INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

THE CONCENTRATION OF NITRIC oxide (NO) that appears in the exhaled breath depends strongly on several factors, including the presence of inflammation (1, 9). The fact that inflammatory diseases, such as bronchial asthma, elevate exhaled NO has generated great interest in using exhaled NO as a noninvasive index of pulmonary inflammation (2). Unfortunately, many early reports collected NO levels under different experimental conditions, and the absolute concentrations, as well as the conclusions, were not consistent. Subsequent work demonstrated that the exhaled NO level also depends on many additional factors, including the exhalation flow rate and the position of the soft palate (which affects nasal cavity contribution) (10, 15). These findings generated formal recommendations by both the American Thoracic Society (ATS) and the European Respiratory Society (ERS) on the conditions under which exhaled NO should be collected (8, 17). Both reports recommend a constant exhalation flow rate during the maneuver (ERS recommends 250 ml/s, the ATS recommends 50 ml/s).

Recently, several groups have demonstrated that exhaled NO arises from both the alveolar and airway regions of the lungs (12, 16, 19, 20); this conclusion is supported by the presence of nitric oxide synthase (NOS) in cells present in both regions (6, 13, 18, 21). The flow rate dependence is due to the source of NO in the airways, and this finding prompted the recommendation of a single constant flow rate in all experimental protocols. However, this recommendation presents a critical limitation in the interpretation of the exhaled NO. Namely, the constant flow rate maneuver cannot provide information regarding the origin of the endogenous NO production (i.e., the relative contribution from the airways and the alveoli). As a result, a single exhalation with a constant exhalation flow rate is inherently nonspecific, since two subjects can potentially have the same exhaled NO concentration yet have different relative contributions from the airways and alveoli. For example, two subjects with different inflammatory diseases (i.e., asthma and interstitial pneumonia) could have identical exhaled NO levels at a constant exhalation flow. The exhaled NO from the patient with asthma would largely arise from the airways, whereas the exhaled NO from the patient with allergic alveolitis (11) (alveolar inflammation) would largely arise from the alveolar region. However, by using only the exhaled concentration at a single expiratory flow as an index, the diseases could not be distinguished.

To avoid this problem, we have previously presented a technique that utilized multiple single-exhalation maneuvers at different constant exhalation flow rates as a means of separately determining airway and alveolar contributions (19, 20). The airway contribution was characterized by the flux from the airway wall (mol NO/s or ml NO/s) and the alveolar contribution by the steady-state alveolar concentration (parts per billion; ppb). Recently, two research groups reported an alternative technique in which the flux from the airway compartment was characterized by two terms: the airway diffusing capacity and either the airway wall concentration (16) or the maximum rate of production of NO by the airways that enters the airstream (maximum flux of NO from the airways) (12, 16). This was achieved by utilizing very low constant expiratory flow rate maneuvers. All of the previous techniques require multiple single exhalations, and the accuracy (or confidence level) of the estimated parameters is positively correlated with the number of single exhalations utilized. Multiple breathing maneuvers are cumbersome and time consuming. Furthermore, constant flow rate maneuvers can be difficult to perform, especially at very low flows and by young subjects.

The goal of this study is to present a new technique to characterize NO exchange parameters. The method involves an appropriate analysis of an individual (i.e., not multiple) single-exhalation maneuver with a variable flow rate. The technique allows 1) estimation of flow-independent parameters characteristic of NO exchange dynamics from a single maneuver and 2) prediction of the plateau NO concentration at a constant exhalation flow rate. The new method of analysis is more versatile because it provides a means to analyze exhaled NO data when flow rate is not necessarily constant. Furthermore, by inducing specific changes in flow rate during a single exhalation, the technique renders a single-exhalation maneuver sufficient to acquire all the necessary information. The focus of this manuscript is to describe the theory underlying the technique, test the technique in two normal subjects (one experienced and one naive to breathing maneuvers), and characterize the intrinsic intramaneuver and intrasubject variability, in particular, the effect of breath-hold time on the variability of the estimated parameters.

