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

磁粒子成像(MPI)是一种依赖于超顺磁性氧化铁纳米粒子行为的成像方式，具有很好的医学应用前景。粒子对高动态磁场的非线性响应感应出在多个接收线圈中测量的电压，从该接收线圈可以重建显示纳米粒子的空间依赖浓度的图像。高的时间和潜在的高空间分辨率使MPI适合于几种体内应用，没有任何相关的有害辐射。MPI目前处于临床前阶段。然而，到目前为止，为了简化建模、数据获取和重建，几个关键的动态方面被排除在考虑之外。在这个合作项目中，我们解决了MPI的三个动态方面，导致了各种动态逆问题：(I)浓度动力学，(Ii)磁场动力学，和(Iii)粒子磁化动力学。实验结果表明，在重建过程中，由于环境动态过程(如心跳)的相互作用和必要的连续测量的重复，浓度(I)的时间变化高度相关，以获得足够的信号质量。因此，我们的目标是开发重建方法，明确考虑浓度的动态行为，以便在例如流量估计或仪器跟踪等应用中显著改善重建结果。安全法规限制了外加磁场的动态部分的幅度，这导致在一个测量周期内产生有限的视场(FOV)。增加FOV并开发在外加磁场(II)中编码的动态测量策略对于当前动物大小，特别是未来人类大小的应用是主要感兴趣的。在这个项目中，我们打算开发一种降低校准成本的策略、有效捕获期望特征的自适应采样方案以及相应的动态重建算法，并进一步解决如何在MPI中正确建模系统功能这一悬而未决的问题。这与粒子在快速变化的外加磁场中的磁化行为(III)有关。这种行为主要是由大量纳米粒子的内尔旋转机制决定的。我们建议解决大型粒子集合的扩展模型中的动态参数识别问题，以实现MPI中基于模型的重建。本项目中解决的不同但相互关联的动力学问题的解决对于MPI方法的进一步发展具有高度的相关性，使其能够进入临床阶段。

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.