(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Cerebrospinal fluid (CSF) flow within perivascular routes (PVS) is essential for maintaining brain health and function. This flow is a part of the glymphatic system, which clears waste products and metabolic byproducts from the brain. The PVS boundaries consist of a non-permeable arterial vessel wall and neural tissue. The arterial vessel peristalsis and the elasticity of the neural tissue are responsible for generating the CSF flow. This article examines the effect of a transverse magnetostatic field and pertinent physiological conditions on CSF flow. It specifically considers the impact of brain elasticity and porosity at the neuroglial layers, arterial wall curvature, and the peristalsis amplitude. The effective Navier–Stokes governing equations describe the peristalsis of CSF flow subjected to a magnetostatic field. The perturbation strategy is utilized to address the governing equations. This leads to a set of equations describing CSF stream-direction velocity, pressure gradient, and neural tissue deformation. The graphical outcomes highlight the significant influence of a range of physiological and flow factors on the behavior of CSF. The key parameters encompass neural tissue porosity and stiffness, neuroglial layer deformation, magnetostatic field strength, and arterial wall curvature. The results reveal that enhancing the magnetostatic field intensity reduces CSF pressure distribution, stream-direction velocity, and arterial deformation. This study is highly significant due to its implications for the development and advancement of different neurological disorders for instance Alzheimer’s disease, meningeal inflammation, neurotrauma, and hemorrhagic stroke.