Effects of lung inflation on pulmonary arterial blood volume in intact dogs.

The isolated effects of alterations of lung inflation and transmural pulmonary arterial pressure (pressure difference between intravascular and pleural pressure) on pulmonary arterial blood volume (Vpa) were investigated in anesthetized intact dogs. Using transvenous phrenic nerve stimulation, changes in transmural pulmonary arterial pressure (Ptm) at a fixed transpulmonary pressure (Ptp) were produced by the Mueller maneuver, and increases in Ptp at relatively constant Ptm by a quasi-Valsalva maneuver. Also, both Ptm and Ptp were allowed to change during open airway lung inflation. Vpa was determined during these three maneuvers by multiplying pulmonary blood flow by pulmonary arterial mean transit time obtained by an ether plethysmographic method. During open airway lung inflation, mean (plus or minus SD) Ptp increased by 7.2 (plus or minus 3.7) cmH2O and Ptm by 4.3 (plus or minus 3.4) cmH2O for a mean increase in Vpa by 26.2 (plus or minus 10.7) ml. A pulmonary arterial compliance term (Delta Vpa/Delta Ptm) calculated from the Mueller maneuver was 3.9 ml/cmH2O and an interdependence term (Delta Vpa/Delta Ptp) calculated from the quasi-Valsalva maneuver was 2.5 ml/cmH2O for a 19% increase in lung volume, and 1.2 ml/cmH2O for an increase in lung volume from 19% to 35%. These findings indicate that in normal anesthetized dogs near FRC for a given change in Ptp and Ptm the latter results in a greater increase of Vpa.     

Characteristics of the upper airway pressure-flow relationship during sleep

In examining the mechanical properties of the respiratory system during sleep in healthy humans, we observed that the inspiratory pressure-flow relationship of the upper airway was often flow limited and too curvilinear to be predicted by the Rohrer equation. The purposes of this study were 1) to describe a mathematical model that would better define the inspiratory pressure-flow relationship of the upper airway during sleep and 2) to identify the segment of airway responsible for the sleep-related flow limitation. We measured nasal and total supralaryngeal pressure and flow during wakefulness and stage 2 sleep in five healthy male subjects lying supine. A right rectangular hyperbolic equation, V = (alpha P)/(beta + P), where V is flow, P is pressure, alpha is an asymptote for peak flow, and beta is pressure at a flow of alpha/2, was used in its linear form, P/V = (beta/alpha) + (P/alpha). The goodness of fit of the new equation was compared with that for the linearized Rohrer equation P/V = K1 + K2V. During wakefulness the fit of the hyperbolic equation to the actual pressure-flow data was equivalent to or significantly better than that for the Rohrer equation. During sleep the fit of the hyperbolic equation was superior to that for the Rohrer equation. For the whole supralaryngeal airway during sleep, the correlation coefficient for the hyperbolic equation was 0.90 +/- 0.50, and for the Rohrer equation it was 0.49 +/- 0.25. The flow-limiting segment was located within the pharyngeal airway, not in the nose.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effect of intravenous papain on tracheal pressure-volume curves in rabbits

To investigate the effects of airway cartilage softening on tracheal mechanics, pressure-volume (PV) curves of excised tracheas were studied in 12 rabbits treated with 100 mg/kg iv papain, whereas 14 control animals received no pretreatment. The animals were killed 24 h after the injection and the excised specimens studied 24 h later. Treated tracheas exhibited decreased ability to withstand negative transmural pressures, reflected in increased collapse compliance: 6.2 +/- 2.1 vs. 2.0 +/- 0.5% peak volume (Vmax)/cmH2O means +/- SD, P less than 0.001, (Vmax = extrapolated maximal tracheal volume), increased kc (exponential constant that reflects the shape of collapse limb of the PV curve): 0.244 +/- 0.077 vs. 0.065 +/- 0.015 (P less than 0.001). The distension limb of the PV curve greater than 2.5 cmH2O transmural pressure (Ptm) was no different. Compliance between 0 and 2.5 cmH2O Ptm was increased in papain-treated rabbits: 4.97 +/- 1.73 vs. 2.30 +/- 0.31% Vmax/cmH2O (P less than 0.001). Tracheal volume, and therefore mean diameter, was decreased at 0 Ptm: 2.7 +/- 0.26 vs. 3.2 +/- 0.27 mm (P less than 0.001). We conclude that airway cartilage softening increases the compliance of the trachea at pressures less than 2.5 cmH2O Ptm.     

