INTRODUCTION

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HUMAN EXTERNAL RESPIRATION is a complex process consisting of at least three component parts: 1) ventilation via airways and lung mechanics; 2) perfusion of lung via the pulmonary circulation; and 3) gas exchange based on the transport of species across the alveolar-capillary barrier and the O₂-CO₂ binding properties of blood. Mathematical modeling to date has focused largely on the component parts, i.e., either exclusively on airway mechanics (14, 23, 25, 54), lung mechanics (18, 49, 50-52), gas exchange (22, 27, 34, 35), pulmonary circulation (8, 9, 26), occasionally on the linkage of any two components (17, 29, 43, 46, 56), but never on a treatment involving all elements collectively. This study attempts to describe the three constituent components concurrently, including the inherent coupling between them.

In an effort to characterize the dynamics of the forced vital capacity (FVC) maneuver in normal human subjects, a nonlinear one-compartment mathematical model of respiration combining airway/lung mechanics, pulmonary blood flow, and gas exchange is presented. Measured intrapleural pressure waveforms generated during the execution of the FVC maneuver were used as model input. The FVC maneuver was chosen as the appropriate driving function, since it involves the generation of full muscular effort covering the full range of admissible lung volumes. A nominal set of model parameter values is derived by using information from a variety of sources, including 1) our previous studies of airway mechanics (20, 40), 2) the pulmonary circulation report of Milnor (37), and 3) the pulmonary gas-transport model of Flummerfelt and Crandall (17). A nonlinear least squares estimation algorithm (Marquardt) was employed to adjust a sensitive subset of model parameters to achieve an acceptable fit to measured data. The ventilation and perfusion models are naturally coupled within the gas-transport model. Additional interactions between intrapleural and alveolar pressures and pulmonary blood volume occur during the FVC maneuver. Specifically, this affects the time course of the observed expired gas (O₂ and CO₂) concentration (see RESULTS).

This study aims to 1) describe a methodology for characterizing data collected during the performance of the FVC maneuver, and 2) provide biophysically based explanations of the interactions between ventilation and perfusion and the concomitant effects on gas exchange. A theoretical basis for physiological interpretation of events occurring during the execution of an FVC maneuver is provided. A subset of output variables predicted by the model and compared against data includes changes in lung volume, airflow at the mouth, and the partial pressures of O₂ and CO₂ in the expired gas. The model also yields predictions of quantities not measured routinely, such as 1) alveolar pressure, 2) excursions in airway resistance and lung compliance, 3) gas composition in the airways, 4) blood perfusion rates, and 5) capillary blood volume variation. Direct measurement of these latter quantities cannot be obtained clinically without invasive procedures. The crucial role of component dynamics during the FVC maneuver is analyzed and discussed. Model-based sensitivity analysis reveals that parameters associated with all three of the forenamed respiratory components affect and influence the data. Feasibility and predictive capability are established by characterizing the data collected from four normal subjects.

	METHODS

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Model Development

View larger version (30K): [in this window] [in a new window]   Fig. 1.   Schematic representation of airway/lung mechanics, gas exchange, and pulmonary circulation system. Symbols are explained in Glossary. A: components of airway mechanics, pulmonary circulation, and gas exchange model. B: pneumatic representation of airway/lung mechanics and gas exchange. C: hydraulic representation of pulmonary circulation.

