Modeling the dynamics of airway constriction: effects of agonist transport and binding

Abstract

Recent advances have revealed that during exogenous airway challenge, airway diameters cannot be adequately predicted by their initial diameters. Furthermore, airway diameters can also vary greatly in time on scales shorter than a breath. To better understand these phenomena, we developed a multiscale model that allowed us to simulate aerosol challenge in the airways during ventilation. The model incorporates agonist-receptor binding kinetics to govern the temporal response of airway smooth muscle contraction on individual airway segments, which, together with airway wall mechanics, determines local airway caliber. Global agonist transport and deposition are coupled with pressure-driven flow, linking local airway constrictions with global flow dynamics. During the course of challenge, airway constriction alters the flow pattern, redistributing the agonist to less constricted regions. This results in a negative feedback that may be a protective property of the normal lung. As a consequence, repetitive challenge can cause spatial constriction patterns to evolve in time, resulting in a loss of predictability of airway diameters. Additionally, the model offers new insights into several phenomena including the intra- and interbreath dynamics of airway constriction throughout the tree structure.

Fig. 1.

A: schematic of airway bifurcation. The airway smooth muscle (ASM) agonist (S) is transported throughout the bifurcation via gas flow. A fraction of the agonist, proportional to the volume concentration of agonist in the respective lumen, is deposited onto the airway epithelium. S_in, S_dep, S_aw, S_out, S_bif and S_alv indicate the amount of agonist that flows into the tree, is deposited onto the airway epithelium, goes through the airway, goes out of the airway, reaches the bifurcation, and reaches the alveoli, respectively. B: schematic of the two-state model for binding kinetics. The deposited agonist diffuses into the airway wall and surrounding smooth muscle. Some agonist binds to smooth muscle receptors before being washed out via the bloodstream. SB and SU, amount of bound and unbound agonist, respectively; α, rate that unbound agonist binds to ASM receptors; β, rate that bound agonist unbinds to ASM receptors; γ, rate of unbound agonist removed by diffusion; δ, rate of absorption. C: free body diagram of the airway wall. Smooth muscle tension (T_AMS) applies a pressure around the outer wall surface, which is added to the outer pressure to determine diameter. P_lumen, lumen pressure.

Fig. 2.

A: impulse response of bound ASM receptors to agonist administration for various parameter combinations. B: normalized pressure-area relation of a single airway segment at generation 4 computed at different times (curves a–c) along a single challenge using the same parameters as in A. C: airway segment resistance in response to an impulse agonist dose during pressure oscillations for various parameter selections. Note that for better visualization, three of the resistance curves have been shifted up.

Fig. 3.

Estimated probability density distributions of the equivalent airway tree resistance after the application of varying levels of uniformly distributed random neural tone.

Fig. 4.

Two-dimensional graphical representations of the airway tree. Colors represent the normalized logarithm of resistance of the corresponding airway, where green shades represent relaxed (low resistance) airways and yellow shades represent constricted (high resistance) airways. A: diameters at peak R_aw after an inhalation challenge of airway tree. B: diameter heterogeneity after a second inhalation challenge after recovery (to 95% reduction from peak R_aw) from the previous challenge.

Fig. 5.

Traces of individual normalized airway diameters in time. Representative airways were selected from generation 6 of the airway tree.

Fig. 6.

A: normalized airway diameters at peak constriction after challenge plotted against their initial diameters. B: normalized pathway resistances at peak constriction plotted against their initial resistance value.

Fig. 7.

Sensitivity of R_aw (A) and SD of pathway resistances (B) to variations in model parameters including binding rate α, unbinding rate β, and rate of agonist absorption on the airway wall δ. The model parameters were normalized such that the baseline values correspond to 1 and the model outputs are also normalized such that their values are 1 at the baseline. The individual values correspond to the peak level of constriction during simulations.