By representing damage induction by ionizing particles and its repair by the cell, the probabilistic two-stage model provides a detailed description of the main processes involved in cell killing by radiation. To link this model with issues of interest in hadron radiotherapy, a simple Bragg peak model is used. Energy loss, its straggling, and the attenuation of the primary particle fluence are represented in a simplified way, based on semi-phenomenological formulas and energy-loss tables. An effective version of the radiobiological model, considering residual (unrepaired) lesions only, is joined with the simple physical model to estimate cell survival along ions' penetration depth. The predicted survival ratios for CHO cells irradiated by carbon ions are presented, showing very good agreement with experimental data.Existing hadrontherapy treatment planning approaches have represented physical processes to a great detail (1) , while biological processes have been accounted for in a schematic manner only (2,3) . The need for developing detailed biology-oriented approaches has been addressed in the probabilistic two-stage model of radiobiological effects (4) , which explicitly takes into account the interplay of DNA damage induction by ionizing particles and its repair by the cell. A simplified version of the model, considering lesions not repaired by the cell only (residual damage), has been applied successfully in studying the effects of single ion tracks by analyzing survival data for irradiation by monoenergetic protons and light ions (5,6) . In the present work, this effective scheme (5) is used together with a simple physical module representing light ions' Bragg peaks, with the aims to estimate the biological effects along penetration depth and make a step towards proposing a biology-oriented treatment planning approach; a more detailed method, representing repair processes explicitly, will be subject of future work.
METHODSThe physical model starts from the energy-loss tables implemented in the SRIM-2003 code (7) . Energy-loss straggling is represented by a corresponding straggling of the actual penetration depth relative to that of a particle obeying the mean energy-loss characteristics; phenomenological range straggling formulas (8) are used in this step. The effect of nuclear reactions is included at the level of attenuating the primary particle fluence only, using nuclear interaction lengths λ reported in Ref. (8) . The products of fragmentation reactions are not followed in the present approach. The effects of scattering phenomena are not reflected, either.As a radiobiological component, the effective scheme based on the probabilistic two-stage model (4) but considering only damage not repaired by the cell (5) is used. The model has been generalized to correspond to Bragg peak irradiation conditions: At given depth x for given incident beam energy E, the single-track a(L) and combined damage probabilities b(L) dependent on LET L, derived in Ref. (5) , are weighted over LET spectra π x,E (L) generated b...