The ensuing attractive force opposes the gravitational force and the sheet will tip in slow motion down towards the horizontal. Similarly, moving a non‐ferromagnetic conducting object in the fringe field gradient will result in resistance to that motion. Make sure the metal you use is non‐ferromagnetic.
Induction from the radiofrequency exposure
In some respects, the calculation of induced E from the RF exposure is easier than for the gradients, because to a good first approximation, we can consider B1 as being uniform in space. The power density PV, follows from a volumetric version of the Ohm’s law relation “power equals voltage times current”:
(2.27)
Specific absorption rate (SAR) is defined as the power deposited in tissue per unit mass given by
(2.28)
ρ is tissue density. In the simplest case of a uniform sphere, the maximum SAR from a rectangular constant amplitude B1 pulse repeated N times is [5]
(2.29)
The duty cycle D is the fraction of time for which the B1 pulse (duration tp) is active within the MRI sequence TR period:
(2.30)
The average SAR is
(2.31)
For a sphere, the average SAR is 0.4 of the peak SAR. In terms of flip angle α, for a rectangular B1 pulse
(2.32)
This illustrates the well‐known result that SAR is proportional to the square of the flip angle (for a given pulse shape), increases linearly with the number of RF pulses and is inversely proportional to the pulse duration and sequence repetition time TR.
In general, calculating SAR for arbitrary geometries requires the use of numerical methods [6]. An additional issue arises as a consequence of Ampere’s law (Maxwell’s fourth equation) for frequencies above 10 MHz, in that the induced E, itself, induces an RF magnetic field opposed to B1 resulting in an overestimation of SAR. Additionally, differing tissue properties, anatomical geometry, and the presence of metallic implants will alter the RF deposition pattern, often resulting in SAR hotspots. The relationship between SAR and heating is non‐linear and heterogeneous and is heavily influenced by the thermal properties of tissue and cooling from perfusion and conduction. These will be considered in Chapter 5.
Wave‐like behavior of B1
Figure 1.26 showed the uniformity of the B1‐field in air produced by a typical birdcage transmit coil. However, the presence of the patient’s tissues affects the nature and amplitude of the field (Figure 2.28). In a dielectric medium the EM wavelength λ has a different value than in air or vacuum and the familiar equation for wavelength (λ = c/f) becomes
(2.33)
Figure 2.28 B1 uniformity map for a head phantom at 7 T showing the effect of (left) non‐optimized and (right) optimized parallel transmission. Figure courtesy of Kawin Setsompop, Massachusetts General Hospital, A.A. Martinos Center for Biomedical Imaging.
where c is the speed of light (3×108 ms−1).
The “wavelength” in air is around 4.7 m at 64 MHz (1.5 T) and 2.3 m at 128 MHz (3 T) and B1 in air is a magnetic field in the near field region with minimal E‐field components, except close to the coil windings and tuning capacitors. However, the dielectric constant, εr of tissues changes the wavelength within the patient. Often the relative permittivity εr of water, with a value stated to be around 80, is used to estimate wavelength in tissue. This reduces the wavelength at 64 and 128 MHz to 0.51 m and 0.26 m. These dimensions are comparable to the patient’s dimensions and also to the body transmit coil dimensions.
Near and far field
In order to better understand the RF interactions, we can consider radio antenna theory. In radio transmission for broadcasting and telecommunications, the RF field is commonly divided into different regions illustrated in Figure 2.29. Closest to the transmitter is the reactive or inductive near field. This is the mode of operation of the MR transmit coil, producing primarily a magnetic B1‐field. This region is said to extend to λ/2π or 0.159×λ. In a 1.5 T scanner this would extend in air to 0.75 m from the iso‐centre and half that distance for a 3 T scanner, encompassing the entire coil volume.
Figure 2.29 Field regions in air and within the patient’s tissues. In the inductive near field zone the B1 magnetic field dominates. In the radiative near field B1 and E1 are highly non‐uniform. For comparison the wavelengths in air and muscle are shown. Top view of the scanner bore.
Figure 2.30 Measurements of B1 and E1 in a gel phantom on axis and off‐axis up to 60 cm from the end of a transmit head coil in tissue equivalent material.
Source [8]. Licenced under CC BY 4.0. Licensee Frontiers.
The radiative near field or Fresnel region extends between one and two wavelengths. At 3 T with a patient in situ, this region will extend from 0.25 to 0.5 m and double those distances in a 1.5 T scanner. In the Fresnel zone the field behavior can become very complex with local maxima and minima. This results in the B and E fields extending
