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Effective Density of Agglomerates

At the time ISDD was developed, the effective density of agglomerates was estimated from parameters describing how primary particles packed to form agglomerates.  DeLoid and colleagues from the Harvard laboratory of Dr. Phil Demokritou developed a simple centrifugation method for measuring the effective density of agglomerates.  This is the preferred method for applying ISDD to the simulation of agglomerates. For many particles, the agglomeration density estimated by the model and the value measured experimentally are similar. For information on the method and its application, please refer to the publications below.
DeLoid, G., J.M. Cohen, T. Darrah, R. Derk, L. Rojanasakul, G. Pyrgiotakis, W. Wohlleben, and P. Demokritou, Estimating the effective density of engineered nanomaterials for in vitro dosimetry. Nat Commun, 2014. 5: p. 3514.
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.

Principles of Use

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.
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., K.R. Minard, G. Orr, W.B. Chrisler, B.D. Thrall, J.G. Pounds, and J.G. Teeguarden, ISDD: A computational model of particle sedimentation, diffusion and target cell dosimetry for in vitro toxicity studies. Part Fibre Toxicol, 2010. 7(1): p. 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.

Dose Translation Across Systems

Applied in conjunction with in vivo dosimetry models such as the Multipath Particle Deposition Model (MPPD), ISDD can be used as the initial step in translating cellular doses of nanoparticles between in vitro and in vivo systems (Teeguarden et al., 2014, below).
Justin Teeguarden with Supercomputer
General Scheme for Translating Doses Across
in vitro and in vitro systems
  This application area can grow as models of systemic particokinetics emerge.
In Vitro-In Vitro Dose Translation
Differences in media viscosity, temperature, and the height of media over cultured cells can influence cellular dose.  Differences in media may also lead to differences in particle corona’s or particle agglomeration states between otherwise similar in vitro systems. Without some understanding of how significant these differences may be, differences in results across systems may be attributed to experimental variability rather than differences in dose.

Translating doses between in vitro systems is relatively straight forward when experimental measures of dose are not available for direct comparison.   Particles should be characterized in the test media. The primary particle size, particle density, and agglomerate particle size should be measured. Ideally, the effective density of the agglomerates should also be measured (see Effective Density of Agglomerates tab). Media height and other parameters should also be acquired in both systems. Using these parameters as inputs, ISDD can be run and predicted doses can be compared and dose-response curves between systems be compared on the same units of dose.
In Vitro-In Vivo Dose Translation
Exposures, be they inhaled concentration (ppm),  oral exposures (mass/kg), injected doses (mass/kg) or other route, cannot be compared directly to exposures in liquid systems (μg/ml).  With advances computational nanomaterial dosimetry, namely ISDD, physiologically based pharmacokinetic (PBPK) models and inhalation particle dosimetry models such as MPPD, comparisons between in vitro and in vivo systems can be made with some confidence.  These comparisons are best made using equivalent measures of dose and exposure between the systems, for example, the surface area of particles delivered to cells.

The framework and process for conducting dose translations across in vitro and in vivo systems is straight forward (see Figure), but can involve additional, non-trivial experimental work.  An example of translation of doses between inhalation exposures in mice, in vitro cell culture studies, and human occupational studies was published by our group (Teeguarden et al., 2014, below). After calculating cellular doses for the in vitro systems (e.g. surface area per cell, or surface area of cells), doses are either measured directly, for example for systemic tissues like the liver, or calculated, for example for the inhalation route. The Multipath Particle Deposition Model, MPPD (ARA, Raleigh NC) is publically available computational dosimetry model for the human, monkey, rat and mouse respiratory tract.  This model can be used, in conjunction with particle/aerosol characteristics, to calculate the delivered dose for particles in units of particle mass, number or surface area per lung surface area, and per macrophage.  These metrics of exposure can then be compared directly to the same metric of exposure calculated for in vitro systems with ISDD, its equivalent, or measured directly.
Teeguarden, J.G., V.B. Mikheev, K.R. Minard, W.C. Forsythe, W. Wang, G. Sharma, N. Karin, S.C. Tilton, K.M. Waters, B. Asgharian, et al., Comparative iron oxide nanoparticle cellular dosimetry and response in mice by the inhalation and liquid cell culture exposure routes. Part Fibre Toxicol, 2014. 11(1): p. 46.

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