Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model ‐ Influence of noisy MRI measurements

MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms are compared for a benchmark problem. In particular, it is shown that noise and other artifacts in the MRI measurements have an influence on certain properties of the flow field, e.g., on the boundary flow and mass conservation.


Introduction
MRI (Magnetic Resonance Imaging) measurements are frequently used in the diagnosis of the cardiovascular system, e.g., intracranial aneurysms. However, they are typically subject to noise and artifacts that disturb the measured flow field. In particular, the precision of the MRI measurements is reduced for velocities in vicinity of the walls. This can largely be attributed to the so-called partial volume effect. The velocities in vicinity of the walls are important for the computation of the wall shear stresses, which are particularly important for the diagnosis of intracranial aneurysms because they are thought to be a measure for the likelihood of rupture of aneurysms. Moreover, mass conservation of the MRI flow field is typically impaired. We investigate these disadvantages of MRI-measured flow fields based on the benchmark introduced in [2], i.e., we compare the MRI measurements to CFD simulations.

Benchmark Problem
We use the geometry depicted in fig. 1 to compare the numerically simulated flow field with MRI measurements. Long sections of in-and outflow reduce the influence of boundary data on the flow near the aneurysm; see [2] for further details.
For the convenience of the reader we now quote verbatim the description of the MRI measurements as in [2]: MRI measurements: The printed model was connected to a pump and introduced into a 3 Tesla MRI system (Ingenia, Philips, Best, The Netherlands). The pump (Acandis, Pforzheim, Germany) was placed outside the magnet room, connected via tubing to the model and generated a continuous flow (rate: 1.76 ml 3 /s) through the phantom. Water and a contrast agent (Dotarem, Guerbet, Villepinte, France) with a concentration of 1.7 mmol/l were used. A three-dimensional gradient-echo sequence with three-directional phase-contrast flow encoding acquisition sequence [1] was used to measure velocities in the model with an isotropic resolution of 0.3 mm, reconstructed to 0.15 mm. The velocity encoding value (VENC) was set to 30 cm/s. To correct for background phases, the measurement was repeated with the pump turned off and the phase subtracted from the first measurement.
Mathematical model: Given a domain Ω and the kinematic viscosity ν we model a fluid using the time dependent incompressible Navier-Stokes equations for a Newtonian fluid. Specifically, we seek to approximately solve ∂u ∂t − ν∆u + (u · ∇)u + ∇p = 0, in Ω, div(u) = 0, in Ω, Inflow Outflow CAD model with a parabolic inflow profile at the inlet, a no-slip condition at the vessel wall and a do-nothing Neumann condition at the outlet. We use a convective-explicit formulation to linearize the Navier-Stokes equations.  Based on a CAD geometry a volume mesh was generated yielding 9.2 million degrees of freedom. The numerical simulation is carried out based on version 3.8.8 of LifeV [3]. The time discretization is done with a BDF-1 scheme and the space discretization with stabilized P 1 -P 1 elements. Specifically, for the inf-sup and convection stabilization the PSPG (Pressure Stabilized Petrov-Galerkin) and SUPG (Streamline-Upwind Petrov-Galerkin) approaches [4] are used. For some more details, see [2]. The presented numerical results are based on steady state solutions and were computed using a kinematic viscosity of ν = 1.0 mm 2 /s. Furthermore a parabolic inflow profile (flow rate: 1.76 cm 3 /s) was prescribed, which results in a peak velocity of a fully developed flow in a straight tube (vessel diameter: 4 mm) of 28.0 cm/s.
In fig. 2, we highlight one key advantage of CFD simulations over MRI measurements. At the position of the depicted slice (left image), the flow profile is almost parabolic. The visual comparison shows a good agreement between the MRI measurement and the CFD simulation (center left images) as is verified by the absolute error. However, the relative error grows towards the boundary. This is to be expected: On the one hand, MRI voxels near the boundary are partially outside of the geometry (partial volume effect, right image), which creates a smearing effect. On the other hand, MRI measurements outside of the geometry are noise, which can introduce artifacts near the boundary. For these reasons and the comparatively lower resolution of MRI images, accurate computations of wall shear stresses can be difficult [1].
In fig. 3, the CFD simulation computes an almost zero flow rate at the interface of the aneurysm and the vessel; in theory this should be identical to zero. The MRI measurement, due to noise, shows a much larger value. In fig. 4, the mean velocities in two sections are given. For the CFD simulation these values are almost identical, whereas the MRI measures significantly different values.
ACKNOWLEDGEMENT: The computations were carried out on the Cologne HPC cluster CHEOPS. ParaView (paraview.org) was used for the visualization.