An optimal control approach to design entire relaxation dispersion experiments

•A general approach is introduced to optimize relaxation dispersion sequences.•Optimizations are based on the relaxation and exchange rate dependence of the detectable signal.•The optimized windowless sequences are both amplitude and phase modulated.•The performance of ideal CPMG sequences is approached by energy-limited sequences.•The physical limits of relaxation dispersion experiments can be explored.

A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.

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