units of STPD, and accounted for changes in gas properties (e.g., viscosity) when using heliox.
Empirical data analysis.
Experimental single-exhalation profiles with preexpiratory breath hold were characterized empirically by CNOpeak, W50, total VI,II, defined as the minimum point (zero slope or dC
NO/dV = 0) in the exhalation profile (29), and AI,II (Fig. 1). In addition, the plateau concentration at a constant flow rate of 50 ml/s (CENO,50), as previously described by the American Thoracic Society (1), was also determined.
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Two-compartment model. A previously described two-compartment model was used to estimate four flow-independent NO exchange parameters: 1) J'awNO (pl/s), 2) DawNO (pl·s–1·ppb–1), 3) CANO (ppb), and 4) mean airway tissue NO concentration, CawNO (ppb) (equal to the ratio of J'awNO to DawNO). A detailed description of the mathematical algorithm to calculate the parameters has been previously described (29).
Trumpet model. The impact of axial diffusion was assessed utilizing a "trumpet model" of the lungs (17) by comparing simulations that included (DNO,air = 0.23 cm2/s for air or DNO,heliox = 0.52 cm2/s for heliox) and excluded (DNO,air = 0) axial diffusion. The structure of the trumpet model (see Fig. 2) is based on Weibel's anatomic data (32) (see APPENDIX for the governing equation and boundary conditions).
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III, defined by
 | (1) |
III is the mean fractional deviation of the model prediction to the experimental data (i.e., the gold standard) in phase III. In a fashion similar to III, A*I,II values are also referenced to an optimal or gold standard determined from experimental data. The new variable is denoted 
III and is defined as
 | (2) |
I,II is interpreted as the fractional deviation from the gold standard (same as III).
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RESULTS |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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There were no differences in CNOpeak, W50, and VI,II with or without 2 min of tidal breathing heliox before the single-exhalation maneuver. Mean (SD) values for CNOpeak, W50, and VI,II in the absence or presence of the 2-min heliox tidal breathing were 52 (20) and 53 (30) ppb, 139 (28) and 124 (27) ml, and 544 (88) and 485 (55) ml, respectively. In addition, mean (SD) values for C*NO,50 in the absence or presence of the 2-min heliox tidal breathing were 10.8 (5.94) and 11.4 (6.53) ppb, respectively, and were not statistically different. ÂI,II for air and heliox were 12,800 and 8,150 ppb·ml, respectively.
CENO,50 is presented in Table 2 for air and heliox. Subject 6 could not adequately perform the constant-exhalation flow-rate maneuver for both air and heliox, and subject 5 could not adequately perform the constant-exhalation flow-rate maneuver in the presence of heliox. Mean CENO,50 was significantly decreased by 45% in the presence of heliox (8.0 ppb compared with 14.6 ppb).
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NO was set to 1,467 pl·s–1·ppb–1 (20, 28). (Note that CANO = J'NO/DNO.) The following three different cases are shown: 1) the trumpet model in the absence of axial diffusion, 2) the trumpet model in the presence of axial diffusion (DNO,air = 0.23 or DNO,heliox = 0.52), and 3) the trumpet model in the presence of axial diffusion (DNO,air = 0.23 or DNO,heliox = 0.52) when J'awNO is increased (J'awNO = 1,100 pl/s) and CANO is set to zero (both at the boundary z = L+ and by setting J'NO equal to zero because J'NO is the product of CANO and DNO; see Glossary and APPENDIX).
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I,II and III significantly deviate from zero and are equal to 0.45 and 0.10 and 0.50 and 0.21, respectively (Fig. 5, C and D).
Increasing J'awNO increases the concentration of NO in all phases of the exhalation profile and thus impacts AI,II and III. Increasing J'awNO by 1.5-fold (J'awNO = 1,100 pl/s) in the presence of axial diffusion (DNO,air = 0.23 cm2/s), holding DawNO and DNO constant (5.03 and 1,467 pl·s–1·ppb–1, respectively), and decreasing the alveolar concentration to zero (CANO = 0 and J'NO = 0) provides the optimal simulation (I,II and III, improve to 0.25 and 0.04, respectively; see Fig. 5C). When this same set of flow-independent parameters is used to simulate heliox (DNO,heliox = 0.52 cm2/s), the trumpet model is able to simulate phase I and II very accurately (I,II improves from 0.50 to 0.03), but the impact on phase III is negligible (III is unchanged from 0.21).
