SME
Bioinstrumentation · Problem type
Larmor frequency in an MRI scanner
Use this for “At what frequency do protons resonate in a 3 T scanner?”
Table
Magnetic field (B)
(T)
Precession frequency (f)
(MHz)
This is an example. Type your own values to start a new problem.
f (MHz)
=
42.58
×
B (T)
Formulas
f
=
42.58
×
B
63.87 = 42.58 × 1.5
Assumptions
•
Hydrogen nuclei (protons) precess at f = (γ ÷ 2π)B, with γ ÷ 2π = 42.58 MHz per tesla.
•
The scanner sends radio waves at this frequency to tip the protons; radio waves at other frequencies do not tip them.
•
Doubling the field doubles the frequency: 1.5 T and 3 T scanners work at about 64 and 128 MHz.
Step-by-step
WE KNOW
B = 1.5 T
FIND
precession frequency (f)
Step 1 · Find precession frequency (f)
Use f = 42.58 × B
Protons precess 42.58 million times a second for each tesla of field.
f
=
42.58
×
1.5
f
=
63.87
MHz
Check
Put the numbers back in. Both sides should match.
63.87 = 42.58 × 1.5 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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