INTRODUCTION

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OUR LABORATORY HAS PREVIOUSLY demonstrated that immature rabbits have greater maximal airway narrowing and greater maximal fold increases in pulmonary resistance and airway resistance (Raw) during bronchoconstriction than mature animals (20, 22, 27). The increased airway narrowing in the healthy immature animal has several similarities to the exaggerated airway response to bronchoconstrictors observed in asthmatic human adults. In addition to the greater sensitivity of the airway response, the immature rabbit does not exhibit a plateau in the pulmonary response to an agonist; instead there is a progressive worsening of pulmonary function with increasing dose. In contrast, the mature animal exhibits a relatively small decrease in pulmonary function with increasing doses of bronchoconstrictors, and there is a plateau in this response such that increasing agonist doses do not produce a further decrease in pulmonary function.

This absence of a plateau in the airway response of the immature rabbit lung is similar to the response observed in a severe asthmatic patient, as well as healthy human infants (26, 33). The presence of a plateau in the response of the mature rabbit is similar to that observed in healthy nonasthmatic adults and other mature species (11, 19, 24, 33). The mechanisms for exaggerated airway narrowing among immature animals and asthmatic subjects have not been identified; however, the similarities of the dose-response curves for these different populations, particularly the absence of a plateau in the response of immature animals and asthma patients, suggest common mechanisms for the exaggerated airway response of immature animals and asthmatic adults.

The degree of airway narrowing during bronchoconstriction is a balance between force generation by the airway smooth muscle (ASM) and the elastic loads that limit ASM shortening. Computational models have been used to evaluate how differences in the mechanical and geometric determinants of airway narrowing might account for the exaggerated airway response observed in asthmatic adults (6, 8, 9, 17, 31, 32). These models have offered insights into the relative importance of different elastic loads, quantity of ASM, and airway wall thickness as determinants of the exaggerated airway narrowing among asthmatic subjects. Our laboratory has previously demonstrated that excised immature rabbit lungs have more distensible airways when assessed by tantalum bronchograms and that isolated immature rabbit lungs also have a lower shear modulus than mature rabbit lungs (22, 29). In addition, our group has reported that anatomically similar airways from mature and immature rabbits differ in the amount of ASM, cartilage, and wall thickness relative to the size of the airway (15). In the present study, we applied a computational model of airway narrowing to investigate maturational differences in airway narrowing. We exchanged between the mature and the immature models the parameters for airway wall compliance, lung shear modulus, quantity of ASM, and wall thickness to evaluate the relative importance of maturational differences in these factors as determinants of the observed greater airway narrowing that occurs in the immature animal.

	MODEL

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The computational model for human airway narrowing with increasing doses of smooth muscle agonist (9) was adapted to assess the dose-response relationship of mature and immature rabbit airways. In this model, Raw is calculated for an airway tree of 17 symmetrically bifurcating generations. The response is the increase in Raw that results from ASM shortening secondary to activation with an agonist. The degree of airway narrowing results from a static force balance in each generation that takes account of the passive tension in the airway wall, the tension generated by the ASM, and airway-parenchymal interdependence. ASM tension is, in part, determined by the amount of ASM in the airway wall. Increased wall area internal to the smooth muscle enhances the effect of muscle shortening on airway narrowing. In addition, an increased wall area external to the smooth muscle may reduce airway-parenchymal interdependence (12, 30). Thus the thickness of the airway wall internal and external to the smooth muscle and that of the muscle itself is also included in the model. We incorporate into the model data of airway size, ASM stress, quantity of ASM within the airway wall, airway wall thickness, airway wall compliance, and the shear modulus of the lung for mature and immature rabbit lungs.

Airway Size

Airway Smooth Muscle

Force generation. Rabbit dose-response data for percent maximal force as a function of acetylcholine (ACh) concentration have been measured for both mature and immature rabbit tracheal smooth muscle (TSM) strips (28). Immature TSM was more sensitive to ACh compared with mature TSM; the dose-response curve for the immature TSM was shifted to the left. We made the assumption that the percent muscle shortening vs. ACh concentration curve would be the same as the percent maximal force curve. A sigmoid-shaped equation was fit to each set of data, and the equations were incorporated into each model. The models have a length-tension curve obtained by fitting a cubic equation to the data of rabbit TSM (14). We assumed that the length at which maximal isometric stress occurs was at Ptp = 5 cmH₂O, as in the human model. The maximal stress generated by ASM is an important determinant of airway narrowing in the model. The maximal stress generated by mature and immature rabbit TSM has been reported to be not significantly different or greater for the mature rabbit TSM (18, 25, 28), with values for isometric tension of ~100 kPa. Maximal isometric stress generation by canine TSM is decreased with tidal stretches compared with measurements under static conditions (5, 23). In addition, our laboratory has demonstrated in rabbits that airway narrowing in vivo during tidal stretching of the lung is less than airway narrowing under static conditions (21). Therefore, the maximal ASM stress generation used in the model should be less than the in vitro isometric value; a value of 85 kPa was chosen for the maximal ASM stress in both models.

