Journal of Applied Physiology
Vol. 82, No. 1, pp. 55-62, January 1997
GAS EXCHANGE, MECHANICS, AND AIRWAYS

Temporal dynamics of acute isovolume bronchoconstriction in the rat

Jason H. T. Bates, Thomas F. Schuessler, Carrie Dolman, and David H. Eidelman

Meakins-Christie Laboratories and Department of Biomedical Engineering, McGill University, Montreal, Quebec, Canada H2X 2P2

ABSTRACT

INTRODUCTION

METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

FOOTNOTES

REFERENCES

ABSTRACT

Bates, Jason H. T., Thomas F. Schuessler, Carrie Dolman, and David H. Eidelman. Temporal dynamics of acute isovolume bronchoconstriction in the rat. J. Appl. Physiol. 82(1): 55-62, 1997.The time course of lung impedance changes after intravenous injection of bronchial agonist have produced significant insights into the mechanisms of bronchoconstriction in the dog (J. H. T. Bates, A.-M. Lauzon, G. S. Dechman, G. N. Maksym, and T. F. Shuessler. J. Appl. Physiol. 76: 616-626, 1994 [Medline] ). We studied the time course of acute induced bronchoconstriction in five anesthetized paralyzed open-chest rats injected intravenously with a bolus of methacholine. For the 16 s immediately after injection, we held the lung volume constant while applying small-amplitude flow oscillations at 1.48, 5.45, and 19.69 Hz simultaneously, which provided us with continuous estimates of lung resistance (RL) and elastance (EL) at each frequency. This procedure was repeated at initial lung inflation pressures of 0.2, 0.4, and 0.6 kPa. Both RL and EL increased progressively after methacholine administration; however, the rate of change of EL increased dramatically as frequency was increased, whereas RL remained relatively independent of frequency. We interpret these findings in terms of a three-compartment model of the rat lung, featuring two parallel alveolar compartments feeding into a central airway compartment. Model simulations support the notions that both central airway shunting and regional ventilation inhomogeneity developed to a significant degree in our constricted rats. We also found that the rates of increase in both RL and EL were greatly enhanced as the initial lung inflation pressure was reduced, in accord with the notion that parenchymal tethering is an important mechanism limiting the extent to which airways can narrow when their smooth muscle is stimulated to contract.

lung impedance; frequency dependence of resistance and elastance; parenchymal tethering; central airway shunting; ventilation inhomogeneity

INTRODUCTION

PREVIOUS STUDIES from our laboratory (2, 3, 11) have shown that a great deal of important physiological information is embodied in the time course of bronchoconstriction during the first minute or so after intravenous agonist injection in dogs. In particular, when bronchoconstriction is tracked by applying small-amplitude flow oscillations to the airway opening at fixed lung volume, we have shown that effects of peripheral lung stiffening, central airway constriction, and development of regional ventilation inhomogeneity can all be inferred in a quantitative fashion. Furthermore, most of these effects are exquisitely sensitive to lung volume, with the rate of reaction increasing dramatically as volume is reduced (2).

We have extended this line of investigation to the rat, which has become a popular model for the study of obstructive lung disease in recent years because of its low cost and ready availability in a number of pure-bred strains. Recently, Lutchen et al. (13) measured transfer impedance in rats between 0.234 and 12 Hz and found evidence of significant parallel inhomogeneities in the lung after bronchoconstriction. We therefore expected that the time course of acute bronchoconstriction in the rat should produce similar insights to those we found previously in the dog (2). In the present study, we measured lung mechanics in open-chest rats by using a computer-controlled small-animal ventilator (SAV) (22) consisting of a piston driven in a cylinder by a linear motor under computer control. We used this device to monitor the evolution of pulmonary impedance at constant lung volume after an intravenous bolus of methacholine (MCh). We also determined how variations in initial lung inflation pressure affected this evolution.