Glossary

Cair	Concentration (ppb) of NO in the airway compartment
Calv,ss	Steady-state alveolar concentration of NO (ppb)
Cexh	Exhaled concentration (ppb)
C	Model-predicted exhaled concentration (ppb)
CI	Inspired concentration (ppb)
tiss,air	Mean (over radial position) concentration of NO within the tissue phase (ppb)
DNO,air	Diffusing capacity (ml · s1 · ppb1) of NO in the airways
F	F statistic test
	Intramaneuver 100(1  )% confidence interval
	Intrasubject 100(1  )% confidence interval
J'NO	Volumetric flux per unit airway volume (ml · s1 · ml1 = ppb/s × 109) of NO
JNO,max	Maximum total molar flux (ml/s) of NO from the airway wall
n	Number of data points
P	Covariance matrix
Ssr	Semi-relative sensitivity index
tDS	Convective transport delay time in the dead space volume
res	Residence time of each differential gas bolus in the airway compartment
V	Axial (or longitudinal) position from the distal region of the airway to the mouth (units of cumulative volume)
Vair	Volume of the airway compartment (ml)
VC	Vital capacity (ml)
VDS	Dead space volume (volume expired before observation of NO signal) (ml)
E	Volumetric flow rate of air during expiration
I	Volumetric flow rate of air during inspiration
YLS	100(1  )% confidence region for the vector of inputs

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Two-compartment model. A simple two-compartment mathematical model has been previously developed to describe the exchange dynamics of NO in the human lungs (19). We will utilize the governing equations of this model in our parameter estimation algorithm and will review only the salient features here. The model is summarized pictorially in Fig. 1 and consists of a rigid tubular compartment representing the airways (trachea-airway generation 17) and a well-mixed expansile compartment representing the alveoli (airway generation 18 and beyond). A tissue layer representing the bronchial mucosa surrounds the airway. Exterior to the tissue is a layer of blood representing the bronchial circulation and serves as an infinite sink for NO (i.e., zero concentration of NO).

View larger version (18K): [in this window] [in a new window]   Fig. 1.   Schematic of two-compartment model used to describe nitric oxide (NO) exchange dynamics. The alveolar compartment has been simplified to represent only the steady-state concentration during exhalation. Parameters are described in the text.

(1)

1

1

9

Flux of NO from airway wall. A previously described description of the exchange dynamics in the airway tissue layer, which incorporates endogenous production, reaction, and diffusion, predicts J'_NO to be a linear function of the bulk gas concentration (19). In agreement with earlier works (12, 16, 19), we assume a uniform distribution for J'_NO along the airway tree (i.e., the same linear dependence between J'_NO and C_air holds throughout the airways). The following linear relationship between J'_NO and C_air then holds (19)

(2)

Thus we will characterize J'_NO with two parameters: J_NO,max and D_NO,air.

Model solution. Assuming a spatially uniform distribution of J'_NO, the solution for C_exh, which follows from Eqs. 1 and 2, has the following form

(3)

where C_in is the inlet concentration to the airway compartment. We can distinguish two different cases

(4)

(5)

Case I represents the emptying of the gas in phases I and II of the exhalation profile (see below). This exhaled gas consists of the inspired gas that has resided only in the airway compartment and has not reached the alveoli. For this case, C_in is simply CI (CI = 0 by ATS guidelines) and _res(t) is calculated from Eq. 4. In other words, the net volume transpired by each bolus is zero and is given by the integral of the flow rate over the time period of interest. The flow signal during this time period would include inspiration (negative flow rate), breath hold (zero flow rate), and expiration (positive flow rate).