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DISCUSSION |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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NO. Impact of Heliox as the Insufflating Gas
NO in the airways is transported by both molecular diffusion (resulting from concentration gradients and random motion of individual NO molecules) and convection (resulting from bulk flow of the insufflating gas). With bulk flow only in the axial direction (i.e., in the absence of mixing), NO transport may be characterized in terms of the Peclet number, Pe, a dimensionless index. Pe corresponds to the ratio of NO mass transport rate by convection (bulk flow) to that by molecular diffusion. Furthermore, Pe is inversely proportional to the molecular diffusivity of NO in the gas phase, DNO,i (i denotes the insufflating gas, either air or heliox) and directly proportional to the product of bulk gas velocity and a characteristic length (usually selected as the airway diameter). The importance of molecular diffusion, relative to convection, increases with decreasing Pe and increasing DNO,i.
At high bulk gas velocities (typical of the larger airways), fluid mixing at airway bifurcations (called axial dispersion) also impacts NO transport rates. Previous work (3, 16, 26) demonstrates that axial dispersion is dependent on flow rate, geometry, and the fluid's physical properties, with mathematical characteristics similar to molecular diffusion. Scherer et al. (16) and others (3, 26) have described the combined effects of molecular diffusion and axial dispersion in terms of an effective diffusivity, D*NO,i. These experiments used nitrogen (with similar physical properties to air) as the insufflating gas. From these data, D*NO,i was correlated as the sum of DNO,i and an axial dispersion term, to account for molecular diffusion and gas mixing at airway bifurcations, respectively. The axial dispersion term was proportional to the product of gas velocity and airway diameter. When air is the insufflating gas, the similarity of air and nitrogen allows axial dispersion's impact to be approximated for an airway branch with known gas velocity and diameter.
When Pe is large (e.g., >10), convection dominates NO transport, relative to molecular diffusion, but axial dispersion retains some influence. For heliox, the precise impact of axial dispersion under these conditions remains unclear. Reynolds number, Re, is a dimensionless index, directly proportional to gas density, and for a specific insufflating gas, Re is also proportional to Pe. Because the data of Scherer et al. and others (3, 16, 26) imply that the relative importance of axial dispersion increases with Re, a gas with lower density will have lower Re and will exhibit less mixing. Therefore, the impact of axial dispersion is expected to be less important for heliox than for air at large Pe. Conversely, when Pe is small (e.g., <0.1) molecular diffusion dominates over both convection and axial dispersion.
At typical exhalation flow rates (e.g., 250 ml/s), the precise impact of replacing air with heliox as the insufflating gas in the larger airways (i.e., generation <5) requires further investigation. However, in the smaller airways, convection and gas mixing are much less important and molecular diffusion dominates. Hence, replacing air with heliox significantly enhances molecular diffusion in the smaller airways and provides a means to study the impact of axial diffusion of NO in the lungs.
Impact of Axial Diffusion on Exhaled NO Concentration
When heliox was used as the insufflating gas in the present study, exhaled NO concentration was decreased in breathing maneuvers spanning a range of static and dynamically changing flow rates. This result is consistent with previous (17) and present simulations (Fig. 5) of a trumpet model that considers axial diffusion and is due to diffusion of NO down the concentration gradient (i.e., from high to low concentration) from the airway to the alveolar region.
The presence of heliox did not impact CNOpeak but reduced W50, VI,II, and AI,II. These findings were confirmed by the trumpet model simulations. The reduced AI,II is due to the reduced W50 (thinner peak causes a small area). The reduced W50 and VI,II are due to depletion of NO in the smaller airways while a constant CNOpeak is maintained (see Fig. 1, which describes how W50 and VI,II are determined). The depletion of NO is a direct result of enhanced axial diffusion of NO from the airways to the alveolar region. The constant CNOpeak is due to a minimal impact of axial diffusion in the larger airways during breath hold. CNOpeak occurs in the first part of the exhaled breath, which is the largest distance from the sink (i.e., the alveolar region) because of axial diffusion. If breath hold time were increased such that a new steady state was achieved in the airway compartment, a lower CNOpeak should be observed. We confirmed this by simulating a 1-h breath hold time using the trumpet model, and CNOpeak decreased by 2% (146 ppb, the ratio of J'awNO/DawNO or CawNO, to 143 ppb). Thus concentrations of NO throughout the airway tree during a breath hold are potentially impacted; however, for breath hold times less than 1 min, the impact is only observed in the small airways.
