Essentials of MRI Safety. Donald W. McRobbie
0.6–1.0
Demagnetizing field and factors
An object’s shape adds a further layer of complexity with great significance for magnetic forces and torques, and hence for MRI safety. Figure 2.13 shows how magnetization of the object in an external B0 generates “virtual poles”, resulting in a “de‐magnetization field” which reduces the apparent value of susceptibility χapp:
(2.8)
Figure 2.13 Demagnetization field within objects magnetized by an external magnetic field: the flatter object (left) creates more ‘virtual poles’ and develops a greater degree of demagnetization.
where di is the demagnetizing factor. For simple shapes (ellipsoids of rotation, cuboids and cylinders) there are three demagnetizing factors: d1 along the principal axis, d2 and d3 along the minor axes. Representative values are shown in Table A1.1 in Appendix 1. Figure 2.14 shows the values of 1/d1 for the axial and 1/d2 (=1/d3) for the radial axes of cylindrical objects. It is the demagnetizing factor that determines the level of magnetization of a ferromagnetic object, rather than the value of χ. For an unsaturated sphere the internal B field is three times the external B0. For elongated objects the internal B can be significantly greater. As a simple rule of thumb, for a cylinder whose length is aligned with B0
Figure 2.14 Reciprocal demagnetization factors for a cylinder: 1/d1 (axial, red line), 1/d2 (radial, blue line). For a cylinder d3 = d2.
If the object is rotated 90° to B0
Figure 2.15 shows the theoretical internal B for ferromagnetic cylindrical objects of various length‐diameter (l/d) ratios and a sphere as they approach 1.5 and 3 T shielded magnets. In each case the saturation value Bsat (=1.6 T) is reached at greater distances from the magnet for the more elongated objects.
Figure 2.15 Predicted internal B for a ferromagnetic sphere and cylinders of differing length/diameter ratios in the approach to 1.5 and 3 T MRI magnets. The material saturates at 1.6 T. The bore entrance is at 0.8 m. The dotted gray line indicates the B0 field strength.
Demagnetizing factors and Bsat are crucial for determining the force and torque on different shaped objects within the scanner’s fringe field.
MYTHBUSTER:
The internal magnetic field or degree of magnetization of a ferromagnetic object is not determined by its magnetic susceptibility but by its demagnetization factors and saturation status.
Example 2.1 Magnetization of a nickel coin
A nickel coin (length = 1 mm, diameter = 1 cm) is inadvertently brought into the MRI examination room. If the external field is 100 mT what is the field within the coin if it is: (a) lying face on to the magnet; (b) edge on to the magnet? Will the coin’s metal saturate?
1 (a) The ratio l/d = 0.1, so from Figure 2.14 or Equation A1.31 and 2.9a
Bsat for nickel is 0.62 T (Table 2.2) so, in this orientation it will be unsaturated.
1 (b) For the end‐on orientation use d2 and Equation 2.9b
This exceeds Bsat so the internal field will saturate at 0.62 T.
Example 2.2 Iron rod in the fringe field
An iron rod of length 10 cm, diameter 2 cm is brought within the fringe field of a MR magnet with B = 100 mT. Will it be saturated if its length is aligned with the field? Iron saturates at around 2 T.
From Figure 2.14 or Equation A1.31 and 2.9a
At this point the metal will not saturate.
FORCES AND TORQUE
The forces upon ferromagnetic objects are paramount for MRI safety.