View larger version (20K): [in this window] [in a new window]   Fig. 2.   Schematic demonstrating the "backward" integration of the flow signal to convert exhalation time to residence time of each exhaled bolus of gas. The concentration of a gas bolus is determined at time t + tDS. By using the flow rate history of the bolus, one can integrate the flow rate signal backward until the volume of the dead space and the airway volume have been traversed. In doing so, one can determine the residence time in the airway compartment. Mathematical details are presented in the text.

Sensitivity analysis. We define the semirelative sensitivity of C_exh with respect to the unknown parameters in the following fashion

(6)

where Y is one of the unknown parameters and the subscript "i" represents the specific parameter. The derivatives are estimated at the nominal values of each parameter. S^sr represents the absolute change of C_exh per fractional change of the corresponding parameter and is useful for 1) providing a useful relative index of comparison between the unknown parameters and their impact on C_exh and 2) determining the confidence region of the estimated parameters. The partial derivatives can be calculated analytically by differentiation of Eq. 2 with respect to the corresponding variable. A necessary condition for an accurate estimation of the parameters of interest is that the model's output should be sensitive enough relative to the intrinsic error of the experimental measurement.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Semirelative sensitivity of Cexh to the 3 input parameters. The shaded region represents the range of airway compartment residence times achieved during a decreasing flow rate maneuver that spans an exhalation flow rate of 300 to 50 ml/s for an airway compartment volume of 200 ml.

Experimental protocol. A series of single exhalation maneuvers were performed on two subjects, one experienced and one naive to performing breathing maneuvers, to determine the feasibility of the new technique. The protocol was approved by the Institutional Review Board at the University of California, Irvine, and the schematic is shown in Fig. 4. The first subject was a healthy male, age 28 yr, body weight 172 lb., vital capacity 5,000 ml, an author on this manuscript (Tsoukias), and experienced at performing breathing maneuvers. The second subject was a healthy male, age 23 yr, body weight 175 lb., and vital capacity 5,200 ml but was not experienced at performing breathing maneuvers. The anatomic airway volume was thus estimated to be 200 ml and 198 ml for the two subjects, respectively (5).

View larger version (23K): [in this window] [in a new window]   Fig. 4.   Schematic of the experimental setup used to collect the exhalation profiles. The flow, pressure, and NO analog signals are captured by the analytical instruments and converted to a digital signal. A series of valves allows NO-free air to be stored in a Mylar bag for inspiration. During the breath hold, the NO analyzer samples from the NO-free air reservoir and the subject maintains a positive pressure of >5 cmH2O by attempting to exhale against a closed valve. As exhalation begins, the NO analyzer then samples from the exhalate and the flow rate is manipulated by a variable Starling resistor while the expiratory effort of the subject remains constant.

Parameter estimation. Identification of the unknown parameters (C_alv,ss, D_NO,air, J_NO,max) is accomplished by nonlinear least-square minimization. Assuming a constant variance error in the measurement renders ordinary least squares sufficient for parameter estimation. Least square minimization of the sum of the residuals (R_LS) between the model's prediction and the experimental data was accomplished with the use of a conjugated direction minimization algorithm.

(7)

View larger version (33K): [in this window] [in a new window]   Fig. 5.   Representative exhaled NO concentration profile following a 20-s breath hold shown as a function of exhaled volume (A) or time (B). The light line represents exhaled NO concentration (parts/billion; ppb), and the dashed line represents the exhalation flow rate (A) or pressure (B). The heavy line represents the best-fit model prediction of the exhalation curve using nonlinear least squares regression. The optimal values for 3 unknown input parameters (Calv,ss, DNO,air, and JNO,max) are shown for this particular maneuver. Parameters and mathematical details are presented in the text.

Identifiability and uncertainty analysis. A high sensitivity is a necessary but not sufficient condition for an accurate estimation of the parameters. Dependence between the parameters may render them unidentifiable even when their sensitivities are significant. Thus, although the sensitivity analysis suggests experimental conditions for improving the estimation of the parameters, a better index is needed to describe the accuracy of our estimation.

