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Gyromagnetic Ratio
A constant for any given nucleus that relates the nuclear MR frequency and the strength of the external magnetic field.
Definition: The ratio of the magnetic moment (field strength = T) to the angular momentum (frequency = v) of a particle.
The gyromagnetic effect happens if a magnetic substance is subjected to a magnetic field. Upon a change in direction of the magnetic field, the magnetization of the substance must change. In order for this to happen, the atoms must change their angular momentum. Since there are no external torques acting on the system, the total angular momentum must remain constant. This mass rotation may be measured. The gyromagnetic ratio is different for each nucleus of different atoms. The value of the gyromagnetic ratio for hydrogen (1H) is 4,258 (Hz/G) (42.58 MHz/T).
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Electron and proton gyromagnetic ratios
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Larmor Equation
The Larmor equation is important because it is the frequency at which the nucleus will absorb energy. The absorption of that energy will cause the proton to alter its alignment and ranges from 1-100 MHz in MRI. The equation states that the frequency of precession of the nuclear magnetic moment is directly proportional to the product of the magnetic field strength (B0) and the gyromagnetic ratio (g). This is stated mathematically as w= gB0.

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Larmor Frequency
The Larmor precession frequency is the rate of precession of a spin packet under the influence of a magnetic field. The frequency of an RF signal, which will cause a change in the nucleus spin energy level, is given by the Larmor equation. The frequency is determined by the gyro magnetic ratio of atoms and the strength of the magnetic field. The gyromagnetic ratio is different for each nucleus of different atoms.
The stronger the magnetic field, the higher the precessional frequency. If an RF pulse at the Larmor frequency is applied to the nucleus of an atom, the protons will alter their alignment from the direction of the main magnetic field to the direction opposite the main magnetic field. As the proton tries to realign with the main magnetic field, it will emit energy at the Larmor frequency. By varying the magnetic field across the body with a magnetic field gradient, the corresponding variation of the Larmor frequency can be used to encode the position. For protons (hydrogen nuclei), the Larmor frequency is 42.58 MHz/Tesla.
See also Larmor Equation.

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Velocity Encoding
(VENC) A specialized technique used for encoding flow-velocities.
The velocity encoding value is given by:
VENC = pi / gamma DELTA M1.
Gamma is the gyromagnetic ratio, and DELTA M1 is the gradient moment and is proportional to the area of the flow encoding gradient waveform.
See also Phase Contrast Sequence, Phase Contrast Angiography, and Bipolar Gradient Pulse.
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