Analytical analysis of multi-pulse NMR

It is well known that in multi-pulse applications in high-resolution NMR and MRI a steady state is reached for the magnetisation vector by the effect of relaxation in combination with the pulse repetition time. In this paper, a mathematical model is developed to understand how the parameters of the pulse sequence and relaxation times T-1 and T-2 affect the behaviour of the magnetisation vector. It will be shown that even under strong simplifying conditions an analytical analysis becomes very complex and only an analytical solution can be found for 90degrees pulses and T-1 = T-2. For other cases a numerical approach is needed. Nevertheless, the basic approach of the mathematical analysis provides a general tool for analytical multi-operator applications. Our results provide a quantitative insight in the process by which the magnetisation relaxes towards the steady-state situation in a multi-pulse sequence. (C) 2004 Elsevier Inc. All rights reserved.