Airway Bistability Is Modulated by Smooth Muscle Dynamics and Length-Tension Characteristics

Abstract

Airway closure has important implications for lung disease, especially asthma; in particular, the prospect of bistability between open and closed (or effectively closed) airway states has been thought to play a prominent role in airway closure associated with the formation of clustered ventilation defects in asthma. However, many existing analyses of closure consider only static airway equilibria; here we construct, to our knowledge, a new model wherein airway narrowing and closure dynamics are modulated by coupling the airway to cross-bridge models of airway smooth muscle dynamics and force generation. Using this model, we show that important qualitative features of airway pressure-radius hysteresis loops are highly dependent on both airway smooth muscle dynamics, and the length-tension relationship. Furthermore, we show that two recent experimental results from intact bronchial segments are both expressions of the same phenomenon: that a monotonically increasing lengthtension relationship, with sharply higher tension at longer lengths, is needed to drive the observed changes in low-compliance regions of the baseline pressure-radius curve. We also explore the potential implications of this finding for airway closure in coupled airway models.

Biological version of Braess' paradox arising from perturbed homeostasis

“…Airway narrowing during an acute asthma exacerbation is driven by contraction of the layer of airway smooth muscle (ASM) surrounding each airway [27]. Activation of the ASM leads to force generation and muscle shortening, and hence airway narrowing; the process is driven by the interaction between muscle force production dynamics and the nonlinear behavior of the airway wall [28,29]. In general, then, one might expect inhaled bronchoconstrictor stimulation of the ASM to lead to reduced ventilation throughout the lung, as ASM activation drives airway narrowing.…”

A Distribution-Moment Approximation for Coupled Dynamics of the Airway Wall and Airway Smooth Muscle

“…Theoretical models have been developed in parallel with these experimental findings in an attempt to understand the complex interaction mechanisms between ASM and the airway wall (17)(18)(19). These efforts are heavily influenced by extensive efforts to model ASM in isolation: specifically, the rich dynamics of ASM are arguably best described by cross-bridge theory, originating with Huxley (20) for striated muscle, adapted to smooth muscle by Hai and Murphy (5,6), and reaching its modern form for ASM with Mijailovich et al (7) and subsequent variants (e.g., (8,9); see (21) for more details on cross-bridge theory and its evolution).…”

“…Several groups have successfully combined cross-bridge PDEs with coupled airway wall models in investigations of key phenomena (17)(18)(19), but thus far only in isolated airways. Unfortunately it is increasingly clear that whole-lung behavior often cannot be easily inferred from isolatedairway behavior (22) and that inter-airway interactions, via both flow coupling and parenchymal interdependence, must be considered.…”

“…We thus proceed as follows: starting from a coupled cross-bridge-airway model (19), we derive the appropriate DM approximation according to Zahalak's approach (31). (Zahalak's original article pre-dates application of crossbridge theory to ASM theory; it describes a detailed application of the DM approximation approach to the original Huxley model, consisting of a single PDE.…”

“…In making this comparison, we are aided by several aspects of the problem: first, that airways are typically subject to an oscillatory pressure environment (viz. breathing), and second, that airway bistability (19,34,35) can provide a natural metric by discriminating between ''open'' and ''closed'' (or effectively closed) airway states. In this way, we are able to establish regions of validity for the DM approximation to the coupled airway-ASM system.…”