Spin Precession 🧲
Larmor precession ω = γB₀, RF pulses, T1/T2 relaxation & the physics of MRI
Physics & equations
Nuclear spin precession: nuclei with non-zero spin (¹H, ¹³C, etc.) behave like tiny magnets. In external field B₀, the magnetic moment precesses around B₀ at the Larmor frequency: ω₀ = γB₀, where γ is the gyromagnetic ratio (e.g. γ/2π = 42.58 MHz/T for ¹H).
RF pulse: a radiofrequency pulse at the Larmor frequency rotates the net magnetisation M by a flip angle θ = γ·B₁·τ_pulse. A 90° pulse tips M fully into the transverse plane for maximum signal; 180° inverts it.
Bloch equations: after the pulse, M relaxes back via T1 (longitudinal/spin-lattice) and T2 (transverse/spin-spin):
dMz/dt = −(Mz − M₀)/T1 | dMxy/dt = −Mxy/T2
MRI uses gradient fields to spatially encode Larmor frequencies; tissues differ in T1/T2 → contrast. Clinical scanners: 1.5 T (63.87 MHz) and 3 T (127.74 MHz) for ¹H.
NMR spectroscopy: chemical shifts in Larmor frequency reveal molecular structure (shielding/deshielding by electron density).