ISDD: A computational model of particle sedimentation, diffusion and target cell dosimetry for in vitro toxicity studies

Abstract

Background: The difficulty of directly measuring cellular dose is a significant obstacle to application of target tissue dosimetry for nanoparticle and microparticle toxicity assessment, particularly for in vitro systems. As a consequence, the target tissue paradigm for dosimetry and hazard assessment of nanoparticles has largely been ignored in favor of using metrics of exposure (e.g. μg particle/mL culture medium, particle surface area/mL, particle number/mL). We have developed a computational model of solution particokinetics (sedimentation, diffusion) and dosimetry for non-interacting spherical particles and their agglomerates in monolayer cell culture systems. Particle transport to cells is calculated by simultaneous solution of Stokes Law (sedimentation) and the Stokes-Einstein equation (diffusion).

Results: The In vitro Sedimentation, Diffusion and Dosimetry model (ISDD) was tested against measured transport rates or cellular doses for multiple sizes of polystyrene spheres (20-1100 nm), 35 nm amorphous silica, and large agglomerates of 30 nm iron oxide particles. Overall, without adjusting any parameters, model predicted cellular doses were in close agreement with the experimental data, differing from as little as 5% to as much as three-fold, but in most cases approximately two-fold, within the limits of the accuracy of the measurement systems. Applying the model, we generalize the effects of particle size, particle density, agglomeration state and agglomerate characteristics on target cell dosimetry in vitro.

Conclusions: Our results confirm our hypothesis that for liquid-based in vitro systems, the dose-rates and target cell doses for all particles are not equal; they can vary significantly, in direct contrast to the assumption of dose-equivalency implicit in the use of mass-based media concentrations as metrics of exposure for dose-response assessment. The difference between equivalent nominal media concentration exposures on a μg/mL basis and target cell doses on a particle surface area or number basis can be as high as three to six orders of magnitude. As a consequence, in vitro hazard assessments utilizing mass-based exposure metrics have inherently high errors where particle number or surface areas target cells doses are believed to drive response. The gold standard for particle dosimetry for in vitro nanotoxicology studies should be direct experimental measurement of the cellular content of the studied particle. However, where such measurements are impractical, unfeasible, and before such measurements become common, particle dosimetry models such as ISDD provide a valuable, immediately useful alternative, and eventually, an adjunct to such measurements.

Figure 1

Important Particle Transport Processes for In Vitro Systems. Depiction of the important processes and system characteristics affecting particle transport rates in liquid containing in vitro systems. Transport of particles ≤ ~10 nm is controlled principally by diffusion, and can become relatively fast at particle sizes less than 10 nm. Transport of particles greater than ~200 nm can also be relatively fast, particularly for dense particles like the metals, and is controlled by sedimentation. Slower transport is expected to occur between 10 and 100 nm, where both diffusion and sedimentation together control transport, but neither process is particularly effective.

Figure 2

Size Class Distribution Data for Iron Oxide Particles. Size class distribution of iron oxide particles measured by high sensitivity DLS. Columns represent number fractions. The line represents the cumulative number fraction.

Figure 3

Simulated Silica Dose. Comparison of observed and ISDD simulated fraction of administered dose associated with cells in culture exposed to varying amounts and concentrations of 35 nm amorphous silica nanoparticles in media with heights varying from 1.1-4.5 mm. Gray bars represent measured values reported in two experiments reported by Lison et al. (2008)[32] in their Figure 5A and 5B.

Figure 4

Iron Oxide MPD Standard Curve. Standard curve for analysis of iron oxide nanoparticles in RAW 264.7 macrophages showing linear responses across a more than 100 fold increase in particle mass.

Figure 5

Simulated Transport of Iron Oxide Agglomerates. Comparison of the modeled and observed transport kinetics of iron oxide agglomerates to RAW 264.7 macrophages. Particle transport was modeled for plausible values of the agglomerate fractal dimension (DF); a DF of 2.3 provided the best correspondence between modeled and observed data. Error bars (visible only on one point) for experimental data reflect standard deviations. The media height was 1.06 mm in this experiment.

Figure 6

Particle Size and Density Effects on Target Cell Dose. Target cell doses calculated using ISDD for cells exposed 24 hours in vitro to 10 μg/mL (3 mL, media height 3.1 mm) of particles with different sizes and densities. Panels A, B and C present target cell AUC on a particle number, surface area and mass basis.

Figure 7

Transport Rates for TiO₂. ISDD calculated fraction of nano and micron scale TiO₂ particles delivered to cells over the duration of a 24 hour in vitro study with a media height 3.1 mm. Different rates of particle transport result in different time-courses for delivery to cells, which is only complete for large particles by 24 hours.

Figure 8

Media Height Effects on the Extent of Transport. ISDD calculated fraction of nano- and micron scale TiO₂ particles delivered to cells over the duration of a 24 hour in vitro study as a function of media height. Increases in media height reduce the fraction of the administered dose reaching cells, particularly for nanoparticles, where diffusion drives transport.

Figure 9

Agglomerate Fractal Dimension Effects on Transport. ISDD calculated rate of transport over a 24 hour in vitro exposure fto Fe₂O₃ agglomerates with, a primary particle size of 34.6 nm, and a fractal dimension of 2.2 (A) or 2.4 (B). The media height was 3.1 mm. Each line represents a different number of particles per agglomerate. Increasing the size and mass of agglomerates decreases diffusion rates, but may not increase sedimentation rates. For more efficiently packed agglomerates (DF = 2.4, bottom panel), but not less efficiently packed agglomerates, increases in agglomeration size can increase the rate and extent of sedimentation.