Improved formulae for signal amplitudes in repeated NMR sequences: applications in NMR imaging

An improved formalism describing the dependence of the signal strength on relaxation times and spin densities in pulsed nuclear magnetic resonance experiments is presented. It is especially applicable to repetitive experiments such as occur in imaging applications. Essentially, it includes long-time spin coherence effects not considered in the algorithms usually adopted. Also, some generalizations of classical concepts are made. Validity criteria are studied using numerical simulations. The algorithm assumes a relatively inhomogeneous main magnetic field, but the computer simulations indicate that the inhomogeneity normally present in magnetic resonance imagers is sufficient. The simulations also indicate that the field gradient pulses applied in the spatial encoding procedure do not necessarily interfere seriously with the validity of the formulae, but complicate the choice of optimal formula and may in some circumstances prevent the spin system from reaching a steady state.