A mathematical model of blood, cerebrospinal fluid and brain dynamics

Abstract

Using first principles of fluid and solid mechanics a comprehensive model of human intracranial dynamics is proposed. Blood, cerebrospinal fluid (CSF) and brain parenchyma as well as the spinal canal are included. The compartmental model predicts intracranial pressure gradients, blood and CSF flows and displacements in normal and pathological conditions like communicating hydrocephalus. The system of differential equations of first principles conservation balances is discretized and solved numerically. Fluid-solid interactions of the brain parenchyma with cerebral blood and CSF are calculated. The model provides the transitions from normal dynamics to the diseased state during the onset of communicating hydrocephalus. Predicted results were compared with physiological data from Cine phase-contrast magnetic resonance imaging to verify the dynamic model. Bolus injections into the CSF are simulated in the model and found to agree with clinical measurements.

CSF dynamic analysis of a predictive pulsatility-based infusion test for normal pressure hydrocephalus

“…Thus, the pulsatility of both arterial and venous blood flow, as well as CSF flow have potential impact on the ICP pulse amplitude, which has been highlighted by several authors. [8,19,20,22,35,36] Modelling the CSF dynamics ICP is a function of the volume of CSF, thus the change in ICP over time depends on the change in volume:…”

Normal and Hydrocephalic Brain Dynamics: The Role of Reduced Cerebrospinal Fluid Reabsorption in Ventricular Enlargement

“…Using a compartmental model, our group has determined that the reduction of CSF flow into the spinal canal in hydrocephalus may be due to a stiffening cerebrospinal system. 17 The soft tissue surrounding the spinal canal is compliant up to a particular threshold. An increase in ICP, perhaps caused by a decrease in CSF uptake through the sagittal sinus, may push the spinal canal to its threshold, limiting the amount of CSF that may be displaced into the canal, and thereby lowering the flow rate through the pontine cistern.…”

Ventricle Equilibrium Position in Healthy and Normal Pressure Hydrocephalus Brains Using an Analytical Model

“…The brain parenchyma is made of different components accounting for the compliance source in form of CSF flow, CSF absorption or drained elasticity which have been incorporated in a variety of compartmental models [16,17]. The brain consists of incompressible interstitial fluid (ISF), brain tissue namely white and gray matter, and blood capillaries.…”