Glossary

CA	Compliance of alveolar compartment, l/cmH2O
Caw(k)i	Concentration of species i in the kth airway compartment, gram-mol/l
Cclp	Compliance of collapsible airway segment, l/cmH2O
Cpc	Compliance of lumped pulmonary capillary region, l/mmHg
Cb(j)i	Total content of gaseous species i in blood in compartment j, ml i/ml blood
	Mean pulmonary capillary compliance during passive breathing, l/mmHg
DLi	Lung diffusing capacity of species i, ml [STPD] · min1 · mmHg1
K1	Linear resistance of upper airways, cmH2O · l1 · s
K2	Flow-dependent resistance of upper airways, cmH2O · l2 · s2
K3	Magnitude of RC at VC = VCmax, cmH2O · l1 · s
Lpc	Length of pulmonary capillary, cm
Nseg	Discretized number of segments in the capillary, 35
Ntot	Total number of gaseous species considered in this study, 3
PAi	Partial pressure of species i in the alveolar space, Torr
PCi	Partial pressure of species i in the collapsible airway, Torr
PDi	Partial pressure of species i in the upper airway (dead space), Torr
Pamsati	Saturated partial pressure of species i in the ambient, Torr
PA	Total pressure in alveolar region, cmH2O
PC	Total pressure in collapsible region, cmH2O
PD	Total pressure in rigid dead space region, cmH2O
PE	Total pressure in the external ambient, cmH2O
Pel	Lung elastic recoil, cmH2O
PelE	Outer envelope of Pel during expiratory phase, cmH2O
PelI	Outer envelope of Pel during inspiratory phase, cmH2O
Pelmax	Pel at VA = V*, cmH2O
PH2O	Partial pressure of water vapor, Torr
Ppl	Intrapleural pressure, cmH2O
Pplmean	Equilibrium intrapleural pressure during tidal breathing, cmH2O
Pplmin	Minimum intrapleural pressure achieved during FVC maneuver, cmH2O
Pplmax	Maximum intrapleural pressure achieved during FVC maneuver, cmH2O
P	Constant characterizing arterial and venous resistance relation to effort (typically, greater than Pplmin), cmH2O
	Spatially averaged intrapleural pressure relative to reference, cmH2O
PS	Standard pressure, 760 mmHg
Ptm	Transmural pressure across collapsible airway, cmH2O
Ptmb	Transmural pressure across pulmonary capillary, cmH2O
Ptmmax	Ptm at VC = VCmax, cmH2O
Pa	Total pressure in pulmonary artery (and arterioles), Torr
Pb(j)i	Partial pressure of species i in blood in segment j, Torr
Ppc	Total pressure in pulmonary capillary, Torr
Pv	Total pressure in pulmonary veins (and venules), Torr
Ppa	Transmural pulmonary arterial pressure relative to Torr
Ppv	Transmural pulmonary venous pressure relative to Torr
Pref	Reference pressure at Tbody, Torr
PEO2	Partial pressure of O2 in expired gas at mouth, Torr
PECO2	Partial pressure of CO2 in expired gas at mouth, Torr
CA	Airflow rate between the collapsible airway and alveolar space, l/s
DC	Airflow rate between the dead space and collapsible airways, l/s
ED	Airflow rate in the upper airways, l/s
	Blood flow rate into pulmonary capillary, l/s
	Blood flow rate out of pulmonary capillary, l/s
RC	Collapsible airway resistance, cmH2O · l1 · s
RL, ti	Pulmonary tissue resistance, cmH2O · l1 · s
Rs	Small airway resistance, cmH2O · l1 · s
Rsa	Parameter characterizing curvature of Rs
Rsc	Rs at V*, cmH2O · l1 · s
Rsc max	Rsc at the instant of Ppl = Pplmax (>0), cmH2O · l1 · s
Rsm	Magnitude of (Rs  Rsc) at minimal alveolar volume, cmH2O · l1 · s
Ruaw	Upper airway resistance, cmH2O · l1 · s
Ra	Pulmonary arterial (and arteriolar) resistance, mmHg · l1 · s
Ra0	Approximately mean Ra during passive breathing, mmHg · l1 · s
Rpc	Pulmonary capillary resistance, mmHg · l1 · s
Rpc0	Magnitude of Rpc at Vpc = Vpcmax, mmHg · l1 · s
Rv	Pulmonary venous (and venuolar) resistance, mmHg · l1 · s
Rv0	Approximately mean Rv during passive breathing, mmHg· l1 · s
Tbody	Body temperature, 310 K
Tam	Ambient temperature, 298 K
TS	Standard temperature, 273 K
V*	Alveolar volume at end inspiration, assuming that  = Pplmin at all times during forced inspiration, liters
Ao	Airflow rate at the mouth detected by pneumotachometry, l/s
VA	Alveolar volume, liters
Vpc	Pulmonary capillary volume, liters
Vpcmax	Maximum pulmonary capillary volume, liters
VC	Collapsible airway volume, liters
VCmax	Maximum collapsible airway volume, liters
VD	Anatomic dead space volume, liters
VL	Total lung volume (=VA + VC + VD), liters
Vcrit	Lung volume at which Rs increases abruptly during forced expiration, liters
V	Parameter characterizing volume dependence of Ra and Rv, cmH2O · l5 · s
V(j)zb	Mean molar-averaged axial velocity of blood flow in capillary segment j, l/s
i	Rate of transfer of species i between blood and alveolar region, ml (STPD) i/min
tot*	Total rate of transfer of all species, ml (STPD)/min
A	Overall density of air in alveolar region, g/l
C	Overall density of air in collapsible airway region, g/l
D	Overall density of air in dead space region, g/l
ref	Overall density of air in ambient under reference conditions, g/l
	Scale factor used to create inspiratory Pel for each subject

Airway/lung mechanics model. The general form is similar to that previously reported (20, 40). A brief review of the model with incorporated modifications is provided below.

