Predictive Models of Diffusive Nanoparticle Transport in 3-Dimensional Tumor Cell Spheroids

The rapidly evolving nanotechnology field highlights the need of better understanding the relationship between nanoparticle (NP) properties and NP transport in solid tumors. The present study tested the hypothesis that the diffusive transport and spatial distribution of NP can be predicted based on the following parameters: interstitial NP diffusivity, NP–cell interaction parameters (cell surface binding capacity, rate constants of association, dissociation, and internalization). We (a) established the models and equations; (b) experimentally measured, in monolayer pharynx FaDu cells, the model parameters for three NP formulations (negatively charged polystyrene beads, near-neutral liposomes, and positively charged liposomes, with respective diameter of 20, 110, and 130 nm); and (c) used the models and parameters to simulate NP diffusion in 3-dimensional (3D) systems. We next measured the NP concentration–depth profiles in tumor cell spheroids, an avascular 3D system, and found good agreement between model-simulated and experimental data in spheroids for the negative and neutral NP (>90% predicted data points at three NP concentrations and three treatment times were within the 95% confidence intervals of experimental data). Model performance was inferior for positive liposomes containing a fusogenic lipid. The present study demonstrated the possibility of using in vitro NP–cell biointerface data in monolayer cultures with in silico studies to predict the NP diffusive transport and concentration–time–depth profiles in 3D systems, as functions of NP concentrations and treatment times. Extending this approach to include convective transport may yield a cost-effective means to predict the NP delivery and residence in solid tumors.