METHODS

Experimental procedures. We studied five adult Brown-Norway rats (weight 290-360 g). The rats were anesthetized with an intraperitoneal bolus of pentobarbital sodium (8.5 mg) and tracheostomized, and the trachea was cannulated with a 14-gauge metal needle. The cannula was connected to the SAV. The rats were then paralyzed: two with an intraperitoneal bolus of pancuronium bromide (8.5 µg) and three with an intraperitoneal bolus of succinylcholine (0.1 mg). The chest was opened widely by midline sternotomy, and a venous line was established for the administration of saline and MCh. Regular mechanical ventilation was performed with the SAV as follows. During inspiration, the piston of the SAV moved forward in a half-sinusoidal fashion, thereby pushing air directly into the lungs of the rat. During expiration, the main valve of the SAV was closed and the cylinder-refill valve was opened so that the cylinder could refill with air as the piston moved back to its starting position. At the same time the expiratory valve, connected to the tracheal cannula via a "Y" piece, was opened to allow the animal to expire passively through a water trap adjusted to maintain a certain positive end-expiratory pressure (PEEP). Tidal volume was 2.5-3.0 ml, and breathing frequency was 100 breaths/min.

The animals were allowed to expire passively to functional residual capacity as determined by PEEP. Flow oscillations into the lungs were then produced by the piston of the SAV for a period of 16 s. A control experiment was performed at each PEEP level by injecting a 0.08-ml bolus of saline intravenously at the start of the 16-s oscillation period. Each control experiment was followed by a bronchoconstriction experiment at the same PEEP, in which a bolus of MCh (0.08 mg in 0.08 ml) was administered intravenously at the start of the 16-s oscillation period. During data collection, the piston position and the pressure inside the cylinder were recorded at 1,024 Hz after they were passed through six-pole Bessel low-pass filters with cutoff at 200 Hz. This high sampling rate was required to accurately control the piston position. After data collection, the data were digitally low-pass filtered (6-pole Bessel) at 30 Hz and decimated to 256 Hz before they were stored on the SAV computer (a 386 personal computer). As soon as data collection was complete, normal ventilation was resumed. Control and bronchoconstriction experiments were performed at PEEP levels of 0.2, 0.4, and 0.6 kPa, with the order randomized for each rat.

The flow oscillations applied to the rats to identify mechanics consisted of the superposition of three distinct frequencies at 1.48, 5.45, and 19.69 Hz. The amplitudes of the oscillations were adjusted to have equal power in flow at each frequency. These frequencies were chosen because they span the range of interest and are mutually prime; i.e., no frequency is an integer multiple of any of the other frequencies so that the impedance identified at each frequency is not affected by harmonic distortion from one of the other input frequencies if the system being identified should happen to be significantly nonlinear (4). The frequencies also satisfied the nonsum nondifference criterion of Suki and Lutchen (24).

SAV calibration. Each data-collection epoch produced 16-s records of piston position calibrated as volume displacement (V) and cylinder pressure (P). However, V consisted of two parts: 1) a volume entering the animal at the trachea (Vtr) and 2) a compressive volume change within the cylinder. Similarly, P consisted of the pressure drop along the flow pathway connecting the cylinder to the animal plus the pressure applied at the animal's trachea (Ptr). The situation is depicted in Fig. 1.

To calculate Ptr and tracheal flow (tr) from P and V, we performed two dynamic calibration maneuvers. First, the SAV piston was oscillated with the composite perturbation signal while the connecting tubing (including the tracheal cannula) was completely blocked (equivalent to having an infinite rat impedance in Fig. 1). P and V were then related by

(1)

where t is time and EG is the gas elastance within the cylinder-tubing assembly. Figure 2A shows an example of the fit provided by the model. The coefficient of determination is 0.991, and the value of EG is 9.9 kPa/ml, which corresponds to a gas volume of ~14 ml, if we assume adiabatic gas compression. To check that this calibration procedure held for each component frequency separately, we determined EG for each frequency by digitally filtering P(t) and V(t) into three bands encompassing the three component frequencies and applied Eq. 1 to each P-V pair. We found that at 1.48 Hz, EG had a value (mean for all 5 rats) of 9.47 kPa/ml. At the other two frequencies of 5.45 and 19.69 Hz, EG had mean values of 10.12 and 9.88 kPa/ml, respectively. Thus EG was essentially independent of frequency over the range we used in our experiments.

