A mathematical framework for the dynamic interaction of pulsatile blood, brain, and cerebrospinal fluid

Abstract

Background: Shedding light on less-known aspects of intracranial fluid dynamics may be helpful to understand the hydrocephalus mechanism. The present study suggests a mathematical framework based on in vivo inputs to compare the dynamic interaction of pulsatile blood, brain, and cerebrospinal fluid (CSF) between the healthy subject and the hydrocephalus patient.

Method: The input data for the mathematical formulations was pulsatile blood velocity, which was measured using cine PC-MRI. Tube law was used to transfer the created deformation by blood pulsation in the vessel circumference to the brain domain. The pulsatile deformation of brain tissue with respect to time was calculated and considered to be inlet velocity in the CSF domain. The governing equations in all three domains were continuity, Navier-Stokes, and concentration. We used Darcy law with defined permeability and diffusivity values to define the material properties in the brain.

Results: We validated the preciseness of the CSF velocity and pressure through the mathematical formulations with cine PC-MRI velocity, experimental ICP, and FSI simulated velocity and pressure. We used the analysis of dimensionless numbers including Reynolds, Womersley, Hartmann, and Peclet to evaluate the characteristics of the intracranial fluid flow. In the mid-systole phase of a cardiac cycle, CSF velocity had the maximum value and CSF pressure had the minimum value. The maximum and amplitude of CSF pressure, as well as CSF stroke volume, were calculated and compared between the healthy subject and the hydrocephalus patient.

Conclusion: The present in vivo-based mathematical framework has the potential to gain insight into the less-known points in the physiological function of intracranial fluid dynamics and the hydrocephalus mechanism.

Keywords: Blood dynamics; Brain; Cerebrospinal fluid dynamics; Hydrocephalus; Intracranial pressure; Mathematical framework; Pulsatile interaction.