Airway dynamics in transition between peak and maximal expiratory flow

Expiratory flow-volume curves with periodic interruption of flow showed flow transients exceeding maximal flow (Vmax) measured on the maximum expiratory flow-volume (MEFV) curve in a mechanical lung model and in five tracheotomized, vagotomized, open-chest, anesthetized dogs. Direct measurement of flow from the collapsing model airway showed that the volume of the flow transients in excess of the MEFV envelope was greater than that from the collapsing airway. Determination of wave-speed flows from local airway transmural pressure-area curves (J. Appl. Physiol. 52: 357-369, 1982) and photography of the airway led to the following conclusions. Flow transients exceeding Vmax are wave-speed flows determined by an initial and unstable configuration of the flow-limiting segment (FLS) with maximum compression in the midportion. The drop in flow from the peak to the following plateau is due to development of a more stable airway configuration with maximum compression at the mouthward end with a smaller area and a smaller maximal flow. When FLS jumps to a more peripheral position, the more distal airways may pass through similar configurational changes that are responsible for the sudden decrease of flow (the "knee") seen on most MEFV curves from dogs.     

Interdependent regional lung emptying during forced expiration: a transistor model

We recognized similarities between isovolume pressure-flow curves of the lung and emitter-collector voltage-current characteristics of bipolar transistors, and used this analogy to model expiratory flow limitation in a two-generation branching network with parallel nonhomogeneity. In this model, each of two bronchi empty parenchymal compliances through a common trachea, and each branch includes resistances upstream and downstream of a flow-limiting site. Properties of each airway are specified independently, allowing simulation of differences between the tracheal and bronchial generations and between the parallel bronchial paths. Simulations of four types of parallel asymmetry were performed: unilateral peripheral bronchoconstriction; unilateral central bronchoconstriction; asymmetric redistribution of parenchymal compliance; and unilateral alteration of the bronchial area-transmural pressure characteristic. Our results indicate that multiple axial choke points can exist simultaneously in a symmetric lung when large airway opening-pleural pressure gradients exist; despite severe nonhomogeneity of regional lung emptying, flow interdependence among parallel branches tends to maintain a near normal configuration of the overall maximal expiratory flow-volume (MEFV) curve throughout a large fraction of the vital capacity; and sudden changes of slope of the MEFV curve ("knees" or "bumps") may reflect choking in one branch in a nonuniform lung, but need not be obvious even when severe heterogeneity of lung emptying exists.     

Noninvasive estimation of pharyngeal airway resistance and compliance in children based on volume-gated dynamic MRI and computational fluid dynamics

Computational fluid dynamics (CFD) analysis was used to model the effect of collapsing airway geometry on internal pressure and velocity in the pharyngeal airway of three sedated children with obstructive sleep apnea syndrome (OSAS) and three control subjects. Model geometry was reconstructed from volume-gated magnetic resonance images during normal tidal breathing at 10 increments of tidal volume through the respiratory cycle. Each geometry was meshed with an unstructured grid and solved using a low-Reynolds number k-ω turbulence model driven by flow data averaged over 12 consecutive breathing cycles. Combining gated imaging with CFD modeling created a dynamic three-dimensional view of airway anatomy and mechanics, including the evolution of airway collapse and flow resistance and estimates of the local effective compliance. The upper airways of subjects with OSAS were generally much more compliant during tidal breathing. Compliance curves (pressure vs. cross-section area), derived for different locations along the airway, quantified local differences along the pharynx and between OSAS subjects. In one subject, the distal oropharynx was more compliant than the nasopharynx (1.028 vs. 0.450 mm(2)/Pa) and had a lower theoretical limiting flow rate, confirming the distal oropharynx as the flow-limiting segment of the airway in this subject. Another subject had a more compliant nasopharynx (0.053 mm(2)/Pa) during inspiration and apparent stiffening of the distal oropharynx (C = 0.0058 mm(2)/Pa), and the theoretical limiting flow rate indicated the nasopharynx as the flow-limiting segment. This new method may help to differentiate anatomical and functional factors in airway collapse.     

