Background

ISDD applies well established, long-used principles of diffusional and gravitational transport of particles in viscous media to calculate the movement of particles from the media to the bottom of a vessel where cells reside. The net rate of transport downward toward the bottom of the vessel is calculated within a single partial differential equation, which is solved numerically to calculate the fraction of material transported from media to the bottom of the vessel. Simulations are conducted using commonly available inputs for monodisperse particles: temperature, media density and viscosity, media height, hydrodynamic particle size in the test media, and particle density. Simulations of agglomerates also require two additional parameters describing how the primary particles are packed to form the agglomerate. The model produces a time-course of particle surface area, number and mass transported to the bottom of the vessel, referred to as the delivered dose, which can be compared to measured values in a cell free environment. The delivered dose can also be compared to measured amounts. Ultimately, ISDD is a computational framework for describing particle transport that can be linked to models describing cellular processes affecting uptake of particles ((Hinderliter et al. (2014)).Particle transport to cells is calculated by simultaneous solution of Stokes Law (sedimentation) and the Stokes-Einstein equation (diffusion).

Appropriate Uses

ISDD is applicable to static liquid systems of poorly soluble particles and their agglomerates.  Primary particles and their agglomerates should be roughly spherical (not rods or fibers). Starting concentrations for the system should be uniform (i.e. well mixed particle solution placed on cells).  

Required Parameters

Media density, media viscosity, media height, media temperature, primary particle diameter, primary particle density, agglomerate characteristics.  Agglomerates can be modeled several different ways: 1) Using measured primary particle characteristics and assumed values of the packing factor and fractal dimension; 2) primary particle characteristics and measured agglomerate density. Parameters are described in detail below and in the model code.

Limitations 

There are a number of limitations to be considered when using ISDD. Particle settling must not generate turbulence (low Reynolds numbers) and dynamic agglomeration or other particle interactions are not accounted for in the model. The model may not be appropriate to apply where advection occurs in the cell culture system or where there has been significant advective or mechanical mixing over the course of the experiment. Formulated for spheres or particles that can be adequately described as spheres, ISDD should not be used for fibers without additional modification and testing. Changes in the agglomeration or aggregation state of modeled particles would be expected to lead to larger discrepancies between modeled and observed target cell doses.

ISDD reports the theoretical total delivered dose, but does not account for particles that may be washed off of cells during processing. The model also does not account for the uptake of particles by cells, which is cell specific. These two factors alone can lead to differences between measured cellular doses and calculated cellular doses. Calculated doses should be interpreted cautiously as the theoretical dose of particles to the cell membrane, where they are assumed to "stick."

Supporting Publications

Teeguarden, J.G., P.M. Hinderliter, G. Orr, B.D. Thrall, and J.G. Pounds, Particokinetics in vitro: dosimetry considerations for in vitro nanoparticle toxicity assessments. Toxicological Sciences, 2007. 95(2): p. 300-12.

Hinderliter, P.M., Minard, K.R., Orr, G. et al. ISDD: A computational model of particle sedimentation, diffusion and target cell dosimetry for in vitro toxicity studies. Part Fibre Toxicol 7, 36 (2010). https://doi.org/10.1186/1743-8977-7-36

Cohen, J.M., J.G. Teeguarden, and P. Demokritou, An integrated approach for the in vitro dosimetry of engineered nanomaterials. Part Fibre Toxicol, 2014. 11: p. 20.