🧠MRI Physics Simulator - Larmor Precession, T1/T2 Contrast, Spin Echo, k-Space

How to use MRI physics simulator

1. 1In Larmor precession, pick a nucleus and field, set B₁ and the flip angle, and switch between the lab and rotating frames
2. 2In T1 / T2 relaxation, tick tissues and switch between 1.5 T and 3 T to see recovery and decay curves and null TIs
3. 3In Weighting & contrast, use presets or drag TR and TE (optionally add an inversion pulse) to see the phantom and tissue signals
4. 4In Spin echo, change TE, T2 and field inhomogeneity to watch dephasing, refocusing and the echo
5. 5In k-space and Noise & safety, try different sampling patterns and estimate FOV, SAR, SNR and projectile force

FAQ

What is the difference between T1-weighted and T2-weighted images?

T1 is the time constant for longitudinal magnetisation to recover; T2 is the time constant for the transverse signal to dephase. With a short repetition time (TR), short-T1 tissues recover more and look bright, so short TR plus short TE gives T1 weighting: fat bright, white matter brighter than grey, CSF dark, good for anatomy. With a long echo time (TE) only long-T2 tissues keep signal, so long TR plus long TE gives T2 weighting: water, oedema and CSF bright, good for pathology. Long TR with short TE mostly reflects hydrogen content: proton-density weighting.

What is k-space, and why is a centre-only image blurry?

Gradient fields make protons at different positions precess at different frequencies and phases, so the received signal is exactly the 2D Fourier transform of the image; the raw data arranged as a matrix is k-space. The centre holds low spatial frequencies that set overall brightness and contrast; the outside holds high frequencies for edges and detail. Keeping only the centre is a low-pass filter, giving a blurry image with contrast intact; keeping only the edges leaves outlines. Skipping every other line halves the field of view and causes wrap-around.

How does a spin echo cancel field inhomogeneity?

Small inhomogeneities in the main field make protons in different places precess at slightly different rates, so phases fan out and the signal decays with T2*. A 180° pulse at TE/2 flips every phase: spins that were ahead are now behind, but they keep their speeds, so they line up again at TE and form an echo. Dephasing from fixed inhomogeneity cancels completely and the echo amplitude follows only the true T2 decay, e^(−TE/T2).

Why is MRI so loud, and what are the safety issues?

The gradient coils carry rapidly switched currents inside a strong field, so the wires feel a Lorentz force F = I·L·B and vibrate like a giant loudspeaker, reaching over 110 dB, hence ear protection. A superconducting magnet is always on, and ferromagnetic objects are pulled hard at the bore entrance: a 1 kg piece of iron can feel tens of times its own weight. Pacemakers, some aneurysm clips and metal fragments can move, heat or malfunction, so everyone is screened. RF also heats tissue, and the SAR limits are harder to meet at higher field.

Are the tissue values and images realistic?

T1, T2 and proton density are typical approximate literature values and can differ by 20% or more between people, regions and methods. The brain image is a synthetic phantom built from ellipses and ripples to show contrast principles, not a real scan, and it does not model blood flow, chemical shift, susceptibility or noise. For chemical shift and spectra, use the NMR spectroscopy tool.