Relaxation (NMR) - Bloch Equations

Bloch Equations

Bloch equations are used to calculate the nuclear magnetization M = (M_x, M_y, M_z) as a function of time when relaxation times T₁ and T₂ are present. Bloch equations are phenomenological equations that were introduced by Felix Bloch in 1946.

Where γ is the gyromagnetic ratio and B(t) = (B_x(t), B_y(t), B₀ + B_z(t)) is the magnetic flux density experienced by the nuclei. The z component of the magnetic flux density B is typically composed of two terms: one, B₀, is constant in time, the other one, B_z(t), is time dependent. It is present in magnetic resonance imaging and helps with the spatial decoding of the NMR signal. M(t) × B(t) is the cross product of these two vectors.

The equation listed above in the section on T₁ and T₂ relaxation can be derived from Bloch equations.