Optimal Experimental Design for Fast and Accurate Relaxation Time Measurements in Magnetic Resonance

Relaxation time constants in magnetic resonance are sensitive probes of molecular structure and dynamics and are critical for achieving spatial contrast in imaging, but measuring relaxation times is generally far more time-consuming than traditional 1D spectroscopic experiments. Furthermore, the accuracy of the measured constants depends on numerous experimental factors. Currently, there are several available methods for designing a relaxation measurement (e.g., linear or logarithmic time spacing), but it is often unclear which method is preferable, how to select the minimum and maximum time points, or how many increments should be used, with all choices affecting the experimental time and the accuracy. Here, we consider optimal experimental designs and show that they maximize information per measurement, leading to more precise estimates for a specified relaxation model while in favorable cases reducing the number of measurements, and potentially the experimental time, required to achieve comparable precision relative to conventional sampling designs. Theoretical results on optimal experimental designs are explored both via simulation studies (for both mono- and multiexponential models) and via experiments for monoexponential $T_1$ measurements on nuclear magnetic resonance systems. We emphasize that the resulting designs are optimal for parameter estimation under an assumed model rather than for model discovery or relaxation-time distribution recovery. We conclude with practical guidelines for improved experimental design for relaxation-time measurements in magnetic resonance while clarifying the limitations of model-based optimal design.