Next, the piston was again oscillated with the test perturbation signal, this time with the connecting tubing completely open to atmosphere (equivalent to having 0 rat impedance in Fig. 1). Now a part of V went into gas compression while the remainder, tr, traveled along the pathway provided by the connecting tubing according to

(2)

where (t) is the time derivative of P(t) and (t) is the time derivative of V(t). The pressure drop along the flow pathway was assumed to be determined by a flow resistance (Rpath) and a gas inertance (Ipath), thus

(3)

where tr(t) is the time derivative of tr(t). Figure 2B shows an example of the fit provided by Eq. 3. The coefficient of determination is 0.959, Rpath is 1.59 × 10³ kPa ^· s ^· ml¹, and Ipath is 2.28 × 10⁵ kPa ^· s^2 · ml¹. We also checked that this procedure was valid for each frequency component separately by applying Eq. 3 to P(t), tr(t), and tr(t) after separating each frequency component in each signal. We found Ipath to have similar values (mean for all rats) of 3.0 × 10⁵, 2.6 × 10⁵, and 2.4 × 10⁵ kPa ^· s^2 · ml¹, at frequencies of 1.48, 5.45, and 19.69 Hz, respectively. Rpath had the identical mean values of 1.5 × 10³ kPa ^· s ^· ml¹ at frequencies of 1.48 and 5.45 Hz. It was somewhat higher (2.2 × 10³ kPa ^· s ^· ml¹) at 19.69 Hz, but the differences between all Rpath values were small compared with our measured rat lung resistance (RL) values under control conditions and negligible after MCh (see RESULTS), thus assuming a fixed value for Rpath for all frequencies would have had no effect on our results.

When a rat was connected to the SAV, we calculated tr by using Eq. 2 with the estimated value of EG. Ptr was calculated with the estimated values of Rpath and Ipath as

(4)

Data analysis. The 16-s records of Ptr and tr were analyzed as follows. First, the running mean of Ptr was calculated with a window length of 2 s to give an estimate of static elastic recoil pressure (Pel). Next, the running means of both Ptr and V(t) were subtracted from the signals themselves to remove zero offsets and low-frequency trends. The edges of each data signal were then extended smoothly to zero as follows. The first 2 s of a signal was concatenated to itself four times and multiplied by a half-cosine bell so that it began at zero and rose smoothly over 8 s to reach the amplitude of the beginning of the data. This contrived signal was then attached to the beginning of the data signal to remove the sharp onset of the latter. A similar process was applied in the reverse sense to the end of the data signal. This produced, finally, a signal of 32 s that began and ended at zero and rose smoothly at both ends to its center 16-s portion, which consists of the original signal. This edge-extension procedure was used to minimize leakage in the frequency domain after Fourier transformation of the records while maintaining the actual data itself intact. We could have reduced leakage by multiplying the data by a Hanning window, but this would have destroyed information near the edges of the data (14).

The edge-extended records of Ptr and tr were then band-pass filtered by calculating the fast Fourier transforms of the complete records, setting all frequency components to zero except those in the band of interest, and then inverse Fourier transforming. Three bands were separated in this way, spanning the frequency ranges 0.5-2.5 Hz, 4.5-6.5 Hz, and 18.5-20.5 Hz. These bands encompassed each of the three frequencies of the composite perturbation V(t) signal. We thus obtained three time domain Ptr-tr signal pairs.

Finally, each Ptr-tr signal pair was analyzed by fitting the model

(5)

where K is a constant, by recursive multiple linear regression with an exponential memory time constant of 0.25 s (2, 3). This gave 32-s signals for RL and lung elastance (EL) at each of the three oscillation frequencies of 1.48, 5.45, and 19.69 Hz. We retained the central 14 s of each, thereby eliminating the irrelevant edge-extended portions together with the first and last seconds provided by the actual data, which were still somewhat affected by Fourier edge effects. This analysis is similar to that used in our previous study in dogs (2), except we included the additional edge-extension procedure in the present study because the duration of the data was much shorter than in the dog study and we wanted to minimize loss of information at the edges.

