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Departments of 1Biomedical Engineering and 2Chemical Engineering and Materials Science, University of California, Irvine, California 92697-2575
Submitted 28 October 2003 ; accepted in final form 29 December 2003
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ABSTRACT |
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 TOP ABSTRACT GlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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gas exchange; pulmonary; mathematical model
), and steady-state alveolar concentration (CANO) (10, 17, 23, 26, 27). Several groups have utilized single-breath (i.e., vital capacity) maneuvers to estimate the flow-independent NO parameters in health and disease and have reported altered NO exchange dynamics in several inflammatory lung diseases (e.g., asthma, cystic fibrosis, allergic alveolitis, scleroderma, and chronic obstructive pulmonary disease) (7, 10, 15, 19, 20, 23). Application of the two-compartment model during tidal breathing has not been explored but may be applicable for young children, intubated subjects, and subjects with compromised lung function who are unable to perform the single-breath maneuvers (6, 24). Analysis of tidal breathing data presents new challenges relative to single-breath maneuvers. Smaller changes in lung volume are often inadequate to overcome sampling system limitations, such as dead space in sampling system plumbing. Each breath occurs over shorter time intervals, which allows less time for NO to accumulate in the airways, compared with single-breath maneuvers. This leads to expired NO levels, which are significantly less than those observed for single-breath maneuvers (1, 8). Analysis of multiple consecutive tidal breaths may partially offset these limitations.
Herein, we characterize NO gas exchange during tidal breathing in terms of two flow-independent parameters: the average volumetric conductive airway flux (
aw NO) and the time-averaged alveolar concentration (
A). We hypothesize that (aw NO and A serve as indexes for NO exchange dynamics in the airway and alveolar regions, respectively. As a first step, these parameters are estimated by comparison of experimental tidal breathing exhalation profiles in healthy adults with the use of a new three-compartment model, which includes two airway sections and one alveolar compartment. Estimates of aw NO and A are compared with analogous parameters determined by using a previously described single-breath technique and the two-compartment model (26, 27): and CANO. Our analysis includes correction of the experimental data for time lags and distortion introduced by the analytic monitoring system. These effects are insignificant for single-breath maneuvers, but profoundly impact low-level tidal breathing data.
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Glossary |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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I,out(t) [parts/billion (ppb)]
, where du is a differential increment in the dummy variable u.
j(t)I,out(t) = Jaw NO,U 1(t) + Jaw NO,L 2(t) + A 3(t) + B
- DawNO Cair = net NO flux into airway compartment air space (pl/s, ml/s)
aw NO
a
s(t,u)
, where s is scaling factor for wavelet transform (s)
jaw NO, A) 
= Residence time, space time, or time constant (s)
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Modifiers |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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aw NO (j = 1) and A (j = 2) or general integer
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METHODS |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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6 to 1% of vital capacity per second) in triplicate, as previously described (27). From these data, we determined the corresponding values of , CANO, and DawNO using nonlinear regression (27). For preexpiratory breath-hold maneuvers, a positive pressure of >5 cmH2O was maintained to prevent nasal contamination, and a Starling resistor (Hans Rudolph, Kansas City, MO) was used to progressively decrease the flow rate during exhalation.
Second, after allowing 1 min of comfortable tidal breathing before collection of data, each subject breathed comfortably in a tidal fashion for a minimum of 3 min (maximum of 5 min). NO was scrubbed from ambient air by using a filter (Ionics, Boulder, CO) to produce "NO-free air," which was used as the inhaled gas. Exhaled NO concentration and flow rate were measured at breathing frequencies of 7-15 breaths/min and alveolar ventilation (A) rates of 6-13 l/min (see Table 2). Subsequently, aw NO and A were determined from the tidal breathing data (see below for details).
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After NO collection, standard spirometric indexes were measured (Vmax229; Sensormedics, Yorba Linda, CA), which included forced vital capacity and forced expiratory volume in 1 s, based on the best performance from three consecutive measurements. All data were obtained with the subjects in the upright position. Table 1 summarizes each subject's physical characteristics, standard spirometry measurements, and conducting airway volumes (Vaw), estimated based on age and ideal body weight (20).
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The experimental monitoring system is shown in Fig. 1A, which measures NO concentration in real-time using a chemiluminesent NO analyzer (NOA280, Ionics), and measures volumetric flow rate and pressure with a pneumotachometer (model RSS100, Hans Rudolph). A digital computer collects data for all three signals at 50 Hz (sampling time = 0.02 s).
