A computational model for expiratory flow

Abstract

A mathematical model of maximal expiratory flow was developed. Coupled equations describing the pressure losses in the flow and the pressure-area behavior of the airway were integrated along the airway from the periphery to the flow-limiting site. Equations describing pressure losses in the flow were adapted from studied of bronchial casts. The bronchial anatomy utilized was that described by Weibel. Bronchial mechanical properties were obtained from measurements in excised human lungs for the central airways and by extrapolations of these data for the peripheral airways. The maximal flow for air and helium predicted by the model agrees with that of five lungs from which mechanical properties were obtained. The model predictions agree with published values of density and viscosity dependence of maximal flow. At high and midlung volumes, maximal flow is determined primarily by the wave-speed mechanism. At low lung volumes, maximal flow is primarily determined by the coupling of viscous pressure losses and airway mechanical properties.

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

“…We begin with the static airway wall model of Lambert et al (10), which is supported by more recent experimental evidence (8,11); qualitatively similar empirical models (23) and solid mechanics models (4) also exist. Rewriting the static model of Lambert et al (10) in terms of airway radius, this gives us…”

“…There are also caveats regarding the construction of the airway wall model, where we have opted for a simple construction based around the static equilibria (1) using the model of Lambert et al (10). Certainly many alternatives are possible.…”

“…This could have profound consequences for our understanding of airway closure in disease. In the absence of activated ASM, the quasi-static airway pressure-radius curve is known to have a characteristic shape, sigmoidal in small airways with a highly compliant region, and progressively flattening for larger airways (e.g., Harvey et al (8), Lambert et al (10), and LaPrad et al (11); see Fig. 1 a for representative curves).…”

Mechanotransduction, asthma and airway smooth muscle

“…The relationship between the diameter and P tm in dissected airways (i.e., τ muscle , P p , and P alv are zero) has been measured by Hyatt et al [22] and was later cast in an analytical relationship by Lambert et al [23]. Especially in central airways, the passive wall tension can become negative at a small diameter and can therefore resist airway collapse.…”

“…During expiration, a positive feedback cycle leading to flow limitation and airway instability can arise in the following way: if the P lumen − P alv pressure difference becomes sufficiently negative, it can lead to a decrease in airway diameter, a subsequent increase in airway resistance and an even more negative P lumen − P alv pressure [20,22,23]. Anafi and Wilson modeled this interdependence between airway resistance, gas flow, and transmural gas pressure difference by a set of simple linear equations [20].…”