(8)

1

(9)

(10)

(11)

(12)

1

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Figure 6 presents the estimated parameters (J_NO,max, D_NO,air, and C_alv,ss, respectively) for each of the five repeated breathing maneuvers (four maneuvers for a 45-s breath hold) for both subjects (subject 1 is shown on left). The mean estimated value with error bars representing the mean (Eq. 11) is also shown. That is, for each maneuver, an independent estimate of the confidence region is estimated from Eq. 11, and the error bar represents the mean of these intramaneuver confidence region estimates. Figure 6 also shows the mean estimated value, with error bars representing the mean (Eq. 12, or intrasubject variability). The mean values for J_NO,max, D_NO,air, and C_alv,ss do not depend on breath-hold time and range from 580 to 600 pl/s, 4.6 to 7.1 pl · s¹ · ppb¹, and 1.8 to 2.2 ppb for subject 1 and 280 to 440 pl/s, 3.7 to 4.1 pl · s¹ · ppb¹, and 0.73 to 1.5 ppb for subject 2. These values compare favorably with those previously reported by our group (19, 20), Pietropaoli et al. (12), and Silkoff et al. (16) using techniques that require multiple-breathing maneuvers.

View larger version (32K): [in this window] [in a new window]   Fig. 6.   Optimal parameter values for JNO,max (A), DNO,air (B), and Calv,ss (C) following 5 repeated decreasing flow rate exhalation breathing maneuvers () following 4 different breath-hold times (10, 20, 30, and 45 s) are shown for 2 subjects. Subject 1 (left) was experienced at performing breathing maneuvers, and subject 2 (right) was naive. , Mean optimal parameter value; error bars are the mean intramaneuver 95% confidence intervals. , Mean optimal parameter value; error bars are the mean intrasubject 95% confidence intervals.

The intramaneuver estimate of J_NO,max steadily improves (as evidenced by a decreasing confidence interval) as the breath-hold time increases from 10 to 30 s. The mean is 17 and 89% for subjects 1 and 2, respectively, at a 10-s breath hold and decreases to 6.5 and 19%, respectively, for a 30-s breath hold. No significant improvement is seen with a 45-s breath hold. The same trend is observed for D_NO,air except the magnitude of the uncertainty is larger. The mean is 89 and 941% for subjects 1 and 2, respectively, at a 10-s breath hold and decreases to 19 and 159%, respectively, for a 30-s breath hold.

A similar, although more modest, trend with breath-hold time is observed for C_alv,ss. The mean improves by increasing the breath-hold time from 10 to 20 s (34 and 280% to 26 and 78% for subjects 1 and 2, respectively) but then remains nearly constant for breath-hold times >20 s. Importantly, there is no statistical difference between the estimated values for any of the parameters at different breath-hold times, only a change in the estimated confidence interval.

The intrasubject estimate of the three parameters consistently improves (as evidenced by a decreasing confidence interval) as the breath-hold time increases from 10 to 20 s with modest or no significant improvement for breath-hold times >20 s. The mean is 25 and 41% for subjects 1 and 2 at a 10-s breath hold that decreases to 13 and 8.3% for a 20-s breath hold, respectively. The mean is 114 and 90% for subjects 1 and 2, respectively, for a 10-s breath hold and decreases to 45 and 32%, respectively, for a 20-s breath hold. For C_alv,ss, the mean is 47 and 63% for subjects 1 and 2, respectively, for a 10-s breath hold and decreases to 28 and 24%, respectively, for a 20-s breath hold.

In general, the mean value for differs from the mean value of because depends inversely on the square root of the number of maneuvers performed (Eq. 12) and on the reproducibility of the experimental conditions and measurements. In addition, it is also of interest to note that the intramaneuver confidence intervals for subject 1 are much smaller than for subject 2, yet the intrasubject confidence intervals are, in general, larger.