Pulmonary circulation model. The pulmonary capillaries were considered as a single tubular compartment of constant length of 0.05 cm (17) and a variable volume. The lumped pulmonary circulation model developed (Fig. 1C ) was based on the following assumptions. 1) Upstream pulmonary arterial pressure (Ppa) and downstream pulmonary venous pressure (Ppv) were assumed to be constant at 15 and 5 Torr, respectively, referenced to intrapleural pressure (26, 58). 2) Pulmonary vascular resistance was partitioned into three components: a proximal, precapillary arteriolar resistance (Ra); a pulmonary capillary resistance (Rpc); and a distal, postcapillary venous resistance (Rv). Perivascular pressure was assumed to be intrapleural pressure for the proximal and distal (extra-alveolar vessels) but alveolar pressure for the capillary (intra-alveolar vessel). The proximal and distal resistances were assumed to be inversely proportional to VA but proportional to the pleural pressure (15, 21), whereas the capillary resistance was presumed to be affected solely by alveolar pressure (37). Blood flow rate into and out of the capillary and respectively) was then governed by the nodal pressure drops (Pa, Ppc and Pv) developed across the corresponding vascular resistances. Consequently, capillary blood volume (Vpc) was modulated by the inequality between blood inflow and outflow and the transmural pressure across the lumped capillary wall.

Gas exchange model. Gas exchange occurring in the constant-volume dead space and variable-volume collapsible and alveolar compartments was described by using species-conservation laws. On the air side of the exchanger, it was assumed that inspired air was instantaneously warmed to body temperature and fully saturated with water vapor. The gaseous mixture was presumed to obey the ideal gas law. On the blood side, the discrete constituents (plasma and erythrocytes) were lumped together and assumed to statistically behave as a uniform, homogeneous phase (3). Within a control volume, the instantaneous specific reactions were then considered to be at equilibrium; relationship between species content and their corresponding equilibrium partial pressures was consequently represented by empirical dissociation curves (12, 28, 48). One-dimensional axial convection provided the sole means for bulk transport of blood and movement of species along the pulmonary circulation; diffusion in the radial and axial directions was ignored. Two-phase flow created due to blood heterogeneity was further disregarded. Transport of gaseous species across the alveolar-capillary membrane, assumed to be solely by diffusion, was characterized by a lumped species lung diffusing capacity (DL_i), which accounted for the total diffusion-resistive path taken by species i (i = O₂, CO₂, N₂) as it diffused across the alveolar-capillary barrier. O₂ was taken up by the blood, and CO₂ was excreted, whereas N₂ (a relatively inert gas) diffused in either direction, depending on the instantaneous overall ventilation-perfusion ratio (39). The contribution of the physiological shunt (35) was neglected. The model used here was directly adapted from Flummerfelt and Crandall (17), with the provision that alveolar pressure was not held atmospheric but, rather, was calculated via the airway mechanics model.

Experimental Pulmonary Measurements

Each experimental episode was recorded after the subject rested adequately (for ~5 min) and followed by several cycles of tidal breathing to ensure full recovery. The end-tidal gas composition was monitored to ensure that the CO₂ level reached 39-40 Torr. When this level was achieved, it was assumed that a steady-state condition had been reached and that the mixed venous blood tension achieved constant nominal values consistent with those commonly reported (59). The duration of the recording episode was <1 min; hence, it was presumed that the mixed venous composition did not change significantly during this time. This seemingly reasonable modeling assumption does require experimental verification, however. Within the noninvasive constraints observed in the pulmonary function laboratory (except for the use of a nasogastric esophageal balloon), it is unlikely that such a measurement could be adopted easily. Four volunteer human subjects with normal lung function (i.e., no respiratory abnormalities) were recruited for this study. Their particulars are listed in Table 1.

Computational Aspects

4

3

View larger version (40K): [in this window] [in a new window]   Fig. 2.   Block diagram of simulation implementation. Intrapleural pressure is input to both the actual system and the mathematical model. Measured output variables are compared off-line against corresponding prediction. A nonlinear least square parameter-estimation algorithm is utilized to modify and estimate model parameter values to minimize discrepancy between measurements and the corresponding model predictions during forced vital capacity (FVC) maneuver.  denotes the Levenburg adjustment parameter. See Glossary for other definitions.

