Spectral stability of the bifurcation state of an arterial model with perivascular soft tissues

We model an artery with perivascular soft tissue as a uniform cylindrical membrane tube surrounded by a flexible substrate with distributed stiffness. We derive the equations of motion of the arterial model, and obtain evolution equation derived in the long wavelength limit from the general equations of motion. We analyze the stability of axisymmetric perturbations at the bifurcation state taking into the consideration of surrounding soft tissue stiffness and constant axial stretch. We observe that the surrounding soft tissues progressively reduce the domain of real valued solutions with increasing constant axial stretch. The results suggest that the stationary solitary wave solution is unstable.