Impact of Axial Diffusion on Flow-Independent NO Parameters
Previous results from our group and others (17, 31), as well as simulations in the present study (Fig. 5), demonstrate that axial diffusion results in a loss of NO produced in the airways to the alveolar region. The result is a decrease in the estimated source of NO from the airways (i.e., J'awNO). This hypothesis is confirmed by the 34% reduction in J'awNO (735 pl/s compared with 485 pl/s) predicted by the two-compartment model, which neglects axial diffusion when heliox replaces air as the insufflating gas and rate of the axial diffusion is increased by 2.3-fold. Thus, to simulate the exhaled concentration observed experimentally with a model that considers axial diffusion, the endogenous source of NO in the airways (i.e., J'awNO) needs to be increased. The present study suggests that 1.5-fold increase (50%) of J'awNO in the presence of air (from 735 to 1,100 pl/s) and a 2.3-fold increase (130%) in the presence of heliox (485 to 1,100 pl/s) combined with a zero alveolar concentration and source (decrease in CANO from 2.5 ppb to 0, and J'NO = 0) is necessary to compensate for the effects of axial diffusion in all three phases of the exhalation profile (Fig. 5).
Of note is the observation that the simulation indexes (i.e., III) for heliox are poorer than air. This is likely due to remaining simplifications of the trumpet model that are exaggerated by the differences between heliox and air. For example, the trumpet model assumes that J'awNO is constant per unit airway volume (resulting in a decrease in J'awNO per unit surface area). This model structure is consistent with reports that the lower airways do not produce as much NO as the larger airways (22) but may not represent the precise distribution. Using the optimal parameter values (J'awNO = 1,100 pl/s and CANO = 0 ppb) and a constant exhalation flow rate of 50 ml/s, the trumpet model predicts the concentration in generation 2 (z = 18.7 cm) to be 10.9 ppb, which is 71% of the exhaled concentration at the mouth (z = 0, 15.4 ppb). Although somewhat higher, this value is comparable to Silkoff et al. (22), who reported that 50% of exhaled NO arises from the upper airways (generations 0–2). If a greater or smaller flux of NO is present in the airways than our model structure, then a greater or smaller, respectively, contribution of axial diffusion on exhaled NO is simulated, which introduces error in the relative impact of axial diffusion. In addition, as mentioned by Van Muylem et al. (31), other factors such as asymmetry of the airway tree and inhomogeneous ventilation may affect the exhalation profile of NO and would differentially impact the simulation of heliox compared with air because of differences in density between the two gases.
Finally, it is important to emphasize that our trumpet model structure limits the simulations of alveolar concentration to a fixed steady-state value. Hence, we cannot rule out the possibility that, even in the presence of a zero alveolar source, the alveolar concentration may be nonzero because of backdiffusion of NO from the airways. This simulation requires a more advanced model in which a separate mass balance on an alveolar compartment is coupled to the mass balance in the airway compartment.
The prediction of a zero or near-zero alveolar concentration in the presence of a zero alveolar source suggests the possibility that previous reports of CANO values that range from 1 to 5 ppb (7, 10, 18, 19, 20) may represent NO in or near the alveolar and respiratory bronchiole region, but the source may be the airways because of backdiffusion. The most commonly used technique to estimate CANO is a plot of NO vs. E (30). For exhalation flow rates >50 ml/s in adults, the slope of this plot is an estimate of CANO and the intercept an estimate of J'awNO. We hypothesized that even if CANO were zero, this plot would predict a positive slope (i.e., a nonzero CANO) because the impact of axial diffusion (and thus loss of NO to the alveolar region) would be reduced as the exhalation flow rate increased. To test this hypothesis and to determine the magnitude of this phenomenon, the trumpet model was used to predict CENO,i (and thus NO) at five different E values (50, 100, 150, 200, 300, and 500 ml/s) by using the optimal set of flow-independent NO parameters (J'awNO = 1,100 pl/s, DawNO = 5.03 pl·s–1·ppb–1, and CANO = 0 ppb) in the presence and absence of axial diffusion.
