Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Ilmenau, Germany.
Med Biol Eng Comput. 2012 Oct;50(10):1081-9. doi: 10.1007/s11517-012-0950-4. Epub 2012 Sep 13.
The problem of estimating magnetic nanoparticle distributions from magnetorelaxometric measurements is addressed here. The objective of this work was to identify source grid parameters that provide a good condition for the related linear inverse problem. The parameters investigated here were the number of sources, the extension of the source grid, and the source direction. A new measure of the condition, the ratio between the largest and mean singular value of the lead field matrix, is proposed. Our results indicated that the source grids should be larger than the sensor area. The sources and, consequently, the magnetic excitation field, should be directed toward the Z-direction. For underdetermined linear inverse problems, such as in our application, the number of sources affects the condition to a relatively small degree. Overdetermined magnetostatic linear inverse problems, however, benefit from a reduction in the number of sources, which considerably improves the condition. The adapted source grids proposed here were used to estimate the magnetostatic dipole from simulated data; the L2-norm, residual, and distances between the estimated and simulated sources were significantly reduced.
从磁弛豫测量中估计磁性纳米粒子分布的问题在这里得到了解决。本工作的目的是确定源网格参数，为相关线性反问题提供良好的条件。这里研究的参数是源的数量、源网格的扩展和源的方向。提出了一个新的条件度量，即引导场矩阵的最大奇异值与平均奇异值的比值。我们的结果表明，源网格应该大于传感器区域。源，以及因此磁激励场，应该指向 Z 方向。对于像我们应用中的欠定线性反问题，源的数量对条件的影响相对较小。然而，对于超定静磁线性反问题，减少源的数量会极大地改善条件。这里提出的自适应源网格用于从模拟数据中估计静磁偶极子;L2-范数、残差和估计源与模拟源之间的距离显著减小。
