Blochvergelijkingen

Blochvergelijkingen, also known as Bloch equations, are a set of differential equations used to describe the time evolution of the macroscopic magnetization of a sample in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). Developed by Felix Bloch in 1946, these equations extend the quantum mechanical description of spins to a macroscopic level by considering the average behavior of a large ensemble of nuclear spins.

The Bloch equations account for three main relaxation processes: T1 relaxation (longitudinal relaxation), T2 relaxation (transverse relaxation), and the effect of an external magnetic field and radiofrequency pulses. T1 relaxation describes the return of the longitudinal magnetization to its equilibrium value after being perturbed. T2 relaxation describes the decay of the transverse magnetization due to spin-spin interactions and inhomogeneities in the magnetic field. The equations incorporate these relaxation times (T1 and T2) as phenomenological parameters.

In their simplest form, the Bloch equations are linear and can be solved analytically under specific conditions, such as in the presence of a constant magnetic field. However, they are often used in more complex scenarios involving time-varying magnetic fields and radiofrequency pulses, which are fundamental to NMR and MRI experiments. The solutions to the Bloch equations provide the time-dependent magnetization components, which are then detected as the NMR signal. They are essential for understanding signal generation, pulse sequence design, and image formation in MRI.