Sensitivity and specificity of the computational model for maximal expiratory flow

The computational model for forced expiratory flow from human lungs of Lambert and associates (J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 52: 44-56, 1982) was used to investigate the sensitivity of maximal expiratory flow to lung properties. It was found that maximal flow is very sensitive to recoil pressure and airway areas but not very sensitive to lung volume, airway compliance, and airway length. Linear programming was used to show that a given air flow-pressure curves was compatible with a fairly wide range of airway properties. Additional data for maximal flow with a He-O2 mixture narrowed the range somewhat. It was shown that the flow-pressure curve contains more information about central than peripheral airways and that information about the latter is obtainable only from flows at recoils less than 2 cmH2O. Parameter ranges compatible with individual flow-pressure curves showed differences that demonstrated that such curves give some indication of individual central airway properties.     

Resistance of intrathoracic airways of healthy subjects during periodic flow.

The resistance and reactance of lower airways were measured as functions of the frequency and amplitude of periodic flow in three healthy subjects by relating flow, produced with a piston pump, to the difference between lateral tracheal and alveolar pressure, estimated plethysmorgraphically. Resistance consistently increased with frequency; reactance was small never exceeding resistance. This result cannot be explained by distortion of velocity profiles by inertia because, in long pipes, resistance increases only when inertial forces are large and reactance exceeds resistance. Theoretical analyses of airway resistance suggested that the results reflected inhomogeneity. In lung models which considered airway wall distensibility and inertial reactance of airways, resistance increased with frequency and inertial reactance was small. These results imply that in health, as in lung disease, resistance is determined by the distribution of resistance and reactance within the lung and is not simply the total resistance of the individual airways. As flow amplitude increased at constant frequency, flow-pressure relationships became distorted and resistance increased, due probably to motion of airway walls and further distortion of velocity profiles     

Venous waterfalls in coronary circulation

Several studies of flow through collapsible tubing deformed by external pressures have led to a concept known as the "vascular waterfall". One hallmark of this state is a positive zero-flow pressure intercept (Pe) in flow-pressure curves. This intercept is commonly observed in the coronary circulation, but in blood-perfused beating hearts a vascular waterfall is not the only putative cause. To restrict the possibilities, we have measured flow-pressure curves in excised non-beating rabbit hearts in which the coronary arteries were perfused in a non-pulsatile way with a newtonian fluid (Ringers solution) containing potent vasodilator drugs. Under these circumstances, vascular waterfalls are believed to be the only tenable explanation for Pe. In physical terms the waterfall is a region where the vessel is in a state of partial collapse with a stabilized intraluminal fluid pressure (Pw). It is argued that the most probable site of this collapse was the intramural veins just before they reached the epicardial surface. In accord with the waterfall hypothesis, Pe increased as the heart became more edematous, but flow-pressure curves also became flatter, implying multiple waterfalls with differing Pws, leading to complete collapse of some of the venous channels. The principal compressive force is believed to have been the interstitial fluid pressure as registered through a needle (Pn) implanted in the left ventricular wall, but a small additional force (Ps) was probably due to swelling of interstitial gels. A method is presented for estimating Ps and Pw. Unlike rubber tubing, blood vessels are both collapsible and porous. Apparently because of increased capillary filtration, Pn was found to increase linearly with the perfusion pressure. Thus, Pw was not the same at all points on the flow-pressure curve. This finding has interesting implications with respect to the concept of coronary resistance.     

Measurement of Outflow Facility Using iPerfusion

Elevated intraocular pressure (IOP) is the predominant risk factor for glaucoma, and reducing IOP is the only successful strategy to prevent further glaucomatous vision loss. IOP is determined by the balance between the rates of aqueous humour secretion and outflow, and a pathological reduction in the hydraulic conductance of outflow, known as outflow facility, is responsible for IOP elevation in glaucoma. Mouse models are often used to investigate the mechanisms controlling outflow facility, but the diminutive size of the mouse eye makes measurement of outflow technically challenging. In this study, we present a new approach to measure and analyse outflow facility using iPerfusion^™, which incorporates an actuated pressure reservoir, thermal flow sensor, differential pressure measurement and an automated computerised interface. In enucleated eyes from C57BL/6J mice, the flow-pressure relationship is highly non-linear and is well represented by an empirical power law model that describes the pressure dependence of outflow facility. At zero pressure, the measured flow is indistinguishable from zero, confirming the absence of any significant pressure independent flow in enucleated eyes. Comparison with the commonly used 2-parameter linear outflow model reveals that inappropriate application of a linear fit to a non-linear flow-pressure relationship introduces considerable errors in the estimation of outflow facility and leads to the false impression of pressure-independent outflow. Data from a population of enucleated eyes from C57BL/6J mice show that outflow facility is best described by a lognormal distribution, with 6-fold variability between individuals, but with relatively tight correlation of facility between fellow eyes. iPerfusion represents a platform technology to accurately and robustly characterise the flow-pressure relationship in enucleated mouse eyes for the purpose of glaucoma research and with minor modifications, may be applied in vivo to mice, as well as to eyes from other species or different biofluidic systems.     