In vivo estimation of tracheal distensibility and hysteresis in normal adults

We used the acoustic reflection technique to measure the cross-sectional area of tracheal and bronchial airway segments of eight healthy adults. We measured airway area during a slow continuous expiration from total lung capacity (TLC) to residual volume (RV) and during inspiration back to TLC. Lung volume and esophageal pressure were monitored continuously during this quasi-static, double vital capacity maneuver. We found that 1) the area of tracheal and bronchial segments increases with increasing lung volume and transpulmonary pressure, 2) the trachea and bronchi exhibit a variable degree of hysteresis, which may be greater or less than that of the lung parenchyma, 3) extrathoracic and intrathoracic tracheal segments behaved as if they were subjected to similar transmural pressure and had similar elastic properties, and 4) specific compliance (means +/- SE) for the intrathoracic and bronchial segments, calculated with the assumption that transmural pressure is equal to the transpulmonary pressure, was significantly (P less than 0.05) smaller for the intrathoracic segment than for the bronchial segment: (2.1 +/- 2.0) X 10(-3) cmH2O-1 vs. (9.1 +/- 2.1) X 10(-3) cmH2O-1. Direct measurements of airway area using acoustic reflections are in good agreement with previous estimates of airway distensibility in vivo, obtained by radiography or endoscopy.     

Modeling expiratory flow from excised tracheal tube laws.

Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area (A(tr)) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. A(tr) was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126-147, 1977) for elastic tubes: Ptm = K(p) [(A(tr)/A(tr0))(-n) - 1], where A(tr0) is A(tr) at Ptm = 0 and K(p) is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.     

Mechanical properties of porcine intralobar pulmonary arteries

The isobaric and isovolumetric properties of intrapulmonary arteries were evaluated by placing a highly compliant balloon inside arterial segments. The passive pressure-volume (P-V) curve was obtained by changing volume (0.004 ml/s) and measuring pressure. The isobaric active volume change (delta V) or isovolumetric active pressure change (delta P) generated by submaximal histamine was measured at four different transmural pressures (Ptm's) reached by balloon inflation. The maximal delta P = 11.2 +/- 0.6 cmH2O (mean +/- SE) was achieved at 30.8 +/- 1.2 cmH2O Ptm and maximal delta V = 0.20 +/- 0.02 ml at 16.7 +/- 1.7 cmH2O Ptm. The P-V relationships were similar when volume was increased after either isobaric or isovolumetric contraction. The calculated length-tension (L-T) relationship showed that the active tension curve was relatively flat and that the passive tension at the optimal length was 149 +/- 11% of maximal active tension. These data show that 1) a large elastic component operates in parallel with the smooth muscle in intralobar pulmonary arteries, and 2) the change in resistance associated with vascular expansion of the proximal arteries is independent of the type of contraction that occurs in the more distal arterial segments.     

Aerosol deposition and flow limitation in a compliant tube

Studies in intact dogs have suggested that aerosol deposition is enhanced in the proximity of a flow-limiting segment (FLS) formed during cough. The mechanism for that observation was investigated using a monodisperse (geometric SD less than or equal to 1.15) fluorescent aerosol produced in a condensation generator. The aerosol was passed through a compliant tube (Penrose) that had been mounted vertically in a two-chamber box. The surrounding pressure (Ps) in the upstream chamber was controlled independent of the surrounding pressure in the downstream chamber, thus allowing development of an FLS near the exit of the upstream chamber. At fixed inlet pressure (P1) and Ps, flow limitation was achieved over a range of 0.1-0.5 l X s-1 by lowering downstream pressure alone (P2). The influence of the FLS cross-sectional geometry on the site of peak deposition was examined because area of an FLS is a function of transmural pressure (Ptm = Px - Ps). For those constriction geometries that did not involve opposing wall contact, the deposition distribution was characterized by a single peak immediately downstream of the constriction. In the most compressed geometries the peak in deposition was diminished and shifted further downstream. Total aerosol deposition was found to be characterized by a dimensionless particle inertia parameter formed as the ratio of particle stopping distance and the minor radius of the elliptical tube cross section. The deposition of small particles with an inertial parameter less than 0.01 was found to be independent of geometry and constriction velocity.(ABSTRACT TRUNCATED AT 250 WORDS)     

Analysis of tracheal mechanics and applications.

