An Eulerian formulation for the computational modeling of phase-contrast MRI

Area of Science:

• Medical Imaging
• Computational Fluid Dynamics
• Biophysics

Background:

• Phase-contrast MRI (PC-MRI) is crucial for assessing flow velocity fields.
• Current PC-MRI simulators often use a Lagrangian approach, which is sensitive to particle density and uniformity.
• This necessitates exploring alternative simulation methods for improved accuracy and efficiency.

Purpose of the Study:

• To develop and validate an Eulerian approach for PC-MRI modeling.
• To provide an alternative to the particle-based Lagrangian method for simulating MRI-reconstructed flow velocity fields.
• To assess the accuracy and feasibility of the Eulerian method in modeling complex flow dynamics.

Main Methods:

• Magnetization motion was modeled using the Bloch equation with an advection term.
• A finite difference method was employed on a fixed grid for computation.
• Spoiled gradient echo sequence was used for k-space sampling, with simulations validated against PC-MRI scans of flow in straight and stenosed cylinders.

Main Results:

• The Eulerian approach accurately reconstructed flow profiles in a straight cylinder with mean errors under 0.5% of maximum velocity.
• Simulations successfully depicted velocity profiles in stenosed cylinders, showing scan parameter-dependent artifacts and intravoxel dephasing.
• Results closely matched those from the Lagrangian approach with adequate particle density.

Conclusions:

• The Eulerian approach is a feasible and accurate method for PC-MRI modeling.
• This method offers a viable alternative to Lagrangian simulations, potentially improving computational efficiency.
• The study successfully demonstrated the capability of the Eulerian method in capturing complex flow phenomena and artifacts.