Systemic pilocarpine increases deposition of and decreases responsiveness to inhaled carbachol in sheep.

The purpose of this study was to determine whether excessive airway secretions could serve as a barrier function against inhaled particulate matter. To increase airway secretions, six conscious sheep were treated with pilocarpine (0.8 mg/kg i.v.). Pilocarpine increased pulmonary resistance (RL) and total aerosol deposition within five breaths (AD5) as determined by the rebreathing of an inert monodisperse aerosol. When RL had returned to baseline, AD5 remained elevated [21 +/- 2% (SE), P < 0.05] and tracheal secretions were increased (237 +/- 77%, P < 0.05) above the values before pilocarpine administration. A carbachol aerosol dose-response curve was carried out at this time and compared with a control carbachol dose-response curve by calculating the dose of carbachol required to increase RL by 400% (PD400). Mean PD400 was increased postpilocarpine by 53 +/- 18 (P < 0.05) and 85 +/- 25% (P < 0.05) when normalized for increased aerosol deposition. Thus, pilocarpine decreased airway responsiveness to inhaled carbachol despite increasing aerosol deposition. The pilocarpine-induced airway hyporesponsiveness to inhaled carbachol is consistent with the hypothesis that excessive secretions have a protective role in the airways.     

Respiratory impedance measured with head generator to minimize upper airway shunt

A new method for measuring total respiratory input impedance (Zrs), which ensures minimal motion of extrathoracic airway walls, was tested over frequencies of 4-30 Hz in 14 normal subjects and 10 patients with airway obstruction. It consists of applying pressure variations around the head, rather than at the mouth, so that transmural pressure across upper airway walls is equal to the small pressure drop across the pneumotachograph. Compared with reference Zrs values obtained by directly measuring airway wall motion with a head plethysmograph and correcting the data for it, the investigated method provided similar values for respiratory resistance at all frequencies (30 Hz, 3.67 +/- 2.24 cmH2O X 1(-1) X s compared with 3.55 +/- 2.00) but slightly overestimated respiratory reactance at the largest frequencies (30 Hz, 2.82 +/- 1.28 cmH2O X 1(-1) X s compared with 2.52 +/- 1.22, P less than 0.01). In contrast, when the data were not corrected for airway wall motion, resistance was largely underestimated, especially in patients (-48% at 30 Hz, P less than 0.001), and the reactance-frequency curve was shifted to the right. The investigated method is almost as accurate as the reference method, provides equally reproducible data, and is much simpler.     

Effects of airway pressure on bronchial blood flow

We studied the effects of increased airway pressure caused by increasing levels of positive end-expiratory pressure (PEEP) on bronchial arterial pressure-flow relationships. In eight alpha-chloralose-anesthetized mechanically ventilated sheep (23-27 kg), the common bronchial artery, the bronchial branch of the bronchoesophageal artery, was cannulated and perfused with a pump. The control bronchial blood flow (avg 12 +/- 1 ml/min or 0.48 ml X min-1 X kg-1) was set to maintain mean bronchial arterial pressure equal to systemic blood pressure. Pressure-flow curves of the bronchial circulation were measured by making step changes in bronchial blood flow, and changes in these curves were analyzed with measurements of the pressure at zero flow and the slope of the linearized curve. The zero-flow pressure represents the effective downstream pressure, and the slope represents the resistance through the bronchial vasculature. At a constant bronchial arterial pressure of 100 mmHg, an 8 mmHg increase in mean airway pressure caused a 40% reduction in bronchial blood flow. Under constant flow conditions, increases in mean airway pressure with the application of PEEP caused substantial increases in bronchial arterial pressure, averaging 4.6 mmHg for every millimeters of mercury increase in mean airway pressure. However, bronchial arterial pressure at zero flow increased approximately one-for-one with increases in mean airway pressure. Thus the acute sensitivity of the bronchial artery to changes in mean airway pressure results primarily from changes in bronchovascular resistance and not downstream pressure.     

Effects of airway versus arterial CO2 changes on lung mechanics in dogs.