Parameter Estimation

For practical reasons, it was necessary to have good nominal values for parameters to ensure convergence of the estimation algorithm. Initial simulations employing parameter values from previous studies (see introductory section) provided initial fits. Further manual adjustment yielded even better fits to the data, ultimately leading to a nominal set of model parameters that was used to initialize the Marquardt scheme (30). The adjustable parameters were chosen based on their known influence on portions of the maximum flow-volume curve associated with the FVC maneuver, as well as parameter variation checks performed in a separate study (not presented here), by using relative sensitivity coefficients to assess the sensitivity of flow and volume to these variations. The estimation algorithm was terminated when the maximum relative change in the adjustable parameters did not exceed 1% on subsequent iterative cycles.

	RESULTS

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Model predictions compared against data for a human subject performing an FVC maneuver are shown in Fig. 3. The last cycle of tidal breathing before the subject exhaled to RV prior to the onset of the FVC maneuver is also shown for reference. Note that the major features of the loop predicted by the model (depicted by solid lines in Fig. 3), such as peak inspiratory flow, initial expiratory upstroke slope, peak expiratory flow, and final expiratory slope, all agree reasonably well with the experimental data.

View larger version (29K): [in this window] [in a new window]   Fig. 3.   Vital capacity maneuver. Model predictions are denoted by solid lines, and the measured data are represented as dots. In B-F, vertical dashed lines (from left to right, marked as e, i, e*, respectively) mark the transition to residual volume (RV), inspiration from RV to total lung capacity (TLC) with full effort, and forced expiration from TLC to RV during FVC. A: plot of maximal flow-volume loop for a subject. B: intrapleural pressure generated by the subject during FVC maneuver. C: alveolar pressure developed. D: flow at mouth. E: lung volume variation from RV. F: collapsible segment volume. See Glossary for other definitions.

Airway Mechanics

Pulmonary Circulation

View larger version (26K): [in this window] [in a new window]   Fig. 4.   Pulmonary circulation description during vital capacity maneuver. Vertical dashed lines in all panels are as defined in Fig. 3. A: nodal pressures (referenced to and transmural pressure (Ptmb) across lumped capillary. B: pulmonary arterial (Ra), capillary (Rpc), and venous (Rv) resistances. C: inlet and outlet blood flow rates through capillary. D: capillary blood volume excursion. E: lumped capillary compliance. See Glossary for other symbol definitions.

In the early part of the expiratory phase (t  e*), Ppc' is low, which causes a greater inlet blood flow compared with outflow; the capillary refills quickly to recover its blood volume lost earlier. As expiration proceeds, however, decreasing VA increases Ra and Rv, which (despite lowered Rpc) lowers the blood flow rates. Inlet and outlet blood flow rates closely match one another, thereby minimizing variation in Vpc toward the end of the FVC maneuver. Capillary blood volume is also constrained to not exceed Vpc_max. The variation in the instantaneous capillary compliance (Cpc) resulting from the nonlinear (sigmoidal-like) shape of the Ptm_b vs. Vpc curve is shown in Fig. 4E. Also note the slight backflow in and in the brief instances when Ppc   either exceeds Ppa (zone-1-like behavior) or is lower than Ppv (zone-3-like behavior), respectively, during the transition from inspiration to expiration.

Resistive and Compliant Properties

View larger version (32K): [in this window] [in a new window]   Fig. 5.   Description of lung and airway characteristics obtained from parameter estimation for subject 1. Dashed-dotted lines corresponds to the episode when subject expired to RV before executing FVC maneuver. Solid line corresponds to when subject executed the FVC maneuver from RV to TLC back to RV. A: static lung elastic recoil characteristic. B: compliance characteristic of the collapsible airway. C: pulmonary capillary compliance characteristic. Note the tapering at higher positive transmural pressures. D: excursion in small airway resistance. Note the difference in behavior during positive (forced expiration) and negative (inspiration) efforts. E: resistance variation in collapsible airways. F: excursion in pulmonary capillary resistance. G: pulmonary arterial and venous resistances. Resistance offered by the capillary region is much greater than that offered by the extra-alveolar arterial and venous resistances. Note the hysteretic behavior exhibited by all the resistances. See Glossary for symbol definitions.

