Airway pressures in an asymmetrically branched airway model of the dog respiratory system

A computer model of the mechanical properties of the dog respiratory system based on the asymmetrically branching airway model of Horsfield et al. (11) is described. The peripheral ends of this airway model were terminated by a lumped-parameter impedance representing gas compression in the alveoli, and lung and chest wall tissue properties were derived from measurements made in this laboratory. Using this model we predicted the respiratory system impedance and the distribution of pressures along the airways in the dog lung. Predicted total respiratory system impedances for frequencies between 4 and 64 Hz at three lung volumes were found to compare quite closely to measured impedances in dogs. Serial pressure distributions were found to be frequency-dependent and to result in higher pressures in the lung periphery than at the airway opening at some frequencies. The implications of this finding for high-frequency ventilation are discussed.     

Respiratory resistance with histamine challenge by single-breath and forced oscillation methods

Relaxed expirations were obtained from five anesthetized dogs under control conditions and during various rates of intravenous infusion of histamine. All volume vs. time curves obtained from 20 ms to 2 s after the start of expiration were poorly described by a single exponential function but were fitted very well by a biexponential function. The resistance of the respiratory system as a function of frequency from 2 to 26 Hz was also determined by the forced oscillation method in the same dogs. Three two-compartment models of the respiratory system were identified from the exponentials fitted to the relaxed expiration data, and the one that had the most plausible parameter values under control conditions consisted of a homogeneous lung compartment connected to a viscoelastic compartment. Although a two-compartment model is arguably appropriate for describing relaxed expirations in normal dogs, physiological considerations suggest that there should be more than two interacting components with histamine infusion. We cannot identify all these components from our data, however. The equivalent complex impedance of the respiratory system was also calculated from the biexponential curves and showed significant variation in resistance over the frequency range from 0 to 2 Hz and negligible variation above 2 Hz. The calculated resistances at 2 Hz were consistently higher than those obtained by the forced oscillation method, which may be due to the nonlinear behavior of the respiratory system during relaxed expiration. We conclude that the single-breath and forced oscillation methods should be viewed as providing complimentary information about respiratory resistance.     

Inverse modeling of dog airway and respiratory system impedances

Mechanical parameters of the respiratory system are often estimated from respiratory impedances using lumped-element inverse models. One such six-element model is composed of an airway branch [with a resistance (Raw) and inertance (Iaw)] separated from a tissue branch [with a resistance (Rt), inertance (It), and compliance (Ct)] by a shunt compliance representing alveolar gas compression (Cg). Even though the airways are known to have frequency-dependent resistance and inertance, these inverse models have been composed of linear frequency-independent elements. In this study we investigated the use of inverse models where the airway branch was represented by a frequency-independent Raw and Iaw, a Raw that is linearly related to frequency and an Iaw that is independent of frequency, and a system of identical parallel tubes the impedance of which was computed from the tube radius and length. These inverse models were used to analyze airway and respiratory impedances between 2 and 1,024 Hz that were predicted from an anatomically detailed forward model. The forward model represented the airways by an asymmetrically branched network with a terminal impedance representative of known Cg, Rt, It, and Ct. For respiratory impedances between 2 and 128 Hz, all models fit the data reasonably well, and reasonably accurate estimates of Cg, Rt, It, and Ct were extracted from these data. For data above 200 Hz, however, only the multiple-tube model accurately fitted respiratory impedances (Zrs). This model fitted the Zrs data best when composed of 27 tubes, each having a radius of 0.148 cm and a length of 16.5 cm.     

Assessment of heterogeneous airway constriction in dogs: a structure-function analysis

Obstructive lung diseases are often characterized by heterogeneous patterns of bronchoconstriction, although specific relationships between structural heterogeneity and lung function have yet to be established. We measured respiratory input impedance (Zrs) in eight anesthetized dogs using broadband forced oscillations at baseline and during intravenous methacholine (MCh) infusion. We also obtained high-resolution computed tomographic (HRCT) scans in 4 dogs and identified 20-30 individual airway segments in each animal. The Zrs spectra and HRCT images were obtained before and 5 min following a deep inspiration (DI) to 35 cmH(2)O. Each Zrs spectrum was fitted with two different models of the respiratory system: 1) a lumped airways model consisting of a single airway compartment, and 2) a distributed airways model incorporating a continuous distribution of airway resistances. For the latter, we found that the mean level and spread of airway resistances increased with MCh dose. Whereas a DI had no effect on average airway resistance during MCh infusion, it did increase the level of airway heterogeneity. At baseline and low-to-moderate doses of MCh, the lumped airways model was statistically more appropriate to describe Zrs in the majority of dogs. At the highest doses of MCh, the distributed airways model provided a superior fit in half of the dogs. There was a significant correlation between heterogeneity assessed with inverse modeling and the standard deviation of airway diameters obtained from HRCT. These data demonstrate that increases in airway heterogeneity as assessed with forced oscillations and inverse modeling can be linked to specific structural alterations in airway diameters.     