Quantity. The area of ASM in the airway wall cross section (WA_m) for generations 1-8 was obtained from morphometric measurements of isolated mature and immature rabbit airway segments (15). The relationship between (WA_m)^1/2 and P_i was linear, as has been found in other studies (17, 31). The amount of muscle in the model airways was represented by the following equations

Values were calculated by generation from the P_i information. For generations beyond generation 8, values were obtained from our unpublished morphometric data from peripheral lung tissue of mature rabbits. This relationship between (WA_m)^1/2 and P_i was also linear. We used the same relationship in the periphery of the lung for the immature model, because our previous study found no significant difference in the relationship between (WA_m)^1/2 and (airway lumen area)^1/2 for mature and immature rabbit airways (27). There is less absolute muscle in any peripheral generation of the immature than in the matching generation in the mature model; however, there is the same amount of muscle for any given P_i

Figure 1A illustrates graphically the cross-sectional area of ASM vs. generation used for the mature and immature models.

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Cross-sectional areas of airway wall compartments and airway lumen vs. generation used in the mature model () and immature model (). Graphical representation are shown of equations in text that were derived by using data in Ref. 15. A: smooth muscle area (WAm) in cross section. B: inner wall area (WAi) in cross section. C: total wall area (WAt) in cross section. D: lumen cross-sectional area when lumen is fully dilated and circular (A).

Elastic Forces

Airway wall. The passive elastic properties of the airway wall are represented in the models by equations that describe the variation of lumen cross-sectional area (A_i) expressed as a fraction () of maximal area (A) vs. transmural pressure (Ptm)

(1)

(2)

The subscript 0 indicates that the value at Ptm = 0, '₀ is the slope of the -Ptm curve at Ptm = 0, and n₁ and n₂ are shape-adjusting parameters. Equations 1 and 2 describe the deformation of an airway at negative and positive values of Ptm, respectively. The equations are hyperbolas. Equation 1 has asymptotes  = 0 and Ptm = P₁, whereas Eq. 2 has asymptotes of  = 1 and Ptm = P₂. A_i vs. Ptm curves were derived from our tantalum bronchogram data from mature and immature excised rabbit lungs for Ptp between 0 and 20 cmH₂O for eight generations of airways (22). In that study, values of ₀ and '₀ were evaluated for the group mean data from both groups of animals. The value of n₂ was poorly defined by the fitting process; therefore, in setting up the model described here, we chose to set n₂ to 100 for all airways. The effect of large variations of n₂ is negligible in the model. There is only one study that obtained sufficient data for Ptp < 0 to inform our choice of n₁ (7). With this study as a guide, we set n₁ to 1.0 for all airways in the mature model and to 10 for all airways in the immature model. The model is weakly sensitive to n₁, and by choosing a greater value for the immature model we emphasize the greater compliance of the airways in that model. Plots of ₀ and '₀ vs. generation number were fitted with an exponential function and a power law, respectively, and these were programmed into the model for generations 1-8

There were no data from that study for generations greater than 8; however, a recently published morphometric study of mature rabbit airways obtained data for ₀ in membranous bronchioles (13). These data were not obtained by generation; however, because P_i was measured, the airway size can be matched to generation in our model. Our choice of model values for ₀ was guided by this study (Table 1). Because there were no data for '₀ beyond generation 8, we extrapolated to generation 10 and then held '₀ constant at the generation 10 value for the more peripheral generations. Representative normalized A_i-Ptm curves are shown in Fig. 2, for which A was calculated as P/4.

View larger version (20K): [in this window] [in a new window]   Fig. 2.   Normalized lumen area (Ai)-transmural pressure (Ptm) curves for generations 1, 3, 5, 7, and 9 (top to bottom) for immature rabbit airways (A) and mature rabbit airways (B). Dotted curves are for generation 15. Ai have been normalized on lumen cross-sectional area when the lumen is fully dilated and circular (A). Graphical representation are shown of equations in text that were derived by using data in Ref. 22.

Parenchymal shear modulus. Airway-parenchymal interdependence is included in the models through the shear modulus for the lung parenchyma (µ), which we have measured in excised mature and immature rabbit lungs (29)

Wall Thickness

For total wall thickness, the plot of WA_t vs. P_i appeared nonlinear, and an exponential fit resulted in a greater value of R². The curves obtained for generations 1-8 were extrapolated to generation 17. The values of WA_t vs. generation used in the models are illustrated graphically in Fig. 1C

The wall area external to the smooth muscle (WA_o) was calculated by subtracting WA_i from WA_t at the P_i of interest.

