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Vermont Lung Center, University of Vermont College of Medicine, Burlington, Vermont
Submitted 22 August 2005 ; accepted in final form 17 October 2005
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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respiratory impedance; computational model; airway hyperresponsiveness; asthma
It may thus serve us better to pursue the development of a set of animal models that collectively encompass the full spectrum of abnormalities seen in asthma but that individually represent only part of this spectrum. This would allow us to examine the effects of each abnormality individually and perhaps even to study the interactions between abnormalities, if more than one can be implemented simultaneously in the same animal. In this sense, the acutely allergically inflamed mouse is a useful representation of one kind of hyperresponsiveness, namely that which occurs when an inflamed mucosa encroaches into the airway lumen. Such encroachment amplifies the increases in airway resistance and airway closure caused by a normal degree of smooth muscle shortening. This is by no means the only mechanism for producing hyperresponsiveness, however, and significant gaps remain in the currently available set of animal models embodying other mechanisms. The goal of the present study was, therefore, to establish a mouse model, complementary to the allergically inflamed preparation, in which hyperresponsiveness is due to enhanced narrowing of the conducting airways.
On the basis of previous work, we hypothesized that increased airway narrowing would occur in mice treated with poly-L-lysine (PLL), an artificial analog of native cationic protein. Our laboratory has previously shown that PLL permeabilizes epithelial cells (28) and that rats treated with intratracheal PLL are hyperresponsive to methacholine that is delivered as an aerosol but not injected intravenously (16). These observations support the notion that PLL increases bronchial responsiveness by an epithelium-dependent mechanism, apparently making the underlying smooth muscle more accessible to an inhaled agonist. Such an effect would be expected to lead to increased contraction of the smooth muscle, and hence exaggerated airway narrowing, when the doses of methacholine are submaximal. By contrast, when the methacholine dose is supramaximal, the airway smooth muscle should contract maximally, regardless of how quickly the agonist is able to traverse the epithelium. Furthermore, at all doses, we would expect airway narrowing to be more rapid than normal, due to enhanced penetration of agonist to the underlying smooth muscle. The PLL-treated mouse should, therefore, constitute a model of airways hypersensitivity. To test these notions, we examined the time course of respiratory impedance following administration of increasing doses of methacholine aerosol to mice pretreated with intratracheal PLL. As in our laboratory's previous study in allergically inflamed mice (29), we interpreted the results by performing equivalent virtual experiments on an anatomically based computational model of the mouse lung.
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METHODS |
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The experimental protocol began with the normalization of lung volume history by the delivery of two deep lung inflations of 1.0 ml followed by 2 min of regular ventilation. Mice were then challenged with an aerosol of PBS for 40 s, achieved by channeling the inspiratory flow from the ventilator through an ultrasonic nebulizer containing PBS. During the challenge, the piston of the ventilator was programmed to deliver a tidal volume of 0.8 ml at a rate of 30 breaths/min. Due to the shunt compliance of the nebulizer chamber, however, the tidal volume actually delivered to the lungs was 
0.6 ml. Following cessation of aerosol delivery, the ventilatory rate and tidal volume were returned to baseline, and measurements of the complex input impedance of the respiratory system (Zrs) were made at regular intervals for the next 3 min. Finally, two more deep lung inflations were given. The above protocol was then repeated three more times with aerosols containing methacholine in PBS at sequentially increasing concentrations of 3.125, 12.5, and 50 mg/ml. Responses were obtained for all concentrations in all animals studied, with the exception of one of the animals in the saline group from which data at 50 mg/ml were not obtained.
During the 3 min following delivery of each aerosol challenge, every 10 s of regular ventilation were terminated in a 1-s passive expiration followed by a 2-s broadband (1–19.625 Hz) volume perturbation, after which ventilation was immediately resumed. The peak-to-peak excursion of the ventilator piston during delivery of these perturbations was 0.17 ml above functional residual capacity, resulting in a volume delivered of 0.14 ml after accounting for gas compression in the ventilator cylinder and connecting tubing. The pressure and flow data obtained during application of the volume perturbations were used to calculate Zrs, which was then fit to a model of lung mechanics using an iterative scheme described previously (29). The model consists of a single airway having a Newtonian resistance (RN) that serves a uniformly ventilated tissue compartment that has a constant-phase impedance. The model is described by the equation (14)
 | (1) |
, and 
couples G and H. Following the approach of Ito et al. (18), we consider f in the above equation to be normalized to the frequency at which 2
f = 1, so that G and H both have the same units as RN, namely cmH2O·s·ml–1. This model has been shown to accurately describe Zrs between 0 and 20 Hz under control conditions and during mild bronchoconstriction (12, 13, 24). Our laboratory has found previously (29) that Iaw has a negligible effect in the mouse lung <20 Hz, no doubt because the mass of the gas in the mouse trachea is so small. Also, the tracheal cannula bypasses a significant fraction of the trachea, and the impedance of the cannula itself is removed in the calculation of Zrs. Consequently, Iaw cannot be estimated reliably from Zrs <20 Hz and so will not be considered further.
