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Week 02: Physical Principles of MRI

Magnetic Resonance Imaging arises from the quantum mechanical spin of protons in water molecules. This week explores static magnetic fields ($B_0$), radiofrequency excitation pulses ($B_1$), nuclear precession at the Larmor frequency, Faraday induction in receiver coils, and how magnetic field gradients enable 2D and 3D spatial encoding.

Interactive Demos & Activities

• Free Induction Decay (FID) & Spin Relaxation

  Faraday Induction & Waveform Simulator · Mxy to FID

  Directly connects the 3D time evolution of precessing and dephasing proton moments to the voltage signal induced in an RF receiver coil via Faraday's Law. Features continuous longitudinal memory across pulses.

• Gradient Encoding Visualizer

  Interactive Spatial Encoding Simulator · Gx, Gy, Gz

  Observe how linear magnetic field gradients make precession frequencies position-dependent, demonstrating slice selection (G_z), phase encoding (G_y), and frequency encoding readout (G_x).

• Pulse Sequence Timing Diagram

  Interactive Timing Diagram · Spin Echo, TR & TE

  A dynamic pulse sequence diagram. Adjust TE to see the 180° refocusing pulse and echo move together; adjust TR to visualize scanner repetition intervals and phase-encode step increments.

• k-space Explorer

  Fourier Reconstruction · Low vs. High Spatial Frequencies

  Vary the fraction of k-space kept to see how central k-space governs coarse contrast while peripheral k-space yields sharp edges, demonstrating Gibbs / truncation ringing.

• 3D NMR Relaxation & Proton Dynamics

  Interactive Three.js 3D Simulator · Bloch Equations

  Explore Bloch equation proton spin dynamics in 3D. Manipulate static field strength ($B_0$), $T_1$ recovery, and $T_2$ decay in real-time. Trigger 90° and 180° RF excitation pulses to watch nutation, precession, and magnetization vector evolution.

• Interactive 2D FFT & K-Space Simulator

  Dual-Canvas Tool · Spatial Domain & K-Space Magnitude

  Draw spatial patterns or test presets (sine gratings, checkerboards, Gaussian blobs, edge filters) to see the instantaneous 2D Fourier transform magnitude spectrum with DC centering and log scaling.

• Spinning Vector Sum Simulator

  Interactive Vector Demo · Phase Coherence

  Adjust rotation frequencies and vector amplitudes to see how multiple precessing magnetic moments combine constructively or destructively to produce the net detected MR signal.

• MRI Safety Course & Force Simulator

  Interactive Safety Module · Fringe Fields & Forces

  Examine the spatial fringe field of superconducting magnets with an interactive magnetic attraction force slider ($F \propto B^2$), review projectile safety, and complete the MRI Safety Certification Quiz.

Topics Covered

• Nuclear Spin & The Larmor Equation: Proton magnetic moments, gyromagnetic ratio ($\gamma = 42.58\text{ MHz/T}$), and resonance.
• RF Excitation & Faraday Induction: Applying a rotating $B_1$ field on-resonance to tip net magnetization into the transverse plane, inducing an alternating voltage in an RF coil according to Faraday's Law.
• Spatial Encoding Gradients: Slice-selection ($G_z$), frequency encoding ($G_x$), phase encoding ($G_y$), and traversal through k-space.