Modeling the Response of Airway Smooth Muscle to Cyclic Loading

Airway smooth muscle (ASM) exhibits complex contractile dynamics and has a highly disordered structure. This contrasts with skeletal muscle which contains ordered arrays of contractile filaments aligned with the long axes of the cells. Models of ASM, however, are often based on Huxley's cross-bridge model, which was developed for skeletal muscle and does not take into account the rheological properties of the non-contractile components of the tissue. Here we use a modeling approach to investigate the relative contributions of tissue viscoelasticity and crossbridge kinetics to the mechanical response of ASM to cyclic loading.Experiments were performed using rat trachealis muscle strips. Breathing was mimicked by applying sinusoidal length oscillations (frequency: 2Hz; amplitude: 1-4%). In unstimulated muscle, peak force during length oscillation followed a typical stress relaxation trajectory. In stimulated muscle, peak force decreased dramatically over the first 5-10 cycles to a level close to the isometric force at the mean length. Furthermore, steady-state peak force decreased as loading amplitude increased. ‘Sighs’ were mimicked by applying a large-amplitude loading cycle (5-25%). Sighs caused a transient but long-lasting reduction in peak force, with the degree of force reduction increasing with sigh amplitude.The response of unstimulated muscle to length oscillation could be reproduced well with a model consisting of a Hill-type contractile element and a parallel elastic element, both in series with a nonlinear Kelvin body (viscoelastic element). In order to reproduce the response of stimulated muscle to length oscillation, cross-bridge kinetics had to be included either using a Huxley-type model or by including first-order cross-bridge attachment and detachment kinetics in the Hill model. The decrement and slow recovery of force after a sigh, however, could not be reproduced by either model, indicating that additional mechanisms are required to explain this phenomenon.