## 4 Control and Monitoring of MRI-Assisted Interventions
### Compatibility and Control Perturbations
#### 4.2.1 MRI-EMFs and Compatibility  
This section aims to illustrate the problem of MRI compatibility of inserted materials related to robotic tools in the scanner scaffold. Such compatibility is associated with image fidelity and accuracy. An MRI-compatible material is not supposed to alter the image.  
An image generated in an MRI scanner is shaped by signals occasioned by the connections of magnetic fields with living tissues. Thus, three different fields are exploited to construct 3-D images. A high static field engenders a vector of magnetization in tissues aligning their protons and quantifying their intensity. Three low-frequency repeated gradient field space-positioning aligned tissue protons fashioned a 3-D spatial reconstruction. Finally, a radiofrequency (RF) field exciting the tissue vector of magnetization allowed its reveal by the scanner, which can be processed and converted into images [16].  
Actually, MRI shows the hydrogen atom nuclei that are detained within the body. A hydrogen nucleus is a proton, which is a mass of positive charge rotating on itself around an axis. Protons are arbitrarily oriented in tissues and spin individually. Therefore, they display zero magnetic field performing out of phase. Considering the MRI theory, tissue protons require three arrangements inside the concerned tissue: aligning protons in a settled direction, rotating them together, and localizing their space distinct origin. These three arrangements could be, respectively, realized by the following: the static magnetic field B\({}_{0}\), excitation by wave RF field B\({}_{1}\) having a frequency corresponding to the natural frequency of protons' rotation f\({}_{\text{L}}\) (Larmor frequency) allowing a resonance action, and 3-D space gradient G(x, y, z) applied to the field B\({}_{0}\), permitting the position distinct values of B\({}_{0\text{d}}\), given by the following:  
\[\text{B}_{0\text{d}}\left(\text{x,y,z}\right)=\text{B}_{0}+\text{G}(\text{x,y, z}) \tag{1}\]  
Figure 1: Schematics of a self-controlled image-guided robotic surgical setting including scanner, tissue-touched zone, surgical tool, position and action processing, and robotic control and actuation.  
Note that the value of f\({}_{\rm L}\) is a function of B\({}_{0}\) and equal to 42.5 MHz per tesla, and the corresponding position distinct values f\({}_{\rm Ld}\) (x, y, z) will be a function of B\({}_{0\rm d}\) (x, y, z) and given by the following:  
\[\rm f_{Ld}\ (x,y,z)=42.5\times 10^{6}\times\ B_{0\rm d}\ (x,y,z) \tag{2}\]  
As mentioned before, the three fields used in MRI, static, gradient and RF, differ in strength, frequency, and presence while operating. Thus, B\({}_{0}\): 0.2-10 T, 0 Hz, permanently present; gradient: 0-50 mT/m, 0-10 kHz, pulses of few ms; and B\({}_{1}\): 0-50 mT, 8-300 MHz (amp. mod. pulses) of few ms. A representation of the three MRI field components is shown in Figure 2.  
The components producing the three fields are normally protected. Those of static and gradient fields are compensated and regulated. The arrangement of the RF field (often birdcage form, see Figure 2c), which is directly related to images, is the most exposed to perturbations mainly due to inserted external matters. Thus, the MRI compatibility of a matter inserted in the scanner scaffold (in the birdcage) is determined by its effect on the distribution of the field B\({}_{1}\); i.e., for an MRI-compatible matter, the field distributions without or in the presence of the matter are identical. Such compatibility could be checked from EMF computations of RF field B\({}_{1}\) distributions in the birdcage (see Section 5.2).