MRI: How You Get Scanned Without Radiation

Unlike X-rays or CT scans, MRI uses no ionising radiation. Instead, it exploits the quantum spin of hydrogen nuclei (protons) in your body's water. A powerful magnet aligns these spins, radio pulses knock them out of alignment, and the signal they emit as they relax reveals stunning soft-tissue detail — all without a single gamma ray.

1. Proton Spin & Magnetic Moments

Every proton (hydrogen nucleus, ¹H) has a quantum property called spin (spin-½). This creates a tiny magnetic moment — each proton is a miniature bar magnet. Your body is ~60% water (H₂O), providing an enormous number of protons to work with.

In no magnetic field: Proton spins are randomly oriented \to no net magnetisation In a strong magnetic field B₀ (e.g., 1.5 T or 3 T): Spins align either parallel (↑, lower energy) or anti-parallel (↓, higher energy) to B₀ Energy difference: ΔE = γ \cdot ℏ \cdot B₀ where γ = 42.576 MHz/T (gyromagnetic ratio of ¹H) ℏ = reduced Planck constant At 1.5 T: ΔE corresponds to f₀ = γ \cdot B₀ = 63.9 MHz At 3.0 T: f₀ = 127.7 MHz (radio frequency range) Population difference (Boltzmann): N↑ / N↓ = exp(ΔE / kT) \approx 1 + 3\times10⁻⁶ at 37°C Only ~3 in a million excess spins align with the field, but with ~10²⁸ protons in the body, the net magnetisation M₀ is measurable

2. Resonance & the RF Pulse

The aligned spins precess (wobble) around B₀ at the Larmor frequency: f₀ = γ · B₀. This is the "resonance" in magnetic resonance.

A short radiofrequency (RF) pulse at exactly the Larmor frequency tips the net magnetisation away from B₀. A 90° pulse rotates M into the transverse plane (perpendicular to B₀). A 180° pulse inverts M completely.

The RF pulse transfers energy only to protons because it matches their resonance frequency exactly — like pushing a swing at its natural frequency.
After the pulse, the transverse magnetisation rotates at f₀, inducing a detectable voltage in a receiver coil (Faraday's law). This is the MR signal — the free induction decay (FID).
The signal frequency (63.9 MHz at 1.5 T) is in the FM radio band — far too low-energy to ionise atoms or break chemical bonds. This is why MRI is safe (no radiation dose).

3. T1 & T2 Relaxation

After the RF pulse, the magnetisation returns to equilibrium through two independent processes:

T1 (longitudinal relaxation, spin-lattice): Mz(t) = M₀ \cdot (1 - e^(-t/T1)) Spins release energy to surroundings ("lattice") M recovers along B₀ direction Fat: T1 \approx 250 ms (fast recovery — strong signal early) Muscle: T1 \approx 900 ms CSF: T1 \approx 4,000 ms (slow recovery — weak signal early) T2 (transverse relaxation, spin-spin): Mxy(t) = Mxy₀ \cdot e^(-t/T2) Spins dephase (lose coherence) due to local field variations Signal decays in transverse plane Fat: T2 \approx 80 ms Muscle: T2 \approx 45 ms CSF: T2 \approx 2,000 ms (maintains signal longest) T2 \leq T1 always. T2* (effective T2) is shorter due to field inhomogeneities: 1/T2* = 1/T2 + 1/T2'

The key insight: different tissues have different T1 and T2 values. Fat recovers quickly (short T1) and dephases slowly. CSF recovers slowly but maintains coherence longest. MRI exploits these differences to create contrast between tissues — without any injected dye in many cases.

4. Gradient Coils & Spatial Encoding

The MR signal from the entire body is useless without spatial information. Gradient coils create small, controlled variations in the magnetic field along x, y, and z axes.

Slice selection (Gz): A gradient along z makes the Larmor frequency vary with position. The RF pulse is tuned to excite only a thin slice (e.g., 3 mm thick). Only protons in that slice resonate and contribute to the signal.
Frequency encoding (Gx): During signal readout, a gradient along x makes each column of the slice precess at a slightly different frequency. The receiver detects all frequencies simultaneously (like hearing a chord), and Fourier transform separates them — each frequency corresponds to a position.
Phase encoding (Gy): Before readout, a brief gradient along y gives each row a different phase advance. The experiment is repeated with different phase-encoding gradient strengths (128–256 steps). Each repetition fills one line of k-space.

