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1 Meakins-Christie Laboratories, McGill University, Montreal, Quebec, Canada H2X 2P2; and 2 Vermont Lung Center, The University of Vermont, Burlington, Vermont 05446
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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We compared the time courses of lung mechanical changes with intravenous (iv) injection vs. aerosol administration of histamine, methacholine, and ACh in dogs. We interpret these results in terms of a spring-and-dashpot model of airway smooth muscle receiving activation via a tissue compartment when agonist is delivered by the iv route and through an additional airway wall compartment when it is delivered by the aerosol route. The model accurately accounts for the principal features of the respiratory system elastance response curves. It also accounts for the differences between iv and aerosol responses, supporting the notion that agonist delivered by aerosol has to traverse a longer pathway to the airway smooth muscle than does agonist delivered iv. The time constants representing diffusive exchange of agonist between compartments were not significantly different for the three agonists, suggesting that the three agonists shared a common principal means of clearance, which was presumably blood flow.
histamine; methacholine; acetylcholine; pulmonary blood flow; bronchial blood flow; pharmacokinetics
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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PRESUMABLY THE MOST RAPID and homogeneous way to deliver a bronchial agonist to the lungs is via a bolus injection into the circulation. The agonist is transported to the lungs through the pulmonary and bronchial circulations and diffuses across the endothelium and extracellular space to reach the airway smooth muscle. It is then cleared by the pulmonary and bronchial blood supplies and also possibly as a result of in situ degradation (8, 9, 21, 22). The dynamics of this process can be observed in the time course of pulmonary mechanics after agonist injection, which exhibits the relatively rapid rise and slower fall characteristic of pharmacokinetic systems (1, 11, 12).
However, bronchial agonists are usually applied to the lungs through the airways as an aerosol (e.g., Refs. 3, 8, 9), because this mimics the mode of delivery of many noxious environmental agents. Aerosol delivery is also less invasive than circulatory administration and thus results in less systemic exposure to the agonist. It seems natural to assume that the delivery of aerosolized agonist to the airway smooth muscle would be slower than by injection because of the time required for the aerosol to pervade the airways and alveoli and to diffuse across the epithelial barrier. Similarly, one might expect the recovery from aerosol to be slower than from intravenous (iv) injection, and indeed this has been observed for histamine (H) in dogs (9).
We hypothesized that a relatively delayed response to aerosol compared with iv delivery should reflect the dynamics of transit of agonist across the airway wall, which is presumably important in determining the efficacy of inhaled medications. Our goal in this study was, therefore, to develop a pharmacokinetic model to account for the kinetics of bronchoconstriction when agonists are administered either iv or by aerosol, with a view to assessing the time constant of airway wall transit. We based our model on measurements of the acute responses in canine lung elastance to both iv and aerosol administrations of H, methacholine (MCh), and ACh.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Experimental.
We performed experiments on five mongrel dogs weighing 16-27 kg.
The dogs were deeply anesthetized with an iv bolus of pentobarbital sodium (28-43 mg/kg). A rigid cannula (20 mm ID) was inserted into
the trachea. Mechanical ventilation was supplied by a volume ventilator
(model 618, Harvard Apparatus, South Natick, MA) by using a tidal
volume of 15 ml/kg at a frequency of 20 breaths/min. Tracheal pressure
(Ptr) was measured via a side tap between the piston and the tracheal
cannula with a piezoresistive pressure transducer (Fujikura FPM-02PG,
Servoflo, Lexington, MA). Flow at the trachea (
) was measured
with a heated Fleisch no. 2 pneumotachograph connected to a
piezoresistive differential pressure transducer (MicroSwitch
163PC01D36, Honeywell, Scarborough, Ontario). The measured signals
(, Ptr) were low-pass filtered at 20 Hz with six-pole Bessel
filters and then sampled at 100 Hz with a 12-bit analog-to-digital
converter (model DT2801-A, Data Translation, Marlborough, MA).
Acquisition of data was performed by using the ANADAT/LABDAT software
package (RHT-InfoDat, Montreal, Quebec).
data was started, and 2 min later a bronchial agonist was given either by iv injection or by
aerosol. Finally, at t > 45 min, data acquisition was
stopped. The next run was begun at t = 60 min. Three
pairs of such runs were performed in total. The first of each pair
involved iv injection of an agonist, whereas the second involved
aerosolization of the same agonist. The three agonists, H, MCh, and
ACh, were used in random order. The iv doses were 1 mg H and 0.25 mg
for both MCh and ACh. The aerosols were generated by an ultrasonic
nebulizer (DeVilbiss 100B), which delivers particles with a mass median
diameter of 0.5-10.0 µm (85% are 4.5-6.0 µm) from
solutions of 50 mg/ml of H and 12.5 mg/ml of both MCh and ACh. Each
aerosol was delivered continuously through a side port in the
inspiratory line of the mechanical ventilator until the peak in Ptr had
reached ~75% of the peak value observed during the previous run with
the injected agonist. This took typically ~1 min. We found that the
final ~25% of the response was manifest after cessation of aerosol;
therefore, the final degree of bronchoconstriction produced by the
aerosol matched that produced by iv injection.
