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Vermont Lung Center, University of Vermont College of Medicine, Burlington, Vermont
Submitted 12 November 2007 ; accepted in final form 11 April 2008
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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airway resistance; airways hyperresponsiveness; airway smooth muscle; airway remodeling
Our laboratory recently developed a computational model of a single airway contracting against the elastic tethering forces of the parenchyma in which it is embedded (5). We showed that this model accurately describes the effects of positive end-expiratory pressure (PEEP) and tidal volume on airway responsiveness in normal animals and also explains much of the effect on airway resistance (Raw) caused by a deep inflation in constricted mice (3), provided the model includes a parameter to account for the stiffness of the airway wall. Thus, by fitting this model to continuous measurements of Raw made at different lung volumes following a bolus injection of bronchial agonist, we can estimate the effective stiffness of the airway wall in vivo. In the present study, we use this approach to investigate whether airway wall stiffness is altered in allergically inflamed mice, a commonly used animal model of asthma.
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METHODS |
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Female BALB/c mice were obtained from Jackson Laboratories (Bar Harbor, ME) at 
8 wk of age. Our studies conformed to the National Research Council Guide for the Care and Use of Laboratory Animals and were approved by the Institutional Animal Care and Use Committee of the University of Vermont.
Acute allergic inflammation.
Our first set of experiments was designed to determine how airway wall stiffness is affected during the acute phase of allergic inflammation. We know that BALB/c mice are hyperresponsive to methacholine during this phase, and computational modeling indicates that this is due to increased thickness of peripheral airway walls (38). The purpose of the present experiments was to determine whether the mechanical properties of the walls are also affected. To produce an acute inflammation, mice were sensitized with an intraperitoneal injection of ovalbumin (20 µg in 2.25 mg alum) on days 0 and 14. They were challenged on each of days 21, 22, and 23 by being placed in a compartmentalized aerosolization chamber and exposed to ovalbumin aerosol (1% in phosphate-buffered saline) for 30 min. Airway responsiveness to a bolus intravenous injection of 137 µg/kg methacholine (0.074 mg/ml in 40 µl saline) was measured (see below) on day 25. This group of mice are referred to as the Acute Ova group (n = 6). The results from these animals were compared with those obtained from an age-matched Acute Control group (n = 6) that was prepared in the same way as the Acute Ova group, except that the control animals were not exposed to ova. We also measured airway responsiveness to three times the dose of methacholine (411 µg/kg) in a second group of control mice, the Acute Control High-Dose group (n = 8), to see if our technique for estimating airway wall stiffness is affected by the degree of bronchoconstriction.
Chronic allergic inflammation. Our second set of experiments was designed to see if allergic inflammation leads to any long-term alterations in airway wall stiffness that persist, even when the acute inflammatory phase is no longer present. We, therefore, subjected BALB/c mice to a more extended ova challenge protocol and waited for the inflammation to resolve before studying their airway responsiveness. Mice were sensitized with an intraperitoneal injection of ovalbumin (20 µg in 2.25 mg alum) on days 0 and 14. They were challenged with 1% aerosolized ovalbumin on days 21, 22, and 23, and then once per week for the following 3 wk. Physiological measurements were performed 4 wk after the final ovalbumin exposure. This group of mice are referred to as the Chronic Ova group (n = 8). As a basis for comparison, we also studied an age-matched Chronic Control group (n = 9) that was not exposed to ovalbumin.
