MRI Physics: Magnet Systems and Superconductivity

1) Main magnet: strong static B0 (creates M0, sets f_L).
2) Shim coils: make B0 uniform.
3) Gradient coils (x, y, z): deliberately vary the field with position for encoding.
4) RF coil: transmits B1 and receives the signal.
Nested from outside in: magnet → shimsradients → RF coil closest to the sample in the room-temperature bore.

Current in many turns gives a strong, uniform field inside: B0 = μ0·N·I/l (Ampère's law).
But heating P = R·I^2: doubling the current doubles B0 and quadruples the heat. A strong resistive magnet needs huge power and cooling; superconducting wire (R = 0) removes the problem.

Permanent: no current, low field (< 1 T). Resistive electromagnet: continuous power, heats up, low field (< 1 T). Superconducting: persistent current in very cold coils, 0.5 T up to 11.7 T (human) and 21.1 T (preclinical).
High-field MRI is always superconducting; the price is cryogenic cooling.

Only while all three hold: T < T_c, B < B_c and J < J_c (critical temperature, field and current density).
The limits trade off: colder operation allows higher field and current. MRI wire is NbTi (most common) or Nb3Sn (tolerates higher fields).
Trap: 4.2 K (liquid helium) is the operating temperature, not "the" critical temperature.

Operate below the curve: at a given temperature the field must stay under B_c(T).
Colder → higher allowed field; warming lowers the limit. Nb3Sn's curve lies above NbTi's, so it reaches higher fields at the same temperature. Some magnets are sub-cooled (e.g., 2.2 K instead of 4.2 K) to push the field higher.

No. Copper's resistance drops but levels off at a small nonzero value; only specific materials (NbTi, Nb3Sn) drop abruptly to exactly zero below T_c.

Once ramped up, the current circulates forever in the zero-resistance loop, so B0 stays on 24/7 without a power supply, including between scans.
Safety consequence: the room is always live.

The coil sits in liquid helium (4.2 K) inside a vacuum-insulated vessel, surrounded by a warmer shield stage (liquid nitrogen 77 K or a cryocooler).
The warmer stage intercepts heat before it reaches the helium; the vacuum and shields separate it from the room-temperature bore where the sample goes.

Conduction (through matter) and convection (moving gas) → blocked by vacuum (supports still conduct a little). Radiation (crosses vacuum) → blocked by reflective radiation shields and multilayer insulation blankets.

Radiated power per area M = ε·σ·T^4 grows with T^4, so warm surfaces radiate vastly more than cold ones.
Doubling T → 16× the radiation. Unshielded room-temperature walls would boil off the helium, hence radiation shields even inside the vacuum.

Heat leaking into the cryostat evaporates liquid helium; refills or recondensing cryocoolers replace it.
The coil itself has no resistive loss, but keeping it cold still costs energy.

A sudden loss of superconductivity: part of the coil becomes resistive, the current heats it, the normal zone spreads, and the stored magnetic energy is dumped as heat. The helium boils off violently and B0 collapses.
Causes: cooling problems (low helium), loss of vacuum, coil fault, or the emergency discharge. Dump resistors help dissipate the energy.

It deliberately quenches the magnet: a last resort only to save a life (e.g., someone pinned by a ferromagnetic object).
It costs at least 500,000 CHF, if the magnet survives. Students never press it: alert the staff.

1) The magnet and its environment are imperfect.
2) The sample itself: materials with different magnetic susceptibility (tissue, air, bone) distort the field, especially at boundaries.

Passive: iron/steel pieces placed in shim trays after mapping the field. Done once at installation, fixed afterwards.
Active: currents in shim coils make adjustable correction fields, set for each sample and region (resistive shims), or fixed superconducting shims set at installation.

First order (x, y, z) cancel linear slopes: field rising steadily across the sample. Second order (z^2, xy, xz, yz, x^2−y^2) cancel curved errors.
These are spherical-harmonic patterns and their fields add. First-order shims have the same shape as imaging gradients, so constant gradient offsets are often used for them.

Both add small z-fields that vary in space. Shims: static corrections that remove unwanted variation. Gradients: deliberate, rapidly switched, known slopes for spatial encoding.

