Interactive figures for teaching MR physics

Spins

Animated, interactive figures for explaining magnetic resonance at the board: Larmor precession, coherence and its loss, the spin echo, chemical shift, and the magnetism of the materials we carry into the scanner room. Every figure runs offline, adapts to the projector, and states its own teaching point.

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One vector, obeying the Bloch equations exactly. Everything else on this page is built out of copies of it.

Larmor Precession & the Rotating Frame Tip the magnetisation with a B₁ pulse, push it off resonance and watch it precess about the effective field, then let T₁ and T₂ pull it home. Switch between the rotating and laboratory frames. Bloch equations · excitation · relaxation

Ensembles and coherence

A receive coil cannot see a single spin. It sees a sum, and the sum only exists when the spins agree.

Spin Ensembles & the Net Magnetisation A lattice of moments, each at its own Larmor frequency, with the vector sum alongside. Switch between equilibrium, coherence and dephasing to see what the coil detects in each. Full controls · all three states Thermal Equilibrium & Random Phase Every moment is precessing and the sample is fully magnetised, yet the coil detects nothing. The figure for the question “why do we need an RF pulse at all?” Polarisation without signal Perfect Coherence The idealised case: one field, one frequency, no fan. The reference point that makes every kind of dephasing legible, and the thing a good shim is buying you. Uniform field · pure T2 Dephasing in Three Dimensions Shade the spheres by their field offset and watch the phase colours sort themselves along the gradient as the sum collapses at T₂*. Then refocus it. T2* · field maps · reversible loss

Dephasing and echoes

Dephasing is ordering, not loss. These figures separate the part you can get back from the part you cannot.

Dephasing & Rephasing Across the Sample Looking down the bore at a slice, with a shim gradient and a susceptibility blob you can dial in. Compare the honest 180° pulse against the impossible “reverse time” button. Field maps · spatial view The Spin Echo & Echo Trains The classic phase fan, opening and closing under a CPMG train. Every echo peak lands on the T₂ curve no matter how bad the shim, which is how T₂ is actually measured. CPMG · measuring T2 Adding Rotating Vectors Fat and water in one voxel, beating in and out of phase. Where you put TE decides whether they add or cancel, which is chemical-shift imaging in one picture. Chemical shift · Dixon · in / opposed phase

Magnetism of materials

The electrons in everything else in the room, and why some of it must stay outside.

Magnetic Domains & Hysteresis An Ising lattice that grows real domains, crosses a real Curie transition, and traces a real hysteresis loop. Raise the temperature and the ferromagnet becomes a paramagnet on the same axes. Ferro vs para · remanence · MR safety