1985
DOI: 10.1016/0303-2647(85)90061-9
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Recent progress in modelling and simulation of three-dimensional tumor growth and treatment

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Cited by 64 publications
(40 citation statements)
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“…This, combined with in vitro experiments using tumor spheroids, sandwich culture, etc., and high power confocal or multiphoton laser microscopy that enables tracking of individual cells in space and time, has brought about the possibility of modeling single-cell-scale phenomena and then using the techniques of upscaling to obtain information about the large-scale phenomena of tumor growth. There are several upscaling techniques; the most popular ones are cellular automata [31,119,120,121,122,123,124,125,126,127,128,129,130,131,132], lattice Boltzmann methods [9,133], agent-based [129,134], extended Potts [135], and the stochastic (Markov chain combined with Fokker-Planck equations) approach [97,134,136,137,138]. As in the case of phase-averaged continuum models discussed in the previous section, the main difficulty with the discrete cell-based models lies in their parameterization, and thus these models are more appropriate for giving qualitative insights, instead of detailed quantitative predictions.…”
Section: Discrete Cell Population Modelsmentioning
confidence: 99%
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“…This, combined with in vitro experiments using tumor spheroids, sandwich culture, etc., and high power confocal or multiphoton laser microscopy that enables tracking of individual cells in space and time, has brought about the possibility of modeling single-cell-scale phenomena and then using the techniques of upscaling to obtain information about the large-scale phenomena of tumor growth. There are several upscaling techniques; the most popular ones are cellular automata [31,119,120,121,122,123,124,125,126,127,128,129,130,131,132], lattice Boltzmann methods [9,133], agent-based [129,134], extended Potts [135], and the stochastic (Markov chain combined with Fokker-Planck equations) approach [97,134,136,137,138]. As in the case of phase-averaged continuum models discussed in the previous section, the main difficulty with the discrete cell-based models lies in their parameterization, and thus these models are more appropriate for giving qualitative insights, instead of detailed quantitative predictions.…”
Section: Discrete Cell Population Modelsmentioning
confidence: 99%
“…Having described their general formulation we will now describe one or two specific examples of automaton models that have appeared in the literature. One of the first models considering discrete cell population migration using a complex cell cycle model, which is still considered to be sophisticated, was that of Duchting and Vogelsaenger [119], who conducted a series of three-dimensional simulations using the model in order to determine the effect of radiotherapy on tumors in a quantitative, well-parameterized manner (see the appendix for the description of their model). Another of the early models that appears to be reasonably well parameterized is that by Qi et al [120], which is one of the least complicated models of its type and describes the minimal cellular automata rules that would reproduce the Gompertz law of cancer growth.…”
Section: Discrete Cell Population Modelsmentioning
confidence: 99%
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“…Stochastic computer tumour models were first developed in the early 1980s and 1990s by groups Donaghey et al, Duechting and Vogelsaenger, Smolle and Stettner, and Kocher [16][17][18][19][20]. These were the first models to peruse individual (or grouped) cell division using Monte Carlo methods, to grow a tumour and simulate radiotherapy, and in some cases start to implement oxygenation-related parameters.…”
Section: Tumour and Treatment Modellingmentioning
confidence: 99%
“…2), we discriminate between grid-based and lattice-free particle methods. Cellular Automata are structured grids where every grid point represents a single cell [4,15]. In single particle models each cell is represented by a particle which can freely move in space [5,35,49].…”
Section: Introductionmentioning
confidence: 99%