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(1) |
. We used Ers as our measure of bronchial response
because it had a better signal-to-noise ratio than Rrs and most likely reflects the same phenomena.
The Ers signals obtained in the present study were smoothed using a
running mean with a 4-s window and then decimated to 1 Hz. The mean
baseline value of Ers (i.e., that value just before onset of
bronchoconstriction) from all dogs for all experimental runs was
2.30 ± 0.29 (SD) kPa/l. The SD of baseline Ers in any one dog was
6%. The Ers signals obtained with both injection and aerosol did not
return to baseline at 30 min after agonist application but instead
plateaued at a level typically about one-third of the peak level above
baseline. This residual degree of bronchoconstriction was only reversed
when the three total lung capacity sighs were given before the next run.
The Ers signals obtained with iv injection of agonist were true impulse
response functions in the sense that an iv bolus represents an
impulsive input compared with the time scale of the response in
mechanics. The Ers signals obtained after aerosol, however, could not
be considered impulse responses in the same way, because the aerosol
was given over a period of ~1 min. Therefore, to make the two sets of
signals comparable, we convolved the iv Ers signals with a unity area
box function having a width of 1 min. This had the effect of spreading
the iv signals in time as if the equivalent dose of agonist had been
infused over 1 min. Henceforth, when we refer to the Ers signals
obtained during iv injection, we mean the signals obtained by
convolving the original signals with the 1-min box function. Figure
1 shows the Ers signals obtained up to 10 min from all dogs (mean ± SD) after both iv injection convolved with the box function (shaded areas) and aerosol (solid areas) for all
three agonists investigated. The baseline values have been set to zero,
and the peak values in each case have been normalized to unity to allow
shape comparison.
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Model development. We first consider the responses to injection (shaded areas in Fig. 1). For all agonists, there is an initial, brief period during which Ers remains at baseline, which we presume reflects the circulatory transit time required for agonist to reach the lungs from the injection site. This is followed by a rapid increase in Ers to a fairly sharply defined peak. The duration of this rising portion is in the order of 1 min, which is the width of the box function we used to convert the response from that of a bolus injection to one representing an infusion over 1 min. Indeed, before convolution, the 20-80% rise times of the iv injection Ers signals were an average of 11 s. This suggests that, once agonist was delivered to the muscle, its response was fully manifest in much <1 min, similar to the rate of contraction of single airways seen in rat lung explants (23). Thus most of the rise time of the convolved Ers was accounted for by the spreading effect of the convolution and thus presumably represents physical delivery of agonist to the airway smooth muscle. By the same token, we presume that physical delivery of agonist to the epithelium was the principle rate-limiting step in the onset of response to aerosol. Our model of Ers dynamics must, therefore, embody the notion that the magnitude of the response is proportional to the local accumulation of agonist at the level of the airway smooth muscle.
We now consider how to link a change in smooth muscle activation to a change in what we actually measured, namely Ers. The relationship between these two quantities is certain to be quite nonlinear. However, the actual changes in Ers that we achieved in our experiments were relatively small, as a fraction of baseline Ers; therefore, we will assume that the change in Ers is proportional to the force generated by the airway smooth muscle. For the same reason, we will also assume that the airway smooth muscle shortens by an amount proportional to the increase in muscle force. This is readily modeled by placing a spring (elastic constant E) in parallel with a force generator (Fig. 2A), where the active force F(t) produced by the generator is proportional to the local accumulation of agonist, whereas the length of the spring can be taken to represent the degree of airway narrowing in some fashion. However, a spring on its own will return to its original unstressed length when the active muscle force is over. Experimentally, Ers did not return to baseline but instead plateaued at a somewhat elevated level (Fig. 1), similar to observations that have been made in previous studies (1, 5). Ers only returned to baseline after we briefly inflated the lungs to 30 cmH2O. To account for this effect empirically in our model, a dashpot (resistance R) is included in series with the spring (Fig. 2A). Now when the muscle shortens, the dashpot moves at a rate proportional to the active force so that the length of the total spring-dashpot assembly (the analog of muscle length) is reduced. Subsequent relaxation of the spring returns the assembly to a shorter length than that which it had initially.