RESULTS

Figure 3 shows Pel obtained at each PEEP after MCh administration. These curves were corrected for the changes in Pel that occurred during control experiments (the control changes were small: 0.02-0.05 kPa over the 16-s oscillation period; we attribute this mainly to continuing gas exchange within the lungs coupled with a respiratory exchange ratio of less than unity). The curves shown are the averages for all rats together with their respective SD values. MCh produced a small increase in Pel of about the same magnitude at each of the three PEEP values studied.

Figure 4 shows RL and EL vs. time at the three different frequencies of 1.48, 5.45, and 19.69 Hz obtained from one of the rats at an inflation pressure of 0.2 kPa. These results typify those obtained from all rats studied. MCh was administered at time 0. The plots show that the reactions in both RL and EL to the drug started at ~5 s and increased progressively throughout the rest of the 16-s measurement period. During the reaction period, the 1.48-Hz component of RL (RL_1.48) was larger than the 5.45-Hz component (RL_5.45), which was in turn larger than the 19.69-Hz component (RL_19.69), but the three quantities (Fig. 4A) increased roughly in parallel. This was in marked contrast to the situation for EL (Fig. 4B), for which the rank ordering of the amount of increase as a function of frequency was opposite to that for RL; i.e., the 19.69-Hz component of EL (EL_19.69) was larger than the 5.45-Hz component (EL_5.45), which was larger than the 1.48-Hz component (EL_1.48). Also, the rates of increase of the three quantities were vastly different, with the reactions being much greater for the higher frequency components of EL.

Figure 5 shows RL_1.48 and EL_19.69 (the components of RL and EL that show the most reaction) vs. time at the three different PEEP values used, from the same rat as in Fig. 4. There is clearly a very large effect of PEEP on responsiveness to MCh in these animals, which was mirrored in all the other rats studied. Table 1 summarizes the data from all the rats by listing the mean values and SDs of RL and EL obtained at all frequencies and all PEEP values from 1-2 s after injection (prereaction values) and from 14-15 s after injection (postreaction values).

Table 1. Resistance and elastance between 1 and 2 s (prereaction) and between 14 and 15 s (postreaction) after MCh injection 0.2 kPa PEEP 0.4 kPa PEEP 0.6 kPa PEEP Resistance, kPa · s · ml1 RL1.48 RL5.45 RL19.69 RL1.48 RL5.45 RL19.69 RL1.48 RL5.45 RL19.69   Prereaction 0.0061 ± 0.0011  0.0050 ± 0.0020  0.0047 ± 0.0004  0.0040 ± 0.0023  0.0031 ± 0.0008  0.0032 ± 0.0005  0.0057 ± 0.0042  0.0029 ± 0.0006  0.0029 ± 0.0003    Postreaction 0.3070 ± 0.2695  0.2649 ± 0.2346  0.2498 ± 0.1844  0.0594 ± 0.0160  0.0472 ± 0.0135  0.0438 ± 0.0148  0.0217 ± 0.0058  0.0143 ± 0.0039  0.0114 ± 0.0032  Elastance, kPa/ml EL1.48 EL5.45 EL19.69 EL1.48 EL5.45 EL19.69 EL1.48 EL5.45 EL19.69   Prereaction 0.202 ± 0.015  0.239 ± 0.046  0.103 ± 0.013  0.153 ± 0.008  0.169 ± 0.013  0.055 ± 0.028  0.186 ± 0.045  0.208 ± 0.011  0.066 ± 0.045    Postreaction 1.147 ± 0.931  2.654 ± 2.418  43.564 ± 76.070  0.333 ± 0.038  0.596 ± 0.127  1.460 ± 0.478  0.225 ± 0.030  0.367 ± 0.056  0.443 ± 0.110 Values are means ± SD. RL1.48, RL5.45, and RL19.69, 1.48-, 5.45-, and 19.69-Hz components of lung resistance, respectively; EL1.48, EL5.45, EL19.69, 1.48-, 5.45-, and 19.69-Hz components of lung elastance, respectively. MCh, methacholine; PEEP, positive end-expiratory pressure.