Virtual experiments.
As previously described (29), we also performed virtual experiments using a computational model of the mechanics of the mouse lung based on the asymmetrical airway branching scheme of Horsfield (11). We assumed Poiseuille flow in each airway to calculate its flow resistance. Together with the mass of gas contained in the lumen, this gives airway impedance (Zaw) as:
 | (2) |
is the density of air. We neglected the influence of airway wall shunting on Zrs by assuming that the airways are rigid during the application of the oscillatory volume perturbations used to determine Zrs.
As in our laboratory's previously study (29), each of the most distal airways terminated in an identical tissue unit with impedance Zti, given in analogy to Eq. 1 by
 | (3) |
(8). The total impedance of the model, Zmod, was calculated by adding the individual Zaw and Zti in series or parallel, as appropriate, at each of the frequencies used to obtain Zrs experimentally. The following Monte-Carlo procedure was used. Sixteen independent determinations of Zmod were made, with the individual values of r in each case being made by random selection from a Gaussian distribution, having mean and standard deviation appropriate for the airway order in question, as determined by Gomes and Bates (11). The final Zmod was the average of the 16 individual Zmod values.
Zmod is thus constrained by the airway tree structure defined by Gomes and Bates (11) and by the forms of Eqs. 2 and 3. We adjusted Zmod to match a given set of experimental data by choosing the values of only three parameters; Hti and , and a scaling factor 
, which was simultaneously applied to all values of r to achieve a uniform relative narrowing or dilatation of all of the model airways.
Once the computational model was adjusted so that Zmod matched baseline Zrs, we made the model bronchoconstrict with a time course similar to a set of experimental data by having the radii of all airways in the model assume a time-varying fraction of their respective baseline values. This fractional time course was calculated as described below. The model also incorporated our previously described mechanism for lung derecruitment (29), whereby any airway narrowing to a specified threshold radius would be closed completely for the remainder of the simulation.
Statistical analysis. Differences in the magnitude or timing of responses to methacholine between the saline and PLL groups were compared by using unpaired t-tests. Differences in the coefficient of determination (a measure of goodness of fit of Eq. 1 to experimental data) between two points along the time course of the methacholine response within a group of animals (either saline or PLL) were compared by using paired t-tests. Differences in the coefficient of determination at the same time point between the two groups were compared by using unpaired t-tests. Statistical significance was taken as P < 0.05. We used the coefficient of determination, a standard measure of goodness of fit, to gauge how well Eq. 1 fit the experimental measurements of Zrs. The coefficient of determination is the fraction of the variance of a data set that is accounted for by the model.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Figure 1 shows the time courses of RN, G, and H following challenge with the three increasing concentrations of methacholine aerosol (the responses are plotted sequentially for ease of comparison, but there was actually a small period of time between the individual challenges, including the 40 s required for aerosol delivery). In both saline and PLL groups, RN shows progressively increasing peaks with each challenge that descend to plateau levels only slightly above baseline (Fig. 1, top). The heights of the peaks in RN are significantly elevated in the PLL group relative to controls at the intermediate concentrations of 3.125 and 12.5 mg/ml, but, at the highest concentration of 50 mg/ml, both groups responded similarly. PLL treatment reduced the time to reach peak response; the maximum value of RN in the PLL group was achieved significantly earlier than in the saline group at methacholine concentrations of 3.125 and 12.5 mg/ml and just failed to reach significance (P = 0.081) at 50 mg/ml. These various observations are mirrored closely in the parameter G (Fig. 1, middle): the peak in each G response tended to be higher in the PLL group compared with the saline group (although not reaching statistical significance) and occurred earlier (significant except for the peak at 12.5 mg/ml methacholine, which was just not significant at P = 0.59). H, on the other hand, showed no initial peak at all in most cases, and a very modest peak in others, leading to slightly elevated plateaus (Fig. 1, bottom). The plateau in the PLL group was significantly higher compared with that in the saline group at 12.5 mg/ml and just failed to be significantly higher (P = 0.067) at 50 mg/ml. The plateaus in RN, G, and H were all abolished by a deep inflation.
