How well do 3D CFD simulations compare with 4D MRI flow measurements in the third ventricle?
- Aurélie Picquot
- Philippe Reymond
- Francesco Santini
- Jelena Block
- Eleonora Fonari
- Theresia Yiallourou
- Bryn Martin
- Nikolaos Stergiopulos
CFD simulations have provided detailed information about the complex flow and pressure field within the cerebrospinal fluid system (Gupta, Soellinger et al. ; Loth, Yardimci et al. 2001; Fin and Grebe 2003; Kurtcuoglu, Poulikakos et al. 2005; Kurtcuoglu, Soellinger et al. 2005; Kurtcuoglu, Soellinger et al. 2007; Gupta, Soellinger et al. 2009). The solutions of these simulations are sensitive to boundary conditions and thus need validation with in vivo measurements. However, validation of 3D CFD flow calculations and MRI CSF flow measurements have been limited to thru-plane pcMR measurements. Recent advancements in MRI flow measurement technology has enabled fast measurement of the 4D flow field within the spinal subarachnoid space (SSS), superior sagittal sinus (Figure 1), and ventricles of the brain (Santini, Wetzel et al. 2009).
The goal of the proposed work is to measure the 3D flow field within the ventricles by 4D MRI and compare the flow field with a 3D CFD simulation based on the same geometry and boundary conditions assuming rigid ventricle walls.
Methods and study outline
- A. in vivo MR measurements
Our approach is to obtain detailed velocity and geometry measurements within the ventricles.
- 4D CSF velocity measurements in the ventricles will be obtained using the protocol developed by Santini et al. (Figure 1) (Santini, Wetzel et al. 2009). Subjects will be asked to lie in the supine position in the scanner bed with a standard 12-channel head coil and neck coil (Siemens Medical Solutions). CSF flow measurements will be performed in healthy volunteers in the spinal SAS (C2 to lumbar if possible), hindbrain, and ventricles with the following imaging parameters: venc = 10 cm/s, TE = 6 ms, TR = 12 ms, flip angle = 70°. Total scan time for each subject will be approximately 20 min.
- Thru-plane phase contrast MR measurements will be obtained at the aqueduct of Sylvius and at the foramen of Monro to establish the flow boundary conditions for the CFD simulation. Velocity mapping will also be obtained at two other planes midway between the aqueduct and foramen. A standard phase contrast velocity mapping sequence will be used to acquire CSF velocity in the aqueduct of Sylvius with slices chosen perpendicular to the aqueduct in its caudal part. Since maximum velocity values in the range of 5 cm/s are expected (Kurtcuoglu, Soellinger et al. 2007), the encoding velocity will be set to 7 cm/s in order to avoid phase wraps. Three measurements will be used to improve the signal-to-noise ratio.
- A high resolution T2-weighted 3D, turbo spin-echo sequence will be used to define the brain ventricles for the CFD simulation.
- B. processing of MR data
The data obtained from the MR measurements will be processed using the following methodologies:
- The 4D MRI data set will be pre-processed using the VeloMap tool by J. block et al. and visualized with EnSight and Matlab software.
- The measured velocity profiles at the aqueduct of Sylvius and foramen of Monro will be manually phase-unwrapped, filtered with a mask (i.e. 5x5 pixels) and smoothed using cubic spline interpolation (Gupta, Soellinger et al. 2009).
- The acquired MR geometry scan of the ventricles will be manually segmented using ? (software) to obtain a three-dimensional representation of the ventricles. The voxel-based segmented structures will be converted to non-uniform rational B-spline surfaces in order to allow for efficient generation of a high-quality computational grid (Gupta, Soellinger et al. 2009).
- C. CFD simulation
CFD simulation will be performed within the region of the third ventricle. A computational mesh will be formed based on the MR geometry scan. CSF velocity profiles obtained at the aqueduct of Sylvius will be imposed with the CSF modeled as an incompressible Newtonian fluid with the same density and viscosity as water at 378K (Loth, Yardimci et al. 2001). Computations will be made using the commercial finite volume CFD solver FLUENT (Fluent Inc., Lebanon, NH, USA).
- D. Comparison of results
The CFD results and 4D MR measurements will be compared qualitatively and quantitatively at various locations within the third ventricle.
Expected results and potential impact
We expect that the 3D CFD calculations, assuming rigid ventricle walls, will agree qualitatively with the 4D MR flow measurements in terms of the location of fluid vortices and velocity gradients within the third ventricle near the aqueduct of Sylvius. However, we expect quantitative agreement to be lacking, particularly near the ventricle walls and at locations further from the aqueduct of Sylvius and at the foramen of Monro. This study will help better understand the potential advantages and drawbacks of the 4D MR scan and CFD calculations assuming a rigid ventricle boundary.
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