We have developed a mathematical model for a tracheal ring that consists of a "horseshoe" of cartilage with its tips joined by a membrane. The ring is subjected to a uniform transmural pressure (Ptm) difference. The model was used to calculate the cross-sectional area (A) of the trachea. Whereas the mechanics of the deformation of the cartilage were analyzed using elastica theory, the posterior membrane was treated as a simple membrane that is inextensible under changes in Ptm. The membrane can be specified to be of any length less than baseline and thus can represent a posterior membrane under tension. The cartilage can have specifiable nonuniform unstressed curvature as well as nonuniform bending stiffness. We have investigated the effect on the tracheal A-Ptm curve of posterior membrane length and tensile force in the membrane, cartilage shape and elasticity, and localized weakening of the cartilage. The model predictions are in good agreement with magnetic resonance imaging data from rabbit tracheas and show that the shape of the horseshoe as well as the posterior membrane force are important determinants of tracheal compliance.     

Airway pressure-volume curve estimated by flow interruption during forced expiration

We attempted to estimate the pressure-volume characteristics of airways downstream from the choke point when the airflow was abruptly interrupted during forced expiration. The change of gas volume of the downstream segment after interruption could be estimated by multiplying the maximum flow (Vmax) immediately before interruption by the interruption time because the Vmax is maintained for a short period after airflow interruption at the mouth, as described in our previous report (J. Appl. Physiol. 66: 509-517, 1989). For the pressure of the downstream segment, we used the mouth pressure itself. Airway compliance, a slope of the pressure-volume curve, was measured in an airway model in eight normal subjects, in six patients with chronic obstructive pulmonary disease (COPD), and in one patient with tracheobronchopathia osteochondroplastica. Airway compliance was 0.96 ml/cmH2O in normal subjects and 2.49 ml/cmH2O in COPD patients. This difference of airway compliance was believed to be caused by the longitudinal expansion of the downstream segment and changes in the properties of the airway wall.     

Evolution of intrathoracic airway mechanics during lung growth

Elastic recoil pressure of the lungs (Pst(L)), maximum expiratory flow rates (MEF), critical transmural pressure of the collapsible flow-limiting segment (Ptm'), and S-segment conductance (Gs) have been determined in 40 healthy subjects, 7-18 yr old. Pst(L), measured at different lung volumes (fractional) from the expiratory quasi-static pressure-volume curves, increases progressively with age. MEF's, at different lung volumes, are closely related to total lung capacity (TLC); the ratios MEF/TLC, at all lung volumes, are independent of age. Ptm' is also independence of age and body height, most values lying between 0 and -15 cmH2O; this finding suggests that the locus and the behavior of the collapsible segment do not change during growth. Gs, in absolute value, increases with growth but, when adjusted for lung size, Gs decreases steadily with age and body height. These relations suggest that, from childhood to adolescence, the air spaces grow disproportionately more than the airway system.     

Effect of flow direction on collateral ventilation in excised dog lung lobes

We determined the effect of flow direction on the relationship between driving pressure and gas flow through a collaterally ventilating lung segment in excised cranial and caudal dog lung lobes. He, N2, and SF6 were passed through the lung segment distal to a catheter wedged in a peripheral airway. Gases were pushed through the segment by raising segment pressure (Ps) relative to airway opening pressure (Pao) and pulled from the segment by ventilating the lobe with the test gas, then lowering Ps relative to Pao. Driving pressures (Ps - Pao) between 0.25 and 2 cmH2O were evaluated at Pao values of 5, 10, and 15 cmH2O. Results were similar in cranial and caudal lobes. Flow increased as Ps - Pao increased and was greatest at Pao = 15 cmH2O for the least-dense gas (He). Although flow direction was not a significant first-order effect, there was significant interaction between volume, driving pressure, and flow direction. Dimensional analysis suggested that, although flow direction had no effect at Pao = 10 and 15 cmH2O, at Pao = 5 cmH2O, raising Ps relative to Pao increased the characteristic dimension of the flow pathways, and reducing Ps relative to Pao reduced the dimension. These data suggest that at large lobe volumes, airways (including collateral pathways) within the segment are maximally dilated and the stiffness of the parenchyma prevents any significant distortion when Ps is altered. At low lobe volumes, these pathways are affected by changes in transmural pressure due to the increased airway and parenchymal compliance.     