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Sampling system model. During exhalation (flow rate, QE m, and time interval, 0 < t < tE m, for breath m), air from the mouth [NO concentration, CM(t)] traverses the mouthpiece assembly entrance dead space (volume, Vds 1 = 135 ml, see Fig. 1), on its way to the sampling point [NO concentration, Cs(t)]. At the sampling point, a small flow of air (Qs = 4.2 ml/s) is collected by the chemiluminescent NO analyzer continuously through a 1.8-mm-diameter sample line (total volume, Vs = 5.5 ml, and space time, s = Vs/Qs 
1.3 s). Although NO is sampled upstream of the pneumotachometer, Qs is small (<5%), relative to QE m, and the impact of this flow rate on parameter estimates is insignificant. On subsequent inhalation (flow, QI m+1, and tE m < t, for breath m + 1), NO-free air is not present at the sampling point until inspired air traverses the mouthpiece assembly exit dead space (volume, Vds 2 = 135 ml). Lag times in both dead space regions are approximated by their respective space times: ds 1m = Vds 1/QE m and ds 2,m+1 = Vds 2/QI m+1. Thus, during exhalation, the Cs(t) lags the mouth in accordance with the relationship, Cs(t) = CM(t - ds 1m), and on subsequent inhalation, residual NO is sampled [i.e., baseline, Cs(t) = 0, is not established] until time t = tE m + ds 2,m+1.
Because the sample line is maintained at laminar flow (Reynolds number is 180 and laminar flow occurs for Reynolds numbers <2,100 in cylinders), air at the tube centerline moves approximately twice as fast as the average bulk flow. This effect significantly delays and distorts the concentration profile input to the NO analyzer (instrument), CI,in(t), which is approximated as a convolution integral of Cs(t), defined by Eqs. A5 and A6 in APPENDIX A (3). At the analyzer, the instrument's response, CI,out(t), is approximated as a first-order system with time constant A = 90 ms (see Eq. A7 in APPENDIX A), as reported by the manufacturer (Ionics). CI,out(t) then corresponds to a theoretically predicted tidal breathing profile, based on the lung models, as discussed below.
Two-compartment lung model. The two-compartment model has been described previously in detail by several research groups, including ours (10, 17, 23, 26), and is currently the accepted model of NO gas exchange. Thus it is the starting point for our analysis of tidal breathing. Briefly, the model approximates the conducting airways (i.e., the trachea and the first 17 airway generations) as a rigid, cylindrical compartment of volume, Vaw, and axial diffusion is neglected. The respiratory bronchioles and alveolar region (generations 18 and beyond) expand and contract to accommodate inspired and expired air. Endogenously produced NO diffuses into the airway compartment at net flux (Jaw NO). These assumptions lead to a differential mass balance for the airway gas-phase concentration of NO, Cair(t,V) (26)
 | (1) |
where t is time, V is cumulative volume, Jaw NO (Cair, V) is the net flux of NO into the airway (a function of Cair and V), and Q is the volumetric flow rate of air [Q = -QI(t) for inhalation and Q = QE(t) for exhalation, see Fig. 1B].
Previous work for single-breath maneuvers (26) approximates Jaw NO as a linear function of Cair, 
. If exhalation proceeds for >10 s, the alveolar concentration is assumed to reach a steady-state value (CANO) (12, 26, 27). Thus NO exchange is characterized by three flow-independent parameters: , DawNO, and CANO. , DawNO, and CANO were determined by using the two-compartment model and the 20-s preexpiratory breath hold and decreasing QE maneuver (27) for all six subjects as a basis for comparison to our characterization of NO exchange dynamics during tidal breathing.
Three-compartment lung model. In our initial analysis, the tidal breathing exhalation profile was often difficult to simulate due to a rapid increase in NO concentration early in exhalation (Phases I and II in Figs. 2, 3, 4). Thus the two-compartment model (26) was expanded for tidal breathing to include two airway sections (i.e., a three-compartment model, as shown in Fig. 1B). This advancement is based on data from Tornberg et al. (24, 25), who demonstrated that the mouth and trachea contribute more exhaled NO than the lower airways by analyzing expired air from both tracheotomized and intubated, mechanically ventilated patients. Earlier studies provide further evidence for this representation. Silkoff et al. (21) demonstrated that the trachea and main bronchi contribute up to 50% of the NO appearing in the exhaled breath. In addition, Dubois et al. (5) collected and analyzed volumes of expired air from different regions of the respiratory tract to obtain data consistent with this hypothesis. Thus the local flux per unit volume is expected to be higher in the mouth and trachea than in the lower portion of the airway compartment. Time and volume-weighted averages of Jaw NO are thus defined over the entire airway compartment (volume, Vaw), the upper 10% (volume, VawU, represents the oropharynx and trachea), and lower 90% of the airway compartment (volume, VawL) as aw NO, Jaw NO,U and Jaw NO,L, respectively. Hence, aw NO is analogous to the breath-hold parameter, , and determined from the relationship, aw NO = (VawU Jaw NO,U + VawL Jaw NO,L)/Vaw, where Vaw = VawU + VawL with the constraints, Jaw NO,U 
Jaw NO,L 0. As aw NO 
Jaw NO,U Jaw NO,L, the three-compartment model reduces to the two-compartment model.