Experimental Protocol
Mice were anesthetized with pentobarbital sodium by intraperitoneal injection (90 ml/kg diluted in phosphate-buffered saline to 5 mg/ml) and tracheostomized, and an 18-gauge cannula was tied into the trachea. The mice were connected to a computer-controlled small-animal mechanical ventilator (flexiVent, SCIREQ, Montreal, Quebec) for mechanical ventilation at 200 breaths/min and a tidal volume of 0.2 ml against a PEEP of 3 cmH2O. The animals were paralyzed with an intraperitoneal injection of pancuronium bromide (0.8 µg/kg). The experimental protocol began with the delivery of a deep breath to an airway pressure limit of 25 cmH2O. Approximately 1 min later, the animals in all five groups were injected with a bolus of methacholine through a catheter placed in the jugular vein. The injection took 1 s to deliver and was followed by 50-µl saline to flush the catheter. At the beginning of injection, regular mechanical ventilation was suspended, and the animals were allowed to expire passively against the external PEEP for 1 s. Immediately after this expiration, a volume perturbation was applied to the lungs by the ventilator piston for 20 s. The perturbation had a peak-to-peak amplitude of 0.1 ml and consisted of 10 repeats of a 2-s signal containing 12 sinusoids, having mutually prime frequencies from 1 to 20.5 Hz and amplitudes that decreased inversely with frequency. Regular mechanical ventilation was resumed immediately after the perturbation sequence was complete. During the application of the perturbation, the volume displacement of the ventilator piston and the pressure inside its cylinder were recorded and stored for subsequent analysis. This methacholine challenge procedure was repeated at PEEP levels of 1, 3, and 6 cmH2O in random order, with 10 min allowed between subsequent methacholine challenges. These maneuvers required that the mice be deprived of normal ventilation for 20-s periods, which is a rather long time for a mouse. One might thus worry about changes in blood gases and possibly neural tone affecting lung mechanics by the end of the measurement period, although we have previously found neural tone to be negligible in mice (30). In any case, both effects would have been mitigated by the volume perturbations that were applied during the measurement period and that had an amplitude of about one-half that of normal tidal volume. Thus by far the major effect on lung mechanics was produced by the methacholine.
At the end of the protocol, a lung lavage was performed by instilling 1 ml of phosphate-buffered saline containing 3.2% sodium citrate into the trachea with a syringe and then withdrawing it back into the syringe (withdrawn volume being 0.8 ml). The lavage fluid was stored on ice for later analysis of cell counts, and the mice were euthanized with an overdose of pentobarbital sodium, followed by opening of the thoracic cavity.
Calculation of Impedance
The pressure and flow data sampled at 128 Hz during application of each volume perturbation were used to calculate the complex input impedance of the respiratory system (Zrs) within a 2-s sliding window that moved across the 20-s data segment in steps of 0.125 s (37) after digital removal of the mechanical effects of the ventilator circuit, as previously described (10). Each estimate of Zrs was fit to the equation of a lung model consisting of a single airway serving a constant-phase viscoelastic tissue unit, the so-called constant-phase model of Zrs (12), described by the equation
 | (1) |
is angular frequency, i = 
; and f is frequency. The exponent 
couples G and H through the expression = (2/
)arctan(H/G) (12). I has negligible effect in the mouse lung <20 Hz and so can be ignored (10). Angular frequency in Eq. 1 is normalized to 0 = 1 rad/s, so that R, G, and H all have units of cmH2O·s·ml–1 (14). We thus obtained time courses for R, G, and H sampled at 8 Hz from 1 to 19 s after each injection of methacholine. Model Fitting
Our computational model of a contracting airway and the method we use to fit it to experimental data have been described in detail previously (4, 5). For completeness, the following is a brief overview. We model an airway in two dimensions as a circular ring of ASM wrapped around an elastic airway wall embedded in homogeneously elastic lung parenchyma. This neglects the fact that at least some ASM cells are oriented at a slight angle to the circumferential direction (19), so that, in reality, ASM contraction may cause changes in airway length as well as radius. This is a complicated issue for which we do not know how to account precisely, so, for the present purpose, we assume that ASM contraction only decreases airway radius by pulling against the parenchymal attachments to the outside of the airway wall. This outward pull comes from two sources: 1) the transpulmonary pressure (Ptp) that is transmitted across the parenchyma when it is undistorted (uniform and isotropic), which is determined by lung volume under the assumption of a constant tissue elastance; and 2) the local distortion of the parenchyma caused by narrowing of the airway, which is assumed to follow the relationship identified by Lai-Fook (15). The inward recoil of the airway wall is determined by its stiffness, which is assumed to arise from a fraction (1 – k) of the airway circumference that expands according to the one-third power of Ptp. The remaining fraction, k, of the circumference is assumed to be inextensible, where 0 < k < 1. Once activated, the ASM follows the classic Hill force-velocity relationship that is hyperbolic when active force (FA) is less than isometric force (F0), and linear when FA 
F0 with slopes matched at F0 (11); thus
 | (2) |
At any point in time, FA is the force that adds to the outward recoil of the parenchyma and the inward recoil of the airway wall to give a net force difference of zero. The explicit expression for FA that this produces is derived in Ref. 5 and is given by
 | (3) |
We used the above equations to calculate how r varies with time when the model was driven with a prescribed volume signal that, when multiplied by lung elastance, produces a time-varying Ptp(t) signal. Initially, the ASM was relaxed so that FA = 0 and r were determined by the force balance between the inward recoil of the airway wall and the outward recoil of the surrounding parenchyma. Once the ASM in the model was activated, FA was given by Eq. 3. A constant level of activation was then assumed so that, at each time step of 0.0625 s, Ptp(t) was used in Eq. 3 to determine FA. The result was substituted into Eq. 2 to provide dr/dt, which was then used to determine r at the next time step using first-order Euler integration. This new value of r was then used in Eq. 3 again to determine the next value for FA, and so on, until a complete time profile of r was produced. Finally, invoking the assumption of Poiseuille flow through the airway, a normalized Raw profile was calculated by raising rTLC/r to the fourth power.
