Biological optimization of heterogeneous dose distributions in systemic radiotherapy.

The standard computational method developed for internal radiation dosimetry is the MIRD (medical internal radiation dose) formalism, based on the assumption that tumor control is given by uniform dose and activity distributions. In modern systemic radiotherapy, however, the need for full 3D dose calculations that take into account the heterogeneous distribution of activity in the patient is now understood. When information on nonuniform distribution of activity becomes available from functional imaging, a more patient specific 3D dosimetry can be performed. Application of radiobiological models can be useful to correlate the calculated heterogeneous dose distributions to the current knowledge on tumor control probability of a homogeneous dose distribution. Our contribution to this field is the introduction of a parameter, the F factor, already used by our group in studying external beam radiotherapy treatments. This parameter allows one to write a simplified expression for tumor control probability (TCP) based on the standard linear quadratic (LQ) model and Poisson statistics. The LQ model was extended to include different treatment regimes involving source decay, incorporating the repair "micro" of sublethal radiation damage, the relative biological effectiveness and the effective "waste" of dose delivered when repopulation occurs. The sensitivity of the F factor against radiobiological parameters (alpha, beta, micro) and the influence of the dose volume distribution was evaluated. Some test examples for 131I and 90Y labeled pharmaceuticals are described to further explain the properties of the F factor and its potential applications. To demonstrate dosimetric feasibility and advantages of the proposed F factor formalism in systemic radiotherapy, we have performed a retrospective planning study on selected patient case. F factor formalism helps to assess the total activity to be administered to the patient taking into account the heterogeneity in activity uptake and dose distribution, giving the same TCP of a homogeneous prescribed dose distribution. Animal studies and collection of standardized clinical data are needed to ascertain the effects of nonuniform dose distributions and to better assess the radiobiological input parameters of the model based on LQ model.