Accounting for Non-Stationary Variability in Magnetic Particle Spectroscopy

Abstract

Magnetic particle spectroscopy (MPS) is an emerging analytical technique with potential for rapid, accessible, and affordable point of care biomarker detection based on magnetic signal fluctuations. Accurate interpretation of MPS signals requires both colloidal stability of nanoparticles in aqueous and complex media and statistical models that appropriately represent experimental variability. Conventional least squares (LS) approaches assume stationary and homoscedastic noise, assumptions which break down in experimental settings due to inherent temporal and within sample variability. This study, investigates the signal variability in 22 nm iron oxide nanoparticles (IONPs) coated with 20 kDa poly(ethylene glycol). We evaluate the validity of the standard linear model and reveal that the least squares approach fails to account for inherent temporal and within sample variability. Repeated measurements under identical treatment conditions reveal substantial structured fluctuations consistent with a non-stationary measurement process. Transformations commonly used to normalize mass loading effects, including harmonic rations, redistribute variance without resolving the underlying variability. A hierarchical mixed effects model is implemented to partition within-run and temporal sources of variation and to provide confidence estimates that reflect the observed variance structure across observation levels. These findings establish a statistical framework for representing intrinsic variability in MPS measurements and support more rigorous interpretation of harmonic signals. Explicit modeling of hierarchical uncertainty is an importation step towards quantitative, reproducible MPS analysis and translation of MPS for sensitive biomarker detection.