🧲 MRI / NMR Physics: Bloch Equations (2D)

🧲 What It Demonstrates

This 2D companion models nuclear magnetic resonance (NMR) — the physical basis of MRI — by integrating the same Bloch equations as the 3D version, drawn on a flat Canvas 2D projection instead of a WebGL scene. 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 through 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 and watch the FID appear.
• Click 180° Inversion for a full inversion recovery — Mz goes to −1, then recovers via T1.
• Choose a tissue preset for realistic 1.5 T T1/T2 values (water, fat, muscle, grey/white matter, CSF).
• Adjust B₀ to see how field strength changes the Larmor frequency (γ·B₀, γ = 42.577 MHz/T for hydrogen).
• Click the left half of the canvas to fire a custom-angle RF pulse (angle = horizontal click position).