%0 Journal Article
%T Using State Variables to Model the Response of Tumour Cells to Radiation and Heat: A Novel Multi-Hit-Repair Approach
%A Stephan Scheidegger
%A Hans U. Fuchs
%A Kathrin Zaugg
%A Stephan Bodis
%A Rudolf M. F¨ąchslin
%J Computational and Mathematical Methods in Medicine
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/587543
%X In order to overcome the limitations of the linear-quadratic model and include synergistic effects of heat and radiation, a novel radiobiological model is proposed. The model is based on a chain of cell populations which are characterized by the number of radiation induced damages (hits). Cells can shift downward along the chain by collecting hits and upward by a repair process. The repair process is governed by a repair probability which depends upon state variables used for a simplistic description of the impact of heat and radiation upon repair proteins. Based on the parameters used, populations up to 4-5 hits are relevant for the calculation of the survival. The model describes intuitively the mathematical behaviour of apoptotic and nonapoptotic cell death. Linear-quadratic-linear behaviour of the logarithmic cell survival, fractionation, and (with one exception) the dose rate dependencies are described correctly. The model covers the time gap dependence of the synergistic cell killing due to combined application of heat and radiation, but further validation of the proposed approach based on experimental data is needed. However, the model offers a work bench for testing different biological concepts of damage induction, repair, and statistical approaches for calculating the variables of state. 1. Introduction In radiation oncology, mathematical models are used to describe clonogenic survival, tumour control probabilities (TCP), or normal tissue complication probabilities (NTCP). The most widely used model for cell survival is the linear-quadratic (LQ) model. The (originally empiric) model was first used by Lea and Catcheside [1] to fit radiation chromosome damage. The model is based on the observation that the logarithmic plot of the surviving cell fraction (with = number of viable cells after and number of cells before radiation) versus radiation dose can be described by a linear and a quadratic dose-dependent term (). Based on this relationship, adaption of doses for hyper- or hypofractionated radiotherapies can be calculated (e.g., application of the BED concept in clinical oncology [2]). There is also a certain need to calculate equivalent doses in the case of application of moderate hyperthermia (40¨C43ˇăC) in combination with radiation (HT-RT). But the extension to combined therapies requires some knowledge of the underlying dynamic processes (radiation and heat induced formation of cellular damages, repair, etc.). Theories about DNA lesion formation or cell survival (e.g., Chadwick and Leenhouts [3]) led to mechanistic interpretations of the LQ
%U http://www.hindawi.com/journals/cmmm/2013/587543/