Magnetic Particle Imaging (MPI) is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the Field-Free Line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitute the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the 2D FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment.

翻译：磁粒子成像（MPI）是一种前景广阔的无创体内成像模态，通过将超顺磁性纳米颗粒暴露于动态磁场中，可实现其空间分布的映射。在场自由线（FFL）扫描拓扑结构中，通过施加在直线上消失的磁场来实现粒子分布的空间编码。当粒子暴露于磁场时，在接收线圈中感生的电压构成信号，由此可重建粒子分布。为避免冗长的校准过程，目前已针对二维FFL扫描拓扑结构开发出基于模型的重构公式。本研究提出了三维FFL的重构公式，并在此基础上提供了基于模型的三维FFL重建算法，通过数值实验对其进行了验证。