🧲 MRI / NMR Physics — Bloch Equations

🧲 What It Demonstrates

This simulator models nuclear magnetic resonance (NMR) — the physical basis of MRI — using the Bloch equations. A net magnetisation vector M = (Mx, My, Mz) starts aligned with the static field B₀ along the z-axis. An RF pulse tips M into the transverse plane, where it precesses at the Larmor frequency and decays due to two independent relaxation processes: T1 (spin-lattice, longitudinal recovery) and T2 (spin-spin, transverse decay). The decaying transverse signal is the Free Induction Decay (FID).

How to Use

• Click 90° RF Pulse to tip M into the transverse plane — watch the FID signal appear.
• Click 180° Inversion for a full inversion recovery — Mz goes to −1, then recovers via T1.
• Choose Tissue Presets to load realistic T1/T2 values for water, fat, muscle, grey/white matter and CSF at 1.5 T.
• Adjust B₀ to see how field strength changes the Larmor frequency (γ·B₀, where γ = 42.577 MHz/T for hydrogen).

Did You Know?

MRI was independently developed by Paul Lauterbur and Peter Mansfield in the 1970s; both shared the 2003 Nobel Prize in Medicine. Unlike CT or X-ray, MRI uses no ionising radiation — it relies entirely on radiofrequency pulses and magnetic fields. A clinical 1.5 T MRI magnet is about 30 000 times stronger than Earth's magnetic field. Different tissues have characteristic T1 and T2 times, which is how MRI creates contrast between grey matter, white matter, CSF and pathology — all without a single drop of contrast agent for many sequences.