DISCUSSION

There are relatively few published studies on the details of respiratory mechanics in the rat, despite the widespread use of this species in bronchopharmacological studies. This is no doubt because of the technical difficulty of making accurate measurements of flow in such small animals. The forced oscillation method has been applied in normal rats, both conscious and anesthetized (8, 9, 19), and the reported values for total system resistance and elastance are of a similar magnitude to our prereaction values (Table 1). However, the study of changes in respiratory mechanics with induced bronchoconstriction in rats has been limited mostly to simple measures of RL and EL obtained by fitting the single-compartment linear model to regular breathing or ventilation data, although the recent study of Lutchen et al. (13) is a notable exception. Our study is the first to investigate the time course of acute changes in rat pulmonary impedance as a function of both frequency and lung volume during induced bronchoconstriction, and was made possible by the development of our computer-controlled SAV (22).

As we expected, the reactions in both RL and EL were highly dependent on the initial PEEP of the lungs before MCh administration (Fig. 5). This kind of effect has been demonstrated previously in humans (5), dogs (1, 2), and rats (6, 17) and is thought to reflect the varying degrees of parenchymal interdependence that occur at different lung volumes; i.e., at high lung volumes, interdependence forces are relatively large and so limit the degree of airway smooth muscle shortening that can occur. This results in a relatively small change in mechanical lung impedance for a given degree of smooth muscle stimulation. Conversely, at low lung volumes the airways are rather more independent of each other so that their respective smooth muscle fibers are free to constrict unhindered. Most studies in this area have investigated the dependence of maximal response on lung volume. In the present study, we were not able to make measurements long enough to determine the maximal response, so instead we use the rate of change in mechanical parameters as our index of responsiveness. Therefore, our results are presumably reflective of the force-velocity relationships of the contracting smooth muscles, where a greater load would result in slower shortening. This relationship would be expected to have a hyperbolic character; this is borne out by our data, which show that the variation in rate of increase of impedance with lung volume is more pronounced at lower volume. Table 1 shows the increases in both RL and EL at all frequencies are much greater going from 0.4 to 0.2 kPa PEEP than going from 0.6 to 0.4 kPa PEEP.

We also found that MCh caused Pel to increase by about the same absolute amount at all three PEEP levels, suggestive of a parallel shift in the static pressure-volume curve of the lung. As we found previously in dogs (2), Pel appeared to approach a plateau relatively early after agonist administration (in this case, at ~10 s), whereas the dynamic impedance parameters continued to increase dramatically. In our previous study (2), we interpreted the changes in Pel as being due to the first passage of agonist through the pulmonary circulation where it constricts peripheral smooth muscle, whereas the subsequent passage of agonist through the bronchial circulation produces the later changes in dynamic impedance. Presumably, the same thing could be happening in the rat over a somewhat compressed time scale due to the smaller size of the animal. Interestingly, however, the changes in Pel in the present study were considerably smaller than those elicited by histamine in dogs under similar conditions (2). This supports the assertion of Lutchen et al. (13) that changes in static elastance in the rat during bronchoconstriction are smaller than those in the dog, possibly reflecting fundamental differences in lung structure between the two species.

Perhaps the most striking result of our study, however, was the different way in which the various frequency components of RL responded to MCh as opposed to the components of EL. In the case of RL, there was a negative dependence on frequency as has been described numerous times before in many species (e.g., Refs. 8, 21), but all three frequency components increased in roughly comparable fashion as the reaction proceeded (Fig. 4A, Table 1). Lutchen et al. made measurements of transfer impedance in rats infused with MCh and also found relatively little effect on the frequency dependence of RL between 1.5 and 5.5 Hz. Their values of RL at these frequencies were a factor of two or so higher than ours, but this is not important given the variability one would expect between different rats. Also, their measurements included the resistance of the tracheal cannula. The situation for EL in our study, however, was very different. Although EL exhibited a positive dependence on frequency as expected, EL_19.69 increased vastly more than EL_5.45, which in turn increased significantly more than EL_1.48 (Fig. 4B, Table 1). In other words, the reaction to MCh in RL was relatively independent of frequency, whereas the reaction in EL was very highly dependent on frequency. We are assuming, of course, that the imaginary part of lung impedance is not influenced unduly by inertance even at the highest frequency of 19.69 Hz that we studied. Oostveen and Zwart (18) found the resonant frequency in closed-chest anesthetized rats to be ~60 Hz, which supports our assumption (although they measured transfer impedance and not input impedance as we did). On the other hand, removal of the chest wall might eliminate an important inertance in the system and so lower the resonant frequency. Indeed, under control conditions (i.e., before reaction to MCh had started) we often found EL_19.69 to be lower than EL_5.45, which suggests that inertance had an influence at the higher frequency as suggested by the transfer impedance measurements made in control rats by Lutchen et al. (13). However, as soon as the reaction to MCh began, we always found that EL values became rank ordered according to frequency (see Fig. 4). Thus it seems that stiffening of the parenchyma with bronchoconstriction increased the resonant frequency so that the imaginary part of impedance below 20 Hz became dominated by elastic rather than inertial factors. Interestingly, Lutchen et al. also found different frequency dependencies for EL before and after MCh infusion in their transfer impedance measurements.