Why MRI is loud: Gradient coils carry pulsed currents (hundreds of amps) in a strong magnetic field. The Lorentz force (F = I×B) causes the coils to vibrate like loudspeakers — producing the characteristic banging, knocking, and buzzing at up to 110 dB. Ear protection is mandatory.

5. k-Space & Image Reconstruction

k-space is the Fourier domain of the image: S(kx, ky) = ∫∫ ρ(x,y) · e^(−i2π(kx·x + ky·y)) dx dy Each MR signal acquisition fills one line of k-space kx ∝ ∫ Gx dt (frequency encoding — fills during readout) ky ∝ ∫ Gy dt (phase encoding — one step per TR) Image = 2D inverse Fourier transform of k-space: ρ(x,y) = FT⁻¹{S(kx, ky)} Centre of k-space: low spatial frequencies → contrast Edges of k-space: high spatial frequencies → sharp edges A 256 × 256 image with TR = 500 ms: Total scan time = 256 × 500 ms = 128 s ≈ 2 min per slice

Faster acquisition techniques include: turbo/fast spin echo (multiple phase-encode steps per TR), echo-planar imaging (EPI — entire k-space in one shot, ~50 ms per slice, used for fMRI), and parallel imaging (GRAPPA, SENSE — using multiple receiver coils to skip phase-encoding steps).

6. Image Contrast & Sequences

Weighting	TR	TE	Fat	Fluid (CSF)	Best for
T1-weighted	Short (~500 ms)	Short (~15 ms)	Bright	Dark	Anatomy, post-contrast
T2-weighted	Long (~2,000 ms)	Long (~80 ms)	Less bright	Bright	Oedema, tumours, inflammation
PD-weighted	Long	Short	Intermediate	Bright	Cartilage, menisci
FLAIR	Long	Long	—	Suppressed (dark)	MS lesions, periventricular
DWI	—	—	—	—	Acute stroke (within hours)

Gadolinium contrast: Paramagnetic gadolinium-based agents (Gd-DTPA) shorten T1 of nearby tissue, making it brighter on T1-weighted images. Used to visualise blood-brain barrier breakdown (tumours, inflammation), vascular imaging (MR angiography), and cardiac perfusion. Unlike iodinated CT contrast, Gd agents carry a small risk of nephrogenic systemic fibrosis in patients with severe kidney disease.

7. The Machine: Magnets, Coils & Helium

Main magnet: Superconducting solenoid wound from NbTi wire, cooled to 4.2 K (−269°C) with liquid helium. Field strength: 1.5 T or 3 T for clinical scanners (60,000× Earth's field). 7 T research scanners exist. The magnet is always on — it takes days to ramp up and costs ~£20,000 in helium to refill.
Helium: A typical MRI scanner contains ~1,700 litres of liquid helium. Helium is a non-renewable resource (extracted from natural gas). Modern scanners (Siemens Free.Max) use helium-free technology: sealed circuits with only 0.7 L of helium and mechanical cryocoolers.
Shim coils: Correct small inhomogeneities in B₀ to achieve uniform field (±1 ppm over the imaging volume). Active shimming uses additional electromagnetic coils; passive shimming uses ferromagnetic plates bolted inside the bore.
RF coils: Transmit the RF pulse and receive the signal. Surface coils (placed on the body part) offer higher SNR than the built-in body coil. Multi-channel phased arrays (32–128 elements) enable parallel imaging and higher resolution.
Cost: A 1.5 T MRI scanner costs £1–2 million. A 3 T scanner: £2–4 million. Annual operating costs (helium, maintenance, electricity): ~£100,000–200,000. A single scan typically costs the NHS ~£200–500.

Safety: The magnetic field is always on and incredibly powerful. Ferromagnetic objects (oxygen cylinders, wheelchairs, scissors) become projectiles near the scanner. All patients and staff are screened for metal implants (some pacemakers are now MRI-conditional). The 5-gauss line (0.5 mT) defines the controlled access zone.