Basic MR Physics and Nuclear Magnetism
Core concepts
Every MR signal begins with nuclear spin. Nuclei with an odd number of protons or neutrons (¹H, ¹³C, ²³Na, ³¹P) possess a net spin angular momentum and a magnetic moment. In a static field B₀ the moments precess at the Larmor frequency: ω = γB₀, or f = (γ/2π)B₀. For protons γ/2π ≈ 42.58 MHz/T, so 1.5 T → ≈63.9 MHz and 3 T → ≈127.7 MHz. At thermal equilibrium, populations follow the Boltzmann distribution; the tiny excess in the lower energy state produces net longitudinal magnetization M₀, which grows with field strength and proton density but is inversely proportional to temperature.
What questions test
Know the difference between spin angular momentum, magnetic moment, and net magnetization. Understand T₁ and T₂ as time constants of recovery and decay, and that T₂* adds static field inhomogeneity (1/T₂* = 1/T₂ + 1/T₂′). Recognize that precession is a rotating frame concept: in the laboratory frame M precesses; in a frame rotating at ω it appears static, which is why RF pulses are described as tipping M by flip angle α.
Traps
- Confusing γ (rad/s/T) with γ/2π (Hz/T); always check units.
- Assuming higher B₀ always gives better SNR without considering SAR and T₁ lengthening.
- Forgetting that a 90° pulse converts M_z fully to M_xy, while a 180° pulse inverts M_z.
Rule of thumb
Larmor frequency scales linearly with field: double B₀, double f. A 3 T scanner resonates protons near 128 MHz; the ¹³C frequency is roughly one-quarter of the proton value.