Determinants of airway hyperresponsiveness—Balance of tonic and phasic contractility of airway smooth muscles of lobular bronchioles

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma, and generally correlates with severity of asthma. Understanding the protection mechanism against excessive airway narrowing and how it breaks down is fundamental to solving the problem of asthma. In this paper we have proposed a stochastic modeling the airway smooth muscle bundle for reproducing AHR such as an increased sensitivity of the airways to an inhaled constrictor agonist, a steeper slope of the dose-response curve, and a greater maximal response to agonist. A large number N of contractile muscle cells was assumed to repeat themselves in between contraction and relaxation asynchronously. Dynamic equilibrium of statistic physics was applied to the system of ASM bundle. Thus, the relation of dose to response of a piece of ASM bundle was described by Φ=tanh(βH) , where β was Boltzman factor and H represented energy of contraction induced by constrictor agents. Each of adjacent pair contractile cells was assumed to have Ising-type of antimagnetic interactions of preference energy J (for the condition of contraction-relaxation) between them. A motion equation for a piece of ASM bundle was described by Φ=N(H-zJΦ , which explained existence of combined tonic and phasic contractions. Based on observations of Venegas et al. [4], airway responsiveness was assumed to be assessable by total volume of the ventilation defects (TVD) of 13NN PET-CT images. Interactions via propagation of Ca ion waves between ASM bundles would cause percolation probability by PΦ=(1+tanh(βH))2/4 along the tree, then the relation of dose βH to TVD was described by TVD=PΦ[1-(1-PΦ)3/PΦ3]-TVD0. TVD0 represented the protection mechanism against excessive airway narrowing, which was determined by the ratio of amplitudes between tonic and phasic contractions, thus the balance of amplitudes between tonic and phasic contractions of peripheral lobular smooth muscles would be the determinant of AHR.