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For healthy adult subjects, DawNO 1-10 pl·s-1·ppb-1, and 
pl/s (9, 17, 20, 23). These estimates for DawNO are made either following a 20-s breath hold or during QE <30 ml/s, in which peak NO values exceed 70 ppb (9, 17, 22, 28). For tidal breathing, typical peak values of Cair range from 2 to 20 ppb; hence, in most cases, 
, and 
. Thus expired NO profiles during tidal breathing are insensitive to DawNO, making DawNO very difficult to determine for tidal breathing. Consequently, for this study, Jaw NO is assumed constant with respect to time and independent of Cair during tidal breathing.
For single-breath maneuvers, the alveolar region is approximated as a well-mixed compartment (9, 17, 23, 26). This assumption predicts that the alveolar gas concentration, CA(t), approaches its steady-state value, CANO, for breath-hold times exceeding 10 s. However, for tidal breathing, alveolar gas exchange is characterized by much shorter contact times, and trends in the alveolar plateau are difficult to discern, due to concentration fluctuations. Thus, for tidal breathing, A is defined as the time-weighted average of CA(t), over the interval, 0 < t < tE m (similar to the breath-hold parameter, CANO, but not necessarily reflecting the steady-state concentration), and Cair(t,V = 0) = A for exhalation. In general, estimates of aw NO and A will vary with each tidal breath; however, averaging these estimates over a sequence of tidal breaths will decrease the uncertainty in the parameter estimate (e.g., smaller standard error of the estimate).
Each tidal breath is analyzed independently, and time is reset to zero at the beginning of each exhalation in a sequence of breaths, designating each breath (inhalation followed by exhalation) by the index m (m + 1 corresponds to subsequent inhalation). QI and QE rate profiles are approximated by their time-weighted averages, QI m and QE m, over their respective time intervals, tI m and tE m. With these assumptions, integration of Eq. 1 leads to algebraic expressions for the exhalation profile at the mouth, CM(t) = Cair(t, V = Vaw), on the interval, 0 
t < tEm, expressed in terms of QI m, QE m, tI m, tE m, and the empirical parameters Jaw NO,U, Jaw NO,L, and A (see Eqs. A1-A4 in APPENDIX A). During exhalation, Cs(t) = CM(t - ds 1m). At the onset of subsequent inhalation (tE m < t = tE m + ds 2,m+1), Cs(t) can be expressed in terms of CM by a similar relationship (see APPENDIX A), and the baseline is assumed to be established at the sampling point [Cs(t) = 0] at time t = tE m + ds 2,m+1. Thus numerical integration of Eqs. A5, A6, and A7 [convolution of Cs(t)] yields CI,out(t) as a linear function of Jaw NO,U, Jaw NO,L, and A, in terms of known functions of time and breathing pattern, which are determined numerically, based on the three-compartment lung model.
Alternatively, if CI,out(t) is specified [e.g., the actual observed experimental data, denoted Cobs(t)], then Cs(t) [and ultimately CM(t)] may be determined numerically, independent of the lung model [i.e., deconvolution of Cobs(t)]. Data filtering facilitates both convolution of Cs(t) (to determine Jaw NO,U, Jaw NO,L, and A) and deconvolution of Cobs(t) [to determine Cs(t) and CM(t) directly from the experimental data], as discussed below.