In Fig. 7, NO plateau concentration (C_exh,ee, concentration at end exhalation) from a constant exhalation flow rate is plotted as a function of E. The model prediction (solid line) is calculated using the mean estimated parameters from the five repeated 20-s breath-hold maneuvers. Mean C_exh,ee values (±95% confidence interval) from the experimental maneuvers with the recommended (8, 17) constant flow rates are also presented. The predicted NO plateau concentrations are in close agreement with the experimental measurements. Importantly, this figure demonstrates that, once the unknown flow-independent parameters have been estimated, the model can be utilized to accurately predict the NO plateau concentration, at least for constant flow rates between 50 and 300 ml/s.

View larger version (22K): [in this window] [in a new window]   Fig. 7.   Cexh at end exhalation is shown as a function of the constant exhalation flow rate for both subjects. Error bars in the experimental data points represent 95% confidence intervals. Two exhalation flow rates are shown (~50 and ~250 ml/s) based on American Thoracic Society and European Respiratory Society recommendations. The solid lines are the model prediction of the end-exhalation Cexh at a constant exhalation flow rate using the mean value of the optimal parameter values determined from the flow rate maneuvers following 20-s breath hold.

In Fig. 8, the effect of V_air in the estimation of the unknown parameters of interest is investigated. The 20-, 30-, and 45-s breath-hold maneuvers were reanalyzed for subject 1 with two smaller values for V_air (100 and 150 ml) instead of the control value of 200 ml. There is a statistically significant difference in the estimation of all three parameters (P < 0.01) with decreasing V_air at each breath-hold time. There is a positive correlation between the estimated values of J_NO,max and D_NO,air with V_air and a negative correlation for C_alv,ss. The percent change in the estimated parameters per milliliter change in V_air has averaged values of 0.2, 1.5, and 0.3% for J_NO,max, D_NO,air, and C_alv,ss, respectively.

View larger version (23K): [in this window] [in a new window]   Fig. 8.   The three estimated parameters [JNO,max (A), DNO,air (B), and Calv,ss (C)] are shown as a function of the choice for Vair for each of three breath-hold times (20, 30, and 45 s); 200 ml is the estimated value of the anatomic dead space for the subject based on the subjects ideal body weight in lb. plus the age in yr. *Statistically different from Vair = 200 ml. #Statistically different from Vair = 150 ml. Statistical significance was determined using a paired Student t-test and P < 0.05.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In this manuscript, we present a new method for the analysis and interpretation of exhaled NO data. This new technique can estimate three flow-independent parameters (J_NO,max, D_NO,air, and C_alv,ss) from a single-exhalation maneuver that can comprehensively characterize the exhalation NO profile. The technique requires only a single-breathing maneuver and is therefore less cumbersome to perform than other techniques, which require multiple-breathing maneuvers. Thus the technique has the potential to be applied to many different diseases and gather information on parameters that will likely provide more specific and sensitive information about NO metabolism and thus inflammation.

The backward integration of the flow signal (Eqs. 4 and 5) provides powerful flexibility, as a specific flow rate profile is not required. One requires knowledge of only the specific exhalation flow rate profile such that the backward integration is possible. Thus the method is very general and can be applied essentially to any given single exhalation profile. However, we utilized an exhalation maneuver with the following characteristics such that our model assumptions and simplifications were still valid, yet we were still able to accurately determine the unknown parameters: 1) the exhalation flow rate pattern produces exhaled boluses of gas with a wide range of uniformly distributed residence times to distinguish alveolar and airway contributions to exhaled NO (i.e., uniquely determine the three unknown parameters), 2) the rate of change in exhalation flow rate is small enough that each bolus of air resides for approximately the same amount of time in the different parts of the airways (i.e., minimal acceleration requirement, see DISCUSSION and APPENDIX below), and 3) easy to perform.

