Optimization of magnetization transfer experiments to measure first- order rate constants and spin-lattice relaxation times

A recent analysis of the optimization of magnetization transfer experiments to estimate first-order rate constants is extended to the design of experiments for measuring these constants and T₁ when both parameters are initially unknown. When the number of measurement times is fixed, an optimal design will consist of a set of measurement times which ensures that the precision of the estimates of the combination of k and T₁ is as small as possible in a worst-case scenario. Simple expressions are given for the parameters that characterize the optimal design.