A mathematical analysis of cerebrospinal fluid pressure in subarachnoid space with poro-elasticity

The entire central nervous system is supplied with blood via the cerebrospinal fluid that circulates in the subarachnoid space, the excess of fluid that secretes around the brain parenchyma that leads to disorders like communicating and non-communicating hydrocephalus. In this work, we developed a simulation on hypothetical in vivo inputs to explain the cerebrospinal fluid circulation, ultimately leading to a pathological condition called hydrocephalus. A mathematical framework was investigated to impose the brain porous spaces due to hydrocephalus. As a result, it leads to identifying neurological activities that include hydrodynamics and nutrient transport diffusivity with enormous pressure changes. We implemented an analytical experiment to justify the physical experiments using the method of novel Perturbation in which the ions are transported through parenchyma via pulsating boundary conditions. The expansion of the SAS barrier between ventricles causes high CSF pressure and traumatic brain injury. When the velocity of the CSF reaches an extreme level, it indicates a higher Womersley number ranging from (25)9 to 13. These results were justified through neurological studies by field researchers.