In agreement with the models described by Pietropaoli et al. (12) and Silkoff et al (16), we assumed in this study that the linear dependence of J'_NO on C_air is constant along the airway tree. In fact, at any given axial position, the flux of NO will depend on many variables in addition to C_air such as tissue thickness, endogenous production and consumption rates, and airway diameter; thus the dependence of J'_NO on C_air does not necessarily remain the same with axial position. Silkoff et al (16) recently demonstrated that D_NO,air for asthmatics was increased relative to healthy subjects even after treatment with corticosteroids. In an earlier study, Silkoff et al. (14) also reported that, in healthy lungs, a significant fraction of exhaled NO arises from the trachea (~45%), suggesting that the larger airways and mouth (~7%) were the primary sources of orally exhaled NO. This does not exclude the lower airways from contributing NO. In fact, the lower airways, together with the alveolar region, must account for the remaining ~48%. Our model (as well as previous models) assumes that the contribution of NO from airways is evenly distributed per unit airway volume. The volume of the trachea (~35-40 ml) accounts for ~20-25% of the physiological dead space (V_air). Thus the larger airways are likely contributing a greater share per unit airway volume in healthy lungs, and the distribution of NO flux (J_NO,max and D_NO,air) may change in disease states. This feature of NO exchange does not invalidate our governing equation but does place a requirement that the exhalation flow rate not change rapidly during the exhalation maneuver.

Rapid changes in the flow will result in significant acceleration (or deceleration) of a differential bolus of gas while traversing the airways. As a result, the bolus of gas will reside for different amounts of time in different parts of the airways, thus rendering our governing equation invalid. The APPENDIX predicts the maximum change in the flow rate during exhalation such that the residence time of any differential gas bolus not change by >10%. Because we cannot preclude a nonuniform NO exchange distribution, such a flow profile minimizes the potential error in the estimation of D_NO,air and J_NO,max.

Our sensitivity analysis (Fig. 3) demonstrates that a range of flow rates (or residence times) is necessary to uniquely determine the three parameters. This can be understood if one considers the limiting cases. At very high flow rates, the residence time in the airway compartment approaches zero, and thus very little NO is absorbed by the exhalate. Thus the exhaled NO concentration approaches that of C_alv,ss. The sensitivity is therefore highest for C_alv,ss at very small airway compartment residence times; however, very little information can be extracted about the airway compartment. Conversely, as the residence time increases, a progressively increasing proportion of the exhaled NO is derived from the airway compartment; thus the parameters that characterize the airway compartment (J_NO,max and D_NO,air) can be uniquely determined.

To estimate D_NO,air, much longer residence times are necessary. This is observed in Fig. 3 and can be explained by Eq. 3. D_NO,air only becomes significant (or impacts J'_NO) when C_air is large enough such that the second term in Eq. 3 becomes significant. Thus the exhalation flow rate must be low such that NO can accumulate in the airways. This increases C_air and decreases the driving force for diffusion of NO in the airstream. One choice in handling this problem is to increase the flow rate range by including smaller flows (higher residence times). Pietropaoli et al (12) and Silkoff et al (16) utilized flows less than 10 ml/s to accomplish estimation of D_NO,air. Alternatively, we utilized a preexpiratory breath hold (limit of zero exhalation flow rate) to achieve long residence times. We believe this alternative provides equivalent information about the airway compartment and is more easily performed by the subject, as well as more easily recorded by the investigator.

An exhalation that spans a wide range of flows may not however be sufficient unless each flow is sustained for a sufficient time to allow a bolus of air to traverse the airways at a specific flow rate. For example a 10 ml/s flow rate in a 150-ml airway will result in an exhaled bolus of gas with a residence time of 15 s. Thus, to characterize the concentration of such a bolus, the flow rate should be sustained for at least 15 s. In a single-exhalation maneuver with a dynamically changing flow rate, lower flows should be sustained for more time than high flows to collect exhaled concentrations that accurately span a wide range of residence times. Ideally, the residence time should also be distributed uniformly over this wide range such as to acquire the same amount of data at any given residence time.

