Symmetric double-helix-fiber model for arterial mechanics considering contracted smooth muscle

The mechanics of contracted smooth muscle in arteries have been widely investigated under axial stretch and intraluminal pressure, yet their behavior under general multiaxial deformation, including shear strain induced by torsion, remains poorly understood. We hypothesize that a constitutive law formulated with nonlinear strain energy functions can accurately describe arterial stress responses not only under orthogonal loading but also under shear deformation, even when parameters are identified solely from pressure–stretch experiments. To test this hypothesis, we developed a symmetric double-fiber constitutive model for passive and noradrenaline-induced contracted states, employing logarithmic or exponential forms for passive stress and a hyperbolic form for active stress. Ten rabbit common carotid arteries were examined under a physiological axial stretch ratio of 1.5 and intraluminal pressure, and model parameters were determined using nonlinear least-squares optimization. Although experiments did not include torsion, the resulting strain energy functions possess full tensorial form, enabling theoretical prediction of shear stresses associated with twist. This extends previous linear analyses of shear behavior to a nonlinear framework. The proposed model therefore provides a new theoretical basis for analyzing arterial mechanics under general multiaxial loading, including torsion, and suggests that future experiments incorporating shear deformation may refine parameter estimation.