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.
Figure 1.27 RF pulse consisting of the carrier (Larmor) frequency multiplied by a shape function or pulse envelope. The example shown is a truncated sinc (sinx/x) function.
This is equal to the area under the curve of the pulse envelope. Three important points arise:
1 for the same pulse shape and duration, the B1 amplitude is proportional to the flip angle;
2 for the same pulse shape and duration, the B1amplitude required to produce a given flip angle is independent of B0;
3 the peak amplitude of B1 alone is not sufficient to characterize the RF exposure.
MYTHBUSTER:
The amplitude of the B1 RF excitation pulse does not depend upon the static field strength B0.
B1+ and B1+rms
The parameter B1+rms is used to characterize the average B1 exposure. The “+” refers to the rotating component of B1 responsible for excitation of the magnetization. An efficient coil should not generate a B1−. RMS stands for root‐mean‐square and is a type of averaging used for time‐varying waveforms. For example, the RMS value for a sinusoidal waveform is 1/√2 or approximately 0.71 of the peak amplitude (Figure 1.28a). B1+rms is defined as
(1.9)
Figure 1.28 (a) the RMS value of a sinusoid is the peak amplitude divided by √2; (b) B1+ RMS for a train of N RF pulses of amplitude B1+, duration τ within time T.
calculated over 10 second intervals (T=10 s). The easiest way to visualize this is to consider a regular train of N rectangular RF pulses (Figure