Ian Sobey(1), Almut Eisentraeger(1), Benedikt Wirth(2) & Marek Czosnyka (3)

(1) Mathematical Institute, University of Oxford, UK

(2) Institute for Numerical Simulation, University of Bonn, Germany

(3) Department of Clinical Neurosciences, University of Cambridge, UK

We have developed a multi-fluid model for flow of cerebro-spinal fluid (CSF) in the brain which has both general application for study of hydrocephalus and particularly here, for simulation of a CSF infusion test. Existing poro-elastic models for CSF flow treat the parenchyma and CSF as a continuum where very slow fluid flow interacts with and can affect the deformation of the underlying elastic substructure. A spherical model with CSF production at the centre of the brain, which allows flow through the aqueduct and very slow flow through the parenchyma before absorption at the outer periphery of the brain, has provided very plausible results for hydrocephalus. However, while that model provides new predictions about the interior state of the parenchyma, it is only applicable for long time scales that neglect blood pulsations on the cardiac cycle time scale. Here we describe our model which, by adding a blood compartment to the usual poro-elastic framework, allows blood pulsations to be included and so to attempt a time accurate simulation of CSF pressure fluctuations in an infusion test.

An infusion test is used to gain data about the CSF system, particularly resistance to absorption and brain compliance. In the test, a saline solution is injected into the CSF system for a fixed period to provide a temporarily elevated CSF production rate. The overall CSF pressure rises to a new plateau value, the level of which provides information about the outflow resistance, and the rate of CSF pressure rise gives information about the compliance.

In order to simulate CSF flow on short time scales we have retained the continuum poro-elastic model but extended the formulation to allow multiple compartments that do not exchange fluid in the continuum region. However, pressure fluctuations of one fluid can affect the pressure of other fluids as well as stress and deformation in the underlying elastic substructure. This results in a model where we can feed into a simulation the correct arterial pressure fluctuations (which are recorded during the infusion test) and then predict CSF pressure fluctuations and compare predictions with recorded values. By varying the physical parameters so as to fit the observed CSF pressure recording, we can provide new and additional predictions of parameters in a particular case, as well as predictions for stress, deformation and fluid content in the parenchyma during and after a test. In this presentation we will outline our multi-fluid model, discuss briefly the methods we use to solve the system of equations and present some results that compare computational predictions with clinical data using both conventional simulation and our multi-fluid model.