Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges, the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due to forces produced by the airway smooth muscle (ASM) wrapped around each airway. The interaction between the muscle and the airway wall is crucial for the airway constriction which occurs during an asthma attack. While crossbridge theory is a well-studied representation of complex smooth muscle dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational cost, even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot be adequately understood by studying isolated airways, this presents a significant limitation. We present results associated with the development of an approximated method (distribution moment approximation) which provides orders of magnitude reduction in computational complexity whilst retaining rich ASM dynamics. This method is then used to model physiological processes such as airway contraction, bronchodilatory effect of a deep inspiration and preliminary results associated with heterogeneity of branched airways.