MRI spin physics

Bloch simulation of a sample of isochromats, viewed in the rotating frame. B0 is along z.

Simulation

t = 0.0 s
0.25×

Display

16³
Hue = phase of Mxy
Saturation = |Mxy|

RF pulse

90°

Pulse sequence

16 TRs of 30° RF → stepped Gy phase-encode → Gx readout (gradient echo) → Gy rewinder → Gz spoiler. The signal is acquired only during the readout windows, shaded in the trace. Raise the speed to play it out faster.

Field

3.0 Hz
0.0 Hz/cm
0.0 Hz/cm
0.0 Hz/cm

The sample spans ±1 cm on each axis; a gradient of G Hz/cm shifts a spin at position x by G·x Hz.

Relaxation

1000 ms
300 ms

Defaults are soft-tissue-like; try T2 ≈ 2000 ms (water/CSF) to keep Mxy around longer.

Try: apply a 90° pulse and watch the spins precess at Δf₀ while T2 slowly attenuates them and Mz recovers (T1). Turn up Gx and the spins fan out (dephase); a 180° pulse refocuses them into a spin echo.

x′ y′ z (B₀)
Signal ⟨Mxy⟩   Re (x′)   Im (y′)