The effects of changes in airway CO2 partial pressure (PAco2) and arterial CO2 partial pressure (Paco2) on lung mechanics were studied in dogs by utilizing unilateral pulmonary artery occlusion and a tracheal divider which allowed separate variation of PAco2 and Paco2. When Paco2 was held at a reasonably normal level, lower than normal PAco2 levels resulted in large compliance decreases, alteration of the complete static pressure-volume curves, and increases in resistance. Invreases in PAco2 to hypercapnic levels did not produce changes. When PAco2 was held at a reasonably normal level, changes in Paco2 levels were positively and directly related to resistance with small and inconsistent effects on compliance and on complete static pressure-volume curves. A combination of low PAco2 and high Paco2 produced large increases in resistance, alterations of the static pressure-volume curve, and decreases in compliance. Vagotomy during the combined stimulus resulted in only a decrease in resistance without change in lung elastic properties. The results suggest that the mechanical effects of airway hypocapnia and systemic hypercapnia are additive. However, small airways effects of low PAco2 appear to be maximal and uninfluenced by the vagally mediated response to Paco2 increases.     

Cholinergic responsiveness of respiratory and vascular tissues in two different rat strains

The airway and systemic arterial smooth muscle responsiveness to cholinergic agents of two strains of rats, Rat Albino (RA) and Brown Norway (BN), was compared in vivo and in vitro. In vivo, we measured the doses of carbachol that induced a 100% increase in lung resistance (PD100 RL), a 50% decrease in dynamic lung compliance (PD50 Cdyn), and the value of systolic blood pressure at the carbachol dose of 10 micrograms (Pa 10 micrograms). In vitro airway smooth muscle and systemic arterial smooth muscle responsiveness was assessed by measuring the maximal response to acetylcholine, the slope of the linear portion of the dose-response curve, and the negative logarithm of the molar concentration of acetylcholine producing 50% of the maximal response (pD2). PD100 and PD50 were about four times greater in BN rats than in RA rats. In contrast, Pa 10 micrograms was 1.5 lower in the BN rats. These differences persisted after bivagotomy. Tracheal pD2 was 25% greater in the RA than in the BN strain. The mean dose-response curve of parenchymal strips of RA rats was situated upward and to the left of the BN curve, but the reverse was observed for aortic smooth muscle dose-response curves. Thus 1) airway smooth muscle responsiveness to cholinergic agents is greater in RA strain than in BN, but the reverse is true for systemic arterial smooth muscle responsiveness; and 2) these differences are not due to factors extrinsic to the smooth muscle, since they occurred in vitro and may depend on different densities of muscarinic receptors.     

Tissue and airway impedance of excised normal, senile, and emphysematous lungs.

We partitioned pulmonary resistance (RL) in excised normal, senile, and emphysematous human lungs at various distending pressures; peripheral resistance (Rp) was measured by means of retrograde catheters and lung tissue resistance (Rti) by means of pleural capsules. By subtracting Rp from RL and Rti from Rp, we obtained, respectively, central (Rcaw) and peripheral (Rpaw) airway resistance. We determined also lung volumes, the elastic recoil pressure-volume curve, and the forced expiratory volume in 1 s-to-vital capacity ratio (FEV1/VC). The functional data were related to morphometry: mean linear intercept (Lm), diameter (d), and density (n/cm2) of membranous bronchioles. In the three groups of lungs, Rti demonstrates a marked negative frequency dependence and increases with transplumonary pressure. In emphysematous lungs, the increase of RL is mainly due to an increase of Rpaw; in addition, Rcaw and Rti are higher than normal. In the group of senile lungs, airway resistances are within normal range, but Rti is slightly increased. FEV1/VC is related to Rpaw and elastic recoil pressure; Rpaw is related to d and n/cm2, and Rti is related to dynamic elastance and to Lm.     

Prediction of maximum expiratory flow rate from area-transmural pressure curve of compressed airway.

The site of greatest airway deformation in dog lungs was located during maximum expiratory flow by use of tantalum bronchography, fiberoptic bronchoscopy, and airway pressure measurements. A series of area vs. transmural pressure curves for each of these segments of the airway was produced after stepwise changes in transmural pressure. Measurements of area were made using cinephotography to elucidate the effect of time on airway compliance. The maximum flow rate was calculated using the t = 0.1 s compliance curve of the airway. An equation was derived so that maximum flow (V) could be calculated from the area (A) and transmural pressure (Ptm) of the flow-limiting segment. This equation, V = K-A square root of Ptm, implied that if V were constant then A must vary as Ptm-1/2. It was demonstrated that the area-transmural pressure curve of the flow-limiting segment showed this relationship between A and Ptm and that the flow calculated from this equation and the data from the A-Ptm curve gave flows identical to those measured during maximum expiration. The phenomena of effort-independent flow and negative effort dependence are also explained in terms of the area-transmural pressure curve of the flow-limiting segment.     

