Nuclear Magnetic Resonance (NMR) is the physical phenomenon underlying MRI. It exploits the quantum mechanical property of nuclear spin to create detailed maps of atomic nuclei in a sample — in MRI, predominantly the ¹H (proton) nuclei in water and fat.

Nuclear Spin

Nuclei with an odd number of protons or neutrons possess a net quantum mechanical spin and an associated magnetic dipole moment \(\boldsymbol{\mu}\). In a static magnetic field \(B_0\), these moments precess around the field axis at the Larmor frequency:

where \(\gamma\) is the gyromagnetic ratio (for ¹H: \(\gamma/2\pi = 42.577\) MHz/T). At 3 T, ¹H precesses at ~128 MHz — in the RF range.

Equilibrium Magnetisation

In a static field \(B_0\), spins align preferentially along the field, creating a bulk magnetisation \(M_0\) parallel to \(B_0\) (the z-axis). This magnetisation is the signal source in MRI.

RF Excitation

A radiofrequency pulse at the Larmor frequency (the B1 field) tips \(M_0\) away from z. A 90° pulse rotates \(M_0\) entirely into the transverse (xy) plane where it precesses and induces a signal in the receive coil. A 180° pulse inverts \(M_0\).

Bloch Equations and Relaxation

After excitation, the transverse magnetisation decays (T2 relaxation — spin-spin interactions) while the longitudinal magnetisation recovers (T1 relaxation — spin-lattice interactions). Different tissues have different T1/T2 values, creating the soft-tissue contrast that makes MRI so powerful. Typical values in brain tissue: T1 ≈ 900 ms, T2 ≈ 80 ms at 3 T.