Spatio-temporal modeling of nanoparticle delivery to multicellular tumor spheroids.

The inefficiency of nanoparticle penetration in tissues limits the therapeutic efficacy of such formulations for cancer applications. Recent work has indicated that modulation of tissue architecture with enzymes such as collagenase significantly increases macromolecule delivery. In this study we developed a mathematical model of nanoparticle penetration into multicellular spheroids that accounts for radially dependent changes in tumor architecture, as represented by the volume fraction of tissue accessible to nanoparticle diffusion. Parameters such as nanoparticle binding, internalization rate constants, and accessible volume fraction were determined experimentally. Unknown parameters of nanoparticle binding sites per cell in the spheroid and pore shape factor were determined by fitting to experimental data. The model was correlated with experimental studies of the penetration of 40 nm nanoparticles in SiHa multicellular spheroids with and without collagenase treatment and was able to accurately predict concentration profiles of nanoparticles within spheroids. The model was also used to investigate the effects of nanoparticle size. This model contributes toward the understanding of the role of tumor architecture on nanoparticle delivery efficiency.