Bayesian estimation to deconvolute single-particle ICP-MS data with a mixed Poisson distribution†

Single-particle ICP-MS (spICP-MS) is an established method for the determination of inorganic nanoparticle (NP) mass distributions and particle number concentrations. However, spICP-MS is not applicable to some cases, especially cases that require distinguishing signals from dissolved ions and signals from relatively small NPs. To deconvolute spICP-MS data, which is obtained by setting the dwell time similar to the particle event duration time, a Bayesian estimation method was developed for spICP-MS analysis using silver (Ag) and silica (SiO₂) NPs. The signal distributions of the spICP-MS data were parameterised using a Bayesian estimation method on the assumption that they could be described by mixed Poisson distributions. Analytical results were then compared to results obtained with conventional criteria. When the instrument parameters were set so that the particle-event duration was within 2 readings and hence did not deviate from the assumptions of the current Bayesian model, better estimation results could be obtained with the Bayesian estimation method than with methods based on conventional criteria, especially for a sample with high particle number concentration. Furthermore, applying the specific informative prior distribution enabled us to obtain reasonable estimation results, even when the signal counts were 6 or less and the background counts were high. Because appropriate NP information was obtained for Ag-NP and SiO₂-NP, the Bayesian estimation method can be universally adopted with inorganic NPs detectable by ICP-MS.