Nanomaterial transport to cells of a particular tissue was captured through the whole-body NM physiologically based pharmacokinetic simulation. For a nanomaterial to reach target tissue cells, it must first bypass the endothelial cell lining primarily through paracellular transport. Here, intercellular gaps are represented by a reflection coefficient, σv. The reflection coefficient built on previous studies by Bungay and Brenner (67), Lightfoot et al. (68), and Lewellen (69), where hydrodynamic transport was captured, which included steric exclusion (ϕ); hindrances to diffusion, drag, and pressure drop across the sphere [G′(α)]; and frictional interactions with the wall [F′(α)]. The NM must travel from the blood vasculature (Cv) to the interstitial space (CIS) through equationdCvdt=QtCLUVVv(QtQL)CV VV(1σV)QLCVVVkadendoCV+(kdesendoAmem)VV (22)where the tissue blood flow (Qt) and lung NM concentration CLUV serve as inputs to this compartment. The NM will interact with the endothelial cell membrane (Amem) of that tissue’s compartment via the adsorption (kadendo) and desorption (kdesendo) rate constants determined from in vitro data. The vasculature reflection coefficient (σV) serves as guidance for the NM to enter the interstitial space given bydCISdt=(1σV)QLCVVISkadCIS+kdesCmem(23)where the individual tissue cells (epithelial and macrophages) will interact with the NM through the predetermined in vitro rate constants kad and kdes for their cell membranes (Cmem). The flow rate into the interstitial space was set to the lymphatic flow rate, and vasculature interstitial volumes (VIS) guided the concentration for this compartment. Once the NM enters the tissue cell membrane compartmentdCmemdt=kadCISkintCmemkdesCmem(24)it will desorb via the desorption rate constant (kdes) or will be internalized into the cell space via the internalization rate constant (kint). Once inside the cell space, the NM can be thus degraded or sequestered within the cellular environment (Ccell).dCcelldt=kintCmemkdegCcell(25)

All tissue compartments here were described as a series of differential equations designed to solve for concentrations using the MATLAB ODE solver.

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