On the basis of the above specifications, we propose a single-exhalation maneuver that includes a preexpiratory breath-hold time, followed by a flow rate pattern that decreases approximately exponentially with volume (see APPENDIX) from ~6% of the VC per second (300 ml/s in our subjects) to ~1% of the VC per second (50 ml/s in our subjects). Such a pattern provides exhaled boluses of gas whose flow rates do not change significantly during their passage through the airways (difference of entering to exiting velocity <10%, see APPENDIX). At the same time, the residence times of the exiting boluses are approximately uniformly distributed over a range between 0.5 and 3 s (see shaded area in Fig. 3). This provides the necessary sensitivity for the estimation of C_alv,ss and J_NO,max.

The dependence of our parameter estimation on the choice of V_air presents a potential problem (Fig. 8). The dependence of the parameters, particularly D_NO,air, on V_air is because the model's prediction for the NO concentration in the airways during breath holding depends on the choice of V_air. For example, if V_air values decrease from 200 to 100 ml, the concentration in the airway compartment will increase more rapidly; thus, to predict the experimental concentration, J_NO,max and D_NO,air would need to decrease (Fig. 8).

However, the parameter most impacted by the choice of V_air is D_NO,air, which is determined primarily from the shape of the exhalation profile in phases I and II (or the breath hold). During a breath hold, the NO emitted into the airway compartment will disperse in either direction due to molecular diffusion and cardiac mixing. On the basis of a molecular diffusion coefficient of 0.27 cm²/s for NO in the gas phase (4), a conservative length for dispersion during the breath hold is 2-4 cm. This axial distance is approximately equal to that between generations 6-15 based on Weibel's symmetric lung model (22). Thus axial dispersion will tend to create a shape for phases I and II similar to that generated if the NO flux was uniformly distributed, thus mitigating the impact of a nonuniform distribution in NO flux. Hence, even if the distribution of NO flux is altered in disease, the choice for V_air should not have a significant impact on the relative change in the parameter estimates due to disease.

Covariance analysis (Eq. 8) provides an a priori estimate (i.e., without the need of multiple maneuvers) for the accuracy of our predictions. Thus it can be utilized as a criterion for rejecting a profile or for specifying sufficient experimental conditions for parameter estimation (flow rate range, breath-hold time). The covariance analysis suggests that a breath-hold time of 20 s in combination with the specific flow rate pattern are adequate for the specific subject in determining the parameters of interest. This theoretical prediction was validated by repeated measurements. Although a longer breath hold time may provide increased accuracy of the estimate of D_NO,air, the gain is minimal and the effort on the part of the patient increases dramatically. A 20-s breath hold may not be possible for those subjects with more advanced lung disease who are hypoxic or hypercarbic, and an alternative technique may be necessary. For example, further characterization of this technique in a given lung disease population may determine that J_NO,max is as good an indicator of disease status as D_NO,air, and thus the breath hold may not be necessary in all patient populations. Additional studies on more normal subjects and those with inflammatory diseases are necessary before a formal recommendation can be made.

Although there was not a significant variation in the mean values of the parameters between subjects 1 and 2, there were differences in the confidence intervals. For subject 2, the intramaneuver confidence intervals were significantly larger than for subject 1. The intramaneuver confidence interval is a positive function of R_LS. Thus a large reflects a large R_LS and, provided that the instrument error did not change between subject testing, can be considered an index of the accuracy or appropriateness of the two-compartment model. Thus there may be significant variation among the normal population in how well the two-compartment model can simulate NO exchange dynamics. In contrast, intrasubject confidence intervals for subject 2 were very similar, or slightly improved, compared with subject 1. is a positive function of the deviation of the estimate from the population mean (Eq. 12); thus it provides an index of the maneuver-to-maneuver reproducibility. Thus our naive subject (subject 2) was able to reproduce the breathing maneuvers to a similar degree as our experienced subject (subject 1). This finding suggests that the maneuver is relatively simple to perform and that patients from many subpopulations may be able to perform the maneuver with minimal training.