The model was driven by a volume signal that varied sinusoidally at a frequency of 1 Hz above the lung volume set by PEEP. The amplitude of the sinusoid was chosen so that it produced simulated excursions in Ptp comparable to the peak-peak pressure excursions measured experimentally in the mice. This neglects any loss of ventilator volume due to gas compression in the ventilator circuit, but, as lung elastance was 20 cmH2O/ml (see below) and the elastance of the gas in the ventilator circuit was 140 cmH2O/ml, this amounts to a volume of loss of 15%, which is unlikely to have a significant bearing on our conclusions. The inflation pressures in the airway at the start of each simulation matched the experimental PEEP levels. Each model simulation was generated by choosing values for the parameters b and F0 in Eq. 2 and k in Eq. 3, and then generating R signals at each of the three PEEP levels of 1, 3, and 6 cmH2O. The model was thus fit simultaneously to the data obtained at each of the three different PEEP levels. The resulting R signals were scaled by a single factor so that they matched, in a least squares sense, the corresponding experimental R signals. The model thus has four free parameters: the scale factor just described together with b, F0, and k. We did not have to include the other wall stiffness parameter (P0 in Eq. 3) as an additional free parameter because, although this parameter is required for the derivation of the model, our laboratory has found previously (5) that the quality of the model fit is very insensitive to its value. Accordingly, we fixed the value of P0 at 10 cmH2O. The best fit values of the four free parameters were found using a grid search, as previously described (5) .
Sensitivity Analysis and Statistics
We determined the sensitivity of each fitted parameter to the data by keeping the other parameters fixed at their best fit values while adjusting the parameter in question on either side of its best fit value until the root-mean-squared residual increased 5% above its minimum value. Comparisons of model parameter values between study groups were made on the basis of overlap between the confidence intervals calculated, as described above.
We also fit the model to the data from each individual animal in each group to make a statistical comparison between parameter values from different groups. Comparison of parameter values between each group and the Acute Control group was performed by unpaired t-test. Statistical significance was taken as P < 0.05.
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RESULTS |
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DISCUSSION |
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Our data also allow us to make an independent assessment of airway wall stiffness by examining how R changes with PEEP at baseline before activation of the ASM by methacholine, as follows. If we assume lung elastance to be constant, then r increases to the one-third power of Ptp, provided the airways behave exactly like the parenchyma. If we further assume that the airways expand isotropically, then R is proportional to the inverse third power of r (an inverse forth power dependence on r coupled with a linear dependence on airway length). Of course, when the airways are stiffer than the parenchyma, the pressure acting to expand the airway, transmural pressure, is not exactly equal to Ptp because of local parenchymal distortion around the airway. Nevertheless, if we assume these two pressures are equal, and that transmural pressure is reflected in the PEEP applied to the lungs, then PEEP is proportional both to the inverse of R and to the cube root of r. Fitting a line to all the baseline values of R in Fig. 3 vs. their respective levels of PEEP, we obtained the linear relationship 1/R = 3.1 + 0.31 x PEEP. This equation predicts that the value of r at a PEEP of 0 cmH2O should be 63% of its value at a PEEP of 30 cmH2O. In other words, k is estimated by this method to be 0.63. By contrast, the values of k estimated by fitting the airway model to the entire time courses of bronchoconstriction lie in the range 0.7 to 0.8 (Fig. 4B). These values are not too dissimilar, however, which is interesting in view of the fact that there is no reason to suspect that they should be the same. The value of k estimate from the R-PEEP relationship reflects airway wall stiffness in expansion when the ASM is relaxed, whereas the active contraction of ASM is opposed by the compressive elasticity of the wall. Importantly, the tensile and compressive moduli of the airway wall are by no means automatically the same, so this issue applies to any method for assessing wall stiffness in expansion, such as one based on directly imaging the airways (9). This issue of tensile vs. compressive elastic modulus has also bedeviled attempts to understand how mucosal buckling opposes smooth muscle shortening (40). Nevertheless, our estimates of k by two different methods suggest that the tensile and compressive moduli of the airway wall in mice are fairly similar.
