ELEC5622 Chap.2 MRI Signal: Spin, Precession and Relaxation
MRI Signal: Spin, Precession and Relaxation
This chapter explains where the MRI signal comes from. Hydrogen nuclei in water behave as tiny magnets that align with the main field and precess at the Larmor frequency. A radio-frequency pulse at that frequency tips the net magnetisation, and two relaxation processes, T1 recovery along the field and T2 decay across it, set how bright each tissue appears.
A worked example ranks four tissues using the lecture's own T1 and T2 table. The physics here underpins Chapters 3 and 4, because pulse-sequence timing and diffusion weighting are both ways of choosing which part of this relaxation behaviour the image shows. Expect both short calculations, such as a transmit frequency or a recovery fraction, and short explanations of why a tissue looks bright or dark.
What this chapter covers
- 01
Nuclei with spin and charge, and why hydrogen dominates
- 02
Net magnetisation and alignment with B0
- 03
Precession and the Larmor equation
- 04
RF excitation and the emitted signal
- 05
T1 recovery and the 63% rule
- 06
T2 decay and loss of phase coherence
- 07
Tissue T1 and T2 values and brightness
Worked example · free
Larmor frequency and longitudinal recovery
- 1ω = γB0 = 42.58 × 3.0 = 127.74 MHz.
- 11,360 ms is 2 × T1, so Mz/M0 = 1 − e^(−2).
- 11 − 0.135 = 0.865, so about 86.5% has recovered.
Key terms
- Larmor frequency
- The Larmor frequency is the rate at which a nucleus precesses around B0, equal to γ times the field strength.
- T1 relaxation
- T1 relaxation is the exponential regrowth of longitudinal magnetisation along B0 after excitation.
- T2 relaxation
- T2 relaxation is the decay of transverse magnetisation as precessing protons lose phase coherence.
- Gyromagnetic ratio
- The gyromagnetic ratio is a nucleus's magnetic moment divided by its angular momentum, 42.58 MHz per tesla for hydrogen.
- Net magnetisation
- Net magnetisation is the vector sum of all proton magnetic moments in a voxel, aligned with B0 at rest.
- Precession
- Precession is the rotation of a proton's magnetic moment around the direction of the main field B0.
MRI Signal: Spin, Precession and Relaxation FAQ
Why does MRI image hydrogen rather than other nuclei?
Hydrogen is the only major element in tissue that is MR sensitive, and it is also the most abundant atom in the body, mostly in water. Other MR-capable nuclei such as carbon-13 or sodium-23 are far scarcer, so their signal is weak.
What happens if the RF pulse is not at the Larmor frequency?
The protons absorb almost no energy because resonance only occurs at the precession frequency. The net magnetisation is barely tipped, so little transverse signal is produced and the receive coils pick up almost nothing.
Why is water dark on T1-weighted images but bright on T2-weighted images?
Water has long T1 and long T2, both 3000 ms in the lecture table. Its slow recovery makes it dark when T1 differences dominate, while its slow decay keeps signal high when the echo is taken late and T2 dominates.
What is the difference between in phase and out of phase?
Protons precessing together are in phase and their transverse components add up to a measurable signal. When they precess separately they are out of phase, their components cancel, and the signal fades; that loss of coherence is what T2 relaxation describes.
Why does MRI not use ionising radiation?
The signal comes from radio-frequency energy absorbed and re-emitted by hydrogen nuclei in a magnetic field, not from X-rays or gamma rays. That is why the lecture lists MRI as safe for people vulnerable to radiation, such as pregnant women and babies.
How strong is a 3 tesla MRI field?
A tesla is one newton per ampere-metre, so in a 3.0 T field a wire carrying 1 A at right angles feels 3.0 N per metre. The lecture compares this with about 5 mT for a refrigerator magnet and 30 to 70 microtesla for the Earth's field.
Exam move
Learn the Larmor equation with the value 42.58 MHz per tesla and practise it at 1.5, 3 and 7 T. Then memorise the T1 and T2 table and the two orderings, noting where the slide's curve exercise and the table disagree about fat. Sketch recovery and decay curves for two tissues and mark where they cross 63% and 37%.
Finally, explain in two sentences why a strong field increases the transmit frequency but not the T1 ordering of tissues, and practise converting between a recovery fraction and a waiting time. When you revise, keep the two axes separate in every sentence: T1 always refers to the z component regrowing, T2 always to the x-y component fading.
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