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(=
R/E) was given a fixed value, as it represents a physical
property of the smooth muscle and the lungs and, therefore, should
presumably not vary with different agonists. We found by trial and
error that a value for of 600 s gave good results. The
remaining model parameters k and c were then
adjusted to produce the best fit between the measured iv Ers curves for
H, MCh, and ACh and the simulated curves. The equations of the model
and their numerical solution are detailed in the APPENDIX.
The aerosol Ers curves (Fig. 1) are smoother and shifted to the right
compared with the iv curves. This suggests that agonist must traverse
an additional compartment when administered as an aerosol. This also
seems reasonable on anatomic grounds, as an aerosol must first
accumulate on, and then penetrate, the mucous and epithelial layer
lining the airway before reaching the interstitium and finally the
airway smooth muscle. We, therefore, postulate the existence of an
airway wall compartment that receives an input of agonist
i(t) from the airway lumen that follows the same
time profile as the iv input from the vasculature. The agonist
concentration in the airway wall compartment is
w(t). The airway wall compartment then
diffusively exchanges agonist with the tissue compartment with a time
constant m (Fig. 2C). The resulting changes in
Ers were simulated in the same way as for the iv administration using the previously determined values of k and c,
except this time the airway wall compartment was included and the value
of m was adjusted to produce the best fit between measured
and modeled curves.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Figure 3 shows the mean normalized
iv data from all animals together with the fits obtained with the model
in Fig. 2B. The means and SDs of the best-fit model
parameters (, c, and k) obtained from
individual animals are given in Table 1.
Figure 3 also shows the mean normalized aerosol Ers curves together
with the best-fit model curves. Table 1 also lists the means and SDs of
the best-fit values of m obtained from individual animals.
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Although the mean value of m for MCh seems higher than for the other agonists (Table 1), there were no significant differences in any model parameter among agonists (P < 0.05, paired t-test).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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The temporal responses to various agonists given both iv and by aerosol have been reported by others (3, 8, 9). However, our study is the first, to our knowledge, to compare the iv and aerosol responses to H, MCh, and ACh by using the same methodology and to try and interpret these responses in terms of a pharmocokinetic-type model. Figure 3 shows that our model accounts for the essential features of the Ers time course for both iv and aerosol administration, including the rapid rise, the transient peak, and the slower recovery. Furthermore, the transformation from the iv to the aerosol response is accurately accounted for (Fig. 3) in terms of a single airway wall compartment (Fig. 2C).
The Rrs signals we obtained in our dogs tended to be rather noisy, often exhibiting spurious oscillations of comparable magnitude to the changes induced by the agonists. We presume this reflected a poor signal-to-noise ratio resulting from the rather small bronchoconstrictive responses that we elicited. In contrast, the Ers signals were considerably smoother, probably reflecting the fact that the majority of the mechanical impedance of the lungs during normal ventilation is elastic rather than resistive. This means that Ers is more precisely determined by the data than is Rrs. We, therefore, used Ers as our measurements of bronchoconstrictive response, rather than the more usual Rrs. It has been shown previously on numerous occasions (e.g., Refs. 1, 2, 6, 14) that bronchoconstriction invariably causes corresponding changes in both Rrs and Ers. Indeed, as far as one could tell from visual inspection of the data from the present study, the Rrs and Ers signals were very similar apart from their different levels of noise, suggesting that they both contained the same information about the dynamics of bronchoconstriction. Our laboratory has previously found this to be the case in dogs receiving much larger doses of bronchial agonist (Fig. 1 of Ref. 12). The reasons why this is so may relate to the fact that the airways and parenchyma are intimately juxtaposed so that a constricting airway will induce stresses in the ajoining parenchyma, thereby making it stiffer. Also, experimental evidence points to bronchoconstriction being an inherently inhomogeneous event (1, 13, 15), which seems reasonable given that airways differ in their mechanical properties, amounts of smooth muscle, and access to the vasculature. Consequently, bronchoconstriction produces regional time constant differences that get worse as the overall level of constriction increases and that produce increases in dynamic lung elastance (1, 14). We thus conclude that either Rrs or Ers can be used as an index of bronchial response to an agonist. Our measurements of Ers also included the elastance of the chest wall. However, we do not believe that significant changes in chest wall mechanics should occur with bronchoconstriction, compared with the changes taking place in the lung; therefore, we took changes in Ers to indicate changes in lung elastance.
