Embodiments of the present disclosure are directed to treatment planning systems for a radiotherapy apparatus. In one implementation, a treatment planning system may include a computational processor configured to apply a set of instructions to an input data set. The input data set may include a three-dimensional dose distribution for delivery by the radiotherapy apparatus to a volume to be irradiated, a three-dimensional volume image characterizing tissue types within the volume to be irradiated, and a set of apparatus parameters which characterize the radiotherapy apparatus. The set of instructions may include a computational process configured to output a treatment plan for delivery of the dose distribution by the radiotherapy apparatus, by optimising a function representing a time-dependent response of the tissue types to an applied radiation.