Data filtering. Exhaled NO concentrations are close to the lower detection limit of the chemiluminescent analyzer, and noise introduced during the monitoring process gives rise to signal fluctuations. Criteria for removal of high-frequency noise (low-pass filtering) is based on comparison of tidal breathing signals with the corresponding baseline reading of the instrument (see APPENDIX B). Low-pass filtering involves Gaussian averaging of adjacent concentration "samples" by using the Gabor transform (13), which are applied to both Cobs(t) and the predicted model result at the instrument, CI,out(t), to obtain two transformed signals, obs(t) and I,out(t), respectively (see APPENDIX B). Transformation of both signals ensures a consistent basis for parameter estimation. In addition to parameter estimates, a correction for baseline drift is applied in the fit I,out(t) to obs(t) (the constant B, defined in Eq. B2, equivalent to a high-pass filter correction).
Parameter estimation and statistical analysis. Jaw NO,U, Jaw NO,L, and A are determined by a least squares fit of I,out(t) to obs(t). Time windows of comparison are translated to align obs(t) and I,out(t) with each other, based on the minimum least squared error criterion, and constraints are imposed on all three parameters: Jaw NO,U Jaw NO,L 0, Finally, the average airway flux is computed as aw NO = (VawU Jaw NO,U + VawL Jaw NO,L)/Vaw, and for each subject, the composite average estimates of aw NO and A are reported for a sequence of M tidal breaths with each breath weighted equally (see APPENDIX B). The reported composite uncertainties for aw NO and A are analogous to the standard deviation (i.e., computed at 68.3% confidence intervals, as discussed in APPENDIX B). Finally, to assess the significance of the relationships between parameters characterizing preexpiratory breath hold and tidal breathing, and CANO were correlated as linear functions of the estimates for aw NO and A.
There were three inclusion criteria for a tidal breath to be included in the parameter estimation algorithm. First, any tidal breath exhibiting a peak NO value early in exhalation exceeding 50 ppb was assumed to have overt nasal contamination and was removed from the analysis (denoted as "Nasal" in Table 2) (24, 25). Second, the breathing pattern is characterized by the flow rate ratio, qm = QI m/QE m, breathing frequency, fB m = 1/(tI m + tE m), and A rate, Am = [QE m tE m - Vaw]fB. Only those breaths for which Am > [Vds 1 + Vds 2]fB were analyzed, which requires tidal volume changes to exceed Vaw + Vds 1 + Vds 2, or tE m > Ea m + E ds 1m + E ds 2m in terms of the airway residence times for exhalation, Ea m = Vaw/QE m. This screening criterion ensures that sufficient air from the alveolar region is observed at the instrument to obtain meaningful A estimates (denoted as "Exh. Vol." in Table 2). Third, to ensure no leakage of air from the mouthpiece (or system plumbing), tidal breaths were removed from analysis, if the calculated lung volume at end inspiration or end expiration varied by >20% (denoted as "Leak" in Table 2).
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RESULTS |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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aw NO = 2,500 pl/s (mean value from healthy adult subjects, see below) and Vaw = 200 ml, with flow rates approximated as time-weighted averages (see Fig. 2A), for a typical breathing pattern, corresponding to qm = QI m/QE m = 1.6, fB m =12.8 breaths/min, and Am = 6.7 l/min. Jaw NO,L and A are varied at representative values, with Jaw NO,U = (Vaw aw NO - VawL Jaw NO,L)/VawU. When aw NO = Jaw NO,U = Jaw NO,L = 2,500 pl/s and A =3.2 ppb, theoretical NO concentration profiles for the two-compartment model are obtained at the mouth, CM(t), the sampling point, Cs(t), the analyzer input, CI,in(t), and analyzer output, CI,out(t) (see Fig. 2B). As a result of sampling system dead space, both CI,in(t) and CI,out(t) are delayed, relative to CM(t) and Cs(t). Four phases, corresponding to the observed NO exhalation profiles, CI,out(t), are designated by roman numerals in Fig. 2, B and C. At the beginning of exhalation, NO-free air is present at the NO analyzer, and a baseline response, denoted as phase I, is observed. The time intervals when expired air, originating from the airway and alveolar compartments, is observed are designated as phase II (Eqs. A1 and A2) and phase III (Eq. A3), respectively. At the beginning of subsequent inhalation, residual NO is observed at the sampling point (designated as phase IV) and represents an artifact of the sampling; hence, phase IV is removed before fitting the model [CI,out(t)] to the experimental data [Cobs(t)].
Figure 2C shows CM(t), Cs(t), and CI,out(t) for the three-compartment model (aw NO 
Jaw NO,U > Jaw NO,L), with aw NO = 2,500 pl/s, A = 3.2 ppb, and Jaw NO,L = 1,000 pl/s, which implies Jaw NO,U = 16,000 pl/s (see APPENDIX A). Initially, the three-compartment model predicts a relatively steep phase II slope for CM(t) (corresponding to expired air from the upper airway section), which decreases significantly as air originating from the lower airway section appears at the mouth. Thus, during phase II, CM(t) is described by one- and two-line segments for the two- and three-compartment models, respectively. This results in higher levels of NO for CM(t), Cs(t), and CI,out(t), particularly during phase II.
