Passive magnetic localization in medical intervention

本文是被动磁定位领域的一篇review，在对被动磁追踪的挑战和远景中的多目标追踪部分和6D定位部分，可以给我们研究方向的指引。

医疗干预中的被动磁定位
Passive magnetic localization in medical intervention [1]
Paper Link
Authors: Zhenglong Sun, etc.
2018，Electromagnetic Actuation and Sensing in Medical Robotics

2. 永磁铁的磁场建模

2.1 磁偶极子模型

磁极子模型因为它的简单而著名。

2.2 充电模型 charge model

它定义两个参数：
It defines two parameters:
体积充电密度：volume charge density:
$${\rho }_m=-▽\cdot \text{M}(A/m^2)$$
表面充电密度：surface charge density:
$${\sigma }_m=\text{M}\cdot \hat{\text{n}}(A/m)$$
where $\text{M}$ is magnetic moment，$\hat{\text{n}}$ is the outward unit normal vector. the magnetic field at ${\text{P}}_s$ can be written as:
$$\text{B}({\text{P}}_s)=\frac{{\mu }_0}{4\pi }{\int }_v\frac{{\rho }_m({\text{P}}_c)({\text{P}}_s-{\text{P}}_c)}{|{\text{P}}_s-{\text{P}}_c{|}^3}\mathrm{d}{v}^{\prime }+\frac{{\mu }_0}{4\pi }{\oint }_s\frac{{\sigma }_m({\text{P}}_c)({\text{P}}_s-{\text{P}}_c)}{|{\text{P}}_s-{\text{P}}_c{|}^3}\mathrm{d}{s}^{\prime }$$
where ${\text{P}}_c$ is the source point (the surface magnetic charge)
For a constant magnetization in a magnet, the volume charge density ${\rho }_m$ equals to zero.

2.3 分布式多极子模型 distributed multipole model

但必须通过适当的校准相应地计算所有参数，由于在这分布式磁偶极子背后没有物理意义。
but all parameters have to be calculated accordingly through proper calibrations, since there is no physical meaning behind the distributed dipoles.

2.4 混合模型 hybrid model

远场用磁偶极子模型，近场用ANN模型。

3. 被动磁追踪原理 principle of passive magnetic tracking

3.1 逆优化理论 inverse optimization method

经常见的方法。

3.2 直接ANN理论 direct ANN method

输入n组$\text{b}$，输出该磁铁的5D pose $(x,y,z,m,n,p)$，监督学习。直接ANN理论能够提供直接前向和快速的计算并有高精度。The direct ANN method is able to provide straightfroward and fast calculation with high accuracy.

5. 被动磁追踪的挑战和远景 Challenges and outlook of the passive magnetic tracking

5.1 多目标追踪 multiple objects tracking

当多个磁目标同时存在于一个自由空间时，叠加原理应用。这个概念简单地表明在空间中的磁场是每个磁源的贡献的和。
When multiple magnetic objects coexist in free space, the principle of superposition applies. This concept simply means that the magnetic field in space is the sum of the contribution due to each magnetic source.
想法在仿真和实验中被证实，但是磁体被假定为固定为静态。磁铁的数量也需要被提前定义和固定。在这个研究方向，期望有一个快速并鲁棒的算法来识别目标的数量同时以合理精度地估计他们的位置信息。
The idea was verified in both simulations and experiments, but the magnets were assumed to fixed in static. The number of magnets also needs to be pre-defined and fixed. Along this research direction, it is expected to have a fast and robust algorithm to identify the number of objects as well as estimate their positional information with reasonable accuracy.

5.2 6自由度追踪 6 DoF tracking

宋报告使用两个相同的垂直对齐的永磁铁的组合在一个无线胶囊内窥镜内。然而，由于磁偶极子的限制，如果两个磁铁互相太近的话，没有唯一解；估计的朝向误差会比较大。因此，两个垂直对齐的磁铁不得不保持一定距离。在被动磁追踪中使能6自由度追踪的另一种理论是采用一种更好的物理模型，能够考虑形状而不仅仅是磁极子模型。但是，由磁铁几何形状导致的磁场不对称的不同是相当有限。所以放大在磁场中这种不对成的一个新想法是用磁铁组合。一个可以预见的限制是处理时间由于使用复杂物理模型的迭代计算。
Song reported using assembly of two identical perpendicular aligned permanent magnets inside a wireless capsule endoscopy. However, due to the limitation of the dipole model, there would be no unique solutions if two magnets are too close to each other; the estimated orientation errors will be large. Thus, the two perpendicular aligned magnets have to be kept at a distance. Another method to enable 6-DoF tracking in the passive magnetic tracking is to adopt a better physical model, which is able to take account of the geometry rather than dipole model. However, the differences in the magnetic field asymmetry caused by the geometry of the magent could be quite limited. One novel idea to amplify such asymmetric in the magnetic field is to use the magnet assembly. One foreseen limitation would be the processing time due to the iterative calculation using the complex physical models.

[1]: Sun, Zhenglong, Luc Maréchal, and Shaohui Foong. “Passive Magnetic Localization in Medical Intervention.” Electromagnetic Actuation and Sensing in Medical Robotics. Springer, Singapore, 2018. 163-187.