It shifts all frequencies equally: the peak moves but cannot get narrower.
Linewidth reflects the spread of local fields, and a constant offset leaves that spread unchanged; only first/second-order (spatially varying) shims narrow the line. Frequency centring moves f_ref instead and does not touch B0 at all.
Trap: a zero-order shim (field offset) is not zero-order phase (an MRS phase correction).

Along z, parallel to B0. Only its strength changes along x, y or z: "Gx" means B_z = B0 + Gx·x.
Units: mT/m (≈ 40 mT/m human, ≈ 500 mT/m small-animal, up to 1 T/m). 1 T/m means a 0.01 T difference across 1 cm.
Trap: Gx does not tilt the field toward x.

Amplitude (mT/m), linearity (constant slope over the field of view) and switching speed: rise time (0 → max, ~120 µs) and slew rate = G_max / rise time (T/m/s).
At a fixed slew rate, a stronger gradient takes longer to reach. Non-linearity distorts images.

Loud: switching currents in B0 feel Lorentz forces, so the coil vibrates (knocking, buzzing). Hot: hundreds of amps in copper → P = R·I^2, hence wide thick copper, water cooling and duty-cycle limits.

The wire loop is the inductor L (stores energy in its magnetic field); capacitors C store energy in their electric field. Energy sloshes between them at f_coil = 1/(2π√(LC)).
Adjustable capacitors set this resonance to the nucleus's Larmor frequency. More C → lower f_coil.

Tuning: set the coil's resonance f_coil to the Larmor frequency of the nucleus.
Matching: make the coil's input impedance equal the 50 Ω of the cable, so RF power enters instead of reflecting back.
Both use variable capacitors and they interact. Impedance is the AC "opposition" including L and C effects, not the DC resistance of the wire.

Its field at the centre is along the loop's normal; that normal must be perpendicular to B0 so B1 is transverse.
A B1 parallel to B0 cannot tip M.

Surface coil (small loop beside the target): easy to build, high sensitivity and B1 efficiency near the loop, but sensitivity falls with depth, B1 is inhomogeneous, small field of view.
Volume coil (surrounds the sample, e.g., birdcage): uniform B1, large field of view, but lower sensitivity and more complex.

Quadrature: two perpendicular modes driven 90° apart → a rotating (circularly polarized) B1 that turns with the spins. About half the power for the same flip angle and up to ~1.4× (√2) sensitivity.
A linear coil's field splits into two counter-rotating halves, and only one of them tips the spins.
Trap: "quadrature detection" in the receiver is a different thing.

B1+ = transmit field: how strongly the coil tips spins at each position (→ local flip angle). B1− = receive sensitivity: how strongly it picks up signal from each position.
Either can make a uniform sample look non-uniform. Coils can transmit and receive, or a volume coil transmits while a surface array receives.

The transmit pulse is enormously stronger than the µV-level MR signal, so a T/R switch protects the receiver. Coil ring-down and receiver recovery take a short time after each pulse.
Then the ADC digitizes the voltage during the acquisition window.

Ferromagnetic objects become projectiles (force and torque); medical devices can fail. The field is always on.
0.5 mT line: limit for people with medical devices/implants. 3 mT: ferromagnetic objects may be attracted. Orange line: no ferromagnetic items beyond it.

Non-ferromagnetic ones: gold, silver, palladium, titanium, brass, (non-magnetic) stainless steel. Iron and many steels are not; some glasses and jewellery hide magnetic parts, so when in doubt, remove them.

No food or drinks in the labs, belongings in the lockers, every magnetic object removed.
Remove belt, wallet, keys, phone, watch, pens, steel-toed shoes, hairpins and jewellery. Nothing ferromagnetic past the orange line: the magnet is always on.

Screening form: checks you carry nothing dangerous near the magnet (implants, devices, metal fragments). Quarantine form: protects the animal facility from contamination, signed every visit: 72 h after a dirty or outside facility before entering, and 72 h after before entering another animal facility.

Liquid helium/nitrogen expand ~700× into gas, displacing oxygen → hypoxia and asphyxia; the cold also burns.
Both are inert gases, so you cannot see, smell or feel a leak, hence oxygen monitors. At an oxygen or cryogen alarm: evacuate and leave the doors open.

RF is non-ionizing but deposits heat in the subject (SAR, W/kg), worst near conductive wires and implants. RF circuits carry high voltage (~300 V). RF also interferes with telecommunications, and outside RF can corrupt the weak MR signal (hence the shielded room).