In a healthy human brain, cerebrospinal fluid (CSF), a water-like liquid, fills a system of cavities, known as ventricles, inside the brain and surrounds the brain and spinal cord. It mechanically stabilises the brain, acts as a space reservoir inside the rigid skull, and is likely to have chemical importance for the extracellular environment of neurons. Abnormalities in CSF dynamics, such as hydrocephalus, are not uncommon and can be fatal for the patient. Thus, the aim of mathematical research in this field is to gain a better understanding of the mechanical behaviour of the brain and the CSF circulation and to find models that accurately describe CSF dynamics and can be used in a clinical environment.
Most models for CSF circulation that are available are quasi-steady, intended for time scales of days and weeks to describe the long-term development of hydrocephalus. My research focuses on a biomechanical simulation of CSF flow based on the theory of poroelasticity, trying to include time dependence in a way that CSF dynamics can also be predicted on time scales of minutes down to fractions of seconds to be able to capture CSF pressure pulsations at heart frequency as well.
For this purpose, a strain dependent permeability is included in a time-dependent spherically symmetric model of the brain, which is then applied to simulate the CSF dynamics during the so-called infusion test. For this standard test in the diagnosis of CSF related diseases, additional fluid is injected into the CSF space at a constant rate, while measuring the pressure continuously.
Future and ongoing research includes the extension of the model by a separate blood compartment, which interacts with the CSF only indirectly through the porous elastic solid. This extra information promises more realistic simulations of the CSF dynamics of the patient.
Different permeability models, nonlinear elasticity, and viscoelastic effects of the solid, as well as a more realistic geometry, are potential extensions of the current model.
See also list of publications.