A Nitric Oxide–Modulated Variable-Order Fractional Maxwell Viscoelastic Model of Cerebral Vascular Walls

It is well known that the mechanical behavior of arterial walls plays an important role in the pathogenesis of vascular diseases. Most studies existing in the literature focus on the mechanical interactions between the blood flow and wall’s deformations. However, in the brain, the smaller vessels experience not only oscillatory forces due to the pulsatile blood flow but also structural and morphological changes controlled by the surrounding brain cells. In this study, the mechanical deformation of the cerebral arterial wall caused by the pulsatile blood flow and the dynamics of the neuronal nitric oxide (NO) is investigated. NO is a small diffusive gaseous molecule produced by the endothelial cells and neurons, which is involved in the regulation of cerebral blood flow and pressure. The cerebral vessel is assumed to be a hollow axial symmetric cylinder whose wall thickness is much smaller than the cylinder’s radius and longitudinal length is much less than the propagating wavelength. The wall is an isotropic, homogeneous linear viscoelastic material described by an NO-modulated variable-order fractional Maxwell model. A fractional telegraph equation is obtained for the axial component of the displacement. Patterns of wall’s deformation are investigated through numerical simulations. The results suggest that a significantly decreased inactivation of the neuronal NO may cause a reduction in the shear stress at the blood-vessel interface, which could lead to a decrease in the production of shear-induced endothelial NO and neurovascular disease.