Magnetic Particle Imaging - Modeling and Solving a Dynamic Inverse Problem

Abstract

Magnetic particle imaging (MPI) is a functional, tracer-based medical imaging technique, which measures the non-linear response of magnetic nanoparticles to a dynamic magnetic field. The visualization of tracer dynamics with high temporal resolution is of particular interest in many applications, e.g. cardiovascular interventions or blood flow measurements. While MPI offers a very high spatial and temporal resolution, the size of its field-of-view is limited by physiological constraints. Multi-patch scans, sequentially scanning smaller subvolumes, so-called patches, allow to increase the total field-of-view. The forward operator, or system matrix, required for image reconstruction can be determined by calibration scans or physical models. Neither measured system matrices nor the standard forward models in MPI account for changes in the tracer concentration during a single scanning cycle. As a result, to date, non-periodic dynamic tracer distributions are mostly reconstructed as a time-series of frames under the assumption of nearly static behavior during the scan of each frame. While being a feasible approach for limited velocities, the reduced temporal resolution and data gaps in multi-patch sequences and the ignorance of dynamics in the forward operators cause motion and displacement artifacts in the case of strong dynamics. In this thesis, we introduce a reconstruction method for dynamic tracer distributions based on a dynamic forward model and a spline representation of the concentration. First, we present the dynamic MPI model and analyze its influence on the measurements and reconstructions with and without noise compared to the static model. Second, we establish the dynamic reconstruction approach for non-periodic motion in multi-patch sequences. Third, the new method is evaluated on the basis of synthetic single- and multi-patch data showing that the dynamic model enables for the reconstruction of fast tracer dynamics from a few frames and the spline approach approximates the missing data, which reduces multi-patch artifacts. Even in the absence of a specific motion model, a reduction of motion and multi-patch artifacts for fast dynamic tracer distributions is achieved.