A structural constitutive model for smooth muscle contraction in biological tissues

• We model smooth muscle contraction in biological tissues.
• We derive an evolution law based on the sliding filament theory.
• We test the model with published isometric and isotonic, uniaxial and biaxial data.

A structural constitutive model that characterizes the active and passive responses of biological tissues with smooth muscle cells (SMCs) is proposed. The model is formulated under the assumption that the contractile units in SMCs and the connected collagen fibers are the active tissue component, while the collagen fibers not connected to the SMCs are the passive tissue component. An evolution law describing the deformation of the active tissue component over time is developed based on the sliding filament theory. In this evolution law the contraction force is the sum of a motor force that initiates contraction, a viscous force that describes the actin–myosin filament sliding, and an elastic force that accounts for the deformation of the cross-bridges. The mechanical response of the collagen fibers is governed by the fiber recruitment process: collagen fibers support load and behave as a linear elastic material only after becoming taut. The proposed structural constitutive model is tested with published active and passive, uniaxial and biaxial experimental data on pig arteries.