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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.

Radiobiological models for estimating normal tissue complication probability (NTCP) are increasingly used in order to quantify or optimize the clinical outcome of radiation therapy. A good NTCP model should fulfill at least the following two requirements: (a) it should predict the sigmoid shape of the corresponding dose-response curve and (b) it should accurately describe the probability of a specified response for arbitrary non-uniform dose delivery for a given endpoint as accurately as possible, i.e. predict the volume dependence. In recent studies of the volume effect of a rat spinal cord after irradiation with narrow and broad proton beams the authors claim that none of the existing NTCP models is able to describe their results. Published experimental data have been used here to try to quantify the change in the effective dose (D(50)) causing 50% response for different field sizes. The present study was initiated to describe the induction of white matter necrosis in a rat spinal cord after irradiation with narrow proton beams in terms of the mean dose to the effective volume of the functional subunit (FSU). The physically delivered dose distribution was convolved with a function describing the effective size or, more accurately, the sensitivity distribution of the FSU to obtain the effective mean dose deposited in it. This procedure allows the determination of the mean D(50) value of the FSUs of a certain size which is of interest for example if the cell nucleus of the oligodendrocyte is the sensitive target. Using the least-squares method to compare the effective doses for different sizes of the functional subunits with the experimental data the best fit was obtained with a length of about 9 mm. For the non-uniform dose distributions an effective FSU length of 8 mm gave the optimal fit with the probit dose-response model. The method could also be used to interpret the so-called bath and shower experiments where the heterogeneous dose delivery was used in the convolution process. The assumption of an effective FSU size is consistent with most of the effects seen when different portions of the rat spinal cord are irradiated to different doses. The effective FSU length from these experiments is about 8.5 +/- 0.5 mm. This length could be interpreted as an effective size of the functional subunits in a rat spinal cord, where multiple myelin sheaths are connected by a single oligodendrocyte and repair is limited by the range of oligodendrocyte progenitor cell diffusion. It was even possible to suggest a more likely than uniform effective FSU sensitivity distribution from the experimental data.

The full potential of biologically optimized radiation therapy can only be maximized with the prediction of individual patient radiosensitivity prior to treatment. Unfortunately, the available biological parameters, derived from clinical trials, reflect an average radiosensitivity of the examined populations. In the present study, a breast cancer patient of stage I-II with positive lymph nodes was chosen in order to analyse the effect of the variation of individual radiosensitivity on the optimal dose distribution. Thus, deviations from the average biological parameters, describing tumour, heart and lung response, were introduced covering the range of patient radiosensitivity reported in the literature. Two treatment configurations of three and seven biologically optimized intensity-modulated beams were employed. The different dose distributions were analysed using biological and physical parameters such as the complication-free tumour control probability (P(+)), the biologically effective uniform dose (D), dose volume histograms, mean doses, standard deviations, maximum and minimum doses. In the three-beam plan, the difference in P(+) between the optimal dose distribution (when the individual patient radiosensitivity is known) and the reference dose distribution, which is optimal for the average patient biology, ranges up to 13.9% when varying the radiosensitivity of the target volume, up to 0.9% when varying the radiosensitivity of the heart and up to 1.3% when varying the radiosensitivity of the lung. Similarly, in the seven-beam plan, the differences in P(+) are up to 13.1% for the target, up to 1.6% for the heart and up to 0.9% for the left lung. When the radiosensitivity of the most important tissues in breast cancer radiation therapy was simultaneously changed, the maximum gain in outcome was as high as 7.7%. The impact of the dose-response uncertainties on the treatment outcome was clinically insignificant for the majority of the simulated patients. However, the jump from generalized to individualized radiation therapy may significantly increase the therapeutic window for patients with extreme radio sensitivity or radioresistance, provided that these are identified. Even for radiosensitive patients a simple treatment technique is sufficient to maximize the outcome, since no significant benefits were obtained with a more complex technique using seven intensity-modulated beams portals.

Background: The spinal cord, known for its strongly serial character and high sensitivity to radiation even when a small segment is irradiated, is one of the most critical organs at risk to be spared during radiation therapy. To compare the sensitivity of different parts of the spinal cord, data for radiation myelopathy have been used., Material and Methods: In the present study, the relative seriality model was fitted to two different datasets of clinical radiation myelitis concerning cervical spinal cord after treating 248 patients for head and neck cancer and thoracic spinal cord after treating 43 patients with lung carcinoma. The maximum likelihood method was applied to fit the clinical data. The model parameters and their 68% confidence intervals were calculated for each dataset. The alpha/beta ratio for the thoracic cord was also was also found to be 0.9 (0-3.0) Gy., Results: The dose-response curve for the more sensitive cervical myelopathy is well described by the parameters D(50)=55.9 (54.8-57.1) Gy, gamma=6.9 (5.0-9.2), s=0.13 (0.07-0.24), whereas the thoracic myelopathy is described by the parameters D(50)=75.5 (70.5-80.8) Gy, gamma=1.1 (0.6-1.6), s=36 (3.3-infinity)., Discussion and Conclusions: Large differences in radiation response between the cervical and thoracic region of spinal cord are thus observed: cervical myelopathy seems to be characterized by medium seriality, while thoracic spinal cord is characterized by a highly serial dose-response. The much steeper dose-response curve for cervical spinal cord myelopathy can be interpreted as a higher number of functional subunits consistent with a higher amount of white matter close to the brain.