1. Contrast Agent Transport Simulation using 4D PC-MRI Derived Flow Fields 

Main problem and approach:

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 Project, 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.

A novel  approach was used,  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).

Methodology:

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:

1. Pre-processing (Segmentation):

4D PC-MRI dataset obtained from in-vivo measurements provides velocity values on a Cartesian mesh.

 2. Numerical solution of the equations 

• A third-order, quadratic  upwind  differencing 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.
  

  Schematic view of tagging system

• A second-order Crank-Nicolson scheme was used for the time discretization. This scheme is implicit which provides stability to the numerical solution.

 

3. Post-processing (Visualization of the results).

A sine function was used  to  simulate  the  heart  pulse  for the artificial velocity data. (as shown in video Below)

 

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.