Our goal now is to try and interpret these various observations in terms of a model of the lung. Such a model must have more than one compartment to account for the frequency dependence of RL and EL. In particular, it must be possible to "bronchoconstrict" the model so as to affect the various frequency components of EL in a widely disparate way (Fig. 4B) while keeping the various components of RL very close to each other (Fig. 4A). We consider first the simplest possibility: a model with two compartments in which bronchoconstriction is achieved only by altering the airway resistances. The compartments of the model can be topologically arranged either in parallel as first suggested by Otis et al. (20) or in series as suggested by Mead (15). Unfortunately, we cannot unequivocally determine which is the appropriate arrangement merely from measurements of air pressure and flow at the airway opening because the parallel and series models can be made to behave identically with appropriate choice of their parameters (23). Nevertheless, it is instructive to consider the extent to which each of the models is physiologically plausible.

A parallel arrangement of the two compartments can exhibit the kind of frequency dependence of elastance we require during bronchoconstriction if the airways serving the two compartments constrict by different amounts, thereby causing the two compartments to have different time constants. This would shunt high-frequency flow to the compartment with the lower time constant. Provided this compartment has a much higher elastance than the other compartment, one would then find a marked increase in elastance with frequency. One might imagine such a situation could occur if bronchoconstriction were very inhomogeneous so that a large fraction of the pulmonary airways became very severely constricted while the remaining small proportion of airways only constricted to a minor degree. In fact, there is strong evidence that bronchoconstriction is highly heterogenous (2, 7, 13), so this scenario is plausible. The problem, however, is that the very mechanism that causes frequency dependence of EL also causes a marked frequency dependence of RL. That is, although the shunting of flow predominately to one compartment increases overall EL in a frequency-dependent manner, the shunted flow also becomes limited to the single airway serving that compartment and this causes a similar dependence of RL on frequency. The only way to avoid this effect on RL is to impose a common central airway that itself has a resistance that is large compared with that of either of the two branches. Although the existence of a dominant central resistance is plausible under control conditions, our results suggest that it must continue to dominate even after bronchoconstriction and this is perhaps more problematic if one suspects that the major reaction is in the periphery.

A series arrangement of the compartments can also be made to account for the frequency dependence of EL we observed if the distal compartment represents the alveolar regions of the lung and the proximal compartment, which is very much stiffer, represents the conducting airway walls. The two compartments are connected by a distal airway, while the proximal compartment connects to the environment via a proximal airway. Such a model has actually been used previously by Jackson and Watson (9) and Oostveen and Zwart (18) to model rat respiratory impedance. When both airways constrict, flow is shunted from the distal to the proximal compartment at high frequencies. This causes a very marked increase in overall model elastance with increasing frequency. The model resistance will remain relatively independent of frequency provided, as with the parallel model above, the proximal resistance remains much larger than the peripheral resistance so that overall resistance is always determined almost entirely by proximal resistance regardless of how much flow is shunted to the proximal compartment. In a modeling study of the dog lung, Lutchen et al. (12) showed that significant shunting to the central airway walls can occur only when constriction of peripheral airways is widespread and severe. In the present study we certainly produced severe constriction by the end of the 16-s isovolume period, as evidenced by the large changes in RL and EL elicited. Therefore, the development of significant central airway shunting seems likely.

