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Heating and energy absorption are difficult to test experimentally, except in simplified phantoms such as homogeneous models filled with fluid. Because these phantoms are so simple, the energy absorption experienced by a phantom may have little relation to the energy absorbed by an actual person, as the body reflects and focuses the RF fields in hard-to-predict ways, as shown by Fig. 3.2 These effects can be thoroughly investigated by simulating realistic heterogeneous models, based on the electromagnetic properties of human tissue.

3. These simulated images of  (a) a cylindrical phantom, (b) a homogeneous head phantom, and (c) a heterogeneous head model are from the Virtual Family (ref. 2), calculated in the CST MICROWAVE STUDIO® simulation software.

Both time- and frequency-domain solvers can be used to simulate RF coils. When human body models are included, however, time-domain methods represent the more practical approach. Figure 4 shows the workflow for tuning and simulating a head coil.3 The first step, simulating each port of the coil in turn, is the most computationally intensive step of the process. However, it only needs to be carried out once. The simulation generates field data and an S-parameter matrix, describing how RF energy propagates through the multiport network.

4. This block diagram represents the simulation workflow for a typical multiple-channel coil.

The coil can then be connected to a tuning circuit (Fig. 5), using a circuit simulator such as CST DESIGN STUDIO™ from Computer Simulation Technology. The software uses S-parameters to tune the circuit elements around the coil without having to run the full-wave simulation again. This produces one tuned and matched field per channel (Fig. 6). The fields from each transmitter can then be combined and, by optimizing the phase and amplitude at each port, the combined field can be made homogeneous in the area of interest.

5. This is the tuning circuit for a head coil simulated in the CST DESIGN STUDIO™.

6. These S-parameters for a tuned coil show good coupling at the desired frequency of 297.2 MHz.

Simulating an empty coil will not provide a full picture of how it will work in practice, however. As mentioned previously, placing a patient in the machine loads the coil and introduces sources of interference, which will affect the EM field distribution. To ensure that the coil produces a homogeneous field inside the subject, the optimizer can also be run with a model inside the coil (Fig. 7), to find a usable field that takes into account the EM properties of the body.

7. This diagram shows a HUGO voxel model being simulated within a head coil.

Once a homogeneous field has been produced, whether with a single-channel or multiple-channel coil, and the results have been verified, the field must be evaluated to remain within the safety guidelines set by the International Electrotechnical Committee (IEC) and standard IEC 60601-2-33. Because it is difficult to determine the temperature distribution inside a patient, the standard way of quantifying MRI safety is by means of the SAR. The SAR is the power absorbed by the body per mass of tissue. There are a number of ways of presenting SAR: averaged over a volume, over a whole organ or structure, or simply as a point-by-point value. There are various legal SAR limits to prevent patients from being exposed to too much RF power during an MRI scan. Post-processing methods can calculate various types of SAR automatically for both standard and worst-case tuning instances, along with other relevant quantities such as the B1+ (transmit) field and the power loss.

The best practice for calibrating a coil is to run simulations using a number of voxel models, evaluate the field distribution and SAR for each one, then find the most critical type of SAR for each model. For example, if the worst-case SAR includes a small but severe hotspot, the point SAR or 10-g average SAR is the most critical one to reduce. If the power loss is evenly distributed across a large area, the SAR averaged across the whole body or a part of it is more likely to be important. If the scan region includes a particularly sensitive organ, the SAR across particular tissue types can be calculated as well to determine how much energy that organ will absorb. Once a designer knows which SAR values are most critical, efforts can be made to reduce those values. Since absorbed power scales linearly with the power of the coil, it’s relatively simple to decrease the power of the coil until all SAR values are within the safe region.

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