Cerebrospinal Fluid Flow in Normal and Hydrocephalic Brains

The flow rates and velocities of cerebrospinal fluid (CSF) in the central nervous system (CNS) can be measured using advanced imaging modalities such as cine-phase-contrast-MRI, but the driving forces behind CSF motion are not fully understood. Recent clinical measurements create the observations necessary to establish a relationship between cerebral blood flow dynamics and pulsatile CSF flow. However, a fundamental mathematical model useful for interpreting and quantifying the dynamic force balances between expanding cerebral vasculature, deformable brain tissue, and displaceable CSF does not yet exist. To bridge the gap between observations of a blood-CSF flow relationship and insight into how these mechanisms occur in reality, this dissertation proposes a multi-scale modeling approach for explaining and quantifying the interactions between expanding vasculature, brain tissue, and CSF. The core hypothesis of this dissertation is that the oscillatory CSF flow is due to pulsating cerebral vasculature expansion. To test this hypothesis, an integrated model of cerebral vasculature, brain tissue, and CSF is presented. Brain and CSF domains were generated from medical images and spatially discretized using the finite volume method. Large arteries of the vasculature network were reconstructed from medical images and an automatic vessel growth algorithm was used to generate regions of microvasculature. The completed vasculature domain was represented as a complex, continuous network of cylindrical tubes. In the model, cerebral blood flow, pressures, and vessel expansion are solved in the entire vascular network. Changes in vessel caliber are transmitted to the brain as a volumetric strain, thus inducing tissue displacement. The deforming brain, in turn, accelerates the CSF throughout the cranial fluid space. The displacement of the brain tissue is governed by a steady-state linear momentum balance with an underlying linear-elastic constitutive model. CSF flow is predicted by solving mass and momentum balances using the SIMPLE (semi-implicit method for pressure linked equations) algorithm for incompressible fluids. Because the CSF space is deformable due to motion along the CSF-brain tissue boundary, the fluid equations are written in an Arbitrary-Lagrangian-Eulerian framework. A mesh displacement scheme was implemented to maintain fluid grid integrity. The model predicts a pulsatile CSF flow pattern that matches in magnitude and timing the in vivo measurements of normal and hydrocephalic patients. Although the close match does not prove the original hypothesis is true, it does provide a rational explanation for the driving forces of intracranial dynamics of the CNS. This extensive undertaking has resulted in the first fully integrated model of vasculature, brain, and CSF, and is an important step toward quantifying complex biomechanical interactions in the brain.