Читать книгу Essentials of MRI Safety - Donald W. McRobbie - Страница 74

The force on an ellipsoid or cylinder aligned to B₀ (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 2.17 shows 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 B₀ is (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 2.18 shows the effect on force of different angulations with respect to B₀. 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.