Recent progress in 3-D computer simulation of tumor growth and treatment

D�chting, Werner

doi:10.1007/bf00046682

Cited by 6 publications

(2 citation statements)

References 5 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mathematical models based on diffusion gained then a large audience, with an increasing number of publications, about four or five per year, see the review by J. Adam in 1989 [1]. The computational effort was minimal, and consisted in producing curves of temporal or one dimensional spatial response, until the contribution by Duchting with 3D computations in 1989 [15]. Specific targetting of angiogenesis modeling as a part of tumor growth was first addressed by Chaplain and Sleeman in 1990 [8].…”

Section: Mathematical Modelingmentioning

confidence: 99%

Two Short Presentations related to Cancer Modeling

Habbal

Jabin

2009

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

View full text Add to dashboard Cite

International audience This paper contains two short presentations related to the mathematical modeling of Cancer. The first part intends to introduce a tumour-immune system interaction, which describes the early dynamics of cancerous cells, competing with the immune system, potentially leading to either the elimination of tumoral cells or to the viability of a solid tumor. The second part of the paper addresses the case where a solid tumor has grown enough to initiate angiogenesis, a process which equips the tumor with its own blood network. Nash game theory is used to model the interaction between activators and inhibitors of the angiogenesis process.

show abstract

Section: Mathematical Modelingmentioning

confidence: 99%

Two Short Presentations related to Cancer Modeling

Habbal

Jabin

2009

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

View full text Add to dashboard Cite

show abstract

“…Models based on cellular automata have been widely utilized in studies related to biological systems [14,15]. Duchting and Vogelsager proposed the application of CA for modeling cancers with radiotherapy effects [16]. Richard et al developed a simple deterministic model based on a cellular automaton [17,18], which is useful to describe the dynamics of a population of proliferating cells.…”

Section: Introductionmentioning

confidence: 99%

Optimization of irradiation interval for fractionated stereotactic radiosurgery by a cellular automata model with reoxygenation effects

Kawahara¹,

Wu²,

Watanabe³

2020

Phys. Med. Biol.

View full text Add to dashboard Cite

The current study aims to determine the optimal irradiation interval of fractionated stereotactic radiosurgery (SRS) by using an improved cellular automata (CA) model. The tumor growth process was simulated by considering the amount of oxygen and the density of blood vessels, which supplied oxygen and nutrient required for cell growth. Cancer cells died by the mitotic death process due to radiation, which was quantified by the LQ-model, or the apoptosis due to the lack of nutrients. The radiation caused increased permeation of plasma protein through the blood vessel or the breakdown of the vasculature. Consequently, these changes lead to a change in radiation sensitivity of cancer cells and tumor growth rate after irradiation. The optimal model parameters were determined with experimental data of the rat tumor volume. The tumor control probability (TCP) was defined as the ratio of the number of histories in which all cancer cells died after the irradiation to the total number of the histories per simulation. The optimal irradiation interval was defined as the irradiation interval that TCP was the maximum. For one fractionation treatment, the ratio of hypoxic cells to the total number of cancer cells kept decreasing until day 16 th after irradiation; whereas the number of surviving cancer cells begun increasing immediately after irradiation. This intricate relationship between the hypoxia (or reoxygenation) and the number of cancer cells lead to an optimal irradiation interval for the second irradiation. The optimal irradiation interval for two-fraction SRS was six days. The optimum intervals for the first-second irradiations and the second-third irradiations were five and two days, respectively, for three fraction SRS. For 4 and 5-fraction treatments, the optimum first-interval was five days, which was similar to three fraction treatment. The remaining intervals should be one day. We showed that the improved CA model could be used to optimize the irradiation interval by explicitly including the reoxygenation after irradiation in the model.

show abstract