Recently, ATS provided recommendations for standardized procedures for the measurement of exhaled NO. They recommended a constant exhalation flow rate maneuver of 50 ml/s and recording of the NO plateau value. The flow rate should be maintained within 10% of this value throughout the exhalation. The recommendations acknowledged that theoretical predictions from our earlier work and others (12, 19) suggest that derivation of additional parameters of potential physiological importance, by analyzing the dependence of C_exh on E, may be achievable.

The significance and utility of the parameters estimated in this study for identification and/or monitoring of inflammatory diseases need to be examined through extensive application of these methods. At this point, such experimental data are limited. Silkoff et al. (16) applied their method in asthmatic subjects with some intriguing results. They found that D_NO,air is fourfold higher in asthmatic patients and that this increase is independent of steroid treatment. In contrast, the NO plateau concentration does not change dramatically between normal subjects and asthmatic patients treated with steroids (9). Perhaps the most promising utility of this technique is to follow patients longitudinally and correlate intrasubject changes in these parameters with important clinical decisions such as therapeutic dose. Thus, if the same V_air is used for a given subject over time [i.e., V_air (ml) = subjects ideal body weight in lb. + age in yr], one should be able to accurately determine changes in NO exchange parameters over time. Finally, there are other techniques such as the single-exhalation CO₂ profile that might be used in conjunction with this technique as an independent assessment of physiological dead space.

An alternative method of describing the linear dependence of J'_NO on the bulk gas phase concentration is to utilize a mass transfer coefficient (or transfer factor) and a concentration difference (16)

(13)

where _tiss,air is the mean (over radial position) concentration within the tissue phase and D_NO,air is equivalent to a mass transfer coefficient or transfer factor. Mathematically, this representation of NO flux is equivalent to Eq. 3, in which J_NO,max = D_NO,air × _tiss,air. Thus the airway compartment is now alternatively characterized by D_NO,air and _tiss,air. We can estimate _tiss,air by taking the ratio of J_NO,max to D_NO,air. For subject 1, the mean values of _tiss,air (with intermaneuver 95% confidence intervals) are 89 ppb (68%), 155 ppb (92%), 152 ppb (63%), and 144 ppb (64%) for 10-, 20-, 30-, and 45-s breath holds, respectively. One estimate from the 10-s breathing maneuver was discarded because it produced a large negative value that greatly skewed the estimate. For subject 2, the mean values of _tiss,air (with intermaneuver 95% confidence intervals) are 85 ppb (124%), 112 ppb (26%), 133 ppb (28%), and 95 ppb (28%) for 10-, 20-, 30-, and 45-s breath holds, respectively. The variance of _tiss,air is similar to the other three parameters, and the mean value does not depend strongly on breath-hold time. Although the mean values for the two subjects are similar to those recently predicted by Silkoff et al. (16), the variance of this data cannot be compared because they report only a intersubject variability for a technique that utilizes multiple-breathing maneuvers.

In conclusion, this study describes a new technique to characterize flow-independent parameters (J_NO,max, D_NO,air, and C_alv,ss), which can characterize NO exchange dynamics in the lungs. The maneuver entails appropriate analysis of only a single-exhalation breathing maneuver that should be tolerated by a wide range of subjects. In addition, our results suggest that the stringent requirements on the flow rate that ATS and ERS recommends are not needed. With proper analysis of a variable flow rate maneuver, one can estimate flow-independent parameters that potentially provide more specificity and sensitivity to disease status. If necessary, one can then use the model to predict the NO plateau concentration at a constant flow (Fig. 7). This could be of importance, especially for young and diseased subjects that have difficulty sustaining a constant expiratory flow. Future studies must address intersubject variability and also must apply this technique in a variety of key populations, including healthy adults and children, and for inflammatory diseases such as bronchial asthma, chronic obstructive pulmonary disease, and cystic fibrosis before its true utility is characterized.