A study of objective functions for organs with parallel and serial architecture.

An objective function analysis when target volumes are deliberately enlarged to account for tumour mobility and consecutive uncertainty in the tumour position in external beam radiotherapy has been carried out. The dose distribution inside the tumour is assumed to have logarithmic dependence on the tumour cell density which assures an iso-local tumour control probability. The normal tissue immediately surrounding the tumour is irradiated homogeneously at a dose level equal to the dose D(R) delivered at the edge of the tumour. The normal tissue in the high dose field is modelled as being organized in identical functional subunits (FSUs) composed of a relatively large number of cells. Two types of organs--having serial and parallel architecture are considered. Implicit averaging over intrapatient normal tissue radiosensitivity variations is done. A function describing the normal tissue survival probability S0 is constructed. The objective function is given as a product of the total tumour control probability (TCP) and the normal tissue survival probability S0. The values of the dose D(R) which result in a maximum of the objective function are obtained for different combinations of tumour and normal tissue parameters, such as tumour and normal tissue radiosensitivities, number of cells constituting a normal tissue functional unit, total number of normal cells under high dose (D(R)) exposure and functional reserve for organs having parallel architecture. The corresponding TCP and S0 values are computed and discussed.