Figure 6 demonstrates the trend in the slope and intercept of NO vs. E in the absence (Fig. 6A) and presence (Fig. 6B) of axial diffusion for different subgroups of the five exhalation flow rates (three of the five flow rates, i.e., 50, 100, and 150 ml/s). In the absence of axial diffusion (equivalent to the two-compartment model) with CANO = 0, the predicted slope is slightly positive (0.36 ppb) when the three lowest flow rates are used and then approaches zero as higher flow rates are used. The slightly positive value at lower flow rates as well as the slight nonlinear relationship (i.e., r2 < 1.0) is due to the fact that, as the flow rate decreases, the airway compartment concentration increases (because of a longer residence time of air in the compartment) and the airway flux decreases slightly (JawNO = J'awNO – DawNO x CNO) as previously described (29). In the presence of axial diffusion with CANO = 0, the slope is 2.1 ppb for a flow rate range of 50–150 ml/s and decreases to 0.4 ppb over the flow rate range of 200–500 ml/s. This value for the slope (0.4–2.1 ppb) is consistent with reported CANO determined by using the slope of the relationship NO vs. E using the two-compartment model, which neglects axial diffusion (7, 10, 18–20). Thus CANO may be near zero for healthy adults, and the reported 1- to 3-ppb range determined from the slope of NO vs. E (7, 10, 18–20) may be an artifact from neglecting axial diffusion.
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APPENDIX |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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The governing partial differential equation for CNO (ppb) is obtained from a mass balance over a differential volume of length 
z:
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Initial and Boundary Conditions
The initial condition for Eq. A1 for inspiration is CNO(z,t = 0) = 0, and for expiration it is equal to the concentration profile just before exhalation (either after the 20-s breath hold for breathing maneuver 1 or end-inspiration for breathing maneuver 2). The boundary conditions for Eq. 1 are as follows:
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| (A3) |
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GRANTS |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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ACKNOWLEDGMENTS |
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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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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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TOPABSTRACTGlossaryMETHODSRESULTSDISCUSSIONAPPENDIXGRANTSACKNOWLEDGMENTSREFERENCES |
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2-agonist inhalation and spirometry in asthma. Am J Respir Crit Care Med 159: 940–944, 1999.This article has been cited by other articles:
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  Y. Kerckx, A. Michils, and A. Van Muylem Airway contribution to alveolar nitric oxide in healthy subjects and stable asthma patients J Appl Physiol, April 1, 2008; 104(4): 918 - 924. [Abstract] [Full Text] [PDF]
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S. C. George How accurately should we estimate the anatomical source of exhaled nitric oxide? J Appl Physiol, April 1, 2008; 104(4): 909 - 911. [Full Text] [PDF]
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P. Condorelli, H.-W. Shin, A. S. Aledia, P. E. Silkoff, and S. C. George A simple technique to characterize proximal and peripheral nitric oxide exchange using constant flow exhalations and an axial diffusion model J Appl Physiol, January 1, 2007; 102(1): 417 - 425. [Abstract] [Full Text] [PDF]
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H.-W. Shin, P. Condorelli, and S. C. George Examining axial diffusion of nitric oxide in the lungs using heliox and breath hold J Appl Physiol, February 1, 2006; 100(2): 623 - 630. [Abstract] [Full Text] [PDF]
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 ATS Workshop Proceedings: Exhaled Nitric Oxide and Nitric Oxide Oxidative Metabolism in Exhaled Breath Condensate. Proceedings of the ATS, January 1, 2006; 3(2): 131 - 145. [Full Text] [PDF]
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H.-W. Shin, P. Condorelli, and S. C. George A new and more accurate technique to characterize airway nitric oxide using different breath-hold times J Appl Physiol, May 1, 2005; 98(5): 1869 - 1877. [Abstract] [Full Text] [PDF]
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