Cancer, tumor growth and invasion

Dynamic density functional theory of solid tumor growth: Preliminary models.

Cancer is a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT) extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth.

Investigation of the migration/proliferation dichotomy and its impact on avascular glioma invasion

Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell proliferation and motility rates. The interplay of proliferation and migration dynamics plays an important role in the invasion of these malignant tumors. We analyze the regulation of proliferation and migration processes with a lattice-gas cellular automaton (LGCA). We study and characterize the influence of the migration/proliferation dichotomy (also known as the “Go-or-Grow” mechanism) on avascular glioma invasion, in terms of invasion speed and width of the infiltration zone. We show that the invasive behavior of the (macroscopic) tumor colony is a highly complex phenomenon that cannot be extrapolated by the sole knowledge of the (microscopic) individual cell phenotype.

Identification of intrinsic in vitro cellular mechanisms for glioma invasion

Invasion of malignant glioma is a highly complex phenomenon involving molecular and cellular processes at various spatio-temporal scales, whose precise interplay is still not fully understood. In order to identify the intrinsic cellular mechanisms of glioma invasion, we study an in vitro culture of glioma cells. By means of a computational approach, based on a cellular automaton model, we compare simulation results to the experimental data and deduce cellular mechanisms from microscopic and macroscopic observables (experimental data). For the first time, it is shown that the migration/ proliferation dichotomy plays a central role in the invasion of glioma cells. Interestingly, we conclude that a diverging invasive zone is a consequence of this dichotomy. Additionally, we observe that radial persistence of glioma cells in the vicinity of dense areas accelerates the invasion process. We argue that this persistence results from a cell-cell repulsion mechanism. When glioma cell behavior is regulated through a migration/proliferation dichotomy and a self-repellent mechanism, our simulations faithfully reproduce all the experimental observations.

Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy

Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antago- nistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction–diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion.

Effect of Vascularization on Glioma Tumor Growth

Cancer describes a group of genetic and epigenetic diseases, characterized by uncontrolled proliferation of cells, leading to a variety of pathological consequences and frequently death. Cancer progression can be depicted as a sequence of traits or phenotypes that cells have to acquire if a neoplasm (benign tumor) is to become an invasive and malignant cancer. A phenotype refers to any kind of observed morphology, function or behavior of a living cell. Hanahan and Weinberg (2000) have identified six cancer cell phenotypes: unlimited proliferative potential, environmental independence for growth, evasion of apoptosis, angiogenesis, invasion, and metastasis. The attempt to define a temporal order of tumor cells acquiring new capabilities remains still unclear in general.


Integrative Physical Oncology

Cancer is arguably the ultimate complex biological system. Solid tumors are microstructured soft matter that evolves as a consequence of spatio-temporal events at the intracellular (e.g., signaling pathways, macromolecular trafficking), intercellular (e.g., cell–cell adhesion/communication), and tissue (e.g., cell–extra- cellular matrix interactions, mechanical forces) scales. To gain insight, tumor and developmental biologists have gathered a wealth of molecular, cellular, and genetic data, including immunohistochemical measurements of cell type-specific division and death rates, lineage tracing, and gain-of-function/loss-of-function mutational analyses. These data are empirically extrapolated to a diagnosis/prognosis of tissue- scale behavior, e.g., for clinical decision. Integrative physical oncology (IPO) is the science that develops physically consistent mathematical approaches to address the significant challenge of bridging the nano (nm)–micro (μm) to macro (mm, cm) scales with respect to tumor development and progression. In the current literature, such approaches are referred to as multiscale modeling. In the present article, we attempt to assess recent modeling approaches on each separate scale and critically evaluate the current ‘hybrid-multiscale’ models used to investigate tumor growth in the context of brain and breast cancers. Finally, we provide our perspective on the further development and the impact of IPO.

How Are the Mathematical and Physical Sciences Contributing to the War on Breast Cancer?

Mathematical modeling has recently been added as a tool in the fight against cancer. The field of mathematical oncology has received great attention and increased enormously, but over-optimistic estimations about its ability have created unrealistic expectations. We present a critical appraisal of the current state of mathematical models of cancer. Although the field is still expanding and useful clinical applications may occur in the future, managing over-expectation requires the proposal of alternative directions for mathematical modeling. Here, we propose two main avenues for this modeling: 1) the identification of the elementary biophysical laws of cancer development, and 2) the development of a multiscale mathematical theory as the framework for models predic- tive of tumor growth. Finally, we suggest how these new directions could contribute to addressing the current challenges of understanding breast cancer growth and metastasis.