a permanent magnet and (b) from an electromagnet."/>
Figure 1.23 Magnetic field lines of force: (a) seen in the pattern of iron filings around a permanent magnet; (b) from an electromagnet.
B0 fringe field
The most uniform and dense grouping of lines of force for an MR magnet (Figure 1.23b) occurs within the bore. As we move away from the bore the lines diverge and consequently the B‐field decreases. We call this region the fringe field. Your scanner manufacturer provides field maps showing fringe field contours at 0.5, 1, 3, 5, 10, 20, 40, and 200 mT [4] (Figure 1.24). These are important for MRI suite design (Chapter 12). A modern MRI system utilizes self‐shielding in order to reduce the spatial extent of the fringe field (Figure 1.25).
Figure 1.24 Fringe field contours at 0.5, 1, 3, 5, 10, 20, 40 and 200 mT for a 3 T MR magnet. Reproduced with permission of Siemens Healthineers.
Figure 1.25 The magnitude of the B0 fringe field (solid lines, logarithmic LH scale) and its spatial gradient dB/dz (dashed lines, linear RH scale) along the z‐axis simulated for shielded 1.5 and 3 T MRI magnets. The vertical lines indicate the locations of the 0.5 mT contour. The iso‐centre is located at z=0, and the bore entrance at 0.8 m.
Fringe field spatial gradient
As we move further from the bore of the magnet, the lines of force diverge, and the fringe field decreases (Figure 1.23b). The amount it decreases with distance is known as the fringe field spatial gradient, specified in T m−1. The fringe field spatial gradient is responsible for the attractive force on ferromagnetic objects. Your manufacturer is required to provide you with information about the fringe field gradient. Figure 1.25 shows how the B0 field and its spatial gradient dB/dz vary along the z‐axis. The fringe field is compressed for the shielded magnet but produces a stronger spatial gradient close to the bore entrance. This is highly significant for projectile safety.
MYTHBUSTER:
The fringe spatial field gradient is always present as long as the main static B0 field exists. It should not be confused with the imaging gradients.
The imaging gradients
Gradient amplitude is measured in mT m−1 (milli‐tesla per meter). When a gradient pulse is applied, e.g. along the x‐axis, the total B experienced at a point x is
(1.6)
Example 1.3 Bz from a gradient
In a 1.5 T MRI system with a gradient amplitude of 10 mT m−1 what is the total magnetic field at a point x = 10 cm from the isocentre?
At a point x = −10 cm, the resultant B‐field is 1.499 T.
The contribution to the overall magnetic field of the gradients is small, but we could not image without them. The strength of the field produced by the gradients decreases rapidly outside the bore of the magnet, and is negligibly small away from the magnet.
As the gradients are switched, they produce time‐varying magnetic fields. The rate of change of field is given by the derivative of B with respect to time, or dB/dt (measured in T s‐1). For a trapezoidal gradient waveform (Figure 1.16)
(1.7)
where ΔB is the change in B produced by the gradient and Δt is the time over which the change occurs. dB/dt is important when considering acute physiological effects, such as peripheral nerve stimulation (PNS). See Chapter 4 .
Example 1.4 Gradient dB/dt
In the example of Figure 1.16 if the peak gradient amplitude is 10 mT and the rise time 0.1 ms, what is the dB/dt?
Radiofrequency field
Figure 1.26 shows simulations of the electric and magnetic fields generated around an eight‐rung birdcage transmit coil [5]. The magnetic B1‐field is highly uniform, whilst the electric field (E) is concentrated around the rungs. In air B1 decreases rapidly beyond the limits of the transmit coil.2 B1 is produced as a pulse consisting of a “carrier” frequency (at the Larmor frequency) multiplied by a shape or envelope (Figure 1.27). The simple rectangular pulses of Equation 1.2 are seldom used in practice and a more general expression for flip angle is
(1.8)
Figure 1.26 Simulated electric (L) and magnetic fields (R) from an eight‐rung birdcage coil. Scale in dB. Source [5], licensee BioMed Central Ltd.
