Larmor frequency, the RF tip, and T1/T2 — contrast is a timing choice.
For MRI physicists · radiographers·8 min
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You will be able to
01Compute f = (γ/2π) B0 for hydrogen at 1.5 T and 3 T.
02Point to T1 recovery and T2 decay on a sketch.
03Say why Ernst angle maximises signal for a given T1 and TR.
Chapter 01
The magnet’s clock
Spins precess at gamma over two-pi times B-zero. Hydrogen at 1.5 tesla is about 64 megahertz; at 3 tesla, about 128. A resonant pulse tips the magnetisation. Off-resonance, nothing tips. That is why a 1.5-tesla protocol is not a 3-tesla protocol with the volume knob up.
Frequency is not a setting. It is B0 times a constant of nature.
Simulation
Larmor frequency — Change the numbers; the scene follows.
Variables
f = 63.8655 MHz
f=2πγB0
Keep thisFrequency is not a setting. It is B0 times a constant of nature.
After a tip, longitudinal magnetisation recovers with T1; transverse magnetisation dies with T2. Short TR and short TE weights T1. Long TR and long TE weights T2. Fat and water, grey and white, tumour and oedema: they differ because their clocks differ.
Simulation
T1 recovery and T2 decay — Change the numbers; the scene follows.
Variables
M_z = 0.2212 a.u.
Keep thisYou do not ‘turn on T2’. You wait for it.
In a spoiled gradient echo, signal versus flip angle has a peak: the Ernst angle, cosine inverse of e to the minus TR over T1. Too small, you waste longitudinal magnetisation. Too large, you saturate. That peak is how a 3D sequence stays loud without cooking the patient.
Simulation
Ernst angle — Change the numbers; the scene follows.
Variables
θ_E = 9.34 °
θE=arccos(e−TR/T1)
Keep thisErnst angle is T1-specific. One angle does not fit the liver and the blood.