How MRI Works — The Physics Explained

Nuclear Magnetic Resonance (NMR)

MRI is built on the quantum mechanical phenomenon of nuclear magnetic resonance (NMR). Certain atomic nuclei (those with odd numbers of protons or neutrons — including ¹H, ¹³C, ³¹P) have a quantum property called spin (I ≠ 0). Spin creates a tiny magnetic dipole moment μ = γIℏ, where γ is the nucleus-specific gyromagnetic ratio.

For hydrogen protons (I = ½): γ = 2.675 × 10⁸ rad·s⁻¹·T⁻¹. When placed in an external magnetic field B₀, the spin can align parallel (lower energy, spin-up |+⟩) or antiparallel (higher energy, spin-down |−⟩). The energy difference:

For a 1.5 T MRI: f₀ = (2.675 × 10⁸ × 1.5) / 2π ≈ 63.9 MHz — in the radio frequency range. For 3 T: f₀ ≈ 127.7 MHz.

At thermal equilibrium, slightly more spins align parallel (Boltzmann distribution), creating a net bulk magnetisation M₀ along B₀ (the longitudinal direction, z-axis). This is small — about 3 spins per million at 1.5 T — but with 10²³ protons in a human body, it's detectable.

Larmor Precession

Like a gyroscope tilted away from vertical, the net magnetisation M precesses around Bâ‚€ at the Larmor frequency fâ‚€. This precession is the fundamental resonance exploited by MRI:

The clinical significance: if you match the frequency of an applied oscillating magnetic field (RF pulse) to the Larmor frequency, the rotating spins absorb energy — resonance. This is the "R" in MRI.

The RF Pulse — Tipping the Magnetisation

An RF pulse at the Larmor frequency is applied perpendicular to B₀. In the rotating reference frame, this appears as a static field B₁ that rotates M away from the z-axis (the flip angle α depends on pulse duration and B₁ amplitude):

• 90° pulse: Rotates M fully into the transverse (xy) plane. Maximum signal detection.
• 180° pulse: Inverts M (used for T1 measurements and spin echo sequences).

Once in the transverse plane, M precesses at ω₀ and induces an oscillating voltage in the receiver coil (by Faraday's law of induction). This signal — the free induction decay (FID) — is the raw MRI data.

T1 and T2 Relaxation

After the RF pulse, the disturbed magnetisation returns to equilibrium via two independent relaxation processes:

T1 — Spin-Lattice (Longitudinal) Relaxation

M_z(t) = M₀(1 − e^−t/T1). T1 is the time constant for longitudinal magnetisation to recover. It reflects how efficiently spins exchange energy with their surroundings (the "lattice"). Fluids have long T1 (~1–4 s); fatty tissues have short T1 (~200–300 ms).

T2 — Spin-Spin (Transverse) Relaxation

M_xy(t) = M₀ e^−t/T2. T2 is the time constant for transverse magnetisation decay — caused by local magnetic field inhomogeneities from neighbouring spins dephasing each other. T2 ≤ T1 always. CSF has long T2 (~2 s); skeletal muscle has short T2 (~30 ms).

By varying the echo time (TE) and repetition time (TR), the MRI operator selects which tissue properties dominate image contrast:

• T1-weighted: Short TR, short TE. Fat is bright, water is dark. Good for anatomy.
• T2-weighted: Long TR, long TE. Water/CSF is bright. Good for oedema and inflammation.
• Proton density (PD): Long TR, short TE. Reflects water content. Good for cartilage.

Gradient Coils — Encoding Position

The key innovation enabling MRI imaging (rather than just spectroscopy) is the gradient coil system. Three sets of gradient coils (Gx, Gy, Gz) add spatially varying fields on top of Bâ‚€:

The Larmor frequency now varies linearly across the body. By applying a selective RF pulse at frequency f₀ ± Δf, only a thin slice (where B is tuned to resonance) is excited — slice selection. Within that slice, additional gradients encode x and y positions via frequency encoding and phase encoding.

Image Reconstruction — Fourier Mathematics

Each data acquisition samples one line of k-space — the Fourier transform of the final image. After collecting many k-space lines (one per TR), a 2D inverse Fourier transform (FFT) reconstructs the image. The time to fill k-space determines scan time:

scan time = TR × number of phase encoding steps × number of averages

Advanced sequences (EPI — Echo Planar Imaging, used in fMRI) fill all of k-space in a single TR, enabling sub-second scan times. Standard anatomical MRI: 3–15 minutes per sequence.

Contrast Agents

Gadolinium-based contrast agents (e.g., gadopentetate dimeglumine) shorten T1 of tissues they penetrate, making those regions appear brighter on T1-weighted images. They accumulate in areas of blood-brain barrier breakdown (tumours, inflammation, active MS lesions) — providing diagnostic specificity unavailable without contrast. Gadolinium is a rare earth metal (atomic number 64) with 7 unpaired electrons, giving it strong paramagnetic properties.

Functional MRI (fMRI)

fMRI exploits the BOLD effect (Blood Oxygenation Level Dependent). Oxygenated haemoglobin (oxHb) is diamagnetic; deoxygenated haemoglobin (deoxyHb) is paramagnetic. Neural activity → local increased blood flow → increased blood oxygenation → reduced local field inhomogeneity → longer T2* → stronger MRI signal. Brain activation maps are constructed by correlating BOLD signal changes with task timing.

Temporal resolution: 1–2 seconds. Spatial resolution: ~1–3 mm. Despite its ubiquity in neuroscience, BOLD fMRI measures blood flow, not electrical activity — there is a 4–6 second hemodynamic delay and the relationship between neural firing and BOLD response is complex and still being characterised.

MRI Safety

MRI is non-ionising — it uses radio waves, not X-rays, and deposits negligible energy in tissue at clinical field strengths. However:

• Projectile effect: The magnetic field exerts enormous force on ferromagnetic objects (steel tools, oxygen cylinders) — these become dangerous projectiles in Zone 3/4 MRI areas. Strict metal screening is mandatory.
• Implant heating: Lead implants, neural stimulators, and some legacy cardiac devices can heat significantly in the RF field. Modern implants are designed to be MRI-conditional.
• Acoustic noise: Rapid switching of gradient coils produces 100+ dB acoustic noise — ear protection is standard.
• 7 T and above (research): At ultra-high fields, peripheral nerve stimulation from gradient switching and specific absorption rate (SAR) limits become more restrictive, but no confirmed long-term biological harm from the Bâ‚€ field alone.

Frequently Asked Questions

How does MRI work simply?

MRI aligns hydrogen spins with a strong magnet, then uses a radio wave to knock them out of alignment. When the radio wave stops, the spins "ring like a bell" at a specific frequency as they realign. Detecting this signal and applying gradient fields allows you to produce a 3D image based on how different tissues ring differently.

Why doesn't MRI use X-rays?

MRI uses radiofrequency electromagnetic waves — a million times less energetic per photon than X-rays. X-rays are ionising (can break chemical bonds and damage DNA); MRI radio waves are non-ionising. That's why MRI is safe for repeated imaging and for pregnant women.

What does the "M" in MRI originally stand for?

"Nuclear Magnetic Resonance Imaging" — NMRI. The word "nuclear" was dropped in the 1980s because it frightened patients who associated it with nuclear radiation (though NMR has nothing to do with nuclear decay).