Three-dimensional pattern generation applied to spheroidal tumor growth in a nutrient medium

Düchting, W.; Vogelsaenger, Th.

doi:10.1016/0020-7101(81)90050-7

Cited by 54 publications

(14 citation statements)

References 7 publications

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“…differential equations-based) models (Wolfram, 1988) (see Section 4.2). Possibly one of the earliest CA models for tumour growth was introduced by Duchting and Vogelsanger (1981) -see Araujo and McElwain (2004) for a detailed history up to the present. Qi et al (1993) made a leap by formulating a stochastic two-dimensional CA that took into account proliferation, nutrient supply, mechanical pressures (and thus motion of cells within the tumour) and immune surveillance rules.…”

Section: Non-traditional Avascular Growth Modelsmentioning

confidence: 99%

Mathematical Models of Cancer

Patel

Nagl

2006

Cancer Bioinformatics

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Modelling and simulation are indispensable for the study of biological systems as dynamical ensembles, made up of a large number of interacting components and exhibiting complex non-linear behaviour. These methods provide the tools for data and knowledge-based in silico predictions of tumour behaviour and hypothesis formulation in both preclinical and clinical settings (see also Chapter 1 and later chapters in this section).The number of mathematical models that describe solid tumour dynamics has increased dramatically since the first instances in the 1920s, and more rapid advances have become possible through the arrival of accessible and fast computation. However, there are no universally accepted models yet, although a large number exist, and none are capable of satisfactorily capturing the rich dynamic behaviour of tumours. Therefore, a real clinical use of mathematical modelling has not yet materialized, and critics have warned that most models of cancer systems are too simplistic and therefore potentially too dangerous for use in the medical field (Byrne, 1999;Gatenby and Maini, 2003). With the advent of post-genomic cancer research, a multidisciplinary research ethos and new computational approaches, this situation is set to change rapidly. Modellers have now reached a juncture where tumour biology is meeting face-to-face with systems science. This chapter will provide an overview of existing mathematical cancer models and the methodologies applied for their development. Ordinary, partial and stochastic differential equation models, as well as phenomenological methods, will be discussed critically and compared with discrete, interaction-based approaches such as cellular automata.Cancer Bioinformatics: From therapy design to treatment Edited by Sylvia Nagl

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Section: Non-traditional Avascular Growth Modelsmentioning

confidence: 99%

Mathematical Models of Cancer

Patel

Nagl

2006

Cancer Bioinformatics

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“…Models utilising MC methods to simulate cell propagation and the effects of oxygenation of radiotherapy response began in the 1980s [6,7]. A stochastic cell-based spatial and/or temporal model in the current era is being perused by researchers such as Stamatakos, Dionysiou, Borkenstein, Harting, Daşu and Titz [8][9][10][11][12][13].…”

Section: Modelling Hypoxic Tumour Responsementioning

confidence: 99%

Altered fractionation outcomes for hypoxic head and neck cancer using theHYP-RTMonte Carlo model

Harriss-Phillips

Bezak²,

Yeoh³

2013

BJR

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Objective: Altered fractionation radiotherapy is simulated on a set of virtual tumours to assess the total doses required for tumour control compared with clinical head and neck data and the doses required to control hypoxic vs well-oxygenated tumours with different radiobiological properties. Methods:The HYP-RT model is utilised to explore the impact of tumour oxygenation and the onset times of accelerated repopulation (AR) and reoxygenation (ROx) during radiotherapy. A biological effective dose analysis is used to rank the schedules based on their relative normal tissue toxicities.

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“…Duchting et al's. work was the first to explore cell by cell modelling of a tumour cell population in a growth medium (tumour spheroids), with the inclusion of cellular oxygenation parameters as well as many cellular kinetic and radiation schedule parameters (six schedules reported on) available for modification by the user [7–10]. Kocher et al's work [11, 12] also considered cellular oxygenation by modelling a regular array of vessels in 3D within a tumour mass, with 3 different schedules simulated.…”

Section: In Silico Cancer Treatment Modelsmentioning

confidence: 99%

In SilicoModelling of Treatment-Induced Tumour Cell Kill: Developments and Advances

Marcu

Harriss-Phillips

2012

Computational and Mathematical Methods in Medicine

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Mathematical and stochastic computer (in silico) models of tumour growth and treatment response of the past and current eras are presented, outlining the aims of the models, model methodology, the key parameters used to describe the tumour system, and treatment modality applied, as well as reported outcomes from simulations. Fractionated radiotherapy, chemotherapy, and combined therapies are reviewed, providing a comprehensive overview of the modelling literature for current modellers and radiobiologists to ignite the interest of other computational scientists and health professionals of the ever evolving and clinically relevant field of tumour modelling.

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Three-dimensional pattern generation applied to spheroidal tumor growth in a nutrient medium

Cited by 54 publications

References 7 publications

Mathematical Models of Cancer

Mathematical Models of Cancer

Altered fractionation outcomes for hypoxic head and neck cancer using theHYP-RTMonte Carlo model

In SilicoModelling of Treatment-Induced Tumour Cell Kill: Developments and Advances

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