Purpose: A solidt umor embedded in host tissue is a three-dimensional arrangement of cells and extracellular matrix that acts as a sink of oxygen andce ll nutrients, thus establishing diffusional gradients. This and variations in vascular density and blood flow typically produce intratumoral regions of hypoxia andac idosis, and may result in spatially heterogeneous cell proliferation and migration.Here,we formulate the hypothesis that through thesemechanisms,microenvironmental substrate gradients may drive morphologic instability with separation of cell clusters from the tumor edge and infiltration into surrounding normal tissue. Experimental Design:We usedc omputer simulations and in vitro experiments. Results:We provide evidence that morphologic instability could be suppressed in vivo by spatially homogeneous oxygen andn utrient supply because normoxic conditions act both by decreasing gradients and increasing cell adhesion and, therefore, the mechanical forces that maintain a well-defined tumor boundary. A properly working tumor microvasculature can help maintain compact noninfiltrating tumor morphologies by minimizing oxygen andn utrient gradients. In contrast, antiangiogenic therapy, by increasing microenvironmental heterogeneity, may promotemorphologic instability, leading to invasive patterns even under conditions inwhich the overall tumor mass shrinks. Conclusions:We conclude that therapeutic strategies focused solely on reduction of vascular density may paradoxically increase invasive behavior. This theoretical model accounts for the highly variable outcome of antiangiogenic therapy inmultiple clinical trials.We propose that antiangiogenic strategies will be more consistently successful when aimedat ‘‘normalizing’’ the vasculature andw hen combinedw ith therapies that increase cell adhesion so that morphologic instability is suppresseda nd compact, noninvasive tumormorphologies are enforced

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.

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC50 concentration). For doxorubicin the effect of hypoxia and hypoglycemia (“nutrient effect”) is isolated and shown to further increase cell inhibition heterogeneity and double the IC50, both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment.

The complex, constantly evolving and multifaceted nature of cancer has made it difficult to identify unique molecular and pathophysiological signatures for each disease variant, consequently hindering development of effective therapies. Mathematical modeling and computer simulation are tools that can provide a robust framework to better understand cancer progression and response to chemotherapy. Successful therapeutic agents must overcome biological barriers occurring at multiple space and time scales and still reach targets at sufficient concentrations. A multiscale computer simulator founded on the integration of experimental data and mathematical models can provide valuable insights into these processes and establish a technology platform for analyzing the effectiveness of chemotherapeutic drugs, with the potential to cost-effectively and efficiently screen drug candidates during the drug-development process.

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The sections in this article are Introduction RES Avoidance A Statistical Model of Nanovector Surface Coverage Modeling the Forces Mediating Protein Approach and Binding Tumoral Vasculature and Hemodynamics An Invasion Percolation Model of Vasculogenesis and Hemodynamics Flow Simulations Using Anderson and Chaplain's Model Particle Dynamics within the Tumoral Vasculature Receptor–Ligand‐mediated Binding Bell's Deterministic Model A Stochastic Model Intratumoral and Cellular Drug Kinetics and Pharmacodynamics A Two‐Dimensional Model of Chemotherapy Refinements of the Model Conclusion

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