Effects of tidal volume and methacholine on low-frequency total respiratory impedance in dogs

The frequency dependence of respiratory impedance (Zrs) from 0.125 to 4 Hz (Hantos et al., J. Appl. Physiol. 60: 123-132, 1986) may reflect inhomogeneous parallel time constants or the inherent viscoelastic properties of the respiratory tissues. However, studies on the lung alone or chest wall alone indicate that their impedance features are also dependent on the tidal volumes (VT) of the forced oscillations. The goals of this study were 1) to identify how total Zrs at lower frequencies measured with random noise (RN) compared with that measure with larger VT, 2) to identify how Zrs measured with RN is affected by bronchoconstriction, and 3) to identify the impact of using linear models for analyzing such data. We measured Zrs in six healthy dogs by use of a RN technique from 0.125 to 4 Hz or with a ventilator from 0.125 to 0.75 Hz with VT from 50 to 250 ml. Then methacholine was administered and the RN was repeated. Two linear models were fit to each separate set of data. Both models assume uniform airways leading to viscoelastic tissues. For healthy dogs, the respiratory resistance (Rrs) decreased with frequency, with most of the decrease occurring from 0.125 to 0.375 Hz. Significant VT dependence of Rrs was seen only at these lower frequencies, with Rrs higher as VT decreased. The respiratory compliance (Crs) was dependent on VT in a similar fashion at all frequencies, with Crs decreasing as VT decreased. Both linear models fit the data well at all VT, but the viscoelastic parameters of each model were very sensitive to VT. After methacholine, the minimum Rrs increased as did the total drop with frequency. Nevertheless the same models fit the data well, and both the airways and tissue parameters were altered after methacholine. We conclude that inferences based only on low-frequency Zrs data are problematic because of the effects of VT on such data (and subsequent linear modeling of it) and the apparent inability of such data to differentiate parallel inhomogeneities from normal viscoelastic properties of the respiratory tissues.     

Mechanical output impedance of the lung determined from cardiogenic oscillations.

The beating heart naturally oscillates the lung because of the close juxtaposition between these organs producing cardiogenic oscillations in flow that can be measured at the mouth when the glottis is open. Correspondingly, if the mouth is occluded, the same phenomenon produces cardiogenic pressure oscillations that can be measured just distal to the site of occlusion. The Fourier-domain ratio of these oscillations in pressure and flow constitutes what we call cardiogenic respiratory impedance (Zc). We calculated Zc between about 1.5 and 10 Hz in relaxed normal subjects at functional residual capacity with open glottis. Zc was insensitive to heart rate changes induced by exercise and had an imaginary part close to zero at all frequencies investigated. Its real part was similar to or smaller than resistance determined by the forced oscillation technique. We speculate that Zc measures the flow resistance of the central and upper airways of the lung. Zc may be useful as a means of obtaining information about lung mechanics without the need for an external source of flow perturbations.     

Oscillatory mechanics of the respiratory system in ozone-exposed rats

The respiratory system impedance of tracheostomized cardiorespiratory disease-free Sprague-Dawley rats was measured from 20 to 90 Hz at constant flow amplitudes in 10 rats exposed to 0.64 ppm (UV) ozone for 7 days, and eight rats exposed to the same level of ozone for 20 days. This data was compared with respiratory system impedence spectra of 24 normal rats obtained in the same manner. When compared with control, the real part (effective resistance) was significantly different at several frequencies in the 7-day group (P less than 0.05), and group means were higher at all frequencies. The 20-day group showed no significant differences in effective resistance. The imaginary part (effective reactance) was significantly lower at higher frequencies (f greater than 36) in both exposure groups (P less than 0.05). When the impedance curves for each individual were fit to a lumped six-parameter model, and the parameters were compared, only the peripheral resistance parameter of the 7-day group was significantly different from control (P less than 0.05). We conclude that ozone exposure at this level causes changes in respiratory system impedance, that these changes consist primarily of decreased reactances at higher frequencies, and that at 7 days these changes can be modeled by an increase in peripheral resistance.     

