Well a main problem is peripheral stimulation i.e. inductive currents that are strong enough to cause irritating sensations in the nervous system (actually, this is not just about gradient strength but much more about the switching times for the gradient). This is a known problem in MRI measurements. Otherwise, going to arbitrarily strong gradients is probably much more limited by apparative issues than by biophysics.

Thank you!

I do not see any safety issue here. The essential thing is the rate of change of the magnetic field, not its spatial gradient: the induced electromotive force around a closed loop is proportional to the time derivative of the magnetic flux through the loop. The gradient of the field does affect magnetic material, but such materials are usually contraindications for performing MRI.

MRI or NMR gradients are small compared to the magnitude of the B0 polarizing field. As a safety issue B0 fields need to be evaluated for the nature of the bio-effects. Currently, these effects have been evaluated in humans up to 8T and approved for human use by the US FDA. Animals scanners have been operating up to 21 T. So far no permanent bio-effects have been observed for the polarizing field, B0.

The field magnitude of the switched field is much smaller but the time varying nature can and does generated currents in conducting media such as tissue. Given the size of MRI gradients it is possible to generate currents that can generate stimulation in peripheral nerves. The sensations can be quite strong and even painful. The static gradient at the end of the MRI magnet is much stronger any of the switched gradients in the MRI. animals or patients tolerate the static gradient well.

The SR limit of 200 T/m/s in MRI is placed there to prevent nerve stimulation. This limit is based on the amplitude of the gradient, frequency, and the length scale over which the gradient is applied. Deep brain stimulation apparatus uses much higher gradients and slew to produce nerve stimulation in brain structures but these are on much smaller length scales.

Thank you all for your kind responses.

I am actually working on MRI model as a support for in-vivo MR experiment. However, while testing the model with experimental data, I got gradient value of around 48200T/m. Is this even possible at all?

Where does this 48200T/m come from?

It is from theoretical calculations!

Michael, can you be more specific? Where would you need a field that changes from zero to 4.82 tesla in 100 micrometers?

I am actually working on a simple model which reports heat transfer into tissues at given SAR values. With this, the MR sequence gives info on the MR signal, relaxation rates and heat transfer. However, for me to maintain SAR of 4 - 10W/kg, i must have to use such amount of gradient based on my calculations. Do you think this value is even realistic? Thank you for your prompt responses!

I am sorry but I am not an expert in SAR estimations. I leave this discussion here.

Thanks a lot, Prof. Risto!

Michael, 48200 T/m is a very high gradient. The largest gradient that I know used in MR is a static 170T/m super con gradient used by R. Kimmich at the University of Ulm studying diffusion in viscous fluids. Your induced gradient term is much high than what is used in MRI. This is more likely to be an issue in transcranial magnetic stimulation procedures. The gradients there are on the order of 1000sT/m but on a very short length scale. Magstim products ( http://www.magstim.com ) are used in a number of facilities for this purpose. You might consider looking there. A while back we built some very small coils that we could generate 1.7 T/A gradients over 2 micrometers. This is the only place I've seen gradients of the size you are simulating. Definitely not in any in vivo system I've had experience using.

MRI concerns about SAR is solely with the RF field generated by the B1 antenna coil. The AC field does generate significant SAR loads that must be accounted for in an active way in the MRI sequence, RF antennas, and in the patient. These SAR loads are orders of magnitude greater than any SAR generated by the switched DC magnetic field gradients.

We have written a review of paediatric imaging which involves some discussion of SAR limits in children (Arthurs OJ, Safety in paediatric imaging, Acta Radiologica 2013 http://www.ncbi.nlm.nih.gov/pubmed/23550188) but there is more literature out there on simulating SAR e.g. http://www.ncbi.nlm.nih.gov/pubmed/15850420 , if that helps ? There may be further references in those articles which may help.

For all practical purposes (and as pointed out by others in this thread) the magnitude limit on gradients is a moot point.

To work through your laundry list in your original posting:

1) B0 is a homogenous field. Any gradients are unwanted and are generally shimmed to be on the order of ppm. 7T has been declared "safe" by the FDA in humans, although there is no hard evidence that this is in fact the limit for a static magnetic field (and some investigators used higher strengths until they reached physical barriers). Moving humans through these fields however (like to load or unload the scanner) may be a nuisance (some people get nauseous).

2) and 3) are the same for absolute magnitude calculations. The limits are generally set by available technology (like H. Morris pointed out at some point you may need superconducting gradients to achieve higher field strengths and time switching those is a challenge) and by the slew-rate limit. Slew-rate dB/dt is limited by the FDA, and is generally below 200T/m/s. With a large magnitude gradient, it will take a long time (in the MR echo time realm) to ramp up a large magnitude under this slew-rate limit, so at some point it becomes unpractical for many reasons.

The magnetic gradient magnitude is not subject to SAR limits (heat deposition is generally an issue for rapidly varying EM-fields such as produced by the B1 RF field, not a static or slowly varying spatial gradient). The dB/dt is an issue of peripheral nerve stimulation and is therefore limited. This is what you need to worry about with magnetic field gradients.

There is some concern with large magnetic gradient magnitudes in implants that experience a mechanical moment in a gradient field and may be displaced, causing physical harm to the patient, but that's a different issue.

So when you talk about SAR effects, you would for all practical reasons look at B1 RF excitation. The FDA limits for that are actually quite useful, as we know how heating affects tissue. One field of research is how spatially varying energy deposition affects the patient, such as with high field MR that requires high RF frequencies. These RF frequencies then will produce spatially inhomogeneous energy deposition.

So if I take your original post about "magnetic gradient magnitude" and your later post about SAR together, then you have to elaborate ("heat transfer" can only happen if you actually temporally modulate the magnitude). As pointed out by me and others, those are usually different concerns.

The frequency and phase encoding gradients are both controlled under dB/dt limitations.

After some research I feel safe to say that 200 T/m/s is not a regulatory limit on  MRI scanners. Since 1998 the FDA has only described an experiential limit of switched magnetic fields in the kHz range for MRI. We are to avoid painful stimuli from peripheral nerve stimulation. If a protocol causes severe discomfort it is classed as a significant risk, and FDA approval is required in addition to IRB approval for human application.  The FDA has adopted ( by reference) the IEC 60601-2-33 2013 3rd edition standards for basic safety and minimum performance of MRI equipment.  The dB/dt limitations there fall in to two branches.  The system must never produce cardiac stimulation, and the system must have a 2 stage limitation based on general empirical or design specific experimental determinations of the threshold of peripheral nerve stimulation. 

Bo spatial gradients are a consequence of equipment design. there are no regulator limits, The 2014 ICNIRP guidelines on static field exposure also include consideration of low frequency magnetic field variations from moving in a spatially varying field. These have been modelled by a number of authors. 

A general concensus appears to be that limiting field variation to less than 2T/sec will avoid vertigo experiences and metallic tastes in 50% of subjects.

PNS values may vary across species