The impact of the instrument response is minimal [compare CI,in(t) with CI,out(t) in Fig. 2B]. However, substantial signal distortion results from NO transport through the sampling line [compare CM(t) and Cs(t) with CI,in(t) in Fig. 2B]. Under these conditions, although the two-compartment model predicts steep leading phase II peaks for both CM(t) and Cs(t), the expected response, CI,out(t), is flattened considerably and actually exhibits a trailing peak during phase III (see Fig. 2B). Often, this behavior was not observed in the experimental data. The three-compartment model elevates NO levels, during phase II for CM(t) and Cs(t), and during both phase II and the beginning of phase III for CI,out(t) (see Fig. 2C). This effect is most pronounced for relatively small values of A and when Jaw NO,U >> Jaw NO,L. Figure 2, D and E, shows the expected response, CI,out(t), for fixed aw NO = 2,500 pl/s and various values of Jaw NO,U and Jaw NO,L, with A = 3.2 and 1.0 ppb, respectively. The additional degree of freedom provided by two airway sections enhances the three-compartment model's ability to fit experimental data. For example, with aw NO = 2,500 pl/s and A = 1.0 ppb, the three-compartment model predicts a peak concentration of NO in phase II for both Jaw NO,L = 500 and 1,000 pl/s (see Fig. 2E), which was often observed experimentally.
Comparison of predicted and experimental concentration profiles. Figure 3 shows observed and filtered data signals [Cobs(t) and obs(t), respectively], as well as predicted concentration profiles, Cs(t) and I,out(t), for typical individual breaths from subjects 1 and 6. Both examples demonstrate the smoothing achieved by filtering. The remaining fluctuations result from small variations in QE, gas-phase axial diffusion, or other phenomena, which are not included in the model.
Subject 1 (Fig. 3A) exhibits a single flat pulse for Cs(t), and the efficacy of a significant baseline offset correction (nearly 2 ppb) is evident. Negative NO concentrations, resulting from a shift in instrument baseline during the course of an experiment, are compensated by least squares parameter estimation, which computes a constant "offset" for each breath. It would be very difficult to determine meaningful parameter estimates for subject 1 without filtering and including the baseline correction, because observed NO concentration levels are close to the lower detection limits of the instrument. In contrast, for subject 6 (Fig. 3B), the best fit to the data predicts a steep leading phase II peak for Cs(t), which is flattened considerably by NO transport through the sampling line and the instrumentation response characteristics [compare Cs(t) to I,out(t) and obs(t) and also see Fig. 2].
Figure 4 compares concentration profiles at the mouth, CM(t), determined theoretically based on the best fit of the data to the three-compartment model, and also by deconvolution (directly from the experimental data). Five tidal breaths are shown for subjects 1 and 6 (Fig. 4, A and B, respectively), with Cobs(t) included for reference. Both subjects exhibit a leading phase II peak for CM(t) and relatively flat phase III plateaus. Meaningful characterization of the leading phase II peak can only be achieved by assuming a heterogeneous NO production mechanism within the conductive airways, as proposed by the three-compartment model (i.e., Jaw NO,U > Jaw NO,L). Fluctuations, evident during phase III, would be even more prominent if Cobs(t) were not prefiltered.
Parameter estimates from tidal breathing data. For all six subjects, a total of 282 tidal breaths were examined (Table 2). Of these, 68, 24, and 4 breaths were removed due to leakage of air from the mouthpiece, inadequate exhaled volume, or nasal contamination, respectively, as described in METHODS. Thus 186 breaths were analyzed for parametric characterization of NO exchange. Table 2 summarizes the specific data for each subject, including the fB, A rate, and QI/QE. Table 3 summarizes the mean values and uncertainties for the tidal breathing parameters, aw NO and A, as well as the mean breathing patterns for each subject. Clearly, aw NO is determined with reasonable precision (standard deviations range from 15-30% and standard errors from 2.3-7.5%). However, A is less well characterized (standard deviations range from 60-100% and standard errors from 10-24%).