Contribution of large airway to the input impedance of the respiratory system

To evaluate the contribution of the large airway to total respiratory impedance, we develop a one-dimensional model of pressure and flow in these airways by coupling conservation of mass and momentum equations with the geometric information obtained by the acoustic reflection technique. We use this model to calculate the impedance of the respiratory system distal to the carina from impedance data estimated at the airway opening by the forced oscillation technique. Simulations show that the real part of the impedance distal to the carina is uniformly decreased from the impedance at the airway opening, indicating a resistive loss, while the imaginary part is increased as a function of frequency. We estimate parameter values for a six-parameter two-compartment lung model and for a three-parameter reduction of this model before and after the application of the upper airway data to the impedance spectrum. Although compliance terms seem to be minimally affected by the manipulation of the data, resistance and inertance terms are influenced in a fashion that suggests that the resistive contribution of the upper airway to total respiratory impedance is significant. Furthermore it appears that the elastic nature of the walls of the upper airway also impact on estimates of total respiratory impedance at the airway opening.     

Lung and chest wall mechanics in rabbits during high-frequency body-surface oscillation

In eight anesthetized and tracheotomized rabbits, we studied the transfer impedances of the respiratory system during normocapnic ventilation by high-frequency body-surface oscillation from 3 to 15 Hz. The total respiratory impedance was partitioned into pulmonary and chest wall impedances to characterize the oscillatory mechanical properties of each component. The pulmonary and chest wall resistances were not frequency dependent in the 3- to 15-Hz range. The mean pulmonary resistance was 13.8 +/- 3.2 (SD) cmH2O.l-1.s, although the mean chest wall resistance was 8.6 +/- 2.0 cmH2O.l-1.s. The pulmonary elastance and inertance were 0.247 +/- 0.095 cmH2O/ml and 0.103 +/- 0.033 cmH2O.l-1.s2, respectively. The chest wall elastance and inertance were 0.533 +/- 0.136 cmH2O/ml and 0.041 +/- 0.063 cmH2O.l-1.s2, respectively. With a linear mechanical behavior, the transpulmonary pressure oscillations required to ventilate these tracheotomized animals were at their minimal value at 3 Hz. As the ventilatory frequency was increased beyond 6-9 Hz, both the minute ventilation necessary to maintain normocapnia and the pulmonary impedance increased. These data suggest that ventilation by body-surface oscillation is better suited for relatively moderate frequencies in rabbits with normal lungs.     

Frequency characteristics of airway and tissue impedances in respiratory diseases

We measured the frequency characteristics (at 10-40 Hz) of airway (Za) and tissue (Zt) impedances in cases of chronic obstructive pulmonary disease [asthmatic bronchitis (AB), chronic pulmonary emphysema (CPE)] and interstitial pneumonitis (IP) by use of an improved random noise oscillation and body box method. The results were then compared with those obtained for normal subjects. The real part of Za was markedly elevated in patients with AB but only slightly elevated in those with CPE. To interpret these data we used an electromechanical analogue including serial inhomogeneity with shunt impedance. From this model we concluded that AB causes both the central and peripheral airway resistances to increase, while CPE brings about a rise mainly in peripheral resistance. In IP patients, only the imaginary part of Zt decreased, which might reflect the decrease in both lung and chest wall compliance. In CPE patients, but not in AB patients, the real part of Zt fell. These data were consistent with the assumption that the decrease in mass per unit volume of lung tissue and hyperinflation of the chest wall in CPE patients might lower the tissue resistances.     

Low-frequency respiratory mechanical impedance in the rat

A modified forced oscillatory technique was used to determine the respiratory mechanical impedances in anesthetized, paralyzed rats between 0.25 and 10 Hz. From the total respiratory (Zrs) and pulmonary impedance (ZL), measured with pseudorandom oscillations applied at the airway opening before and after thoracotomy, respectively, the chest wall impedance (ZW) was calculated as ZW = Zrs - ZL. The pulmonary (RL) and chest wall resistances were both markedly frequency dependent: between 0.25 and 2 Hz they contributed equally to the total resistance falling from 81.4 +/- 18.3 (SD) at 0.25 Hz to 27.1 +/- 1.7 kPa.l-1 X s at 2 Hz. The pulmonary compliance (CL) decreased mildly, from 2.78 +/- 0.44 at 0.25 Hz to 2.36 +/- 0.39 ml/kPa at 2 Hz, and then increased at higher frequencies, whereas the chest wall compliance declined monotonously from 4.19 +/- 0.88 at 0.25 Hz to 1.93 +/- 0.14 ml/kPa at 10 Hz. Although the frequency dependence of ZW can be interpreted on the basis of parallel inhomogeneities alone, the sharp fall in RL together with the relatively constant CL suggests that at low frequencies significant losses are imposed by the non-Newtonian resistive properties of the lung tissue.     

