# Numerical Simulation of Bloch Equations for Dynamic Magnetic Resonance Imaging

## TL;DR

This paper develops a numerical simulation framework for MRI based on modified Bloch equations, analyzing its mathematical properties and discretization methods to improve imaging of flowing spins.

## Contribution

It introduces a well-posedness analysis and discretization strategies for the modified Bloch equations in MRI, including discontinuous Galerkin methods and adaptive time-stepping.

## Key findings

- Validated the numerical approach on basic examples
- Established well-posedness of the modified Bloch problem
- Demonstrated effectiveness of discretization methods

## Abstract

Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semidiscretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.