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Seven different radiobiological dose-response models have been compared with regard to their ability to describe experimental data. The first four models, namely the critical volume, the relative seriality, the inverse tumor and the critical element models are mainly based on cell survival biology. The other three models: the Lyman (Gaussian distribution), the parallel architecture and the Weibull distribution models are semi-empirical and rather based on statistical distributions. The maximum likelihood estimation was used to fit the models to experimental data and the χ2-distribution, AIC criterion and F-test were applied to compare the goodness-of-fit of the models. The comparison was performed using experimental data for rat spinal cord injury. Both the shape of the dose-response curve and the ability of handling the volume dependence were separately compared for each model. All the models were found to be acceptable in describing the present experimental dataset (p > 0.05). For the white matter necrosis dataset, the Weibull and Lyman models were clearly superior to the other models, whereas for the vascular damage case, the Relative Seriality model seems to have the best performance although the Critical volume, Inverse tumor, Critical element and Parallel architecture models gave similar results. Although the differences between many of the investigated models are rather small, they still may be of importance in indicating the advantages and limitations of each particular model. It appears that most of the models have favorable properties for describing dose-response data, which indicates that they may be suitable to be used in biologically optimized intensity modulated radiation therapy planning, provided a proper estimation of their radiobiological parameters had been performed for every tissue and clinical endpoint.

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 (ΔPapprox.) and those calculated by the RayStation show close agreement, which proves the high importance of the D50 parameter in specifying clinical response levels. Finally, the presented findings show that the behavior of ΔPapprox. looks sensible because, for both of the models that were used (Poisson and Probit), it significantly approaches the real ΔP 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.

This present paper presents an analytical description and numerical simulations of the influence of macroscopic intercell dose variations and intercell sensitivity variations on the probability of controlling the tumour. Computer simulations of tumour control probability accounting for heterogeneity in dose and radiation sensitivity were performed. An analytical expression for tumor control probability accounting for heterogeneity in sensitivity was also proposed and validated against simulations. The results show good agreement between numerical simulations and the calculated TCP using the proposed analytical expression for the case of a heterogeneous dose and sensitivity distributions. When the intratumour variations of dose and sensitivity are taken into account, the total dose required for achieving the same level of control as for the case of homogeneous distribution is only slightly higher, the influence of the variations in the two factors taken into account being additive. The results of this study show that the interplay between cell or tumour variation in the sensitivity to radiation and the inherent heterogeneity in dose distribution is highly complex and therefore should be taken into account when predicting the outcome of a given treatment in terms of tumor control probability.

There are many tools available that are used to evaluate a radiotherapy treatment plan, such as isodose distribution charts, dose volume histograms (DVH), maximum, minimum and mean doses of the dose distributions as well as DVH point dose constraints. All the already mentioned evaluation tools are dosimetric only without taking into account the radiobiological characteristics of tumors or OARs. It has been demonstrated that although competing treatment plans might have similar mean, maximum or minimum doses they may have significantly different clinical outcomes (Mavroidis et al. 2001). For performing a more complete treatment plan evaluation and comparison the complication-free tumor control probability (P+) and the biologically effective uniform dose (D ) have been proposed (Kallman et al. 1992a, Mavroidis et al. 2000). The D concept denotes that any two dose distributions within a target or OAR are equivalent if they produce the same probability for tumor control or normal tissue complication, respectively (Mavroidis et al. 2001)...