Dynamic Inverse Problems in Magnetic Particle Imaging (D-MPI)

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Magnetic particle imaging (MPI) is an imaging modality with promising medical applications that relies on the behavior of superparamagnetic iron oxide nanoparticles. The particles' nonlinear response to a highly dynamic applied magnetic field induces a voltage measured in multiple receive coils from which an image showing the spatially dependent concentration of the nanoparticles can be reconstructed. A high temporal and a potentially high spatial resolution make MPI suitable for several in vivo applications without any associated harmful radiation.MPI is currently in the preclinical phase. However, several crucial dynamic aspects have been left out of consideration so far to simplify modeling, data acquisition and reconstruction. In this collaborative project, we address three dynamic aspects of MPI resulting in a variety of dynamic inverse problems: (i) concentration dynamics, (ii) magnetic field dynamics, and (iii) particle magnetization dynamics.Experimental results indicate that temporal changes of the concentration (i) are highly relevant during the reconstruction due to an interplay of environmental dynamic processes (like the heart beat) and the necessary repetition of sequential measurements to obtain sufficient signal quality. Thus, we aim for developing reconstruction methods which take the dynamic behavior of the concentration explicitly into account in order to significantly improve the reconstruction results in applications like, for example, flow estimation or instrument tracking.Safety regulations limit the amplitudes of the dynamic part of the applied magnetic field which results in a limited field-of-view (FOV) during one measurement cycle.Increasing the FOV and developing dynamic measurement strategies encoded in the applied magnetic field (ii) is of major interest for current animal-size and particularly for future human-size applications. In this project, we intend to develop a strategy to reduce the calibration costs, adaptive sampling schemes to capture the desired features efficiently and respective dynamic reconstruction algorithms.We further address the still unsolved problem of modeling the system function in MPI properly. It is related to the particles' magnetization behavior (iii) in the rapidly changing applied magnetic field. The behavior is mainly determined by Néel rotation mechanisms of large ensembles of nanoparticles. We propose to solve dynamic parameter identification problems in extended models for large ensembles of particles to enable model-based reconstruction in MPI.The solution of the different but interrelated dynamic problems addressed in this project are highly relevant for further developments of the MPI methodology enabling an entry into the clinical phase.