Thus it appears that a case can be made for both parallel and series models. Indeed, there is published evidence that both kinds of compartmentalization actually occur in the constricted rat lung. For example, other investigators have identified series models of the rat lung (9, 18) and have partitioned airway resistance almost equally between central and peripheral components. In addition, Lutchen et al. (13) have presented convincing evidence of severe inhomogeneity of airway constriction in rats infused with MCh. This means that the appropriate model for our results should consist of at least three compartments: a central compartment and two parallel peripheral ones. We thus simulated the impedance of the model shown in Fig. 6. The central compartment of this model was assigned a fixed elastance of 15 kPa/ml, whereas the central resistance followed an exponential time course of 0.005e^0.2t kPa ^· s ^· ml¹. The two peripheral compartments were assigned fixed elastances (E₁ and E₂) of 16 and 0.1 kPa/ml, respectively, implying that one compartment was 160-fold larger than the other (assuming uniform intrinsic tissue properties). Their respective resistances, R₁ and R₂, followed exponential time courses with R₂ (0.002e^0.25t kPa ^· s ^· ml¹) starting off 160-fold smaller than R₁ (0.16e^0.1t) but increasing substantially more quickly. This had the effect of producing a progressively increasing inhomogeneity during bronchoconstriction, with most of the lung shutting down rapidly and so causing ever more flow to be shunted to the remaining small portion.

The model impedance was calculated over a 16-s period by using the above parameter time courses. Total model resistance (real part of impedance) and elastance (imaginary part of impedance multiplied by negative angular frequency) at the same three frequencies as used in our rat experiments are plotted in Fig. 7 and show strong similarities to the experimental results given in Fig. 4. The effect of initial PEEP on rate of change of RL and EL (as seen in Fig. 5) can be simulated simply by altering the rates of exponential increase in the individual airway resistances of the model. These similarities between our simulations and the real data do not, of course, mean that we have proven anything conclusively. There are certain to be other physiologically plausible ways we could have altered the model parameters to simulate bronchoconstriction that would have produced similar results. Nevertheless, our model study does demonstrate how both parallel inhomogeneity of bronchoconstriction and central airway shunting could simultaneously play important roles in determining the changes in rat lung impedance during acute induced bronchoconstriction. It is also interesting that we were able to achieve realistic simulations of the time course of bronchoconstriction by having only the model airway resistances increase while the compartmental elastances remained constant. This is in keeping with the hypothesis favored by some investigators (2, 11, 16) that the most important effect elicited by bronchoactive drugs is constriction of conducting airways, with relatively little reaction occurring within the lung parenchyma itself.

In conclusion, we have studied pulmonary mechanics in anesthestized paralyzed open-chest rats at three different oscillation frequencies and at three different lung volumes during acute induced bronchoconstriction by using our recently developed SAV. We found that both RL and EL increased with bronchoconstriction under all conditions but that the frequency dependence of EL became very much more marked than that in RL. We interpreted these findings in terms of a three-compartment lung model in which particular time courses of constriction of central and peripheral airways produced both inhomogeneous ventilation of the two peripheral compartments and shunting of the applied oscillations into the central airway compartment. We also found that the increases in both RL and EL exhibited a strong inverse relationship to the initial inflation pressure of the lungs, which supports the notion that the forces of parenchymal interdependence exert an important influence on the extent to which airway smooth muscle can shorten when stimulated. This profound dependence of airway responsiveness on PEEP shows that it is critical to control for lung volume when studying the responsiveness of the lungs to bronchial agonists.

ACKNOWLEDGEMENTS

The authors acknowledge the financial support of the Medical Research Council of Canada, the J. T. Costello Memorial Research Fund, the Montreal Chest Hospital Research Institute, and the Canadian Network of Centres of Excellence in Respiratory Health (Inspiraplex). J. H. T. Bates and D. H. Eidelman are chercheur-bousiers of the Fonds de la Recherches en Santé du Québec.

FOOTNOTES

Address for reprint requests: J. H. T. Bates, Meakins-Christie Laboratories, 3626 St. Urbain St., Montreal, Quebec, Canada H2X 2P2.

Received 19 March 1996; accepted in final form 26 August 1996.

REFERENCES