An Integrated Computational/Experimental Model of Tumor Invasion

Abstract

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability. (Cancer Res 2006; 66(3): 1597-604)

Nonlinear Modeling and Simulation of Tumor Growth

“…By considering a characteristic diffusion constant for nutrient D n ≈ 10 −5 cm 2 /s and a nutrient consumption rate υ U ≈ 1 min −1 (the latter from the observation that brain cells run out of glucose and die on that time scale), a characteristic nutrient diffusion length L ≈ 200 − 300µm is obtained. This is consistent with the observed thickness of the viable rim of cells in tumor spheroids in vitro [2,74]. For the simulation illustrated in Fig.…”

“…In vivo, for example, malignant glioma (brain tumor), apoptosis is probably negligible (λ A = 0) since mutated clones after the initial selection has occurred are typically characterized by suppression of the p53 pathway and enhanced proliferation [137], and even normal glial cells are immortal. From experiments [74] on growth of glioblastoma cell lines (the most malignant and proliferative brain tumors) as multicellular millimeter-size spheroids in vitro, it was observed that typically mitosis rate λ M ≈ 0.3 day −1 , that rate of volume loss in the necrotic core is comparable or less than the rate of volume gain from mitosis, hence the choice λ N = 0.25, and finally that minimum nutrient concentration for cell viability is a small fraction of outer uniform concentration in growth medium [74], hence the choice of a value for n N 1 (although the value of this parameter may be affected by the difficulty of reproducing the in vivo conditions in vitro). Dimensionless nutrient concentration in the blood is chosen as n C = 1, i.e., in equilibrium with the concentration in the undisturbed tissue environment.…”

“…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.…”

The impact of adhesion on cellular invasion processes in cancer and development

“…Most early work in this area involved the incorporation of adhesion via a surface tension on the tumour boundary (Byrne & Chaplain 1996;Chaplain 1996;Cristini et al 2003;Frieboes et al 2006Frieboes et al , 2007Friedman 2007;. This representation of adhesion is indirect: there is no explicit modelling of cell-cell or cell-matrix contact.…”

Intratumoral Spatial Distribution of Hypoxia and Angiogenesis Assessed by 18F-FAZA and 125I-Gluco-RGD Autoradiography

“…Indeed, some studies have demonstrated that antiangiogenic therapy may interrupt the delivery of chemotherapeutic drugs to tumors (5) and diminish the effects of radiation therapy (6). In fact, computer simulations suggest that conventional treatment, including antiangiogenic therapies, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability (7) and selecting for more malignant cells with increased metastatic potential (8). Unfortunately, some cancer cells may survive in this abnormal microenvironment and regrow to recurrent disease or become the origin of metastatic seed.…”