MATHEMATICAL MODELING OF THERMO-SOLUTAL TRANSPORT IN PULSATING FLOW IN THE HYDROCEPHALUS

Abstract

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Hydrocephalus is an asymmetric and unusual cerebrospinal fluid flow in the lateral ventricular portions. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. Mathematical models of transport in the hydrocephalus, which constitutes an excess of fluid in the cavities deep within the brain, enable a better perspective of how this condition contributes to disturbances of the CSF flow in the hollow places of the brain. Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Thermophysical and mass transfer effects are therefore addressed in this paper to quantify the transport phenomena in pulsatile hydrocephalus CSF transport with oscillating pressure variations that characterize general neurological activity and transitions from one functional state to another. A new mathematical model is developed which includes porous media drag for brain tissue and solutal diffusion (concentration) effects. A classical Laplace transform method is deployed to solve the dimensionless model derived with appropriate boundary conditions. The analysis reveals that with increasing permeability of the subarachnoid space, the CSF velocity is increased, and a significant fluid flux enhancement arises through the brain parenchyma as the pressure of the fluid escalates drastically due to hydrocephalus disorder. Stronger thermal buoyancy (Grashof number) also results in deceleration in the flow. CSF temperature is reduced with progression in time. Particle (e.g. ion) concentration is suppressed with increasing Schmidt number. As heat conduction parameter increases, there is a substantial depletion in CSF velocity with respect to time. Increasing Womersley parameter displaces the CSF velocity peaks and troughs. The present effects are beneficial in determining the thermo-fluidic transport mechanism of the pathological disorder hydrocephalus. Also, the present results are compared with those clinical studies for some cases. We have confirmed that our validity provides a decent justification with the neurological studies.