To the extent that this computational model captures the essential aspects of reality, our results are clear: allergic inflammation, either acute or chronic, does not change the effective stiffness of the airway wall in BALB/c mice (Fig. 4B). Interestingly, we did find a small but still statistically significant change in k compared with control values when triple the dose of methacholine was given to normal mice (Fig. 4B). As both Acute Control groups of mice received identical treatments before methacholine challenge, this difference in k between the low and high doses of methacholine likely reflects nonlinear effects. In particular, as r decreases, the wall tension required to induce further narrowing also decreases as a consequence of the Laplace law (5), all other things being equal. This could make it appear as if wall stiffness decreases with increasing levels of bronchoconstriction, which would explain why k was slightly smaller in the control mice receiving the higher dose of methacholine. This may also explain the trend for k to be lower in the Acute Ova group than in control (P = 0.085), with the degree of constriction again being greater in the former group. In any case, the roughly 10% decrease in k that we found in the Acute Control High Dose group (Fig. 4B) is likely of minor importance physiologically compared with the changes in mechanical load that even small changes in lung volume would present to the ASM.
The most notable consequence of ova treatment observed in the present study was a marked AHR in the acutely inflamed animals (Fig. 3), as has been reported previously (33). The value of bF0 was substantially elevated relative to controls (Table 1 and Fig. 4). Furthermore, the methacholine responses we observed in the Acute Ova group were similar in magnitude to those in the Acute Control High Dose group (Figs. 3 and 4), suggesting an elevated level of ASM activation in the Acute Ova group. However, although the responses in R were robust, particularly at low PEEPs, H increased very little over the 20-s measurement period, even in the inflamed animals (Fig. 2, bottom). We have previously found a similar lack of effect of intravenous methacholine on H in BALB/c mice (39), which stands in marked contrast to what happens when the mice are challenged with an aerosol of methacholine. With aerosol, H increases substantially, even in control animals, and in allergically inflamed mice the hyperresponsiveness in H is proportionally greater than that in either R or G, even when the fractional increases in R are not as great as in the present study (38). We have shown that these increases in H are due mainly to closure of small airways in the lung periphery (22, 38). Interestingly, H was clearly somewhat elevated in the acutely inflamed animals (Fig. 2, compare bottom panels), suggesting that these animals had either some degree of baseline airway closure (22, 38), or alterations in the intrinsic elastic properties of the parenchyma secondary to the distortion caused by airway constriction (32). However, H increased only minimally following intravenous challenge, suggesting that few additional lung units were de-recruited during the ensuing bronchoconstriction. The modest rises in G in Fig. 2 (middle) thus likely reflect heterogeneity of airway narrowing (2, 23). We, therefore, conclude that the effects of methacholine injection in both normal and allergically inflamed BALB/c mice are largely limited to narrowing the conducting airways, while causing essentially no closure of peripheral airways (22). Why this should be, when aerosol delivery of methacholine is clearly so effective at causing airway closure, is not entirely clear. Perhaps one possibility is that the saline carrier in the aerosol adds to the fluid layer lining the small airways, leading to enhanced liquid bridge formation. In any case, our results agree with those of Nagase et al. (27), who found that methacholine was more evenly distributed and caused fewer effects on tissue viscance when delivered intravenously than by aerosol in rats.
We also found a significantly increased central airway responsiveness in the Chronic Ova group (Figs. 3), although the effect was not nearly as pronounced as in the acutely inflamed animals (Fig. 4). We suspect that this reflects the fact that, in the Chronic animals, the acute inflammatory process induced by ova treatment was well on the way to being resolved, as evidenced by the return of the cell counts toward control levels (Fig. 1). Of course, to be sure of this, we would have to perform a more complete time course study, and also possibly examine the airway wall for histological evidence of remodeling. Those issues aside, however, our data suggest that the hyperresponsiveness we observed in the Acute Ova animals was related to the presence of active inflammation in the lungs rather than the progressive accrual of any permanent structural changes.
