Displaying similar documents to “Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology.”

Stochastic models of progression of cancer andtheir use in controlling cancer-related mortality

Marek Kimmel, Olga Gorlova (2003)

International Journal of Applied Mathematics and Computer Science

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A construction of a realistic statistical model of lung cancer risk and progression is proposed. The essential elements of the model are genetic and behavioral determinants of susceptibility, progression of the disease from precursor lesions through early (localized) tumors to disseminated disease, detection by various modalities, and medical intervention. Using model estimates as a foundation, mortality reduction caused by early-detection and intervention programs can be predicted under...

The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids

Simon D. Angus, Monika J. Piotrowska (2010)

Applicationes Mathematicae

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A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis...

Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth

Jan Poleszczuk, Urszula Foryś (2009)

Applicationes Mathematicae

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We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe...

Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model

Maciej Cytowski, Akio Ito, Marek Niezgódka (2009)

Banach Center Publications

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In the present paper, we consider an approximate system of one-dimensional simplified tumor invasion model, which was originally proposed by Chaplain and Anderson in [chaplain-anderson-03]. The simplified tumor invasion model is composed of PDE and ODE. Actually, the PDE is the balance equation of the density of tumor cells and the ODE describes the dynamics of concentration of extracellular matrix. In this model, we take into account that the random motility of the density of tumor...

Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis

V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan, V. Selitser, Z. Agur (2010)

Mathematical Modelling of Natural Phenomena

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Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules...

Tumour angiogenesis model with variable vessels' effectiveness

Jan Poleszczuk, Iwona Skrzypczak (2011)

Applicationes Mathematicae

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We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical...

Application of Hybrid Models to Blood Cell Production in the Bone Marrow

N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

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A hybrid model of red blood cell production, where cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models, is proposed. Spatial organization and regulation of red blood cell production (erythropoiesis) are investigated. Normal erythropoiesis is simulated in two dimensions, and the influence on the output of the model of some parameters involved...