Thomas Puiseux^{1,2}, Anou Sewonu^{1,3}, Ramiro Moreno^{1,3,4}, Simon Mendez^{2}, and Franck Nicoud^{2}

^{1}SPIN UP, Toulouse, France, ^{2}IMAG, Univ. Montpellier, CNRS, Montpellier, France, ^{3}I2MC, INSERM U1048, Toulouse, France, ^{4}ALARA Expertise, Strasbourg, France

The present study proposes a novel approach to efficiently simulate 4D Flow MRI acquisitions in realistic complex flow conditions. Navier-Stokes and Bloch equations are simultaneously solved with Eulerian-Lagrangian coupling. A semi-analytic solution for the Bloch equation as well as a periodic particle re-injection strategy are implemented to reduce the computational cost. The Bloch solver and the velocity reconstruction pipeline were first validated in a steady flow configuration. The coupled 4D Flow MRI simulation procedure was validated in a complex pulsatile flow phantom cardiovascular-typical experiment. Besides, we compared simulated MR velocity data with experimental 4D Flow MRI measurements.

To identify the largest velocity error contribution, the highest error patterns were compared to the highest CFD acceleration patterns in figure 4. The high visual correlation confirms that acceleration-induced artifacts contribute for the main errors. Note also that the sparse particles distribution near the inlet boundary induces high velocity error.

The velocity error produced by MRI simulation with respect to CFD was qualitatively compared to the error raised between MR measurements (

1. Bittoun et al, MRI, 1984.

2. Stoecker et al, MRM, 2010.

3. Puiseux et al., NMR Biomed., 2019.

4. Mendez et al, IFMBE, 2015.

5. Bittoun et al, MRM, 2000.

6. Thunberg et al, MRM, 2000.

(a) Flow phantom schematic representation in the coronal plane annotated with locations of surfaces of interest. (b) Schematic diagram of the experimental setup.

Main steps of the CFD-MRI simulation procedure. BC: Boundary conditions. The grey block corresponds to the simulation framework kernel, while the red/blue blocks are inputs/outputs to the simulation.

Comparison in the XZ-middle plane between **u**_{SMRI} and ||**u**_{CFD}|| at four different phases during the cycle.

Threshold of (**left)** phase-averaged CFD acceleration and **(right)** L2-norm error of the SMRI velocity. **a)**. t/T_{p}=0.44 and **b).** t/T_{p}=0.91.

Velocity L2-norm error in the XZ-middle plane of the **(left)** experimental and **(right)** simulated MRI at peak systole t/T_{p}=0.44. The L2-norm error is calculated based on the downsampled phase-averaged CFD velocity.