The effect of VA on Rs is shown in Fig. 5D, where the lower curve is traced during inspiration and the upper curve during active expiration (with positive The transition point in the Rs curve during expiration where the slope changes corresponds to a critical volume (V_crit; assumed to be 70-80% of FVC), below which the caliber of the peripheral airways is considered to be sensitive to the surrounding positive intrapleural pressure during forced expiration (Fig. 5D ). Incorporation of this property is purely a modeling construct, necessary to produce the strong concavity observed in the flow-volume loop following peak expiratory flow (e.g., see Figs. 3A, 8A-C, and 10A ). RC is similarly described by two curves, traversed differently on inspiration and expiration (Fig. 5E ). The model-predicted excursions in Rpc, Ra, and Rv shown in Fig. 5, F and G, agree qualitatively with trends reported in Ref. 37. Clearly, pulmonary vasculature is dominated by transmural effects due to changes in alveolar pressure and the capillary resistance during the FVC maneuver.

Isovolume Pressure-Flow (IVPF) Description

View larger version (15K): [in this window] [in a new window]   Fig. 6.   Isovolume pressure-flow relationship evaluated for subject 1. Various levels of expiratory effort were simulated by scaling expiratory intrapleural pressure waveform. Symbols denote simulation results, whereas dashed line was manually traced. VC, vital capacity.

Effect of Perfusion on Gas Exchange

View larger version (24K): [in this window] [in a new window]   Fig. 7.   Effect of changing perfusion rate on expired PO2 and PCO2 in expired gas at mouth during FVC maneuver for subject 1. The same corresponding to the reference case (see Fig. 3B ) was used for all cases presented here. A similar qualitative effect is observed for other subjects (results not shown). A: effect on expired O2. B: effect on expired CO2. See Glossary for symbol definitions.

Intersubject Variability

1

View larger version (29K): [in this window] [in a new window]   Fig. 8.   Comparison of model prediction against data for the VC maneuver performed by 3 other volunteer subjects, provided for reference. Note that volumes are normalized with respect to body surface area (BSA). A: flow-volume loops. B: time course of expired PO2. C: time course of expired PCO2. See Glossary for symbol definitions.

Model-generated spirogram indexes for all four subjects compared against data are depicted in Table 3, again indicating a reasonable agreement for all the subjects and further demonstrating the good fits achieved for the flow-volume loops in general.

Component Resistances

View larger version (32K): [in this window] [in a new window]   Fig. 9.   Contribution of component resistances for the FVC maneuver for all volunteer subjects (A-D ). Differences in type of effort generated are reflected in variation in in the 4 subjects. Note that RC dominates beyond peak expiratory flow, whereas effects of Rs are increasingly apparent only at low lung volumes. Upper airway resistance contributes only to peak expiratory flow. Vcrit occurs toward early part of the forced expiratory phase in all subjects. See Glossary for symbol definitions.

Sensitivity Analysis

In general, an increase in airway resistance tends to lower peak flow rates as well as impede airflow into and out of the alveolar compartment. The effects are more pronounced during expiration because of the greater magnitude of resistance encountered and are reflected in the expiratory portion of the flow-volume loop. Slower deflation of the lung assists in maintaining lower vascular resistances and increases perfusion, albeit to a very small extent. Because expiration is forceful in this maneuver, the contents of the alveolar compartment are quickly emptied out. Alveolar composition is not significantly affected, thereby resulting in no marked differences in O₂ and CO₂ composition observed at the end of the FVC maneuver. This is unlike during tidal breathing when decrease in the upstroke slope leads to lower end-tidal CO₂ composition. During forced expiration, these small differences are, in general, attenuated, and insignificant effects on expired-gas tracings are observed.

In contrast, alterations in alveolar compliance result in marked variation in resulting lung volume changes for the same intrapleural pressure variation. This causes marked changes in alveolar composition and is reflected in the final levels of gas composition observed in the expired gas. Alveolar composition is dictated by the extent of gas exchange occurring across the alveolar-capillary membrane and is mainly governed by the ratio of perfusion to ventilation. Changes in parameters describing pulmonary circulation cause alterations in perfusion rates which, in turn, modify gas-exchange rates, alter alveolar composition, and significantly affect the time course of the expired-gas composition.

A more detailed sensitivity analysis is conducted by altering the functional descriptors for the resistances and compliances. A summary of the qualitative effects of the individual component parameters and the resulting correlation between model parameters and property attributes of the physiological variables is provided in Table 4. This is useful in eliciting mechanistic insight into resulting system behavior. Detailed illustrations for a sample subset of the parameters listed in Table 4 are depicted in Figs. 10 and 11.