Taken at face value, the findings of the present study might seem to suggest that allergic inflammation merely induces a transient hyperresponsiveness of the ASM, without significantly affecting any other mechanical aspects of the lung. However, these results stand in marked contrast to our previous finding that H increases proportionately more than R in allergically inflamed mice when methacholine is delivered as an inhaled aerosol. Using an anatomically based computational model of the mouse lung, we showed that these earlier findings can be ascribed entirely to an increase in the number of small peripheral airways that close during bronchoconstriction in the inflamed animals as a result of a thickened epithelium and increased secretions (22, 38). In other words, the increased R response seen in inflamed mice caused in response to methacholine aerosol can be explained entirely by the geometrical amplification that occurs when the airway walls become thickened, so that a given degree of smooth muscle shortening leads to an increased amount of small airway closure. In other words, the ASM itself in the allergic animals appears to respond normally (38). How, then, do we reconcile this apparent dichotomy between airway responsiveness measured using aerosol vs. intravenous challenge in inflamed mice? Our laboratory's previous study (38) shows that the ASM in inflamed mice seems to contract normally in response to an aerosol challenge, while, in the present study, it seems that intravenous challenge causes ASM contraction to be excessive compared with control mice (Fig. 3), even when there is almost no evidence of airway closure (Fig. 2).
A possible clue to the resolution of the above conundrum is suggested by the fact that the responsiveness in R seen in the Acute Ova group (Fig. 3B) is similar to that observed in the Acute Control High Dose group (Fig. 3A). Thus, even though the Acute Control High Dose group received three times the dose of intravenous methacholine as the Acute Ova group, it is as if the amount of methacholine that actually reached the ASM in each case was similar. In other words, our results are compatible with more methacholine having reached the ASM in the Acute Ova mice compared with the Acute Control mice, despite both groups having received the same injected dose (Fig. 3A). Of course, we did not measure vascular leak in our study. However, in a previous study, Lee et al. (18) found a marked increase in plasma extravasation into the lung, as quantified by Evan's blue dye, in the same acute allergic mouse model as we used in the present study. It is thus plausible that increased delivery of methacholine to the ASM of the Acute Ova animals could have occurred as a result of their general inflammatory state, because endothelial leak is a known consequence of inflammation (28). That is, if the pulmonary vascular endothelium in the inflamed mice was more leaky than normal, then more of the injected methacholine could have passed into the interstitum of the lung, and thence to the ASM, compared with what would have occurred in the less permeable control animals. If this is true, then the hyperresponsiveness of the acutely inflamed mice could be a reflection of increased delivery of agonist to the ASM, rather than having anything to do with the responsiveness of the ASM itself. Interestingly, Larson et al. (16) showed that the methacholine responsiveness of isolated ASM from ovalbumin-exposed BLAB/c mice is not different from normal animals, which also fits with our laboratory's previously advanced notion (38) that acute allergic inflammation in the BALB/c mice represents an animal model of normal ASM in an abnormal lung. On the other hand, increased ASM mass has been reported in animal models of asthma (13), and this might be accompanied by a simultaneous decrease in contractile proteins (26), perhaps as a result of the ASM cells assuming a more secretory phenotype (29). This combination of factors could leave the overall contractile ability of the ASM essentially unaltered from normal, even though the ASM itself would be quite abnormal.
We can formalize the above notion about differences in methacholine delivery by drawing on a theoretical model that our laboratory developed previously to account for differences in bronchoconstriction dynamics in dogs subjected to aerosolized vs. injected bronchial agonists (17). In that study, we observed that the onset and decay of bronchoconstriction were relatively delayed following aerosol delivery. By simulating the delivery of agonist via the aerosolized and injected routes in terms of passage through various compartments, we were able to accurately model the relative time courses of bronchoconstriction resulting from the two modes of delivery. In particular, we estimated that the time constant of diffusion of agonist across the airway wall in dogs is in the order of 60 s. In the mouse, the transfer rate across the airway wall would presumably be faster, because the relevant tissues are thinner and the corresponding diffusion distances shorter. Nevertheless, assuming that the same model structure applies in mice, our previous studies with aerosolized methacholine (22, 38) and the results of the present study together suggest that acute allergic inflammation affects airway responsiveness in mice by modifying the accessibility of the ASM to methacholine. In particular, the present study suggests that, in inflammation, there may be a decreased barrier presented to injected methacholine by a leaky capillary wall, while our laboratory's previous study with aerosol challenge (38) indicates that inflammation may actually increased the barrier to methacholine presented by a thickened airway wall.
