A theoretical study of the effect of airway smooth muscle orientation on bronchoconstriction

Abstract

If airway smooth muscle shortened in vivo to the extent that it does in vitro, then maximal bronchoconstriction would result in complete closure of virtually all airways. The fact that this does not happen indicates the existence of inhibitory mechanisms preventing maximal muscle shortening. There are many factors potentially limiting shortening in vivo. In this study we investigated one of these factors, the orientation of the smooth muscle around the airway wall. The airway was modeled as a cylinder of given wall thickness around which the muscle was wound as a spiral. The longitudinal and circumferential elasticities of the airway were embodied in a 2 x 2 matrix of elastic coefficients. We investigated smooth muscle shortening under three conditions: 1) a longitudinally stiff airway, 2) a circumferentially stiff airway, and 3) a longitudinally and circumferentially compressible airway. In case 1, for a given degree of smooth muscle shortening, airway resistance increased markedly with increasing pitch of the smooth muscle spiral. On the other hand, the muscle tension required to elicit a given change in resistance also increased markedly with pitch. In case 2, the effect with increasing pitch was reversed. In case 3, resistance first increased and then decreased as spiral pitch increased. Similarly, the muscle tension required to elicit a given change in resistance first increased and then decreased with pitch. These results suggest that the orientation of the smooth muscle about the airway may be very important in determining airway responsiveness.