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Abstract

Understanding tumor development crossing multiple spatial-temporal scales is of great practical importance to better fighting against cancers. It is hard to attack this problem with pure biological means. In recent decades, computer-based modeling and simulation techniques have been playing an increasingly important role in addressing it. After reviewing the literature, however, we notice that existing tumor models are either highly simplified or too complicated to be scaled to large tumor systems.

In light of these problems, we have developed a software environment TUGME to facilitate the multi-scale modeling and simulation of tumor development based on the agent-based method. The most important feature of this software environment is its flexibility which enables straight-forward model reuse and extension. Tumor models of TUGME are hybrid as discrete and continuous approaches are coupled to model the discrete and continuous nature of the tumor system. TUGME is highly modularized, thus changing one module only requires few or no modifications to the others.

Using TUGME, we have simulated the avascular growth of a multicellular tumor spheroid system of the tumor cell line, EMT6/Ro. Our tumor models treat individual tumor cells as single agents. The cell morphology and topology are represented by a 3D Voronoi tessellation. Cell motion, which is driven by mechanical interactions between a cell and its surroundings, is modeled using Newton's second law. Oxygen and glucose are treated as nutrients for cell energy production. Their transport and metabolism by cells are described by reaction-diffusion equations. Cell proliferation is defined considering the availability of both oxygen and glucose as well as the availability of space as its controllers. Based on these models, a series of simulations have been carried out. Good agreements between our simulations and experiments indicate the applicability of TUGME and the validity of our tumor models. In addition, the investigation of the invasive tumor morphology under different nutrient conditions shows that a lower nutrient concentration gives rise to a rougher tumor surface.

One of the key challenges of agent-based multi-scale cancer modeling and simulation is the sharp increase of the computational cost of model solving with increasing system size (the number of tumor cells). According to our tests, the main computational bottleneck of our tumor models consists in solving the linear system of cell motion. To better understand this problem, we look into the properties of the matrix of the linear system. Our conclusion is that its matrix is extremely sparse, symmetric and positive-definite. These properties can help find a more efficient solver for the linear system. This work can be important reference for people who intend to work on individual-cell-oriented cancer modeling.