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International Conference on Mathematical Biology and

Annual Meeting of The Society for Mathematical Biology,

July 27-30, 2009

University of British Columbia, Vancouver

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Program

Poster PS54A
Harald Kempf
Frankfurt Institute for Advanced Studies
Title Spatio-temporal dynamics of tumour spheroid irradiation
Abstract We present an agent-based approach to the modelling of cellular dynamics within tumour spheroids during irradiation treatment. Our model aims at bridging the gap between theory and experiment and thus is based on experimentally accessible parameters. Within our agent-based approach cells are represented as instances of a C++ cell-class. Each cell advances through a realistic cell cycle in response to external and internal stimuli such as the concentration of nutrients and the pressure upon the cell by neighbouring cells. The model makes use of a dynamic Delaunay triangulation in order to derive the cell neighbourhood topology while its dual, a Voronoi tessellation, is employed in order to calculate the contact surfaces between adjacent cells. Cell-cell interaction is handled within the contact model of Johnson, Kendal and Roberts which employs experimentally accessible parameters such as cell elastic modulus and Poisson\'s ratio. Forces acting on a cell are summed up and integrated using Newton\'s equation in an overdamped approach. An adaptive integration stepsize algorithm is employed in order to maximize performance. In a first approach we use a stochastic model for cell damage upon irradiation: Defined probabilities exist for the occurrence of cluster damage or non-lethal damage to a cell\'s DNA. Affected cells show a reaction depending on the radiation characteristics, local tissue oxygenation, DNA content and cell status. After irradiation cells with complex cluster damage to their DNA will undergo interphasic death. Cells with non-lethal damage to their DNA will rest at the G2/M-checkpoint until successfully repaired or undergo clonogenic death if repair failed multiple times. Damage repair capability depends on availability of nutrients amongst other factors. Accumulation of multiple repairable hits to the DNA in a cell will also lead to interphasic death. As a results of irradiation treatment a dynamic reaction is triggered in the tumour system which can be studied in detail. Reoxygenation of the tumour volume and a decrease in pressure due to cell necrosis lead to excessive regrowth after irradiation as previously quiescent cells are reactivated. A distinct resynchronisation of the cell cycle is observed which can be exploited within fractionated irradiation treatment. The inability of DNA-damaged cells to pass the G2/M-checkpoint leads to an accumulation of cells in the G2 phase interchanging the ratio of cells in G1 to cells in G2. Fractionation of the radiation dose changes the degree of tumour control considerably depending on the applied fractionation scheme. Results of our simulation environment are directly comparable to experimental results. Ultimate goal is a model which is able to relate the deposited radiation dose to the dynamical effects of partial tumour destruction. Such a model could be used to optimise treatment planning and to determine a tumour control probability.
CoauthorsMarcus Bleicher, Michael Meyer-Hermann
LocationWoodward Lobby (Monday-Tuesday)