This simulator builds an MR image from first principles: tip a magnetization vector with RF pulses, watch it precess and relax in a rotating frame, encode spatial position into k-space one phase-encode line at a time, and reconstruct a real 2D Fourier image from the acquired data. Five tabbed sections take you from the magnetization lab through k-space and image reconstruction, sequence and contrast controls, a verification bench, and a knowledge check.
• Magnetization lab (01): a 3D spin ensemble view with Scanner & spins / Spin ensemble camera views and Auto orbit; a 90° excitation (y), 180° refocus (x), and Invert 180° (y) pulse buttons, plus a custom-pulse control to apply a chosen flip angle about the y-axis; Run spin echo; Play/Advance 10 ms stepping and Reset equilibrium; a live spin readout and spin-time display. • K-space & image (02): Acquire one line, Complete acquisition and Clear acquisition controls for building a k-space grid and reconstructed image incrementally, with live acquisition diagnostics. • Encoding & contrast (03): sequence and acquisition settings, a contrast laboratory with four presets — Spoiled GRE, T1-style SE, T2-style SE and PD-style SE — a contrast formula/note readout, and timing/spatial-encoding controls. • Experiments & tests (04): a 22-check automated verification bench (Run 22 checks) confirming the signal chain behaves correctly, plus guided lessons. • Learn & quiz (05): model scope and references, and a 12-question knowledge check. • Export data, Expand and a guided tour button that walks through all six core components.
The rotating frame removes the rapid Larmor carrier precession from the display so you can see the underlying dynamics — offsets and relaxation remain visible after removing the carrier, which is the whole point of viewing magnetization in the rotating frame rather than the lab frame. An ideal 90° pulse applied to equilibrium magnetization rotates it into the transverse plane without destroying its length, producing transverse magnetization that can induce a measurable signal; T1 recovery then governs how longitudinal magnetization returns toward equilibrium, while T2 decay governs how transverse magnetization dephases and decays.
A spin echo's 180° refocusing pulse can reverse static, non-random frequency-offset dephasing (like field inhomogeneity), which is why an ideal echo intensity is exp(−1) (about 0.368) of its initial value at TE = T2 under full relaxation — but 180° refocusing cannot undo true, irreversible T2 decay itself, which is why T2 loss persists across the echo regardless of how well static offsets refocus.
Central k-space samples dominate broad image structure (contrast and overall shape), while outer k-space samples carry fine spatial detail — no single k-space sample corresponds to a single image pixel, because Fourier encoding mixes contributions from the entire object into every sample. The reconstructed complex image comes from an actual inverse Fourier transform of the acquired k-space data, and magnitude display of that complex result is subject to a known bias: magnitude noise is biased away from zero even when the underlying complex noise has zero mean, because magnitude cannot be negative.
The four contrast presets — spoiled GRE, T1-weighted SE, T2-weighted SE and PD-weighted SE — each combine different TR/TE/flip-angle choices to emphasize a different physical contrast mechanism; the Ernst angle control specifically maximizes one compartment's spoiled-GRE signal at a fixed TR, which is a signal-optimization concept distinct from optimizing tissue contrast. Increasing the number of excitations (NEX) from 1 to 4 quadruples acquisition time but only reduces noise by a factor of two (a square-root relationship from independent averaging) — a fundamental signal-to-noise/time tradeoff in real MRI.
A spin echo's 180° refocusing pulse reverses static, non-random dephasing caused by field inhomogeneity, but it cannot reverse true T2 relaxation, which is an irreversible loss of transverse magnetization coherence due to random spin-spin interactions. That is why, under full relaxation, an ideal echo's amplitude at TE = T2 is exp(−1) — about 36.8% of its initial value — rather than fully recovering to the initial amplitude.
Central k-space samples (low spatial frequencies) dominate the image's broad structure and overall contrast, while outer k-space samples (high spatial frequencies) carry fine spatial detail and edges. No individual k-space sample corresponds to a single image pixel — Fourier encoding mixes information from across the whole object into every sample, and the full 2D inverse Fourier transform is needed to recover the spatial image.
The Ernst angle is the flip angle that maximizes a given tissue compartment's signal in a spoiled gradient-echo (GRE) sequence at a fixed repetition time (TR). It is a signal-optimization concept, not a contrast-optimization one — maximizing raw signal at the Ernst angle does not automatically maximize the contrast difference between two different tissues.
Each acquisition contributes independent, zero-mean noise. Averaging N independent measurements reduces the noise standard deviation by a factor of the square root of N, not by a factor of N itself — so going from NEX=1 to NEX=4 quadruples scan time but only halves the noise, which is a fundamental tradeoff in MRI acquisition planning.