Читать книгу Essentials of MRI Safety - Donald W. McRobbie - Страница 77

For a saturated metal the magnetization within the material is at a maximum so once saturation occurs B₀ becomes irrelevant, and the maximum force is

(2.13)

Here, for a given object, the only variable is the gradient of the B₀ fringe field, which itself changes over distance from the magnet. The shape of the object is no longer a significant factor as it has been completely magnetized. Figure 2.19a shows the relative forces from a 1.5 and 3 T shielded magnet on 0.1 kg ferromagnetic objects which saturate at 1.6 T. State of saturation is more significant than field strength. The object’s shape is a key factor. You will get closer to the magnet holding a sphere without it being wrenched from your grasp than you would with an elongated object of the same mass. Figure 2.19b, plotted on a logarithmic scale, shows the force on each object at greater distances from the iso‐centre, compared to the gravitational force of around 1N. A length‐diameter ratio of 50 corresponds to the geometry of a Birmingham gauge 21 hypodermic needle. The force on the needle exceeds that of gravity around two meters from iso‐centre, half a meter further than for a spherical object of the same material and mass. Needles and scissors constitute two of the most hazardous objects around MRI scanners.

Figure 2.19 Predicted translational force on spherical and cylindrical 0.1 kg objects along the z‐axis: (a) linear plot; (b) logarithmic scale. The bore entrance is at 0.8 m. The objects have density of 8000 kg m⁻³ and χ = 1000 with B_sat = 1.6 T.