Recent progress in modelling and simulation of three-dimensional tumor growth and treatment

Düchting, W.; Vogelsaenger, Th.

doi:10.1016/0303-2647(85)90061-9

Cited by 63 publications

(40 citation statements)

References 6 publications

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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%

“…In this section we describe the model due to Duchting and Vogelsaenger [119] (see Figure 7). Each cell can stay in each stage for a given amount of time before moving to the next stage.…”

Section: Appendixmentioning

confidence: 99%

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Mathematical Models of Avascular Tumor Growth

Roose¹,

Chapman²,

Maini³

2007

SIAM Rev.

513

353

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Abstract. This review will outline a number of illustrative mathematical models describing the growth of avascular tumors. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modeling of avascular tumor development are outlined together with a list of key questions.

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Section: Discrete Cell Population Modelsmentioning

confidence: 99%

Section: Discrete Cell Population Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Models of Avascular Tumor Growth

Roose¹,

Chapman²,

Maini³

2007

SIAM Rev.

513

353

View full text Add to dashboard Cite

show abstract

“…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%

Monte Carlo radiotherapy simulations of accelerated repopulation and reoxygenation for hypoxic head and neck cancer

Harriss-Phillips

Bezak²,

Yeoh³

2011

BJR

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Objective: A temporal Monte Carlo tumour growth and radiotherapy effect model (HYP-RT) simulating hypoxia in head and neck cancer has been developed and used to analyse parameters influencing cell kill during conventionally fractionated radiotherapy. The model was designed to simulate individual cell division up to 10 8 cells, while incorporating radiobiological effects, including accelerated repopulation and reoxygenation during treatment. Method: Reoxygenation of hypoxic tumours has been modelled using randomised increments of oxygen to tumour cells after each treatment fraction. The process of accelerated repopulation has been modelled by increasing the symmetrical stem cell division probability. Both phenomena were onset immediately or after a number of weeks of simulated treatment. Results: The extra dose required to control (total cell kill) hypoxic vs oxic tumours was 15-25% (8-20 Gy for 562 Gy per week) depending on the timing of accelerated repopulation onset. Reoxygenation of hypoxic tumours resulted in resensitisation and reduction in total dose required by approximately 10%, depending on the time of onset. When modelled simultaneously, accelerated repopulation and reoxygenation affected cell kill in hypoxic tumours in a similar manner to when the phenomena were modelled individually; however, the degree was altered, with non-additive results. Simulation results were in good agreement with standard linear quadratic theory; however, differed for more complex comparisons where hypoxia, reoxygenation as well as accelerated repopulation effects were considered. Conclusion: Simulations have quantitatively confirmed the need for patient individualisation in radiotherapy for hypoxic head and neck tumours, and have shown the benefits of modelling complex and dynamic processes using Monte Carlo methods.

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“…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%

SEM++: A particle model of cellular growth, signaling and migration

et al. 2014

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We present a discrete particle method to model biological processes from the sub-cellular to the inter-cellular level. Particles interact through a parametrized force field to model cell mechanical properties, cytoskeleton remodeling, growth and proliferation as well as signaling between cells. We discuss the guiding design principles for the selection of the force field and the validation of the particle model using experimental data. The proposed method is integrated into a multiscale particle framework for the simulation of biological systems.

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Recent progress in modelling and simulation of three-dimensional tumor growth and treatment

Cited by 63 publications

References 6 publications

Mathematical Models of Avascular Tumor Growth

Mathematical Models of Avascular Tumor Growth

Monte Carlo radiotherapy simulations of accelerated repopulation and reoxygenation for hypoxic head and neck cancer

SEM++: A particle model of cellular growth, signaling and migration

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