Density dependence of maximal expiratory flow before and during tracheal constriction in dogs

The effect of carbachol-induced central bronchoconstriction on density dependence of maximal expiratory flow (MEF) was assessed in five dogs. MEFs were measured on air and an 80% He-20% O2 mixture before and after local application of carbachol to the trachea. Airway pressures were measured using a pitot-static probe, from which central airway areas were estimated. At lower concentrations of carbachol the flow-limiting site remained in the trachea over most of the vital capacity (VC), and tracheal area and compliance decreased in all five dogs. In four dogs, decreases in choke point area predominated and produced decreases in flows. In one dog the increase in airway "stiffness" apparently offset the fall in area to account for an increase in MEF. Density dependence measured as the ratio of MEF on HeO2 to MEF on air at 50% of VC increased in all five dogs. Increases in density dependence appeared to be related to increases in airway stiffness at the choke point rather than decreases in gas-related airway pressure differences. Lower concentrations produced a localized decrease in tracheal area and extended the plateau of the flow-volume curve to lower lung volumes. Higher concentrations caused further reductions in tracheal area and greater longitudinal extension of bronchoconstriction, resulting in upstream movement of the site of flow limitation at higher lung volumes. Density dependence increased if the flow-limiting sites remained in the trachea at mid-VC but fell if the flow-limiting site had moved upstream by that volume.     

Relationship of airway narrowing, compliance, and cartilage in isolated bronchial segments.

Structural components of the airway wall may act to load airway smooth muscle and restrict airway narrowing. In this study, the effect of load on airway narrowing was investigated in pig isolated bronchial segments. In some bronchi, pieces of cartilage were removed by careful dissection. Airway narrowing was produced by maximum electrical field stimulation. An endoscope was used to record lumen narrowing. The compliance of the bronchial segments was determined from the cross-sectional area of the lumen and the transmural pressure. Airway narrowing and the velocity of airway narrowing were increased in cartilage-removed airways compared with intact control bronchi. Morphometric assessment of smooth muscle length showed greater muscle shortening to acetylcholine in cartilage-removed airways than in controls. Airway narrowing was positively correlated with airway compliance. Compliance and area of cartilage were negatively correlated. These results show that airway narrowing is increased in compliant airways and that cartilage significantly loads airway smooth muscle in whole bronchi.     

Tidal Stretches Differently Regulate the Contractile and Cytoskeletal Elements in Intact Airways

Recent reports suggest that tidal stretches do not cause significant and sustainable dilation of constricted intact airways ex vivo. To better understand the underlying mechanisms, we aimed to map the physiological stretch-induced molecular changes related to cytoskeletal (CSK) structure and contractile force generation through integrin receptors. Using ultrasound, we measured airway constriction in isolated intact airways during 90 minutes of static transmural pressure (Ptm) of 7.5 cmH₂O or dynamic variations between Ptm of 5 and 10 cmH₂0 mimicking breathing. Integrin and focal adhesion kinase activity increased during Ptm oscillations which was further amplified during constriction. While Ptm oscillations reduced β-actin and F-actin formation implying lower CSK stiffness, it did not affect tubulin. However, constriction was amplified when the microtubule structure was disassembled. Without constriction, α-smooth muscle actin (ASMA) level was higher and smooth muscle myosin heavy chain 2 was lower during Ptm oscillations. Alternatively, during constriction, overall molecular motor activity was enhanced by Ptm oscillations, but ASMA level became lower. Thus, ASMA and motor protein levels change in opposite directions due to stretch and contraction maintaining similar airway constriction levels during static and dynamic Ptm. We conclude that physiological Ptm variations affect cellular processes in intact airways with constriction determined by the balance among contractile and CSK molecules and structure.     

Deceleration time of systolic pulmonary venous flow: a new clinical marker of left atrial pressure and compliance.

