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Two-Dimensional Chemotherapy Simulations Demonstrate Fundamental Transport and Tumor Response Limitations Involving Nanoparticles

J. Sinek, H. Frieboes, X. Zheng and V. Cristini
University of California, Irvine, US

virtual cancer, in silico chemotherapy, tumor simulation

Zheng et al. (2004) developed a multiscale, twodimensional tumor simulator with the capability of showing tumoral lesion progression through the stages of diffusion-limited dormancy, neo-vascularization (angiogenesis) and consequent rapid growth and tissue invasion. In this paper we extend their simulator to describe delivery of chemotherapeutic drugs to a highly perfused tumoral lesion and the tumor cells’ response to the therapy. We perform 2-D simulations based on a self-consistent parameter estimation that demonstrate fundamental convective and diffusive transport limitations in delivering anticancer drug into tumors, whether this delivery is via free drug administration (e.g., intravenous drip), or via 100 nm nanoparticles injected into the bloodstream, extravasating and releasing the drug that then diffuses into the tumoral tissue, or via smaller 1–10 nm nanoparticles that are capable of diffusing directly and targeting the individual tumor cell. Even in a best-case scenario involving: constant (“smart”) drug release from the nanoparticles; a homogenous tumor of one cell type, which is drug-sensitive and does not develop resistance; targeted nanoparticle delivery, with resulting low host tissue toxicity; and for model parameters calibrated to ensure sufficient drug or nanoparticle blood concentration to rapidly kill all cells in vitro; our analysis shows that fundamental transport limitations are severe and that drug levels inside the tumor are far less than in vitro, leaving large parts of the tumor with inadequate drug concentration. A comparison of cell death rates predicted by our simulations reveals that the in vivo rate of tumor shrinkage is several orders of magnitude less than in vitro for equal chemotherapeutic carrier concentrations in the blood serum and in vitro, and after some shrinkage the tumor may achieve a new mass equilibrium far above detectable levels.We also demonstrate that adjuvant anti-angiogenic therapy “normalizing” the vasculature may ameliorate transport limitations, although leading to unwanted tumor fragmentation. Finally, our results suggest that small nanoparticles equipped with active transport mechanisms (e.g., chemotaxis) would overcome the predicted limitations and result in improved tumor response.

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