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Research Papers

# Three-Dimensional Computational Modeling of Subject-Specific Cerebrospinal Fluid Flow in the Subarachnoid Space

[+] Author and Article Information
Sumeet Gupta

Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

Michaela Soellinger, Peter Boesiger

Institute for Biomedical Engineering, University of Zurich, CH-8006 Zurich, Switzerland; ETH Zurich, 8092 Zurich, Switzerland

Dimos Poulikakos

Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerlanddimos.poulikakos@ethz.ch

Vartan Kurtcuoglu1

Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerlandvartan.kurtcuoglu@ethz.ch

1

Corresponding author.

J Biomech Eng 131(2), 021010 (Dec 10, 2008) (11 pages) doi:10.1115/1.3005171 History: Received October 23, 2007; Revised August 25, 2008; Published December 10, 2008

## Abstract

This study aims at investigating three-dimensional subject-specific cerebrospinal fluid (CSF) dynamics in the inferior cranial space, the superior spinal subarachnoid space (SAS), and the fourth cerebral ventricle using a combination of a finite-volume computational fluid dynamics (CFD) approach and magnetic resonance imaging (MRI) experiments. An anatomically accurate 3D model of the entire SAS of a healthy volunteer was reconstructed from high resolution T2 weighted MRI data. Subject-specific pulsatile velocity boundary conditions were imposed at planes in the pontine cistern, cerebellomedullary cistern, and in the spinal subarachnoid space. Velocimetric MRI was used to measure the velocity field at these boundaries. A constant pressure boundary condition was imposed at the interface between the aqueduct of Sylvius and the fourth ventricle. The morphology of the SAS with its complex trabecula structures was taken into account through a novel porous media model with anisotropic permeability. The governing equations were solved using finite-volume CFD. We observed a total pressure variation from $−42Pato40Pa$ within one cardiac cycle in the investigated domain. Maximum CSF velocities of about $15cm∕s$ occurred in the inferior section of the aqueduct, $14cm∕s$ in the left foramen of Luschka, and $9cm∕s$ in the foramen of Magendie. Flow velocities in the right foramen of Luschka were found to be significantly lower than in the left, indicating three-dimensional brain asymmetries. The flow in the cerebellomedullary cistern was found to be relatively diffusive with a peak Reynolds number $(Re)=72$, while the flow in the pontine cistern was primarily convective with a peak $Re=386$. The net volumetric flow rate in the spinal canal was found to be negligible despite CSF oscillation with substantial amplitude with a maximum volumetric flow rate of $109ml∕min$. The observed transient flow patterns indicate a compliant behavior of the cranial subarachnoid space. Still, the estimated deformations were small owing to the large parenchymal surface. We have integrated anatomic and velocimetric MRI data with computational fluid dynamics incorporating the porous SAS morphology for the subject-specific reconstruction of cerebrospinal fluid flow in the subarachnoid space. This model can be used as a basis for the development of computational tools, e.g., for the optimization of intrathecal drug delivery and computer-aided evaluation of cerebral pathologies such as syrinx development in syringomelia.

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## Figures

Figure 1

(a) CSF space anatomy (T2 weighted MRI image) and pathways in the intracranial cavities. (b) Schematic of trabeculae bridging the SAS between arachnoid and pia layers.

Figure 2

3D reconstruction of the SAS using anatomic MRI. (a) Anatomical MRI slices were segmented to produce (b) a 3D model of the SAS. (c) The current investigation domain. (d) Detailed anatomy of the superior cranial SAS.

Figure 3

Velocity profiles at the boundaries as obtained using velocimetric MRI at (a) the pontine cistern, (b) the cerebellomedullary cistern, and (c) the spinal SAS. (d) Measured volumetric flow rates at each boundary. (e) Magnitude image at pontine cistern with segmented basilar artery.

Figure 4

Porous media representation of the SAS, (a) Representative porous model for CFD, (b) Representative unit cell and permeability directions, (c) permeability variation with porosity (The number of “RUCs” across a channel can be more than one)

Figure 5

CSF volumetric flow rates from CFD simulations at LFL, RFL, and FM

Figure 6

Normal velocity (m/s) contours at LFL

Figure 7

Stream traces colored by velocity magnitude (m/s). Particles are injected at Plane A intersecting the basal pontine and cerebellomedullary cisterns.

Figure 8

Velocity profiles at different cross sections within the domain. α is the Womersley number. (Cross sections are scaled differently at different time steps for better representation of the vectors.)

Figure 9

Velocity magnitude (m/s) contours in the SAS during one complete cardiac cycle (The velocity range in this figure has been chosen in order to best visualize the flow field.)

Figure 10

Relative pressure (Pa) contours in the SAS during one complete cardiac cycle. The pressure values are given with respect to zero reference pressure at the superior end of the fourth ventricle.

Figure 11

Transient deformation and deformation rate of cranial SAS during one complete cardiac cycle

Figure 12

Results of the independence studies. Pressure along a critical path in the treated domain as calculated (a) with different meshes, (b) at different time steps, and (c) with different time periods. (d) Pressure contours on a critical plane in the domain as calculated with different meshes.

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