Nuclear Spins in a Magnetic Field
When placed in a strong magnetic field (1.5-7 Tesla), hydrogen nuclei in tissue align with or against the field, creating a net magnetization vector M₀. A radiofrequency pulse at the Larmor frequency tips this magnetization into the transverse plane, where it precesses and induces a signal in the receiver coil. The magnitude and timing of this signal encode tissue composition.
T1 and T2 Relaxation
After excitation, two independent relaxation processes restore equilibrium. T1 (spin-lattice) relaxation returns longitudinal magnetization toward M₀ — fast in fat (~250 ms), slow in CSF (~4000 ms). T2 (spin-spin) relaxation causes transverse magnetization to dephase — long in fluid (~2000 ms), short in liver (~40 ms). These differences create the rich soft-tissue contrast unique to MRI.
The Spin-Echo Sequence
The workhorse spin-echo sequence applies a 90° excitation pulse followed by a 180° refocusing pulse at TE/2. The refocusing pulse reverses static dephasing, producing an echo at time TE that depends only on true T2 decay. By repeating every TR milliseconds, the sequence samples T1 recovery between excitations. Short TR emphasizes T1 differences; long TE emphasizes T2 differences.
Choosing Contrast in Practice
Radiologists select TR and TE to highlight specific pathologies. T1-weighted images (TR ~500 ms, TE ~15 ms) excel at anatomical detail and post-gadolinium enhancement. T2-weighted images (TR ~4000 ms, TE ~100 ms) reveal edema, tumors, and inflammation as bright regions. This simulator shows how the signal equation S = M₀(1 − e^(−TR/T1))e^(−TE/T2) responds to each parameter in real time.