The benefits of a Bayesian analysis for the characterization of magnetic nanoparticles

Abstract

Magnetic nanoparticles offer a unique potential for various biomedical applications, but prior to commercial usage a standardized characterization of their structural and magnetic properties is required. For a thorough characterization, the combination of conventional magnetometry and advanced scattering techniques has shown great potential. In the present work, we characterize a powder sample of high-quality iron oxide nanoparticles that are surrounded with a homogeneous thick silica shell by DC magnetometry and magnetic smallangle neutron scattering (SANS). To retrieve the particle parameters such as their size distribution and saturation magnetization from the data, we apply standard model fits of individual data sets as well as global fits of multiple curves, including a combination of the magnetometry and SANS measurements. We show that by combining a standard least-squares fit with a subsequent Bayesian approach for the data refinement, the probability distributions of the model parameters and their cross correlations can be readily extracted, which enables a direct visual feedback regarding the quality of the fit. This prevents an overfitting of data in case of highly correlated parameters and renders the Bayesian method as an ideal component for a standardized data analysis of magnetic nanoparticle samples.

Using small-angle scattering to guide functional magnetic nanoparticle design

“… 153 Regarding the calculation of interparticle correlations in MNP assemblies to resolve short- and long-range order Monte-Carlo simulations can be employed as demonstrated recently for artificial spin ice. 387 For data fitting, tools based on Bayesian statistics are developed to improve the predicitive power of model fits of neutron reflectometry 388 and SANS 389 data and maximize the information density. Similar to modelfits also inverse Fourier transforms are usually ill-posed problems, and thus similiar approaches have been introduced in recent years to find the most probable solution 390 or by using image processing inspired approaches such as the singular value decomposition 132 or fast iterative method to reveal the real-space 2D correlations.…”

Using small-angle scattering to guide functional magnetic nanoparticle design

“…153 Regarding the calculation of interparticle correlations, on the other hand, to resolve short-and long-range order in MNP assemblies Monte-Carlo simulations can be employed as demonstrated recently for artificial spin ice. 387 For data fitting, improved tools are developed such as Bayesian approaches for improving model fits of neutron reflectometry 388 and SANS 389 data to increase the predictive power of the fits and maximize the information density. Similar to model-fits also inverse Fourier transforms are usually ill-posed problems, and thus new approaches have been introduced in recent years that improve data analysis either by applying Bayesian analysis to find the most probable solution 390 or by using novel approaches such as the singular value decomposition 132 or fast iterative method to reveal the real-space 2D correlations 391 .…”

From Single-Core Nanoparticles in Ferrofluids to Multi-Core Magnetic Nanocomposites: Assembly Strategies, Structure, and Magnetic Behavior

“…Recently, Bersweiler et al [247] took the analysis a step further by including Bayesian analysis in the characterization of magnetic nanoparticles. These were spherical iron oxide nanoparticles [246]; permission conveyed through Copyright Clearance Center, Inc.).…”