1. Contrast Agent Transport Simulation using 4D PC-MRI Derived Flow Fields Ali Bakhshinejad, Roshan M. D'Souza, Loic Boussel, Vitaliy L. Rayz bakhshi3@uwm.edu Co-registration of the base-line (gray) and follow-up (black) lumenal geometries showing the regions occupied by thrombus [3] (b): CFD- predicted region of increased flow residence time (shown in red). ●Aneurysmal disease of blood vessels, causing a local vessel dilatation, presents a danger of vessel rupture resulting in severe blood loss (hemorrhage). ●Previous studies showed that blood flow residence time is an important biomechanical factor affecting aneurysm growth and thrombus deposition (clotting). ○Traditionally, contrast agent injection is the most common method for estimation of the filling and washout times in aneurysms. ○Another approach is patient-specific Computational Fluid Dynamic (CFD) modeling based on non-invasive MR imaging data. ■In this work, the boundary conditions required for numerical solution were obtained from phase-contrast magnetic resonance imaging (PC-MRI), which provided velocity measurements in the arteries supplying the aneurysms. ●In the current work we use a novel approach, where the contrast transport is simulated by solving the advection-diffusion equation using velocities measured in patients with time-resolved, phase-contrast MRI velocimetry (4D Flow MRI).

2. Contrast Agent Transport Simulation using 4D PC-MRI Derived Flow Fields Ali Bakhshinejad, Roshan M. D'Souza, Loic Boussel, Vitaliy L. Rayz bakhshi3@uwm.edu An artificial dataset generated for testing the numerical algorithm. Blue areas show the generated random noise in the areas without flow, and the red area represents a blood vessel. Schematic view of tagging system. ●Flow residence time can be assessed by modeling transport of a virtual contrast agent. In order to compute the concentration of virtual contrast, the advection-diffusion equation is solved, using three-dimensional velocity field measured with 4D PC-MRI. ●This method can be categorized into three steps: ○Pre-processing (Segmentation) ○Numerical solution of the equations ○Post-processing (Visualization of the results). Pre-processing (Segmentation) Numerical Solution ●A third-order, quadratic upwind di ff erencing scheme (QUICK) was employed to interpolate velocities on the walls of each voxel using two neighboring voxels in each direction. A first-order UPWIND scheme was used for the voxels at the boundaries. ●4D PC-MRI dataset obtained from in-vivo measurements provides velocity values on a Cartesian mesh. ●A second-order Crank-Nicolson scheme was used for the time discretization. This scheme is implicit which provides stability to the numerical solution.

3. Contrast Agent Transport Simulation using 4D PC-MRI Derived Flow Fields Ali Bakhshinejad, Roshan M. D'Souza, Loic Boussel, Vitaliy L. Rayz bakhshi3@uwm.edu Post-processing (Visualization of the Results) ●A sine function was used to simulate the heart pulse for the artificial velocity data. ●The virtual contrast quickly fills the center of the vessel, where the velocities are relatively high, while its flow near the walls is substantially slower, due to the lower velocities in the near-wall region. Future Work ●The present work is the early stage of the method development. Therefore, in the process of advancing the method, we need to improve the accuracy of the numerical algorithm in order to calculate the concentration of the virtual contrast. Also, more advanced post-processing modules are required for the accurate calculation and visualization of the flow residence time.