Figure 1 suggests that the recovery from ACh was slightly more rapid than from the other two agonists. This is what we would expect given the more rapid enzymatic degradation of ACh (20). Similar observations were obtained by Kelly et al. (9) for iv administration of the three agonists, although, again, their time constants were somewhat different from ours, perhaps because of differences in experimental methods and dose of agonists. There are plenty of reasons for suspecting that the clearance rates should be different for all three agonists, as the enzymes responsible for local degradation of H and MCh and ACh are different (9). Cartier et al. (3) found that recovery from aerosolized MCh was much slower than that from aerosolized H in humans, although this contrasts with the iv results of Kelly et al. (9), perhaps because of species and methodological differences. It has also been shown that pulmonary blood flow influences recovery from H but not MCh and ACh (9), whereas bronchial blood flow affects recovery from H (8) and MCh (21). Despite this, however, there were no significant differences in the values of c for any of the agonists (Table 1). This may have been due to the large variability in the values of the model parameters among animals. Such variability could have obscured any differences among parameters because of differences in clearance mechanisms. Even so, the essential similarities of the values of c lead us to conclude that a common predominant mechanism was responsible for the clearance of all agonists in our experiments, and the obvious candidate is blood flow.
Our data clearly show (Fig. 1) that recovery is slower for aerosol delivery than for iv. Kelly et al. (9) made similar observations for H in dogs and concluded that this was due to a greater volume of distribution for the aerosol than for the injected agonist. Our model incorporates a specific mechanism whereby this greater distribution volume is achieved, namely the presence of an additional compartment representing the airway wall and any other structures that a drug must traverse when delivered by aerosol as opposed to iv (Fig. 2C). Such an additional compartment seems reasonable on anatomic grounds, as an aerosol must first accumulate on, and then penetrate, the mucous and epithelial layer lining the airway before reaching the interstitium and finally the airway smooth muscle. The effect of this compartment is both to delay the peak in the response and to slow its subsequent decay (Fig. 3). The parameter m represents diffusive exchange of agonist across the airway wall compartment and has a value in the order of 1 min, albeit with large interanimal variation (Table 1). This quantity presumably has significance for the efficacy of drug delivery by aerosol and would be expected to change with alterations in the thickness of the airway wall and associated components. For example, damage to the epithelium by cationic proteins (4) might be expected to decrease m.
Our model is extremely simplistic. For example, the spring-and-dashpot muscle representation in Fig. 2A neglects many details that have been shown to pertain to real airway smooth muscle, such as plasticity to length changes (7). However, for our present purposes, we merely require a construct that behaves empirically like the contractile machinery activated during our experiments. A key feature of our data is that Ers recovered to an elevated level (Fig. 1) that was only returned to baseline with a deep lung inflation. This phenomenon may be due to some regions of the distal lung becoming closed off during bronchoconstriction and only being reopened with a large inflation. Such closure was postulated to account for some of the observations in our previous study of the acute time course of bronchoconstriction to H in the dog (1). Also, the recent computer modeling studies of Lutchen et al. (13) support the notion that bronchoconstriction is attended by diffuse closure of lung units.
A key assumption we made in developing the aerosol model is that the delivery of agonist from the tissue compartment to the airway smooth muscle compartment is the same for both aerosol (Fig. 2B) and iv (Fig. 2C) administration. This is almost certainly not precisely the case in practice. Studies in rats, for example, have shown different patterns of constriction in the lung and different signatures of change in mechanical impedance with the two modes of administration (15, 16, 18). However, we have no idea how to incorporate such mode-dependent effects into our model or even whether they are important compared with the processes for which we have accounted. We, therefore, assume that they are not important and offer as support for this notion the fact that the model curves fit the mean data well (Fig. 3) and seem to be able to account for the differences between iv and aerosol dynamics with only a single addition parameter (m).
