ISD3: a particokinetic model for predicting the combined effects of particle sedimentation, diffusion and dissolution on cellular dosimetry for in vitro systems

BACKGROUND: The development of particokinetic models describing the delivery of insoluble or poorly soluble nanoparticles to cells in liquid cell culture systems has improved the basis for dose-response analysis, hazard ranking from high-throughput systems, and now allows for translation of exposures across in vitro and in vivo test systems. Complimentary particokinetic models that address processes controlling delivery of both particles and released ions to cells, and the influence of particle size changes from dissolution on particle delivery for cell-culture systems would help advance our understanding of the role of particles and ion dosimetry on cellular toxicology. We developed ISD3, an extension of our previously published model for insoluble particles, by deriving a specific formulation of the Population Balance Equation for soluble particles. RESULTS: ISD3 describes the time, concentration and particle size dependent dissolution of particles, their delivery to cells, and the delivery and uptake of ions to cells in in vitro liquid test systems. We applied the model to calculate the particle and ion dosimetry of nanosilver and silver ions in vitro after calibration of two empirical models, one for particle dissolution and one for ion uptake. Total media ion concentration, particle concentration and total cell-associated silver time-courses were well described by the model, across 2 concentrations of 20 and 110 nm particles. ISD3 was calibrated to dissolution data for 20 nm particles as a function of serum protein concentration, but successfully described the media and cell dosimetry time-course for both particles at all concentrations and time points. We also report the finding that protein content in media affects the initial rate of dissolution and the resulting near-steady state ion concentration in solution for the systems we have studied. CONCLUSIONS: By combining experiments and modeling, we were able to quantify the influence of proteins on silver particle solubility, determine the relative amounts of silver ions and particles in exposed cells, and demonstrate the influence of particle size changes resulting from dissolution on particle delivery to cells in culture. ISD3 is modular and can be adapted to new applications by replacing descriptions of dissolution, sedimentation and boundary conditions with those appropriate for particles other than silver. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s12989-018-0243-7) contains supplementary material, which is available to authorized users.