Bloch equations

Bloch Equations are a set of macroscopic equations that are used in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) to calculate the response of magnetization within a sample to an external magnetic field. They were first introduced by Felix Bloch in 1946.

Overview

The Bloch Equations describe the behavior of nuclear magnetization in the presence of both a static and a time-dependent magnetic field. They are named after Swiss physicist Felix Bloch, who was awarded the Nobel Prize in Physics in 1952 for his work in the field of quantum mechanics and nuclear magnetic resonance.

Mathematical Formulation

The Bloch Equations are a set of three differential equations that describe the time evolution of the magnetization vector M = (Mx, My, Mz) in a magnetic field. The equations are given by:

dM/dt = γM × B - (M - M0)/T1 in the z direction dM/dt = γM × B - M/T2 in the x and y directions

where γ is the gyromagnetic ratio, B is the magnetic field, T1 is the spin-lattice relaxation time, T2 is the spin-spin relaxation time, and M0 is the equilibrium magnetization.

Applications

The Bloch Equations are fundamental to the understanding and application of NMR and MRI. They are used to calculate the response of a sample to a magnetic field, which is crucial in the imaging process in MRI and the spectroscopic analysis in NMR.

See Also

• Nuclear magnetic resonance
• Magnetic resonance imaging
• Felix Bloch
• Spin-lattice relaxation
• Spin-spin relaxation