Since the discovery of X-ray tomography in the 1970s, imaging techniques have continuously revolutionized medical diagnostics. Nowadays, there are a variety of tomographic procedures in the clinical environment, which are applied differently due to their specific advantages and disadvantages. The most important procedures are computed tomography (CT), magnetic resonance imaging (MRI), and various functional technologies such as PET (positron emission tomography) and SPECT (single photon emission computed tomography).
In the early 2000s, a new tomographic technique was developed based on tracking iron oxide nanoparticles in the human body. This technique, called Magnetic Particle Imaging (MPI), is radiation-free, highly sensitive, and offers very high temporal resolution.
This makes MPI predestined for the diagnosis of cardiovascular diseases. Another important application is in the cath lab, where MPI can enable three-dimensional navigation in the vascular tree using specially marked catheters.
In the joint project MPI², model-based methods and their efficient algorithmic implementation are being researched. In addition to the university partners from Aschaffenburg University of Applied Sciences, Hamburg-Eppendorf University Medical Center and Saarland University, the consortium is complemented by industrial partners. In addition to SCiLS and the Center for Radiology and Endoscopy at UKE Hamburg-Eppendorf, the MPI equipment manufacturer of the first commercially marketed scanner Bruker BioSpin is also supporting the work in the consortium.
ZeTeM (Prof. Dr. Peter Maaß, Dr. Tobias Kluth) is responsible for the coordination and management of the image reconstruction subproject. To determine the particle distribution, MPI exploits the magnetization property of the metallic nanoparticles. First, a static magnetic field is applied outside the object, which drives the magnetization of the particles inside the object into saturation almost everywhere in the site. Only along a certain trajectory of field-free points are there environments where the strength of the magnetic field allows a measurable change in the magnetization of the nanoparticles. This change in magnetization is produced by superposition with a second, dynamically varying, external magnetic field that causes the desired displacement of the field-free point.
A major concern in the development of new reconstruction techniques for MPI is the inclusion of a high degree of uncertainty in the model used. This is due to the lack of a mathematical model of sufficient quality to date. The measurement of a system matrix to describe the relationship between particle concentration and potential measurement is necessary for this reason. This time-consuming calibration process has to be replaced or the calibration effort has to be reduced significantly. For this purpose, models that include particle relaxation are investigated on the one hand, and on the other hand robust methods motivated by the total least squares approach are investigated that simultaneously reconstruct additional unknown model parameters in addition to the determination of the particle concentration. The actually linear inverse problem becomes a nonlinear problem, which has to be analyzed and solved.
