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Where does the MRI signal come from? This section explores the basic physics of magnetic resonance imaging.

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Larmor Equation

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What is the Larmor equation?

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For a particular magnetic field strength, the (resonant) frequency of precession can be calculated via the Larmor equation. The Larmor equation may be derived using classical physics or quantum mechanics. It links these two descriptions of nuclear magnetic resonance, and is fundamental to MRI physics. The Larmor equation is

ω0 = γ B0

where ω0 is the angular frequency of precession of protons in an external magnetic field, γ is a proportionality constant called the gyromagnetic ratio, and B0 is the strength of the external magnetic field. γ = 2.67*108 radians s-1 T-1. In some texts the right-hand side of the equation is negative; this simply depends on the direction in which a positive rotation is defined.

We may also write f0 = γ B0, where γ = 42.56 MHz T-1 (γ = γ/2π).

Example: the Larmor frequency f0 for a 1.5 T magnet is 1.5(T)*42.56(MHz T-1) = 63.8 MHz.

Further reading on this topic:
Books: MRI From Picture to Proton p107, MRI The Basics p26
Online: Hyperphysics

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