Airway Length

	METHOD

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The models were programmed over a sufficient range of agonist to produce a plateau in resistance at a Ptp of 5 cmH₂O. For calculations of Raw, flows of 5 and 25 ml/s were used with the immature and mature models, respectively, because these values are similar to in vivo data. The models were run with the airway compliances for mature and immature animals exchanged to assess the influence of airway mechanics on airway narrowing. The models were also programmed with the mature and immature shear moduli exchanged to evaluate the effect of maturational differences in airway-parenchymal interdependence. To investigate the influence of airway wall structure on airway narrowing, the models were run with a 50% increase in airway wall thickness internal to the ASM, as well as a 25% increase in ASM.

	RESULTS

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The dose-response curves for the mature and immature models are shown in Fig. 3; the responses are expressed as the fold increase in Raw from baseline. The immature airway response has greater sensitivity to the agonist than the mature model, requiring a smaller agonist dose [1.9 vs. 2.6; log (ACh) × 10⁹ M] to produce a twofold increase in Raw. In addition, the immature model has significantly greater maximal fold increase in Raw (8.3 vs. 5.0).

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models.

The effects of exchanging airway compliances between the mature and the immature models are illustrated in Fig. 4. Maximal airway narrowing in the mature model with the immature airway compliance increased significantly, and the magnitude of the response of this modified mature model became similar to the magnitude of the maximal response of the initial immature model with the immature airway compliance. In addition, the maximal airway narrowing of the immature model with the mature airway compliance decreased significantly, becoming similar to the maximal response of the mature model with the mature airway compliance. For both immature and mature models, exchanging airway wall compliances did not change the agonist dose required to produce a twofold increase in Raw; the sensitivity remained unchanged.

View larger version (15K): [in this window] [in a new window]   Fig. 4.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses for the immature model with the mature animal's airway compliance and the mature model with the immature animal's airway compliance.

Exchanging the shear moduli for the mature and immature models increased the maximal airway's response of the mature model and decreased the maximal airway's response of the immature model; however, the effect of exchanging these elastic loads was significantly smaller than the effect of exchanging airway compliances (Fig. 5).

View larger version (13K): [in this window] [in a new window]   Fig. 5.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses for immature model with the mature animal's shear modulus and the mature model with the immature animal's shear modulus.

Exchanging the values for total wall area and the percentage of smooth muscle produced only small changes in the maximal airway narrowing for each model (Fig. 6). Increasing the quantity of ASM by 25% produced a greater maximal response in both models; however, there was proportionately a greater increase in the airway response of the immature model (Fig. 7). Similarly, exchanging between the two models the wall area internal to the smooth muscle and the wall area of the airway produced only small changes in maximal airway narrowing (Fig. 8). A 50% increase in the wall area internal to the smooth muscle produced a greater increase in the maximal airway response of the immature than the mature airway model, although the effect of increasing internal wall thickness was smaller than the effect of increasing ASM (Fig. 9).

View larger version (13K): [in this window] [in a new window]   Fig. 6.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses for the immature model with the mature animal's fraction of smooth muscle in the airway wall (WAm and WAt) and the mature model with the immature animal's fraction of smooth muscle in the airway wall (WAm and WAt).

View larger version (11K): [in this window] [in a new window]   Fig. 7.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses with a 25% increase in smooth muscle in the airway wall (1.25 × WAm) for the immature and the mature models.

View larger version (13K): [in this window] [in a new window]   Fig. 8.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses for the immature model with the mature animal's wall thickness and wall area internal to the airway smooth muscle (WAt and WAi) and the mature model with the immature animal's wall thickness and wall area internal to the airway smooth muscle (WAt and WAi).

View larger version (12K): [in this window] [in a new window]   Fig. 9.   Comparison of airway responses (fold increase in airway resistance) vs. log (ACh × 109 M) for immature and mature rabbit models, as well as the airway responses with a 50% increase in the wall area internal to the airway smooth muscle (1.5 × WAi) for the immature and the mature models.

	DISCUSSION

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The models described here for the dose-response behavior of rabbit airway narrowing successfully reproduce the main features of in vivo airway reactivity in mature and immature animals. The immature model is more responsive to agonist than the mature model, and the magnitude of the maximal responses is similar to that observed in vivo. Among the mechanical determinants that we have data for and have incorporated into the model of airway narrowing, our results strongly suggest that the greater compliance of immature airways can be an important factor contributing to the greater airway narrowing of immature animals. In contrast to airway compliance, maturational differences in the shear modulus of the lung, the thickness of the airway wall relative to the airway size, and the fraction of smooth muscle in the airway wall do not appear to account for maturational differences in airway narrowing.

