Evaluation of the generalized gamma as a tool for treatment planning optimization

Purpose: The aim of that work is to study the theoretical behavior and merits of the Generalized Gamma (generalized dose response gradient) as well as to investigate the usefulness of this concept in practical radiobiological treatment planning. Methods: In this study, the treatment planning system RayStation 1.9 (Raysearch Laboratories AB, Stockholm, Sweden) was used. Furthermore, radiobiological models that provide the tumor control probability (TCP), normal tissue complication probability (NTCP), complication-free tumor control probability ( P + ) and the Generalized Gamma were employed. The Generalized Gammas of TCP and NTCP, respectively were calculated for given heterogeneous dose distributions to different organs in order to verify the TCP and NTCP computations of the treatment planning system. In this process, a treatment plan was created, where the target and the organs at risk were included in the same ROI in order to check the validity of the system regarding the objective function P + and the Generalized Gamma. Subsequently, six additional treatment plans were created with the target organ and the organs at risk placed in the same or different ROIs. In these plans, the mean dose was increased in order to investigate the behavior of dose change on tissue response and on Generalized Gamma before and after the change in dose. By theoretically calculating these quantities, the agreement of different theoretical expressions compared to the values that the treatment planning system provides could be evaluated. Finally, the relative error between the real and approximate response values using the Poisson and the Probit models, for the case of having a target organ consisting of two compartments in a parallel architecture and with the same number of clonogens could be investigated and quantified. Results: The computations of the RayStation regarding the values of the Generalized Gamma and the objective function ( P + ) were verified by using an independent software. Furthermore, it was proved that after a small change in dose, the organ that is being affected most is the organ with the highest Generalized Gamma. Apart from that, the validity of the theoretical expressions that describe the change in response and the associated Generalized Gamma was verified but only for the case of small change in dose. Especially for the case of 50% TCP and NTCP, the theoretical values (Δ P approx. ) and those calculated by the RayStation show close agreement, which proves the high importance of the D 50 parameter in specifying clinical response levels. Finally, the presented findings show that the behavior of Δ P approx. looks sensible because, for both of the models that were used (Poisson and Probit), it significantly approaches the real Δ P around the region of 37% and 50% response. The present study managed to evaluate the mathematical expression of Generalized Gamma for the case of non-uniform dose delivery and the accuracy of the RayStation to calculate its values for different organs. Conclusion: A very important finding of this work is the establishment of the usefulness and clinical relevance of Generalized Gamma. That is because it gives the planner the opportunity to precisely determine which organ will be affected most after a small increase in dose and as a result an optimal treatment plan regarding tumor control and normal tissue complications can be found.