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

Abstract

Zheng et al. (2004) developed a multiscale, two-dimensional 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.

Nonlinear simulation of the effect of microenvironment on tumor growth

“…Consequently, our results support the contention of Cristini et al (2005) that treatments that seek to normalize the tumor vasculature (by selectively "pruning" weak blood vessels with targeted anti-angiogenic therapy) may stabilize the tumor morphology by providing the tumor with increased access to nutrient. Since such treatments may also increase the accessibility of the tumors to chemotherapeutic agents (Jain, 2001;Sinek et al, 2004), our results provide additional support for the use of targeted anti-angiogenic therapy as an adjuvant therapy to chemotherapy and resection. This is currently under investigation.…”

“…hypoxic) conditions may lead to instability. Zheng et al did not fully investigate the interaction between the growth progression and the tumor microenvironment, but their work served as a building block for recent studies of the effect of chemotherapy on tumor growth by Sinek et al (2004) and for studies of morphological instability and invasion by Cristini et al (2005) and Frieboes et al (2006b). Hogea et al (2006) have also begun investigating tumor growth and angiogenesis using a level set method coupled with a continuous model of angiogenesis.…”

Nonlinear Modeling and Simulation of Tumor Growth

“…These results support the contention [55] that treatments that seek to normalize tumor vasculature (by selectively "pruning" weak blood vessels with targeted anti-angiogenic therapy) may stabilize tumor morphology by providing increased access to nutrient. Since such treatments may also increase the accessibility to chemotherapeutic agents [105,188], our results provide additional support for the use of targeted anti-angiogenic therapy as adjuvant to chemotherapy and resection.…”

“…As in [59], Zheng et al found that low-nutrient (e.g., hypoxic) conditions could lead to morphological instability. Their work served as a building block for recent studies of the effect of chemotherapy on tumor growth by Sinek et al (2004) [188] and for studies of morphological instability and invasion by Cristini et al, (2005) [55] and Frieboes et al (2006) [74]. Hogea et al (2006) [97] have also begun exploring tumor growth and angiogenesis using a level set method coupled with a continuum model of angiogenesis.…”

Computational modeling of brain tumors: discrete, continuum or hybrid?

“…Using a continuum approach, Cristini and co-workers have established a series of exploratory investigations on mathematical analysis of morphologic stability in growth and invasion of highly malignant gliomas [17,18,25,26,53,56,73]. They propose that tumor tissue dynamics can be simply regulated by two dimensionless parameters: one quantifies the competition between local cell proliferation (contributing to tumor mass growth) and cell adhesion (which tends to minimize the tumor surface area), while the other one represents tumor mass reduction related to cell death.…”