Our study has a number of limitations that must be considered. First and foremost, the inferences we have made about airway wall stiffness are based on a structurally very simple model of a single airway embedded in uniform elastic parenchyma. This neglects all of the heterogeneity among airways of different sizes and generations that is known to characterize the lung, and it makes numerous simplifying assumptions about the dynamics of ASM contraction and parenchymal mechanics (5). It also assumes a particularly simple mathematical form for the stiffness of the airway wall (35), which is certain to be a gross oversimplification of reality. Indeed, our laboratory recently showed that, even though this model accounts for much of the transient dynamics in R following a deep lung inflation in constricted mice (3), there appears to be significant effects due to tissue viscoelasticity in these dynamics for which the model does not account. Nevertheless, this model, with only four free parameters, is able to describe the dynamics of onset of bronchoconstriction for the entire lung at three different PEEP levels simultaneously, and under a variety of different conditions (Fig. 3). We, therefore, suspect that, had there been an important change in the effective stiffness of the airway wall in any of our study groups, we should have picked up at least some change in the value of the parameter k.
The other major limitation of our study concerns the nature of the inflammatory mouse models we studied. Even the chronic model was developed over a very short time scale, even compared with the lifetime of a mouse, let alone a human, and, therefore, is assailable on many fronts in terms of relevance to human disease. However, our purpose here is not to defend these preparations as valid models of asthma, but rather to investigate them in their own right, because allergically inflamed mice are widely used in studies of AHR (7). On the other hand, there is an essentially limitless number of sensitization and challenge protocols to which one could expose a mouse to generate inflammation, and we may have by no means chosen the best examples. This applies particularly to the chronic model we used here. Whereas the acute protocol has been well established by us and other groups, our particular choice of chronic exposure protocol was more arbitrary, and different protocols have been used by other groups. Inman and colleagues (20, 33), in particular, have been able to demonstrate sustained changes in lung function following chronic ovalbumin exposure in mice, so applying the methods of the present study to these mouse models could be a productive area for future research. It would also be interesting to apply our model-fitting approach to other situations in which altered airway wall stiffness might be expected, such as the decorin-deficient mice recently shown to have an abnormal responsiveness to PEEP (31). The bottom line is that, just because we failed to show functional evidence of a change in airway wall stiffness in the particular chronic model we investigated, this in no way means that we would not find such evidence in a different model. By the same token, our results do not mean that increased airway wall stiffness is not a common feature in human asthma.
In conclusion, we measured the time course of Raw immediately following intravenous methacholine injection in acutely and chronically inflamed mice. We estimated the effective stiffness of the airway wall in these animals by fitting to the Raw profiles a computational model of a dynamically narrowing airway embedded in elastic parenchyma. Effective airway wall stiffness was estimated from the model fit and found not to change from control in either the acute or chronic inflammatory groups. The chronically inflamed animals responded to intravenous methacholine almost identically to controls. The acutely inflamed mice, however, were hyperresponsive in terms of Raw, which we interpret as reflecting increased delivery of methacholine to the ASM through a leaky pulmonary endothelium. These results further support the notion that acutely inflamed BALB/c mice represent an animal model of functionally normal ASM in an abnormal lung.
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APPENDIX |
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GRANTS |
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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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J. H. T. Bates, S. R. Bullimore, A. Z. Politi, J. Sneyd, R. C. Anafi, and A. -M. Lauzon Transient oscillatory force-length behavior of activated airway smooth muscle Am J Physiol Lung Cell Mol Physiol, August 1, 2009; 297(2): L362 - L372. [Abstract] [Full Text] [PDF]
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), together with two stylized model curves, both of which fit the data equally well. The solid curve has a low value of b and a high value of F0, whereas the dashed curve has a high value of b and a low value of F0.