In our models of airway narrowing, the magnitude of airway narrowing is a balance between force generation by ASM and the elastic loads that limit airway narrowing. Using existing morphometric and physiological data for immature and mature rabbits, our comparison of model predictions demonstrates greater maximal fold increases in Raw for the immature animal. Two of the mechanical determinants of airway narrowing that are included in the models are the airway wall compliance and the shear modulus of the lung; both of these elastic loads are lower for the immature than the mature animal. Our models suggest that the greater compliance can be an important determinant of greater airway narrowing in the immature animal; exchanging airway compliances greatly magnified the airway response in the mature model and diminished the airway response in the immature model. In the models presented here, maximal muscle shortening is produced in peripheral airways but not in the most peripheral airways because of our choice of the distribution of the resting airway size at a Ptm of 0 cmH₂O (₀). Recently published data demonstrate that the smallest airways from mature rabbits are relatively more open at Ptm values of 0 cmH₂O than somewhat larger airways (13); thus we chose increasing values of resting airway caliber and greater stiffness for the most peripheral generations (Table 1). There are presently no comparable data available for immature rabbits, so we used similar estimates for the immature model. However, more compliant peripheral airways in the immature rabbit could further contribute to greater airway narrowing in the immature animal. To assess whether extrapolation of our data from the first eight generations to the more peripheral airways altered our interpretations of the model results, we also evaluated the models truncated at generation 8. The same qualitative results were present. The maximal fold increases in resistance were greater in the immature than the mature model with their own airway wall compliances, although the magnitudes of the maximal increases in resistance are smaller in the absence of the peripheral airways. Exchanging airway compliance between immature and mature in the truncated model also produced the same qualitative results, although smaller in magnitude. The immature model with the mature airway wall compliance decreased the maximal response, and the mature model with the immature airway wall compliance increased its maximal response, which exceeded that of the immature with the mature compliance. Therefore, both the full and the truncated models yield qualitatively similar results, demonstrating the importance of maturational differences in airway wall compliance on the greater maximal airway narrowing observed in the immature animal.

Exchanging shear moduli between the mature and the immature models made the airway responses more similar; however, this effect on maturational differences in airway responsiveness was relatively small compared with the effect of exchanging airway wall compliances. The small effect of changes in the shear modulus in the rabbit model is similar to the relatively small effect on airway narrowing of altering the shear modulus in the human model (10).

In our rabbit models, airway wall thickness had a relatively small effect on airway reactivity, particularly in the mature model (Fig. 9). This finding in the rabbit contrasts to the greater importance that airway wall thickening has on airway reactivity in patients with asthma (8, 31, 32). This difference between the rabbit and the human models may relate to the proportionately thinner airway walls relative to the size of the airway for rabbits compared with humans. The slopes of the relationship of wall area and airway size for mature and immature rabbits are similar, but approximately one-half that for nonasthmatic human adults, which is significantly lower than the slope for asthmatic adults.

Although exchanging the quantity of ASM within the airway wall produced only minor changes in maturational differences in airway narrowing, the magnitudes of the airway responses for both models were very sensitive to the quantity of ASM. An increase of the smooth muscle area by 25% produced large increases in the airway responses of both mature and immature animals, a finding similar to that observed in the model of human airway narrowing. On the basis of in vitro data in TSM, we chose the same maximal stress for mature and immature ASM (4, 18). Our models of airway narrowing demonstrate that the immature model is more sensitive than the mature model to the nonspecific agonist dose, which is consistent with in vivo observations. The difference in model sensitivity of airway narrowing reflects the greater in vitro sensitivity of immature TSM force generation to agonists, which we have incorporated into our models (4, 28).

Our model of airway narrowing for rabbits has incorporated a homogenous symmetrically branching airway tree that undergoes homogenous airway narrowing. Several more complex models of airway narrowing have demonstrated that heterogeneity in the distribution of airway properties and heterogeneity of airway narrowing within the airway tree can greatly amplify the magnitude of the overall airway response to bronchoconstriction (2, 3). In contrast to the relatively symmetric airway branching pattern present in humans, rabbits have a very asymmetric, monopodal branching pattern (16). This asymmetric branching in the rabbit may further magnify the effects of heterogeneity of the airway response. Because immature animals exhibit greater airway narrowing and airway closure, the impact of an asymmetric airway tree on airway responsiveness may also contribute to the observed maturational differences in airway responsiveness.

In summary, we have developed models of airway narrowing for mature and immature rabbits on the basis of extensive morphometric and physiological data. Our results strongly suggest that the mechanical properties of the airway, that is, greater compliance of the immature airway, can be an important factor contributing to the greater airway narrowing of the immature animal.