### Myths and maths in MRI safety 1

The British Institute of Radiology recently published three information sheets on MRI safety. Myths and maths was one of them. In this series I’d like to expand on themes of that sheet. More details can be sourced from my book Essentials of MRI Safety.

Myth: the various magnetic fields involved in MRI- the static field (B0), switched gradients and radiofrequency (RF)- are different entities, to be treated differently when considering MR safety.

Maths: they are all magnetic fields. They display different spatial characteristics and frequencies, but they are all subject to the same physical laws of magnetisation and induction. Only the relative strength of these two interactions vary.

BIR information sheet

The table above summarises the magnetic field exposures involved with MRI. It is a common approach to consider these separately. So, for example, the static field B0 is considered to be the cause of the mechanical forces (torque or twisting forces, and the translational force in the spatial gradient of the B0 fringe field dB/dz). These apply generally but are only significant for ferromagnetic materials. When considering metallic items the B0 spatial gradient is considered as the source of the Lenz Law anti-motive force (i.e. a resistance to movement). This also occurs in a uniform field if the angle of the object’s long axis changes with respect to the B0 field lines- for example, in the opening and closing of a metallic heart valve. Lenz Law forces occur for all electrically conducting materials. Turning to bio-effects, B0 is considered to be the underlying cause for sensations of vertigo and more occasionally nausea.

If we think of the imaging gradients (Gx, Gy, Gz), they are responsible for acoustic noise generation, electric field induction in tissues and metallic objects, including: guidewires, leads, and electrodes. The rate of change of these magnetic fields is also the physical cause of peripheral nerve stimulation (PNS).

The radiofrequency (RF) exposure (B1)? Well, everyone knows that RF is responsible for tissue and implant heating.

That’s a lot to learn and remember!

The common approach to MRI safety is to consider the influence of each of these components separately. This is not wrong; it is logical and, indeed, my book Essentials of MRI Safety takes the same approach. But on further reflection of the underlying physics it seems to me that fundamentally there are only two interactions- and these occur any time that a magnetic field exists.

Magnetic fields do two things only: magnetisation and induction.

MAGNETISATION

We are used to the term magnetisation through our detection of nuclear magnetisation as the MR signal. At the macroscopic (and atomic/electronic) level, all objects become magnetised when they encounter an external magnetic field. It is the interaction of the object’s magnetic moment (equal to magnetisation times volume) with the B0 field that determines magnetic torque, and with the B0 spatial gradient dB/dz that determines the translational force. That’s it. As simple as that. If the material magnetises strongly then the forces will be strong. Diamagnetic and paramagnetic materials exhibit minimal magnetisation so the forces on them are small. For ferromagnetic objects it does not ultimately matter if they are saturated or unsaturated- as it is magnetisation only that determines the forces. The laws of physics are not different in either case.

INDUCTION

Induction is what happens whenever a magnetic field is changing with time. Movement through the spatial gradient of B0 is experienced as a time variation or dB/dt. Lenz Law forces are therefore caused by induction and apply to all electrical conductors. The imaging gradients and RF are both time-varying magnetic fields. The outcome of induction is the generation of an internal electric field. This is the underlying interaction responsible for peripheral nerve stimulation, ECG artefacts, the hydrodynamic effect, electrical interference on active devices, and RF heating. Yes, all those diverse effects result from one basic interaction- induction. Larger current (or electric field) paths and higher frequencies will result in greater degrees of induction, i.e., larger induced electric fields. The frequency and strength of these determines the outcome: motion resistance, stimulation, interference or heating.

The Lorentz force (on current-carrying wires) can also be considered as a particular case of induction. The Lorentz force is responsible for the generation of acoustic noise- and is deemed to be the underlying physiological mechanism that causes vertigo.

CONCLUSIONS

All phenomena associated with magnetic field exposure result from either magnetisation or induction. So, when faced with a new scenario, ask these questions:

• Is any part or component likely to become strongly magnetised?
• What opportunities for induction are presented?
• What is the likely magnitude and frequency of the interaction?

In summary, magnetic fields do two things only: they cause magnetisation and induction. Everything else follows from these.

Isn’t that (conceptually at least) quite simple?