Models for the bystander effect in gradient radiation fields: Range and signalling type.

Bystander responses to radiation are responsible for a significant fraction of cell death, but are not included in the conventional linear-quadratic (LQ) radiobiological model. Strong dose gradients in radiation fields affect the distribution of bystander signals and can be used to decrease the survival of cancer cells. Predictive models incorporating bystander effects are needed to design the dose gradients in modulated fields to improve cancer treatments. Fundamental questions concern the nature and range of bystander signalling. Some authors propose bystander signals are carried by diffusing molecular factors expressed into the extracellular medium and that strong dose gradients drive their diffusion. Others propose bystander effects occur between neighbouring cells through gap-junctions, leaving no universal agreement. Here we test three assumptions concerning the effective range of bystander signals using both average and local measures of survival. Model 1 assumes short range signalling (e.g. gap-junction mediated) proportional to the local dose gradient, without relying on diffusion across the extracellular medium; Model 2 assumes metabolite diffusion governed by Fick's second law with either negative or both signs of bystander effect; Model 3 assumes that the extent of signal production is dependent on the average of the dose gradient over the field and that the signals have long range distribution. A single bystander parameter for each model was fitted to observed average survival of cancer cells in uniform and modulated fields. All models gave better fits than the classical LQ model. Model 2 fitted best with one sign of bystander effect on survival. Model 3 gave the best overall fit of average survival. The models were then used to predict local survival and survival as a function of dose in modulated fields, using independent datasets, without changing the bystander parameter. Model 3 gave the best overall prediction. This study demonstrates that the bystander effect can be controlled by design of the radiation field modulation.