First off -- sorry for a rather terse initial comment last night whilst I was trying to get to sleep! This explanation (a) won't be on my phone; and (b) will have a lot more detailed added.

B1 is the oscillating RF magnetic field that is responsible for both delivering power into the sample / patient, and once their nuclei have received that and undergone the magnetic resonance phenomenon, they emit RF at the same frequency. We / the MRI community divide this field into two: B1+ and B1-, for transmit and receive (and they also happen to be left and right-handed circularly polarised fields). It's worth pointing out that a physical device -- a lump of copper with capacitors in it -- called an RF coil transmits B1+ and receives B1-. Because we want B1+ to be homogeneous and uniform and B1- to be sensitive, in the last ~20 years, most clinical scanners now have a separate "body coil" for transmission and multiplee anatomically shaped ones ("breast/thoracic/spine/knee/ankle/wrist/whatever-coils") for reception. Multiple because you can noise-optimise the size of each little loop, and you can also do tricks ("parallel imaging" or "compressed sensing") to exploit their different spatial locations and speed up the scan.

Now, at low field, say at 1.5 T (a typical clinical MRI scanner's field), the Larmor frequency for protons that are most often of interest to the operator of the scanner is objectively low (about 60 MHz for 1.5T). By 'objective low', I mean "its wavelength is a fair bit longer than the instrument". Mathematically, if you took a course that involved Maxwell's equations, we're in the quasi-static regime: \nabla \times B = µ0 ( J + \epsilon_0 ∂E/∂t) and at low field ∂E/∂t ≈ 0 compared to J. So, Biot-Savart's law works for describing the coils – you put a current in them (and quite a large one -- 1-3 kV voltages are not unusual for transmit inside a body coil on a device that has a minimally low resistance) and get a magnetic field out. Everything is DC, doesn't interact, and that magnetic field is what permeates through the patient. The optional difference in electronics aside, there's no substantial difference between B1+ and B1- and all is hunky-dory and comparatively well understood.

Now, at high fields, a bunch of stuff happens. Firstly, the frequency goes up -- at ~12 T, it is ~500 MHz -- and with that, the wavelength goes down. At 12T (or 9.4T, or 7T, the other commonly-used high-field strengths where this is relevant), it's well below the size of a person, and rather than having a quasi-static problem, you now have a full-wave electrodynamic problem in which you can't just ignore the displacement current, ∂E/∂t ≠ 0. As well as making it harder to design RF coils, this actually means that you cannot ignore the fact that it's a wave -- to a first approximation you'll get nodes and anti-nodes in the tissue on a human length-scale. Not only that, but all of the really important electrodynamic parameters -- the µr's and \epsilon_r's that determine what speed the wave propagates at, and so on -- are (a) actually complex numbers; (b) different in different tissue types / diseases; and (c) not as well measured at high field as they are at low field. Another effect emerges from this at ultrahigh field: B1 twist. B1+ starts being ≠ B1-* (where the * denotes complex conjugation) and you get some rather "interesting" patterns appear. [1] From an electrical engineering point of you, you've got a near-field antenna design problem into a fundamentally unknown electrodynamic environment (unknown, because to some extent you are measuring it! Is that a cystic, fluid-filled region in the brain, or a dense, cellular tumour?)

So, at ultrahigh field, the only thing you can do is change your approach completely. Rather than having one homogeneous, optimised transmission device, you have multiple -- transmitting in parallel ('pTx') -- and change the phases and amplitudes between them to optimise the homogeneity in the response. This has the downside that you have to be careful not to accidentally start to heat your patient, and so throw in a lot of work, simulations and measurements about safety here. Rather than looking like a loop of wire, coils now tend to look like e.g. fractionated dipole antennas -- which makes them very sensitive to their electrodynamic tuning and exactly the value of µr and \epsilon_r (or equivalently the conductivity) of the sample. Fat is different here to muscle, and that difference is bigger at ultrahigh field...so you now see people selling "dielectric pads", foam-wrapped pads of a material with a favourable \epsilon_r to literally pad around the patient if you have a problem. These too have their own safety concerns, so you end up spending a week running a full-wave FEM simulation of Maxwell's equations prior to destructive heating testing before doing it on a human. The whole thing becomes a bit of a pain.

[1/2 -- I never knew HN had a comment character limit until now!]