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The Glazier–Graner–Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study

Ariel Balter, Roeland M.H. Merks, Nikodem J. Poplawski, Maciej Swat and James A. Glazier. 2008. The Glazier–Graner–Hogeweg Model: Extensions, Future Directions, and Opportunities for Further Study. In: Katarzyna A. Rejniak, Alexander Anderson and Mark Chaplain (eds). Single Cell Based Models in Biology and Medicine. Birkhaüser-Verlag, Basel, Boston and Berlin. Series “Mathematics and Biosciences in Interaction.” Chapter (ii).3. pp. 137-150.

One of the reasons for the enormous success of the Glazier–Graner–Hogeweg Model (GGH ) model is that it is a framework for model building rather than a specific biological model. Thus new ideas constantly emerge for ways to extend it to describe new biological (and non-biological) phenomena. The GGH model automatically integrates exten-sions with the whole body of prior GGH work, a flexibility which makes it unusually simple and rewarding to work with. In this chapter we discuss some possible future directions to extend GGH modeling. We discuss off-lattice extensions to the GGH model, which can treat fluids and solids, new classes of model objects, approaches to increasing computational efficiency, parallelization, and new model-development platforms that will accelerate our ability to generate successful models. We also discuss a non-GGH, but GGH- inspired, model of plant development by Merks and collaborators, which uses the Hamiltonian and Monte-Carlo approaches of the GGH but solves them using Finite Element (FE) methods. doi:10.1007/978-3-7643-8123-3_7

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