[2/2 -- see above about not knowing HN had a character limit!]

Now, for B0. The simple explanation is this: as alluded to above, we're all made of very different stuff. Bone, air, fat and muscle all have very different electrodynamic properties. At their interfaces, there's a "rule" that comes from Maxwell's equations† that means that you _must_ have a discontinuity in both the normal component of the electric (D) field in media and the tangential component of the magnetic field (H). This isn't negotiable, under the assumption that your patient does not have a net overall charge or current flowing through them. What this means, practically, is you get tiny bound surface charges or currents appearing at the interface of different materials. These then change the magnetic field homogeneity -- how B_0 varies over space -- because they create magnetic fields that add to it (the principle of superposition). Remember, all of MRI is based on having extremely homogeneous fields so that you can make a mapping between frequency and phase of your signal to the space of your sample. Inhomogeneities destroy that -- they can e.g. make two places look the same if they should be different, for example. B0 homogeneity is a big problem: we need the field to be uniform across the sample.

Practically, what that means is twofold. One, for big changes -- caused by air, or a dental filling typically -- you get large, far-field effects that distort the image macroscopically. The maxillary and ethymoid sinuses (in the front of your face) together with the hard palette make it harder to image certain regions of the brain -- the bits that are basically directly above the roof of your mouth. This is _entirely_ due to the difference in the dielectric properties of air and "meat". Lung imaging with MRI is very, very challenging (but possible!). What works well for the brain does _not_ work at all, really, on the long -- and especially not at ultrahigh field. Even something as "simple" as cardiac imaging becomes more difficult, because the heart contains oxygenated and deoxygenated blood in close proximity -- and they have different dielectric properties.

Secondly, all tissue on a microscopic level is inhomogeneous. Cells have bilayers and a complex microstructure. Organs have microstructures made up of different types of cells. The liver has a a beautiful microstructure, and a lot of iron in it. This causes a decrease in the effective static field inhomogeneity -- which manifests itself in terms of an NMR relaxation parameter called T2* -- meaning, in short words, that the MRI signal vanishes more quickly over time than it does at lower fields. That's why livers tend to look a bit darker than their surrounding organs on some types of MRI scans. If you play a single RF pulse and acquire signal on an NMR tube of pure water in a chemistry lab, you'll get a voltage you could measure with a hand-held AC voltmeter appearing for seconds after the initial excitation. Put a sphere of water in a 12T MRI scanner, and frankly you're doing well to have signal there after ~500 ms. In vivo, that's likely to be ~30-50 ms. That makes actually doing the experiments hard - your [gradient-echo] signal vanishes quickly.

The whole B0 homogeneity thing is a coupled problem, best solved by considering Laplace's equation for the scalar magnetic potential (\nabla^2 \psi = 0). This famously has a solution space that can be expressed as an infinite sum of spherical harmonic functions. So, MRI scanners (yes, even clinical ones!) have a series of loops of wire that generate B-fields that approximate the first few spherical harmonics -- in Cartesian coordinates, they're weird things like x^2-y^2 and look like the pictures of the orbitals for electrons inside a hydrogen atom, if you've ever seen that. Patient goes in scanner, B0 field inhomogeneity is measured, magic regression‡ works out the right coefficients to dial a current into each coil, and the field is magically more homogeneous.

Now, the trouble with this is that the spherical harmonics are a sum until infinity. And you can't build an infinite number of coils. The first few components get you most of the way there...but not all. And again, at higher field building effective shim coils, working out what your artefact is and where it comes from, and so on, all become more difficult.

</end lecture>

MRI is complicated -- it spans mathematics, physics, chemistry, engineering, biochemistry, and medicine. Frankly, that's why I like working in it as an academic area -- there's always something to learn. There are about 6000 others who do so technically, and we have a big, week-long worldwide conference once a year to both teach this stuff (where I have lectured) in quantitative detail, and show off our latest and greatest results (the usual big "evil" companies typically take academic work and put it in their products -- which I find rewarding, as it means your work can have a difference quickly and you don't have to deal with the FDA). I'm sure CEA / ISEULT will present there and I am genuinely excited that their mega-machine has finally been built. But there are a lot of challenges to overcome. Of course, there are also a huge number of opportunities -- it is (hopefully!) going to make it possible to image at higher spatial resolution, and also be much better for MR spectroscopy, and reveal information about low concentrations of biomolecules. But I guess the main point of my comment originally last night was trying to convey "the journey is really just beginning" and not "expect this in your local hospital in five years time".

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[1] https://sci-hub.st/10.1002/cmr.b.21319

† Specifically Gauss's law and Ampere's law at the boundaries for the D or H fields giving rise to the rule that there must be a discontinuity in D, with the difference normal components being equal to the bound surface charge density; and the difference in the tangential part of the H field being equal to the bound surface current. Putting these together with the constitutive relationships for D and H, and you get that the surface current is equal to B_{tangential, 1} / µ_1 - B_{tangential, 2} / µ_2 = J_s. In biology, µ is approximately fixed...so the surface current changes.

‡ Or a patient graduate student / radiographer...