Mathematical modeling and analysis of the pulsating flow of the cerebrospinal fluid

This study presents a mathematical model analyzing the cerebrospinal fluid (CSF) flow velocity, wall shear stress, and flow rate within the subarachnoid space, treating it as a porous medium in a channel. Understanding CSF dynamics is essential for neurological health, particularly in drug delivery, hydrocephalus, and neurodegenerative diseases. The perturbation technique is applied to transform the non-linear partial differential equation into an ordinary differential equation, which is then solved analytically. The findings reveal that the no-slip boundary condition and laminar pressure-driven flow in the constrained spaces lead to a parabolic velocity profile. The results indicate that the CSF flow velocity increases with increasing Darcy number and decreases with frequency, emphasizing the role of the porous resistance and pulsatile effects. A reduction in the flow rate at higher frequencies leads to impaired CSF circulation, directly contributing to inadequate waste clearance from the brain, a factor known to drive conditions such as Alzheimer’s disease and other neurodegenerative disorders. Furthermore, decreased shear stress with a higher Darcy number has significant clinical consequences, as excessive mechanical forces on the brain and spinal cord structures accelerate the progression of disorders like syringomyelia and traumatic brain injuries. These insights provide a critical foundation for developing targeted therapies for CSF-related abnormalities and optimizing treatments, such as intrathecal drug delivery.