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Comparison of tidal breathing and single-breath parameters. Mean and standard deviations for the flow-independent parameters for the single-breath maneuvers are provided in Table 3. Ranges for standard deviations for and CANO are 14-28 and 24-132% and the range for standard errors are 10-20 and 17-93%, respectively. A plot of aw NO vs. is shown in Fig. 5A and A vs. CANO in Fig. 5B for the six subjects. There is a high degree of correlation (r2 value > 0.95, P value < 0.001) for both pairs of parameters. The slope of aw NO vs. is 3.3 and is statistically >1.0 (line deviates to the left of the 45° line), and the slope for A vs. CANO is 0.45 and is statistically <1.0 (line deviates to the right of the 45° line).
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Comparison of airway and alveolar parameters. A plot of aw NO VS. A from tidal breathing is shown in Fig. 5C for the six subjects and demonstrates a high degree of correlation (r2 value = 0.99, P value < 0.001). However, single-breath parameters from the two-compartment model, and CANO, are also highly correlated (r2 value = 0.89, P value < 0.005, Fig. 5D).
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DISCUSSION |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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aw NO, which is analogous to the previously described , determined from single-breath maneuvers (9, 17, 23, 27). The alveolar region is characterized by a A, which is similar to CANO, determined from single-breath maneuvers. Our results show that aw NO and A are well correlated with and CANO, respectively (see Table 3 and Fig. 5). However, estimates of aw NO are significantly higher than those of , and estimates of A are less than those of CANO. These observations are likely due to altered gas-exchange dynamics in tidal breathing, which exploit simplifications in the lung model. For single-breath maneuvers, such as those used in this study, which utilize a preexpiratory breath hold, accumulation of high-NO levels (>70 ppb) in the airway leads to a marked peak observed at the beginning of exhalation (20, 27). During the breath hold, evidence of heterogeneous production of NO in the airway is mitigated due to axial or longitudinal diffusion, as well as the analysis technique, which considers only the total amount of NO exhaled in phases I and II (27). In contrast, a single tidal breath is completed within a shorter time interval, and much lower levels of NO are present within the airway compartment at the onset of exhalation, which results in a flat exhalation profile. In addition, heterogeneous rates of NO production in the airways become more prominent.
Consistent with this concept is our observation during tidal breathing of NO levels at the beginning of exhalation (phase I) that are higher than those predicted by the two-compartment model. Although low levels of nasal NO may have been present, breaths exhibiting NO concentrations exceeding 50 ppb were assumed to result from overt nasal contamination and were removed from our analysis. Thus, although a small level of nasal contamination cannot be ruled out, a more likely explanation is a higher rate of NO production in the upper airways, as described by other workers (5, 21, 24, 25). Thus the present study partitioned the airway compartment into an upper region (trachea and oropharynx) comprising 10% of the total Vaw, and a lower region comprising the remaining 90% of the Vaw. This representation leads to the three-compartment model (two airway compartments and one alveolar compartment).
We do not explicitly report estimates for Jaw NO,U and Jaw NO,L; however, despite considerable intersubject variation and higher than expected estimates for aw NO, their relative values (i.e., the ratios Jaw NO,U/aw NO and Jaw NO,L/aw NO) are consistent with recently published experimental data for multiple-breath, constant-flow rate maneuvers (24) (data not shown). Further partitioning of the airway compartment is possible and may result in a more accurate prediction of the observed exhaled signal. However, this comes at the cost of additional unknown parameters. Although, based on previous experimental results, partitioning the airway into 10 and 90% fractions is arbitrary. Hence, alternate partitioning into different fractions should also be considered. In either case, the simple three-compartment model is capable of simulating higher NO levels at the beginning of exhalation.
Although the three-compartment model can successfully simulate the shape of experimental NO concentration profiles for tidal breathing, estimates for the volume-weighted NO flux within the airway compartment determined from tidal breathing data (aw NO) are approximately threefold higher than estimates determined from single-breath maneuvers (). In addition, estimates for the A are smaller than those for CANO estimated from the single-breath maneuver. A possible explanation is the impact of axial diffusion of NO, which is neglected in the two- and three-compartment models. During a preexpiratory breath hold, NO excreted within the airway may be transported to the alveolar region by axial diffusion (i.e., "NO losses" to the alveolar compartment), resulting in reduced levels of NO in expired air (18, 29), reduced apparent airway wall flux of NO, and possibly an increase in the CANO. Because axial diffusion is neglected, the two-compartment model may underestimate by two- to fivefold (18, 29). However, tidal breathing allows much less time for axial diffusion to proceed, because inhalation is immediately proceeded by subsequent exhalation. Thus NO losses due to axial diffusion are likely to be significantly lower for tidal breathing than those for preexpiratory breath hold, resulting in a larger predicted airway compartment flux and a smaller alveolar concentration. Although gas flow mixing patterns and velocities differ between tidal breathing and a single-breath maneuver, radial NO transport between the airway wall and the air is tissue-phase limited (26). Thus there are no intrinsic reasons why the airway flux during tidal breathing would be larger than during a single breath, and future studies must consider axial diffusion in lung models as a potentially important mode of transport for NO.