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, Hti, and of 0.83, 1,800 cmH2O·s·ml–1, and 0.1, respectively. To match the data from the present control animals at baseline as closely as possible, the values of and Hti had to be changed slightly from those used in our laboratory's previous study, possibly reflecting subtle differences in animal size or developmental history: was increased by 9%, and Hti was decreased by 11%. We also found that the simulated values of G were too high if we retained the value of 0.1 for that we used in our laboratory's previous study (29). However, this value of was taken from a published study of dog lung strips that used single-frequency length oscillations, because data from mouse lung strips were not available at the time of our laboratory's previous study. Recently, Fust et al. (9) fit the model in Eq. 1 to the mechanical impedance of isolated strips of mouse lung tissue subjected to uniaxial broadband length oscillations up to 20 Hz, and found a value for of 0.042. We, therefore, used this value of in the present computational model and obtained simulated time courses for RN, G, and H that reproduce the main features of the experimental measurements in both the saline group (Fig. 3) and the PLL group (Fig. 4).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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In the present study, we made a number of findings that are relevant to the foregoing. First, we found that intratracheal PLL caused elevations in RN and G but only at the low and intermediate concentrations of methacholine; at the highest concentration of 50 mg/ml, the responses of RN and G in the PLL and saline groups were similar (Fig. 1, top and middle). In other words, the dose-response curves for RN and G were shifted to the left, indicating an increase in the sensitivity of the airways to methacholine, but not in their peak responsiveness. A second and contrasting observation is that, although PLL also increased the methacholine responsiveness of H (Fig. 1, bottom), the effect became progressively more pronounced with increasing methacholine concentration. Thus our data indicate that, between 12.5 and 50 ml/ml methacholine, a progressively increasing degree of peripheral airway closure took place in the PLL group without a corresponding increase in the degree of airway narrowing. A possible explanation is that incomplete reopening of closed airways between challenges and the accumulation of airway secretions may have caused closure to increase over time. Indeed, the inability of agonist aerosol to fully penetrate a lung partially obstructed from a previous challenge has been postulated to account for the existence of a plateau in the methacholine responsiveness of a normal lung (3).
The above results are compatible with the notion that intratracheal PLL causes airway hypersensitivity by compromising the barrier function of the epithelium, an ability shared by other cationic proteins (6, 7). Our laboratory introduced this notion previously to explain why intratracheal PLL causes exaggerated increases in lung resistance and elastance measured in rats at a single frequency when methacholine is delivered as an aerosol, but not when it is injected intravenously (16). PLL has been previously shown to lower the electrical conductivity of epithelial cell layers (28), which presumably reflects damage either to the cell membrane or to the tight junctions between cells. A permeabilized epithelium presumably allows more luminally applied agonist to make its way to the smooth muscle before being cleared or degraded, resulting in enhanced muscle shortening, excessive airway narrowing, and increased airway resistance. This notion is further supported by our finding that the peaks in RN and G from the PLL group occurred earlier than the corresponding peaks in the saline group (Fig. 1). Such an effect would be expected if the challenging agonist were able to reach the airway smooth muscle more easily, and hence more quickly, than normal. By contrast, our laboratory has previously argued (29) that the relatively delayed peak in RN seen in inflamed BALB/c mice reflects the increased transit time required for an agonist to cross a swollen, thickened epithelium. An effect of PLL solely on the epithelium, and not on the airway smooth muscle itself, would also mean that the maximum ability of the muscle to narrow the airways would be unchanged, which is indeed what we observed; the response of the PLL-treated animals to 50 mg/ml methacholine, which likely approached a supramaximal dose, was similar to that of the saline-treated controls.
To put the above interpretation in the context of our current understanding of lung structure, we now examine the data in light of our computational model of mouse lung mechanics (29). This model serves as a virtual laboratory for reproducing experiments in silico and allows us to determine the consequences of particular hypotheses about mechanisms of hyperresponsiveness. To use the computational model effectively, we must simulate data under conditions as close to those used experimentally as possible, because Eq. 1 does not fit the experimental spectra of Zrs(f) perfectly; small systematic deviations between Zrs(f) and the fit provided by Eq. 1 attest to the obvious fact that the lung is a much more complex system than that represented by Eq. 1. Furthermore, as bronchoconstriction develops, the adequacy of Eq. 1 as a description of lung mechanics is likely to change. However, although the goodness of fit provided by Eq. 1, as measured by the coefficient of determination, was significantly lower in both groups at the peak and plateau of the response to 50 mg/ml methacholine compared with baseline, the differences were relatively small. This suggests that Eq. 1 continued to describe the experimental data adequately, even during bronchoconstriction. Furthermore, by generating Zrs(f) data using the computational model at the same values of f as used experimentally, we are able, at least insofar as the model is a good representation of the real lung, to reproduce any variations in parameter values due to variations in the ability of Eq. 1 to describe the experimental data.