Low-frequency pulmonary impedance in rabbits and its response to inhaled methacholine.

We assessed pulmonary mechanics in six open-chest rabbits (3 young and 3 adult) by the forced oscillation technique between 0.16 and 10.64 Hz. Under control conditions, pulmonary resistance (RL) decreased markedly between 0.16 and 4 Hz, after which it became reasonably constant. Measurements of alveolar pressure from two alveolar capsules in each rabbit showed that the large decrease of RL with increasing frequency below 4 Hz was due to lung tissue rheology and that tissue resistance was close to zero above 4 Hz. Estimates of resistance and elastance, also obtained by fitting tidal ventilation data at 1 Hz to the equation of the linear single-compartment model, gave values for RL motion that were slightly higher than those obtained by forced oscillations at the same frequency, presumably because of the flow dependence of airways resistance. After treatment with increasing doses of aerosolized methacholine, RL and pulmonary elastance between 0.16 and 1.34 Hz progressively increased, as did the point at which the pulmonary reactance crossed zero (the resonant frequency). The alveolar pressure measurements showed the lung to become increasingly inhomogeneously ventilated in all six animals, whereas in the three younger rabbits lobar atelectasis developed at high methacholine concentrations and the alveolar capsules ceased to communicate with the central airways. We conclude that the low-frequency pulmonary impedance of rabbits exhibits the same qualitative features observed in other species and that it is a sensitive indicator of the changes in pulmonary mechanics occurring during bronchoconstriction.     

Modeling of respiratory system impedances in dogs

Mechanical impedances between 4 and 64 Hz of the respiratory system in dogs have been reported (A.C. Jackson et al. J. Appl. Physiol. 57: 34-39, 1984) previously by this laboratory. It was observed that resistance (the real part of impedance) decreased slightly with frequency between 4 and 22 Hz then increased considerably with frequency above 22 Hz. In the current study, these impedance data were analyzed using nonlinear regression analysis incorporating several different lumped linear element models. The five-element model of Eyles and Pimmel (IEEE Trans. Biomed. Eng. 28: 313-317, 1981) could only fit data where resistance decreased with frequency. However, when the model was applied to these data the returned parameter estimates were not physiologically realistic. Over the entire frequency range, a significantly improved fit was obtained with the six-element model of DuBois et al. (J. Appl. Physiol. 8: 587-594, 1956), since it could follow the predominate frequency-dependent characteristic that was the increase in resistance. The resulting parameter estimates suggested that the shunt compliance represents alveolar gas compressibility, the central branch represents airways, and the peripheral branch represents lung and chest wall tissues. This six-element model could not fit, with the same set of parameter values, both the frequency-dependent decrease in Rrs and the frequency-dependent increase in resistance. A nine-element model recently proposed by Peslin et al. (J. Appl. Physiol. 39: 523-534, 1975) was capable of fitting both the frequency-dependent decrease and the frequency-dependent increase in resistance. However, the data only between 4 and 64 Hz was not sufficient to consistently determine unique values for all nine parameters.     

Respiratory mechanics in the normal dog determined by expiratory flow interruption

We recently proposed an eight-parameter model of the respiratory system to account for its mechanical behavior when flow is interrupted during passive expiration. The model consists of two four-parameter submodels representing the lungs and the chest wall, respectively. The lung submodel consists of an airways resistance together with elements embodying the viscoelastic properties of the lung tissues. The chest wall submodel has similar structure. We estimated the parameters of the model from data obtained in four normal, anesthetized, paralyzed, tracheostomized mongrel dogs. This model explains why lung tissue and chest wall resistances should be markedly frequency dependent at low frequencies and also permits a physiological interpretation of resistance measurements provided by the flow interruption method.     