Estimates of aw NO are correlated with those for A (see Fig. 5C), and estimates of are correlated with those for CANO (see Fig. 5D). Thus parameter estimates, corresponding to the conductive airways and alveolar regions, are dependent on each other for both single-breath and tidal-breathing maneuvers. This suggests that airway and alveolar NO are coupled either metabolically (i.e., subjects with higher airway NO production also produce more alveolar NO) or physically through mixing of gas from each compartment. For example, NO produced from the airways is transported to the alveolar region by convection and diffusion; thus a subject with high-airway NO production may artificially increase the alveolar NO concentration, leading to a positive correlation. These hypotheses may be addressed in future work through more advanced modeling (e.g., including axial diffusion) and experimental techniques.
It is clear that the signal-to-noise ratio in exhaled NO during tidal breathing is smaller than during a single-breath maneuver with a preexpiratory breath hold. However, data filtering, combined with analyzing multiple tidal breaths, can offset this disadvantage. Within a single subject, the standard deviation of the airway flux or the alveolar concentration is similar in tidal breathing and a single-breath maneuver (result of data filtering); however, the standard error of the estimate is substantially improved in tidal breathing due to the fact that many tidal breaths are sequentially analyzed (range of 19-52 breaths, mean of 31). In the case of the single-breath maneuver, only three breathing maneuvers are performed. It is also interesting to note that the time to collect 30 tidal breaths is similar to that to collect three single breaths (5 min), yet no specific training or effort on the part of the subject is needed. The drawback of the tidal breathing analysis is the inability to estimate DawNO.
Our sampling system model accounts for important sources of time lags and distortion in tidal breathing, which are inherent to the experimental monitoring system (e.g., instrument response, laminar flow dispersion, transit times in plumbing, etc.). We have also corrected for misalignment of predicted and experimental concentration profiles. However, we have not attempted to optimize the analytic monitoring system. Our results suggest that monitoring system errors (e.g., mouthpiece lags and distortion in the sampling line) may significantly impact the shape of observed tidal breathing concentration profiles, and these errors propagate when multiple breaths are analyzed sequentially. Future investigation should lead to development of techniques for optimization of sampling system instrumentation and thus minimize the impact of systematic errors on experimental measurements.
The analysis of exhaled NO during tidal breathing provides an opportunity to characterize new subject populations who are incapable of performing single-breath maneuvers. Our results provide an initial assessment of tidal breathing to partition exhaled NO into airway and alveolar regions. Our analysis suggests that estimates of aw NO and A can provide region-specific information with improved accuracy (reduced standard error), yet less effort and training needed of the subject relative to the single-breath maneuver with a preexpiratory breath hold. Such information may be useful for detection of inflammatory diseases (e.g., asthma), which are characterized by additional NO production in the lower airways and alveolar region. Thus the assumption, Jaw NO,U > Jaw NO,L, may not hold for certain disease states (12, 21). Our simplified model does not include features such as axial diffusion or flow rate variability, which may be significant sources of error. Thus future work should focus on the development of more rigorous models, which will improve our characterization of NO gas exchange during tidal breathing. In addition, improved analytic instrumentation and implementation of more sophisticated filtering techniques may reduce the signal-to-noise ratio in the observed exhalation profile and thus further enhance parameter estimates. Despite these difficulties, the observation and analysis of multiple tidal breaths allows one to average parameter estimates, which offers a significant advantage relative to single-breath techniques.
