Synopsis

Electromagnetic (EM) fields are one of the fundamental forces in nature, which provide us an insight into the physics of MRI. In the presentation, we will have an overview of the interactions between the EM fields and human body. Audience are expected to understand the basic EM fields and Maxwell equations, the interaction variation with frequency, numerical method election and FDTD procedures to interpret the interactions qualitatively and quantitatively, and a summary of EM simulation applications in MRI.

TARGET AUDIENCE

OUTCOME/OBJECTIVES

Theory and METHODS

A. Fields and Maxwell Equations

Electromagnetic fields are one of the fundamental forces in nature. It has the following components and physical constants:

1. Electric field E: generated by electric charges and described by Gauss’s Law for Electricity.
2. Electric flux density D: also called displacement current, with an associated magnetic field determined by Faraday’s Law.
3. Permittivity ε: E=D/ε. ε =ε_r ε₀, where ε₀ is permittivity of free space, and ε_r is the relative permittivity of this material to free space.
4. Magnetic flux density B: generated by moving charges or current, defined by Biot-Savart Law.
5. Magnetic field H: determined by Ampere’s Law.
6. Permeability µ: B= µH. μ=μ₀ μ_r, where μ₀=4π x 10^-7 henry/m is the permeability of free space, μ_r is the relative permeability of the material to free space.
7. Others: I electric current, J electric current density, Z wave impedance, λ wave length.

EM fields are described by Maxwell Equations, and determined by currents on MRI RF Coils directly and indirectly through wave propagation. Due to the uniqueness of Maxwell Equations, current distribution on MRI RF coil can used to evaluate the quality of an EM simulation. Initial Conditions and Boundary Conditions are essential for EM fields estimation within human body.

B. High Frequency and Low Frequency

We typically call 3T (corresponding to a Larmor frequency of 123MHz) MRI or above high frequency. The interactions between EM fields and human vary with frequency.

At low frequency, the circuit size is much smaller than λ such that the current magnitude on a MRI RF coil does not vary along the coil. Current distribution is not much affected by the human body loaded in the RF coil. Lumped circuit theory and Biot-Savart Law may be used for low frequency MRI.

An electrical problem is said to be of high frequency if its largest circuit dimension is more than λ/10. Current magnitude varies in high frequency along the circuit due to the wavelength effect and standing wave patterns. Human body should always be considered as an integral part of the circuit at high frequency.

Tissue conductivity increases and the permittivity decreases with frequency, resulting in more power loss and less uniform fields within tissues. Intrinsic impedance variation results in EM wave reflection at tissue/tissue or air/tissue boundaries. Decreased Uniformity and higher power loss resulted Safety Concerns are the key challenges for high frequency MRI.

C. Numerical Methods

The interactions between MRI RF coils and human body through EM fields are complicated problems, requiring numerical methods to interpret the phenomena qualitatively and quantitatively.

Finite Element Method (FEM) and Finite Difference Time Domain (FDTD) are popular numerical tools in MRI. For FEM method, the storage and calculation operations are proportional to NC^3.3, where NC is the total number of cells in the numerical domain. For FDTD, the storage is proportional to NC, and the operations is proportional to NC*N, where N is the number of time steps. Therefore, FDTD is expected to be faster at high frequency MRI where the body usually has to be meshed into millions of cells for accurate SAR and Temperature estimation. Furthermore, FDTD can better take use of the parallel computing technology, limited only by the number of operations per time step (order of 100M).

The choice of method depends on project needs.

D. Simulation procedures for MRI

• The first thing in EM simulation is to define the project goals, and know the resources for the project. These affect the rest of the simulation.
• FDTD models should be as close as possible to the physical structure, including the dimensions, the circuit format, the body meshes. For example, all the decoupling and matching circuitry in general should be included in the RF array simulation.
• In setting up simulation parameters, note the exact parameters from a physical coil may not warranty meaningful results. Some input parameters may have to be measured before the assembly of the whole coil and even require EM simulation assistance, such as the resistive loss of an array element.
• During simulation, key parameters may need to be monitored.
• Results may be used to adjust the input parameters such as the lumped element value to achieve more accurate simulation. Some may be fairly complicated and better be done with other tools such as Matlab.

For high Q-factor resonant structures, it may require iterative effort to simulate the EM phenomena. For example, to tune/match/decouple a 16-ch head array, it might take 3 rounds along the coil geometry.

The described iterative EM optimization procedure can be substituted with EM-Circuit Co-Simulation method^1-3, which optimizes the S-parameters after EM calculations of non-resonant circuits, at the cost of interim larger storage and memory requirement. For arrays with large number of channels, the Co-Simulation method can achieve a speeding factor of 10-40.

Applications of EM Simulations in MRI

EM numerical simulation may be used for the following purposes:

• RF coil design, including coil type and geometry/parameter optimization
• RF coil performance evaluation to understand the electrical and thermal safety. The performance should be documented and may be used for coil diagnosis.
  
• Exploration and Explanation of MRI physics.

CONCLUSION

Acknowledgements

References

1. Zhang R, Xing Y, Nistler J, and Wang J. Field and S-Parameter Simulation of Arbitrary Antenna Structure with Variable Lumped Elements. ISMRM 2009: 3040.
2. Kozlov M,Turner R. Fast MRI coil analysis based on 3-D electromagnetic and RF Circuit co-simulation. JMR 200 (2009):147-52.
3. Beqiri A, Hand JW, Hajnal JV, Malik SJ. Comparison between Simulated Decoupling Regimes for Specific Absorption Rate Prediction in Parallel Transmit MRI. MRM 74 (2015): 1423-1434.