Using the computational model described above, we were able to accurately reproduce the data from both the saline (Fig. 3) and PLL (Fig. 4) groups, with the fractional airway narrowing in the model being determined in each case (Fig. 2) by the corresponding experimental values of RN. In other words, exactly the same model structure accounted for both data sets, implying that the only effect of PLL treatment was to cause a greater degree of smooth muscle shortening at intermediate doses of methacholine. By contrast, the model representing allergically inflamed mice, with an 18-µm lining inside the airways and an 18% increase in the closure threshold radius (29), did a poor job of accounting for the experimental data from the PLL mice (Fig. 4) in two critical ways. First, to get the simulated RN from the inflamed model to match the experimental values in the PLL mice, we had to reduce the degree of airway narrowing to 60% of that used with the control model (Fig. 2). There is no plausible explanation for why a substantially reduced degree of smooth muscle shortening should occur in PLL-treated mice, particularly as our previous studies have indicated that precisely the opposite is what actually occurs. Second, we found that, even with this reduced airway narrowing, the simulated H profiles were elevated substantially above those observed experimentally (Fig. 4). We, therefore, conclude that the computational model that we used previously to account for the methacholine responsiveness of allergically inflamed mice has no relevance for the PLL-treated animals of the present study. Taken together, the above simulation results support the conclusion that greater airway narrowing occurred in the PLL mice than in controls at methacholine concentrations of 3.125 and 12.5 mg/ml but that the PLL mice behaved similarly to controls at baseline and at 50 mg/ml methacholine.
Thus our results indicate that the BALB/c mouse treated with intratracheal PLL is a model of enhanced sensitivity of the airways to methacholine, as we originally hypothesized. This stands in stark contrast to our previous findings in mice with allergic airway inflammation that exhibited hyperresponsiveness predominantly in H, indicating an effect confined to the lung periphery (29). However, our conclusions are based on mathematical models of the lung, which embody assumptions that are always open to question. The model (Eq. 1) that we fit to measurements of Zrs assumes a particularly simple lung structure, but this is necessary in order for the parameters of the model to be uniquely identifiable from the data. Accordingly, this model assigns a central role to RN and peripheral roles to G and H. A key component of our study was then to further refine these roles using virtual experimentation with an anatomically based computational model. Nevertheless, we must bear in mind that the strength of these interpretations rests on the many assumptions inherent in the computational model. For example, the model is based on the airway tree structure of a strain of mouse (11) that is different from that used in the present study. We assumed the airways are rigid, which neglects their ability to change volume in response to applied variations in pressure (10, 26). We assumed Poiseuille flow in the airways, which neglects the possible presence of entrance effects, flow unsteadiness, and turbulence (17, 23). We also assume that it is appropriate to narrow all airways in the model by the same fraction to simulate bronchoconstriction, whereas, in reality, airways narrow heterogeneously (1, 22, 27). Testing these assumptions remains an important area for future research.
In summary, we have studied the time course of induced bronchoconstriction in BALB/c mice treated with intratracheal PLL. We found an increased response in the central airways at submaximal doses of methacholine aerosol, which we were able to accurately reproduce in an anatomically based computational model of the mouse lung simply by increasing the degree of airway narrowing. Moreover, we interpret these results as reflecting a reduced barrier function of the epithelium caused by the PLL, allowing for easier and more rapid access of aerosolized agonist to the underlying smooth muscle. This represents a completely different manifestation of enhanced bronchoconstriction to that found in the allergically inflamed mouse (29), underscoring the fact that airway hyperresponsiveness can occur by a variety of mechanisms (4). Which of these mechanisms has the most relevance for human asthma remains an open question, but studying different animal models that embody the various possibilities may help in finding the answer.
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GRANTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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, Saline-treated animals (n = 6); 
, animals treated with poly-L-lysine (PLL; n = 6). The three time courses are shown consecutively to save space, but there was actually a 40-s aerosol delivery period before each peak in the responses shown. The vertical dotted lines bracket parameter values obtained following deep lung inflations given to reestablish baseline conditions. *Significant differences in parameter values between groups at time points indicated, P < 0.05. +Significant differences in timing of the indicated response peaks between the two groups, P < 0.05.