Measurement of interrupter resistance in rabbits exposed to methacholine aerosols.

We studied the effect of increasing airway resistance on equilibration of airway and alveolar pressure during passive expiratory airflow interruption. In 10 anesthetized and paralyzed rabbits, airway and alveolar pressures were compared before and after airway resistance was increased with methacholine. In all studies, airway pressure rose to equilibrate with alveolar pressure immediately after the interruption (delta Pinit) regardless of increases in airway resistance. The pressures then remained equal during the interruption while gradually increasing to plateau (delta Pdiff). Before methacholine exposure, delta Pdiff was small (0.6 +/- 0.3 cmH2O). Steady-state resistance calculated from the sum of delta Pinit and delta Pdiff was similar to airway resistance calculated from delta Pinit alone. After methacholine, increased airway resistance was accompanied by increased delta Pdiff (2.0 +/- 0.5 cmH2O), causing disproportionate increase in steady-state resistance. delta Pdiff increases were equal in the airway and alveoli, implying resistive changes distal to the sampled alveoli. Thus increasing airway resistance did not delay pressure equilibration across airways. However, increases in airway resistance were accompanied by tissue resistive changes that were greater than the increases in airway resistance.     

A model of the mechanics of airway narrowing

To examine the interaction between airway smooth muscle shortening and airway wall thickening on changes in pulmonary resistance, we have developed a model of the tracheobronchial tree that allows simulation of the mechanisms involved in airway narrowing. The model is based on the symmetrical dichotomous branching tracheobronchial tree as described by Weibel and uses fluid dynamic equations proposed by Pedley et al. to calculate inspiratory resistance during quiet tidal breathing. To allow for changes in lung volume, we used the airway pressure-area curves developed by Lambert et al. The model is easily implemented with a spreadsheet and personal computer that allows calculation of total and regional pulmonary resistance. At each airway generation in the model, provision is made for airway wall thickness, the maximal airway smooth muscle shortening achievable, and an S-shaped dose-response relationship to describe smooth muscle shortening. To test the validity of the model, we compared pressure-flow curves generated with the model with measurements of pulmonary resistance while normal subjects breathed air and 20% O2-80% He at a variety of lung volumes. By simulating progressive airway smooth muscle shortening, realistic pulmonary resistance vs. dose-response curves were produced. We conclude that this model provides realistic estimates of pulmonary resistance and shows potential for examining the various mechanisms that could produce excessive airway narrowing in disease.     

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.     

Airway anesthesia effects on hypercapnic breathing pattern in humans

Minute ventilation (VE) and breathing pattern during an abrupt increase in fractional CO2 were compared in 10 normal subjects before and after airway anesthesia. Subjects breathed 7% CO2-93% O2 for 5 min before and after inhaling aerosolized lidocaine. As a result of airway anesthesia, VE and tidal volume (VT) were greater during hypercapnia, but there was no effect on inspiratory time (TI). Therefore, airway anesthesia produced an increase in mean inspiratory flow (VT/TI) during hypercapnia. The increase in VT/TI was compatible with an increase in neuromuscular output. There was no effect of airway anesthesia on the inspiratory timing ratio or the shape and position of the curve relating VT and TI. We also compared airway resistance (Raw), thoracic gas volume, forced vital capacity, forced expired volume at 1s, and maximum midexpiratory flow rate before and after airway anesthesia. A small (0.18 cmH2O X l-1 X s) decrease in Raw occurred after airway anesthesia that did not correlate with the effect of airway anesthesia on VT/TI. We conclude that airway receptors accessible to airway anesthesia play a role in hypercapnic VE.     

Airway stability and heterogeneity in the constricted lung.

The effect of bronchoconstriction on airway resistance is known to be spatially heterogeneous and dependent on tidal volume. We present a model of a single terminal airway that explains these features. The model describes a feedback between flow and airway resistance mediated by parenchymal interdependence and the mechanics of activated smooth muscle. The pressure-tidal volume relationship for a constricted terminal airway is computed and shown to be sigmoidal. Constricted terminal airways are predicted to have two stable states: one effectively open and one nearly closed. We argue that the heterogeneity of whole lung constriction is a consequence of this behavior. Airways are partitioned between the two states to accommodate total flow, and changes in tidal volume and end-expiratory pressure affect the number of airways in each state. Quantitative predictions for whole lung resistance and elastance agree with data from previously published studies on lung impedance.     

