Elucidating Dynamics of Fluid Interactions in the Brain using a Mathematical Model

Background: Major pathological conditions that may evolve after a traumatic brain injury are hydrocephalus and cytotoxic or vasogenic edema, leading to an elevated intracranial pressure (ICP) and decreased cerebral blood flow (CBF). The rigid cranium enclosing the brain creates a distinctive complex environment. To prevent an ICP raise, any increase in fluid of one component of the brain must inflict an equivalent decrease in other component. To understand the brain fluids complex interactions in transitions from normal dynamics to pathological conditions, a mathematical model was developed.

Method: An equivalent electrical circuit, representing brain fluid dynamics, was built using a lumped parameter model technique. The model included three components: blood, cerebrospinal fluid (CSF) and brain tissue. A system of nonlinear ordinary differential equations, representing the electrical model, was solved numerically.

Results: The model reproduced physiological and pathological behavior of intracranial fluids affecting ICP and CBF. All modeled pathological conditions showed ICP elevation and CBF reduction. Induced Hydrocephalus resulted in ventricular CSF accumulation affecting ICP and CBF. Induced Cytotoxic and vasogenic edema resulted in elevation of brain tissue fluid volume and pressure thereby diminishing CBF.

Conclusions: The results show a well-known and studied behavior of intracranial fluids in hydrocephalus and edema. The model allows investigation of the complex fluid movement and interactions in various physiological conditions, such as exploration of how changes in the intracranial blood supply affect the CSF circulation dynamics and is affected by ICP changes.