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APPENDIX A: PULMONARY AND MONITORING SYSTEM MODELS |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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A, Eq. A1 is integrated to obtain the exhalation profile at the mouth, CM(t) = Cair(t,V = Vaw)
 | (A1) |
 | (A2) |
 | (A3) |
where Ea m = Vaw/QE m and Ea,U m = VawU/QE m are the exhalation residence times of the entire airway and upper 10% of the airways, respectively; Vaw = VawU + VawL; and Vaw aw NO = VawU Jaw NO,U + VawL Jaw NO,L (Jaw NO,U, Jaw NO,L, and A are determined from experimental data). Because this implies that VawU = 0.1 Vaw and VawL = 0.9 Vaw, if any two of the parameters, aw NO, Jaw NO,U, and/or Jaw NO,L, are specified, the third parameter is fixed (i.e., aw NO = 0.1 Jaw NO,U + 0.9 Jaw NO,L). If Jaw NO,U = Jaw NO,L = aw NO, Eqs. A1 and A2 reduce to
 | (A4) |
The response of the mouthpiece assembly dead space is approximated as a plug flow; thus, at the sample point, Cs(t) = CM(t - ds 1m), for 0 < t < tE m. On subsequent inhalation (t > tE m and flow, QI m+1), NO-free air first traverses dead space volume, Vds 2. Thus, if tE m > Ea m + E ds 1m + E ds 2m, Eq. A3 implies Cs(t) = A + aw NO/QE m, for tE m t < tE m + I ds 2,m+1 and Cs (t > tE m + I ds 2,m+1) = 0 (see Fig. 1A).
Expired air, entering the sample line (Vs = 5.5 ml, at Qs = 4.2 ml/s, corresponding to space time, s = Vs/Qs 1.3 s), is maintained at laminar flow. This results in a delayed and distorted input to the analyzer, CI,in(t). Because the length-to-diameter ratio of the sample line is large, this effect is approximated in terms of a convolution integral (3)
 | (A5) |
 | (A6) |
The analyzer's response, CI,out(t), is modeled as a first-order system, characterized by the time constant, A = 90 ms (i.e., 200 ms required to reach 90% of full scale response), which is also a convolution integral (2)
 | (A7) |
With Cs(t) known and CI,in(t) determined from Eqs. A5 and A6, numerical integration of Eq. A7 yields CI,out(t) as the linear function of the model parameters: CI,out(t) = Jaw NO,U G1(t) + Jaw NO,L G2(t) + A G3(t), where G1(t), G2(t), and G3(t) are known (numerically determined) functions of time and breathing pattern. Thus Jaw NO,U, Jaw NO,L, and A are determined by fitting CI,out(t) to Cobs(t). Alternatively, if CI,out(t) is specified, or its equivalent in terms of Cobs(t), then Cs(t) and CM(t) may be determined numerically, independent of the lung model, by deconvolution (analogous to numerical differentiation). Fluctuations in the observed experimental data make direct implementation of either convolution or deconvolution difficult. Fortunately, some of these fluctuations may be filtered from Cobs(t) to facilitate these two techniques (see APPENDIX B).
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APPENDIX B: DATA FILTERING, PARAMETER ESTIMATION, AND UNCERTAINTY ANALYSIS |
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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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obs(t) and I,out(t), respectively
 | (B1) |
 | (B2) |
where 
, 
, s is a scaling facor (s = 0.1-0.3 s, for filtration frequencies of 1-3 Hz, respectively), and B is a correction for baseline drift (i.e., equivalent to a crude high-pass filter correction).
With CI,out(t) determined from Eqs. A1, A2, A3, A5, and A7, Eq. B2 yields
 | (B3) |
where 1(t), 2(t), and 3(t) are known, numerically determined functions of time.
We determine Jaw NO,U, Jaw NO,L, and A by minimizing the least squared error between obs(t) and I,out(t) and translate the time scale of I,out(t) to achieve the best fit, imposing the constraints Jaw NO,U Jaw NO,L 0 and A 0. The overall procedure is illustrated in Fig. 6. Alternatively, numerical deconvolution of Cobs(t) yields Cs(t) and CM(t) directly from the experimental data.
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Uncertainty analysis. We report estimates of aw NO and A for each subject as the average values determined from each sequence of M tidal breaths, and and CANO from single-breath maneuver in triplicate, weighting each breath equally. Composite uncertainties, j (
), are then computed as
 | (B4) |
where 
is the variance of the means from the sequence of M tidal breaths or three single breaths, and jm are the uncertainties of individual tidal breaths or single breaths at 68.3% confidence, based on the t-statistic (14). Thus j is analogous to the standard deviation, but includes allowances for both breath-to-breath variation and individual breath distributions.
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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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TOPABSTRACTGlossaryModifiersMETHODSRESULTSDISCUSSIONAPPENDIX A: PULMONARY AND...APPENDIX B: DATA FILTERING,...REFERENCES |
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; B: 
, where 
is the slope), and for C and D the intercept is a variable. Error bars represent SE of the mean.