A model of the radiation-induced bystander effect based on an analogy with ferromagnets. Application to modelling tissue response in a uniform field

We propose a model of the radiation-induced bystander effect based on an analogy with magnetic systems. The main benefit of this approach is that it allowed us to apply powerful methods of statistical mechanics. The model exploits the similarity between how spin-spin interactions result in correlations of spin states in ferromagnets, and how signalling from a damaged cell reduces chances of survival of neighbour cells, resulting in correlated cell states. At the root of the model is a classical Hamiltonian, similar to that of an Ising ferromagnet with long-range interactions. The formalism is developed in the framework of the Mean Field Theory. It is applied to modelling tissue response in a uniform radiation field. In this case the results are remarkably simple and at the same time nontrivial. They include cell survival curves, expressions for the tumour control probability and effects of fractionation. The model extends beyond of what is normally considered as bystander effects. It offers an insight into low-dose hypersensitivity and into mechanisms behind threshold doses for deterministic effects.