Estimation of Individual Growth Curves by Empirically Weighted Least Squares

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance-covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.     

Tracking of airway and tissue mechanics during TLC maneuvers in mice.

A tracking impedance estimation technique was developed to follow the changes in total respiratory impedance (Zrs) during slow total lung capacity maneuvers in six anesthetized and mechanically ventilated BALB/c mice. Zrs was measured with the wave-tube technique and pseudorandom forced oscillations at nine frequencies between 4 and 38 Hz during inflation from a transrespiratory pressure of 0-20 cmH2O and subsequent deflation, each lasting for approximately 20 s. Zrs was averaged for 0.125 s and fitted by a model featuring airway resistance (Raw) and inertance, and tissue damping and elastance (H). Lower airway conductance (Glaw) was linearly related to volume above functional residual capacity (V) between 0 and 75-95% maximum V, with a mean slope of dGlaw/dV = 13.6 +/- 4.6 cmH2O-1. s-1. The interdependence of Raw and H was characterized by two distinct and closely linear relationships for the low- and high-volume regions, separated at approximately 40% maximum V. Comparison of Raw with the highest-frequency resistance of the total respiratory system revealed a marked volume-dependent contribution of tissue resistance to total respiratory system resistance, resulting in the overestimation of Raw by 19 +/- 8 and 163 +/- 40% at functional residual capacity and total lung capacity, respectively, whereas the lowest frequency reactance was proportional to H; these findings indicate that single-frequency resistance values may become inappropriate as surrogates of Raw when tissue impedance is changing.     

Theoretical and experimental evaluation of the effects of an argon gas mixture on the pressure drop through adult tracheobronchial airway replicas

Argon has the potential to be a novel inhaled therapeutic agent, owing to the neuroprotective and organoprotective properties demonstrated in preclinical studies. Before human trials are performed, an understanding of varying gas properties on airway resistance during inhalation is essential. This study predicts the effect of an 80% argon/20% oxygen gas mixture on the pressure drop through conducting airways, and by extension the airway resistance, and then verifies these predictions experimentally using 3-D printed adult tracheobronchial airway replicas.The predicted pressure drop was calculated using established analytical models of airway resistance, incorporating the change in viscosity and density of the 80% argon/20% oxygen mixture versus that of air. Predicted pressure drop for the argon mixture increased by approximately 29% compared to that for air. The experimental results were consistent with this prediction for inspiratory flows ranging from 15 to 90 slpm. These results indicate that established analytical models may be used to predict increases in conducting airway resistance for argon/oxygen mixtures, compared with air. Such predictions are valuable in predicting average patient response to breathing argon/oxygen mixtures, and in selecting or designing delivery systems for use in administration of argon/oxygen mixtures to critically ill or injured patients.     

Augmentation of parasympathetic contraction in tracheal and bronchial airways by PGF2 alpha in situ

We studied the effect of exogenous prostaglandin F2 alpha (PGF2 alpha) on airway smooth muscle contraction caused by parasympathetic stimulation in 22 mongrel dogs in situ. Voltage (0-30 V, constant 20 Hz) and frequency-response (0-25 Hz, 25 V) curves were generated by stimulating the cut ends of both cervical vagus nerves. Airway response was measured isometrically as active tension (AT) in a segment of cervical trachea and as change in airway resistance (RL) and dynamic compliance (Cdyn) in bronchial airways. One hour after 5 mg/kg iv indomethacin, a cumulative frequency-response curve was generated in nine animals by electrical stimulation of the vagus nerves at 15-s intervals. Reproducibility was demonstrated by generating a second curve 7 min later. A third frequency-response curve was generated during active contraction of the airway caused by continuous intravenous infusion of 10 micrograms X kg-1 X min-1PPGF2 alpha. Additional frequency-response studies were generated 15 and 30 min after PGF2 alpha, when airway contractile response (delta RL = +2.8 +/- 0.65 cmH2O X 1(-1) X s; delta Cdyn = -0.0259 +/- 0.007 1/cmH2O) returned to base line. Substantial augmentation of AT, RL, and Cdyn responses was demonstrated in every animal studied (P less than 0.01 for all points greater than 8 Hz) 15 min after PGF2 alpha. At 30 min, response did not differ from initial base-line control. In four animals receiving sham infusion, all frequency-response curves were identical. We demonstrate that PGF2 alpha augments the response to vagus nerve stimulation in tracheal and bronchial airways. Augmentation does not depend on PGF2 alpha-induced active tone.