A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

Abstract

Abstract. The invasive capability is fundamental in determining the malignancy of a solid tumor. Revealing biomedical strategies that are able to partially decrease cancer invasiveness is therefore an important approach in the treatment of the disease and has given rise to multiple in vitro and in silico models. We here develop a hybrid computational framework, whose aim is to characterize the effects of the different cellular and subcellular mechanisms involved in the invasion of a malignant mass. In particular, a discrete Cellular Potts Model is used to represent the population of cancer cells at the mesoscopic scale, while a continuous approach of reaction-diffusion equations is employed to describe the evolution of microscopic variables, as the nutrients and the proteins present in the microenvironment and the matrix degrading enzymes secreted by the tumor. The behavior of each cell is then determined by a balance of forces, such as homotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and is mediated by the internal state of the individual, i.e. its motility. The resulting composite model quantifies the influence of changes in the mechanisms involved in tumor invasion and, more interestingly, puts in evidence possible therapeutic approaches, that are potentially effective in decreasing the malignancy of the disease, such as the alteration in the adhesive properties of the cells, the inhibition in their ability to remodel and the disruption of the haptotactic movement. We also extend the simulation framework by including cell proliferation which, following experimental evidence, is regulated by the intracellular level of growth factors. Interestingly, in spite of the increment in cellular density, the depth of invasion is not significantly increased, as one could have expected.

The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology

“…Their results agree with the in vitro and in vivo experiments conducted in [3,[25][26][27] and with other tumor-models predictions without considering haptotaxis [17,20,21,[28][29][30] and with haptotaxis [31][32][33]. Simulation results show that increases in both MDE secretion rate and the haptotaxis coefficient promote invasion [34] and inhibiting haptotaxis or the proteolysis result in less disperse invasion fronts [35] which is found in vitro case as well.…”

A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue

“…In our case, the proliferation of stalk cells, fundamental for sprout elongation, is regulated by long-range diffusing VEGF-A activity (which, instead, do not influence their migratory response due to the delta/notch-mediated lateral inhibition, as previously seen). For each cell Σ σ such as τ (Σ σ ) = S, we therefore define the present probability P Σσ for cell Σ σ to undergo mitosis with the following functional form, which resembles that used in similar approaches [54,70]:…”

On a structured multiscale model for acid-mediated tumor invasion: The effects of adhesion and proliferation

“…Most of them describe individual cell behavior and are discrete -in their majority lattice based (e.g., [29,59], also see [15] for a comprehensive review) or off-lattice (see e.g., [18,53]). The so-called hybrid models have a semidiscrete character: They specify the evolution of cells in a discrete, individual-based way and couple it to that of some tactic signal (e.g., chemoattractant concentration, density of ECM fibers), the latter being modeled in a continuous way via some reaction-(diffusion) equation, see e.g., [2,36,54]. (Semi)discrete models provide the framework for very detailed descriptions of the mechanical and biochemical processes involved in adhesion-mediated cell migration.…”