Impedance measurement during air and He-O2 breathing before and after salbutamol in normal subjects

Total respiratory resistance and reactance from 4 to 52 Hz were determined by the method of forced pseudorandom noise oscillation in 20 normal male subjects before and after inhalation of 0.200 mg salbutamol (albuterol) and before and after the subjects were equilibrated with 80% He-20% O2. During air breathing, there was a statistically significant decrease of resistance values at lower frequencies after inhalation of salbutamol. When the subject was equilibrated with 80% He-20% O2, total respiratory resistance markedly decreased at all frequencies, and a negative frequency dependence of resistance was observed between 8 and 20 Hz. Resistance values further decreased during He-O2 breathing after inhalation of salbutamol. After inhalation of salbutamol, reactance values increased during air and He-O2 breathing. The density-dependent decrease of the real part of impedance can be explained by a decrease of turbulence in the larger airways. The bronchodilating effect of salbutamol was not influenced by a change in the physical properties of the inhaled gas. During He-O2 breathing, reactance values significantly decreased, resulting in an increase of resonant frequency due to a decrease of inductive reactance. It is concluded that an increase in the capacitance of the respiratory system must be supposed to explain the increase in reactance values after inhalation of the beta-adrenergic agonist salbutamol.     

Relationship of central and peripheral airway resistance to lung volume in dogs

We could not reconcile reported relationships between lung resistance measurements and lung volume with bronchographic and anatomic studies showing that airway diameters change monotonically with lung volume and that small airways change diameter proportionately at least as much as large ones. Accordingly we measured central and peripheral airways resistances with a new technique. The relevant pressures were measured with a tracheal cannula, a wedged retrograde catheter, and two parenchymal needles in seven open-chested dogs while pleural pressure was oscillated at 1 Hz. In contrast to previous studies, the volume dependency of peripheral resistance was at least as great as that of central resistance with vagi intact, the volume dependencies of central and peripheral resistances were not abolished by vagotomy, and neither resistance increased systematically at high volumes. Volume dependency of central resistance resembled predictions for isotropic expansion of airways with vagi cut but increased with bronchomotor tone. These results fit generally with bronchographic data. Previous studies may have been affected by volume dependency due to "tissue resistance" and catheter phase lags.     

Effect of body posture on respiratory impedance

The effects of posture on the mechanics of the respiratory system are not well known, particularly in terms of total respiratory resistance. We have measured respiratory impedance (Zrs) by the forced random noise excitation technique in the sitting and the supine position in 24 healthy subjects. Spirometry and lung volumes (He-dilution technique) were also measured in both postures. The equivalent resistance (Rrs), compliance (Crs), and inertance (Irs) were also calculated by fitting each measured Zrs to a linear series model. When subjects changed from sitting to the supine position, the real part of Zrs increased over the whole frequency band. The associated equivalent resistance, Rrs, increased by 28.2%. The reactance decreased for frequencies lower than 18 Hz and increased for higher frequencies. Consequently, Crs decreased by 38.7% and Irs increased by 15.6%. All of these parameter differences were significant (P less than 0.001). A covariance analysis showed that a significant amount of the postural change in Rrs and Crs can be explained by the reduction of functional residual capacity (FRC). This indicates that the observed differences on Zrs can in part be explained be a shift of the operating point of the respiratory system induced by the decrease in the FRC.     

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.     

Effects of posture and bronchoconstriction on low-frequency input and transfer impedances in humans.

We simultaneously evaluated the mechanical response of the total respiratory system, lung, and chest wall to changes in posture and to bronchoconstriction. We synthesized the optimal ventilation waveform (OVW) approach, which simultaneously provides ventilation and multifrequency forcing, with optoelectronic plethysmography (OEP) to measure chest wall flow globally and locally. We applied an OVW containing six frequencies from 0.156 to 4.6 Hz to the mouth of six healthy men in the seated and supine positions, before and after methacholine challenge. We measured mouth, esophageal, and transpulmonary pressures, airway flow by pneumotachometry, and total chest wall, pulmonary rib cage, and abdominal volumes by OEP. We computed total respiratory, lung, and chest wall input impedances and the total and regional transfer impedances (Ztr). These data were appropriately sensitive to changes in posture, showing added resistance in supine vs. seated position. The Ztr were also highly sensitive to lung constriction, more so than input impedance, as the former is minimally distorted by shunting of flow into alveolar gas compression and airway walls. Local impedances show that, during bronchoconstriction and at typical breathing frequencies, the contribution of the abdomen becomes amplified relative to the rib cage. A similar redistribution occurs when passing from seated to supine. These data suggest that the OEP-OVW approach for measuring Ztr could noninvasively track important lung and respiratory conditions, even in subjects who cannot cooperate. Applications might range from routine evaluation of airway hyperreactivity in asthmatic subjects to critical conditions in the supine position during mechanical ventilation.