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Grid-based cancer growth simulations

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Competition for available nutrients is known to be crucial for cancer development. Based on this fact, a model is proposed that can describe the manifold of morphologies and growth rates characteristic of tumoral growth. The formulation of a consistent set of rules governing the microscopic interactions leads to a system of coupled nonlinear iteration equations. These equations contain both deterministic and stochastic terms and are amenable to direct numerical simulation. They allow us to test the effects of such parameters as the availability, diffusivity, and binding rate of nutrients and the mobility, death, and multiplication rates of cancer cells on tumor morphology and development. Detailed numerical solutions are presented.
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The power of modern computers allows the modeling and simulation of complex biological systems. The last decade has seen the emergence of a growing number of simulations of the immune system. In this article, Franco Celada and Philip Seiden present a model that, they suggest, is rich enough to allow computer experiments to be used as practical adjuncts to the usual biological experiments, at a saving of cost and time.
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The self-regulatory interactions between cells and the vascular system are mediated by signals propagating at a finite speed. In order to build up a physical model of these processes, several features, such as storing of internal energy, nonclassical nonlinear behavior, and delay and threshold effects, have to be taken into account. Considering cells as particles in different metabolic states according to their internal energy, we have developed a model based on the local interaction simulation approach. Several numerical results, in qualitative agreement with biological observations, illustrate the applicability of the model and the method to implement it.
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We present a hybrid cellular automata-partial differential equation model of moderate complexity to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism. The model allows both temporal and two-dimensional spatial evolution of the system under investigation and is comprised of biological cell metabolism rules derived from both the experimental and mathematical modeling literature. We present numerical simulations that display behaviors which are qualitatively similar to those exhibited in tumor-immune system interaction experiments. These include spherical tumor growth, stable and unstable oscillatory tumor growth, satellitosis and tumor infiltration by immune cells. Finally, the relationship between these different growth regimes and key system parameters is discussed.
Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy
  • N Bellomo
  • E De Angelis
  • L Preziosi
N. Bellomo, E. De Angelis, and L. Preziosi. Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy. Jounal of Theoretical Medecine, 5(2):111-136, 2003.