Calculation of radiofrequency electromagnetic fields and their effects in MRI of human subjects

Abstract

Radiofrequency magnetic fields are critical to nuclear excitation and signal reception in magnetic resonance imaging. The interactions between these fields and human tissues in anatomical geometries results in a variety of effects regarding image integrity and safety of the human subject. In recent decades, numerical methods of calculation have been used increasingly to understand the effects of these interactions and aid in engineering better, faster, and safer equipment and methods. As magnetic resonance imaging techniques and technology have evolved through the years, so to have the requirements for meaningful interpretation of calculation results. Here, we review the basic physics of radiofrequency electromagnetics in magnetic resonance imaging and discuss a variety of ways radiofrequency field calculations are used in magnetic resonance imaging in engineering and safety assurance from simple systems and sequences through advanced methods of development for the future. Key words: MRI; electromagnetics; radiofrequency; signal; noise; SAR; safety Only 10 years ago, the task of reviewing the literature on radiofrequency (RF) field calculations performed with an attempt to consider the human subject in magnetic resonance imaging (MRI) would be a seemingly manageable task, and could even be comprehensive without being prohibitively long. The combination of increasing reliance on numerical calculations and increasing complexity of RF techniques and technology in MRI makes this much more challenging today. In this work, the fundamental roles of the RF fields in MRI are discussed before a basic example calculation of signal-to-noise ratio (SNR) and specific energy absorption rate (SAR) for a particular imaging sequence in a sphere of biological tissue is presented using analytical methods. Following a brief transition, an attempt to review the literature on current applications with emphasis on breadth more than depth is given. It is hoped that the end result will provide enough basic understanding to the reader that with further study of the references provided he or she may be comfortable pursuing calculations for new purposes, continuing to advance the frontiers of MRI. RF MAGNETIC FIELDS FOR MRI: NUCLEAR EXCITATION AND SIGNAL RECEPTIONIn MRI, a variety of magnetic fields is applied to the human body to manipulate the magnetic moments of nuclei in the tissue so that they produce a detectable RF signal. An equation often used to describe the behavior of the net nuclear magnetization vector (M) in the presence of a general applied magnetic field (B) at a single location is the Bloch equation, sometimes written aswhere g is the gyromagnetic ratio, T 1 and T 2 are the longitudinal and transverse relaxation rates, respectively, M 0 is the magnitude of the net nuclear magnetization at rest, proportional to the strength of a given z-oriented static magnetic field (B 0 ), and a i , a j , and a k are unit vectors in the x, y, and z directions. The first term on the right-hand-side (including the cross product) indicates t...

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“…The amount of transmission power required also increases with, to a good approximation, the square of the static magnetic field strength, and furthermore is difficult to calculate because of the variations in the magnetic and electrical field distributions (Collins and Wang, 2011). This difficulty often leads to over-conservative estimations of SAR, further limiting the use of some rf pulses.…”

Improvement of Electromagnetic Field Distributions Using High Dielectric Constant (HDC) Materials for CTL-Spine MRI: Numerical Simulations and Experiments

“…The MRI signal is affected by both the transmit RF magnetic fields and the receive magnetic fields, as shown in the following equations [24]: $$S\propto M_t{B}_1^{-\ast }$$ $${\mathrm{bold-italicB}}_1^{-}=\frac{({\mathrm{bold-italicB}}_x-j{\mathrm{bold-italicB}}_y)\ast }{2}$$ where S is the signal, M t is the transverse magnetization, and ${\mathrm{bold-italicB}}_1^{-\ast }$ is the complex conjugate of the rotating RF magnetic field in receive mode, respectively. Whereas, ${\mathrm{bold-italicB}}_1^{+}$ is the rotating RF magnetic field in transmit mode defined as ( B x + jB y ) / 2 [9], [24].…”

Consideration of the effects of intense tissue heating on the RF electromagnetic fields during MRI: simulations for MRgFUS in the hip

“…Due to the strong dependence of tissue electrical properties on temperature (Lazebnik et al , 2006; Zurbuchen et al , 2010), it is important to consider the potential effects of intense tissue heating on the RF electromagnetic fields during MRI, as can occur in MRgFUS. Changes of the RF electromagnetic fields resulting from the changes in tissue electrical properties during an MR scan may affect, for example, both the efficacy of RF pulses and the MRI-induced specific absorption rate (SAR) pattern (Collins and Wang, 2011). To the best of our knowledge, however, a study of the potential effects of intense tissue heating on the RF electromagnetic fields during MRI has not previously been performed.…”