Dynamic range and noise considerations in pattern search optimal fitting of experimental data: a case study using field-cycling NMR relaxometry of liposomal formulations

Abstract

When physical information is extracted from experimental data using a theoretical model, anoptimal fitting procedure becomes essential. In this context, the experimental design,complexity of the physical model and choice of fitting criteria can significantly influence thederived parameters. The consistency of the model itself does not guarantee the results. This isdetermined by both the experimental approach and the intricacies of the fitting optimizationprocedure. In this manuscript, we employ box-constrained mathematical optimizationalgorithms to elucidate critical aspects of the fitting process, which may substantially influencethe reliable extraction of the physical quantities of interest. As a case study we consider 1Hspin-lattice nuclear magnetic resonance relaxometry studies carried out on liposomes. Ourinvestigation reveal that this technique can provide, in a single experiment, information aboutthe elastic properties of the membrane and the diffusion of the lipids within it. Usingexperimentally-generated synthetic data, we analyze the robustness of the pattern searchalgorithm in recovering the physical parameters of interest in a 7D space. We examinenoise-effects and the advantages of extending the dynamic range of the experiment.