Donald W. McRobbie - Essentials of MRI Safety

1 (a) The ratio l/d = 0.1, so from Figure 2.14or Equation A1.31 and 2.9a

B sat 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 B sat so the internal field will saturate at 0.62 T .

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.

The forces upon ferromagnetic objects are paramount for MRI safety. “Magnet safety” should be ingrained into our behavior and consciousness. In this section we consider forces and torques on objects, conducting wires, and electrical circuits. The former is relevant for all implants, MR accessories and objects brought into the MR environment; the latter is relevant for active implants.

For diamagnetic and paramagnetic materials where |χ| is very small, we do not have to consider the demagnetizing factors. If we assume only the z‐axis component, then the magnetic force on a paramagnetic object is

(2.10)

For a diamagnetic material the force will be negative, i.e. repulsive. Figure 2.16shows plots of B, dB/dz and their product B .dB/dz along the z‐axis for simulations of 1.5 and 3 T shielded magnets. Note that the locations of the maximum values of dB/dz and B .dB/dz do not necessarily coincide. For a paramagnetic or diamagnetic object the maximum force is exerted at the location of the maximum field‐gradient product, near to the bore entrance. The figure shows B‐field values on‐axis, but in general the spatial gradient and product values are greatest around the edge of the bore circumference.

Figure 2.16 B, dB/dz and product B .dB/dz along the z‐axis for: (a) a shielded 3 T magnet (b) a shielded 1.5 T magnet with bore length 1.6 m. The horizontal axis is distance from the iso‐centre. The bore entrance is at 0.8 m. Simulation for illustration only.

The translational force within the bore is not a maximum but is close to zero.

What is the force on a 1 litre bag of saline brought towards the bore of a magnet with B = 1 T and dB/dz = 5 T m −1?

This is a repulsive force but is 2700 times less than the force due to gravity, so is negligible .

The situation for a ferromagnetic object is complicated by two additional factors: demagnetization factors which depend strongly upon geometry, and saturation : the degree of magnetization sustainable by the metal. In this section we quote the final results as applied to a cylinder or ellipsoid with equal minor axes (1). Appendix 1provides a full derivation.

The force on an ellipsoid or cylinder aligned to B 0(z‐axis) at an angle θ, made from a soft ferromagnetic material with χ >> 1, e.g. nickel, iron, or martensitic or ferritic stainless steel, is

(2.11)

The force is proportional to the product of B and dB/dz. It is striking that it does not depend upon magnetic susceptibility as long as χ >> 1, a consequence of the demagnetizing fields. As we have seen, most strongly ferromagnetic objects will saturate close to the scanner bore entrance. Figure 2.17shows the relative forces on cylinders with length to diameter (l /d) ratios ranging from 0 (a flat disk) to 50 (like a knitting needle) and a sphere in the region where the metal is unsaturated. For a long cylinder aligned with z, the maximum force with the object aligned to B 0is (from Equation A1.31)

(2.12)

Figure 2.17 Predicted translational force (logarithmic scale) on spherical and cylindrical 0.1 kg unsaturated objects at distances remote from the iso‐centre along the z‐axis. The bore entrance is at 0.8 m. The objects have density of 8000 kg m −3, χ = 1000 and B sat= 1.6 T. The force due to gravity is approximately 1 N.

This formula is handy for a quick worst case estimation if you do not know the demagnetization factor or the saturation field.

Figure 2.18shows the effect on force of different angulations with respect to B 0. For objects with a length‐diameter ratio greater than one the maximum force occurs with the greatest alignment to the field (θ = 0°). For flatter objects, the greatest force occurs for an angle of 90°, that is with the planar surface perpendicular to B.

What is the maximum force on an iron rod of length 10 cm, diameter 2 cm in the fringe field of a MRI magnet with B = 100 mT and dB/dz = 0.6 T m −1? The material is unsaturated.

The material is unsaturated (see Example 2.2), so use Equation 2.12

By contrast the gravitational force is

The magnetic force is approximately eight times the force due to gravity at this point .

Figure 2.18 Influence of angulation of ferromagnetic objects with respect to the B 0direction. The objects have density of 8000 kg m −3weighing 0.1 kg with χ = 1000 and B sat= 1.6 T. B = 0.1 T and dB/dz = 0.5 T m −1. The effect of saturation at around 30° is evident for the longest object. Simulation for illustration only.