View larger version (27K): [in this window] [in a new window]   Fig. 10.   Effect of airway mechanics parameters during FVC. Parameters describing subject 1 were used as baseline for all cases. For each scenario, only 1 of parameters was modified while all others were unchanged. Same driving intrapleural pressure (shown in Fig. 3B ) was used in all cases. A and C: effect on flow-volume loop. B and D: effect on PCO2 at the mouth during forced expiration. See Glossary for symbol definitions.

View larger version (30K): [in this window] [in a new window]   Fig. 11.   Effect of modifying vascular parameters during FVC. Parameters describing subject 1 were used as baseline for all cases. For each scenario, only 1 of parameters was modified while all others were maintained unchanged. Same driving intrapleural pressure (shown in Fig. 3B ) was used in all cases. A and D: effect on inlet blood flow rate. B and E: effect on outlet blood flow rate. C and F: effect on PCO2 at the mouth during forced expiration. See Glossary for symbol definitions.

Effect of airway mechanics parameters. SMALL AIRWAY RESISTANCE. Obstructed small airways exaggerate the concavity of the MEFV curve. This is illustrated by adjusting a couple of model construct parameters describing Rs.

Effect of vascular parameters. The effect of modifying selected parameters describing the pulmonary vasculature during the FVC is shown in Fig. 11. The flow-volume loop was not affected by the perturbation of the vascular parameters. The control case is depicted by the solid line in Fig. 11. A decrease in the vascular resistances [simulated by setting either Ra₀ (in Eq. 15A,c), Rv₀ (in Eq. 15A,d ), or Rpc₀ (in Eq. 15A,e) to 50% of baseline] increases the inlet (Fig. 11, A and D ) and outlet (Figs. 11, B and E ) blood flow rates. This causes a higher CO₂ transfer to the alveolar space and results in higher values of end-expiratory PE_CO2 (Fig. 11, C and F ). Because Rpc dominates vascular resistance, reduction of this resistance greatly affects blood flow rates. The coupling between the alveolar volume and extra-alveolar resistances at lower lung volume was investigated through variation of the nominal parameter V (Eqs. 15A,c and 15A,d ). A reduction in V to one-half of its nominal value effectively reduces Ra and Rv, thereby resulting in increased blood flow rates.

Regional parameter sensitivity. The comparative effects of the sensitive model parameters can be localized to specific regions in the flow-volume loop and expired-gas concentration temporal profiles and are schematically depicted in Fig. 12. Regions of the flow-volume loop influenced by the particular parameter during the inspiratory and expiratory phases are shown in Fig. 12A. RC has a dominant effect during most of the FVC maneuver, whereas Rs effects (via model parameters Rs_m and Rs_a) are more evident at lower lung volumes. The drop in airflow following expiration is mainly dictated by V_crit and Rs_{c max} (parameters that affect Rs). Ruaw strongly influences peak inspiratory and expiratory flow rates as well as the initial upstroke in forced expiration. Parameters describing compliance of the collapsible segment (Ptm_max and VC_max) and the alveolar region ( and V*) affect the inspiratory phase. Effects of parameteric changes on the flow-volume loop are also reflected in the expired-gas composition profile, as shown in Fig. 10, B and D.

View larger version (28K): [in this window] [in a new window]   Fig. 12.   Schematic representation of localization of contribution of model parameters to flow-volume loop and FVC capnogram (expired PCO2 in expired gas at mouth during FVC maneuver). A: effect on flow-volume loop. B: effect on expired CO2 waveform at mouth. See Glossary for symbol definitions.

	DISCUSSION

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To develop a mathematical model that emulates the functional behavior of the respiratory system, it is essential to characterize the airways and lung and alveolar-capillary gas transport. The lumped model presented consists of nonlinear resistive-compliant airway and alveolar compartments interacting with pulmonary vascular compartments. Measured pleural pressure was used to drive the model, and a nonlinear parameter-estimation scheme was employed to identify model parameters that yielded good agreement between model predictions and experimental data. The FVC maneuver was chosen to illustrate the excursion over the full range of permissible lung volumes. After the system under the vital capacity maneuver has been identified, it should be possible to predict its behavior during other breathing maneuvers, i.e., tidal breathing and panting, holding the parameter set unchanged (not shown here).

Airway/Lung Mechanics

To obtain concavity of the flow-volume loop past peak expiratory flow, it was necessary to incorporate two parameters, V_crit and Rs_{c max}, which describe the abrupt increase in Rs due to the effects of positive (Fig. 5D ). V_crit corresponds to a critical lung volume below which this effect is apparent. The increase in magnitude in Rs when lung volume equals V_crit is then c