The curvilinearity of the atrial pressure-volume curve implies that atrial compliance decreases progressively with increasing left atrial (LA) pressure (LAP). We predicted that reduced LA compliance leads to more rapid deceleration of systolic pulmonary venous (PV) flow. With this rationale, we investigated whether the deceleration time (t dec) of PV systolic flow velocity reflects mean LAP. In eight patients during coronary surgery, before extracorporeal circulation, PV flow by ultrasonic transit time and invasive LAP were recorded during stepwise volume loading. The t dec was calculated using two methods: by drawing a tangent through peak deceleration and by drawing a line from peak systolic flow through the nadir between the systolic and early diastolic flow waves. LA compliance was calculated as the systolic PV flow integral divided by LAP increment. Volume loading increased mean LAP from 11 +/- 3 to 20 +/- 5 mmHg (P < 0.001) (n = 40), reduced LA compliance from 1.16 +/- 0.42 to 0.72 +/- 0.40 ml/mmHg (P < 0.004) (n = 40), and reduced t dec from 320 +/- 50 to 170 +/- 40 ms (P < 0.0005) (n = 40). Mean LAP correlated well with t dec (r = 0.84, P < 0.0005) (n = 40) and LA compliance (r = 0.79, P < 0.0005) (n = 40). Elevated LAP caused a decrease in LA compliance and therefore more rapid deceleration of systolic PV flow. The t dec has potential to become a semiquantitative marker of LAP and an index of LA passive elastic properties.     

Parenchymal interdependence and airway response to methacholine in excised dog lobes

The objective of this investigation was to determine the minimum transpulmonary pressure (PL) at which the forces of interdependence between the airways and the lung parenchyma can prevent airway closure in response to maximal stimulation of the airways in excised canine lobes. We first present an analysis of the relationship between PL and the transmural pressure (Ptm) that airway smooth muscle must generate to close the airways. This analysis predicts that airway closure can occur at PL less than or equal to 10 cmH2O with maximal airway stimulation. We tested this prediction in eight excised canine lobes by nebulizing 50% methacholine into the airways while the lobe was held at constant PL values ranging from 25 to 5 cmH2O. Airway closure was assessed by comparing changes in alveolar pressure (measured by an alveolar capsule technique) and pressure at the airway opening during low-amplitude oscillations in lobar volume. Airway closure occurred in two of the eight lobes at PL = 10 cmH2O; in an additional five it occurred at PL = 7.5 cmH2O. We conclude that the forces of parenchymal interdependence per se are not sufficient to prevent airway closure at PL less than or equal to 7.5 cmH2O in excised canine lobes.     

Noninvasive determination of upper airway resistance and flow limitation.

We have shown that a polynomial equation, FP = AP3 + BP2 + CP + D, where F is flow and P is pressure, can accurately determine the presence of inspiratory flow limitation (IFL). This equation requires the invasive measurement of supraglottic pressure. We hypothesized that a modification of the equation that substitutes time for pressure would be accurate for the detection of IFL and allow for the noninvasive measurement of upper airway resistance. The modified equation is Ft = At3 + Bt2 + Ct + D, where F is flow and t is time from the onset of inspiration. To test our hypotheses, data analysis was performed as follows on 440 randomly chosen breaths from 18 subjects. First, we performed linear regression and determined that there is a linear relationship between pressure and time in the upper airway (R2 0.96 +/- 0.05, slope 0.96 +/- 0.06), indicating that time can be a surrogate for pressure. Second, we performed curve fitting and found that polynomial equation accurately predicts the relationship between flow and time in the upper airway (R2 0.93 +/- 0.12, error fit 0.02 +/- 0.08). Third, we performed a sensitivity-specificity analysis comparing the mathematical determination of IFL to manual determination using a pressure-flow loop. Mathematical determination had both high sensitivity (96%) and specificity (99%). Fourth, we calculated the upper airway resistance using the polynomial equation and compared the measurement to the manually determined upper airway resistance (also from a pressure-flow loop) using Bland-Altman analysis. Mean difference between calculated and measured upper airway resistance was 0.0 cmH2O x l(-1) x s(-1) (95% confidence interval -0.2, 0.2) with upper and lower limits of agreement of 2.8 cmH2O x l(-1) x s(-1) and -2.8 cmH2O x l(-1) x s(-1). We conclude that a polynomial equation can be used to model the flow-time relationship, allowing for the objective and accurate determination of upper airway resistance and the presence of IFL.