Dynamic range and noise considerations in Pattern Search optimal fitting of experimental data: a case study using Field-Cycling NMR Relaxometry of liposomal formulations

Fast field-cycling nuclear magnetic resonance relaxometry has been consolidated as an experimental technique that can be used to infer about the molecular dynamics in many different materials. In some cases, experiments should be extended into a low Larmor frequency regime, where environmental and internal local fields should be taken into account. In turn, as a model-dependent technique, the use of a validated physical model is mandatory, as it is the used criteria to fit the data. 1H spin-lattice relaxometry studies carried out in liposomes revealed that this technique can provide, in a single experiment, information about the elastic properties of the membrane, and the diffusion of the lipids within it. In this manuscript we use specific box-constrained mathematical optimization algorithms to analyze the relevance of the dynamic range of the experiment, in a case where the low-frequency regime may coexist with the local internal fields of the sample. The use of automated optimal methods facilitated the understanding of relevant features concerning the fitting process, that may strongly affect the extraction of the physical quantities of interest.