Interestingly, our study shows that the bronchoconstrictive response to a short application of bronchial agonist is transient, regardless of whether the application is by injection or by aerosol. Thus even though there is a period of a few minutes around the peak aerosol responses in Fig. 1 when Ers is not changing very rapidly (particularly for H and MCh), the responses all begin to decay immediately after peaking, without there being any clear plateaus at the peak. Cartier et al. (3) measured the response to aerosolized H and MCh in humans and reported response plateaus of ~17 and 75 min, respectively, before recovery. These recovery times are very much greater than ours, and we are not sure how to account for differences of this magnitude, especially as our recovery times are similar to those of other investigators (9). A possible explanation is that Cartier et al. (3) defined the plateau arbitrarily as being the time during which their response was within 20% of the maximum; thus the response was actually recovering slowly during the designated plateau phase. Also, they measured their responses in terms of lung conductance, which is the inverse of resistance and, consequently, appears to change less near the plateau than does resistance. In any case, a true steady-state level of bronchoconstriction is only likely to be achieved during the continuous application of agonist at some constant rate. Nevertheless, it is generally held that the response to aerosol agonist exhibits a plateau for some time during which a maximal response measurement can be made (3). That this is not so has significant practical implications for the measurement of bronchial responsiveness in animals and humans, because the usual practice in such measurements (e.g., Ref. 17) is to deliver a bronchial agonist by aerosol and then assess lung mechanics at some point after cessation of aerosol when the bronchoconstrictive response is considered to be fully manifest. It is clearly important to know when the maximum response occurs and to time measurements carefully with respect to this event to be able to compare results between challenges.
In summary, we studied the time courses of Ers after iv and aerosol administration of H, MCh, and ACh in dogs. We interpreted our data in terms of a model consisting of three interconnected compartments interfacing with a simple spring-and-dashpot model of airway smooth muscle mechanics. We found that the time constants of intercompartmental exchange and clearance were similar for all three agonists, which supports the notion that the principal mechanisms responsible for agonist dynamics were the same for all substances. We also estimate that the time constant of transport of agonist across the airway wall is in the range of 0.5-2 min. Even though this model is a grossly oversimplified representation of the myriad compartments that must actually be involved in agonist kinetics, we suggest that it captures the important global steps involved in the process of agonist exchange. In particular, it shows how a single, additional compartment is all that is required to transform an iv response curve into an aerosol curve. Finally, both iv and aerosol responses were transient, with no stable plateau being achieved, which has practical implications for the common practice of assessing bronchial responsiveness to inhaled agents.
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APPENDIX |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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The equation describing the rate of change of agonist in the
tissue compartment in the iv model (Fig. 2B) is
![V<SUB><IT>s</IT></SUB> <FR><NU>d<IT>s</IT>(<IT>t</IT>)</NU><DE>d<IT>t</IT></DE></FR><IT>=q</IT>(<IT>t</IT>)<IT>+&agr;</IT>[<IT>a</IT>(<IT>t</IT>)<IT>−s</IT>(<IT>t</IT>)]](/content/vol89/issue5/fulltext/2023/img002.gif)
|
(2) |
is a rate constant for exchange between the tissue
and airway smooth muscle compartments. The a(t)
and s(t) quantities are shown in Fig.
2B. Rearranging Eq. 2 gives
![<FR><NU>d<IT>s</IT>(<IT>t</IT>)</NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>q</IT>(<IT>t</IT>)</NU><DE>V<SUB><IT>s</IT></SUB></DE></FR><IT>+</IT><FR><NU><IT>&agr;</IT></NU><DE>V<SUB><IT>s</IT></SUB></DE></FR> [<IT>a</IT>(<IT>t</IT>)<IT>−s</IT>(<IT>t</IT>)]](/content/vol89/issue5/fulltext/2023/img003.gif)
|
(3) |
![=i(t)+<FR><NU>1</NU><DE>k</DE></FR> [a(t)−s(t)]](/content/vol89/issue5/fulltext/2023/img004.gif)
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![<FR><NU>d<IT>a</IT>(<IT>t</IT>)</NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>k</IT></DE></FR> [<IT>s</IT>(<IT>t</IT>)<IT>−a</IT>(<IT>t</IT>)]<IT>−</IT><FR><NU><IT>1</IT></NU><DE><IT>c</IT></DE></FR><IT> a</IT>(<IT>t</IT>)](/content/vol89/issue5/fulltext/2023/img005.gif)
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(4) |
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(5) |
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(6) |
Equations 3-6 were integrated at 100 Hz by using first-order Euler integration, with i(t) as described in the text and with the values of the model parameters chosen to achieve a best fit between the simulated and measured Ers curves.
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ACKNOWLEDGEMENTS |
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The authors acknowledge the financial support of the Medical Research Council of Canada, the J. T. Costello Memorial Research Fund, the Fonds de la Recherche en Santé du Québec, and the Canadian Network of Centres of Excellence in Respiratory Health (Inspiraplex). A.-M. Lauzon is a Parker B. Francis Fellow.
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FOOTNOTES |
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Address for reprint requests and other correspondence: J. H. T. Bates, Colchester Research Facility, 208 South Park Drive, Suite 2, Colchester, VT 05446 (E-mail: jhtbates{at}zoo.uvm.edu).
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.
Received 21 January 2000; accepted in final form 16 June 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
|
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1997
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