To accurately describe the radiation response over a wide dose and ionization density range Binomial and Poisson statistics have been combined with the recently developed potentially Repairable-Conditionally-Repairable (RCR) damage response model and the combination is shown to have several advantages for the accurate description of the cell survival at both low and very high doses and LET's, especially when compared with the classical Linear and Linear Quadratic cell survival models. Interestingly, the potentially and conditionally repairable damage types of the RCR model may also be linked to the two major radiation damage repair pathways of eukaryotic cells namely Non Homologous End Joining (NHEJ) and Homologous Recombination (HR) respectively. In addition it describes the damage interaction of low and high LET damage in different dose fractions more accurately than any other model (cf. (6) and Fig. 7d). This is of considerable importance when describing the response of tumors and normal tissues during pencil beam scanning with light ion beams where low and high LET dose fractions from the plateau and Bragg peak can interact synergistically when being delivered quasi simultaneously. In conclusion, considering the unique biological properties of light ion beams such as their increased effect on hypoxic tumors, their microdosimetric energy deposition heterogeneity and their pencil beam energy deposition kernels the largest clinical advantages are obtained with medium LET beams (≍ 20–50 eV/nm). This applies even for radiation resistant tumors, at least when the goal is to maximize tumor cure with minimal adverse reactions in normal tissues.

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.

This study was carried out in order to derive the radiobiological parameters of the dose-response relation for the obliteration of arteriovenous malformation (AVM) following single fraction stereotactic radiotherapy. Furthermore, the accuracy by which the linear Poisson model predicts the probability of obliteration and how the haemorrhage history, location and volume of the AVM influence its radiosensitivity are investigated. The study patient material consists of 85 patients who received radiation for AVM therapy. Radiation-induced AVM obliterations were assessed on the basis of post-irradiation angiographies and other radiological findings. For each patient the dose delivered to the clinical target volume and the clinical treatment outcome were available. These data were used in a maximum likelihood analysis to calculate the best estimates of the parameters of the linear Poisson model. The uncertainties of these parameters were also calculated and their individual influence on the dose-response curve was studied. AVM radiosensitivity was assumed to be the same for all the patients. The radiobiological model used was proved suitable for predicting the treatment outcome pattern of the studied patient material. The radiobiological parameters of the model were calculated for different AVM locations, bleeding histories and AVM sizes. The range of parameter variability had considerable effect on the dose-response curve of AVM. The correlation between the dosimetric data and their corresponding clinical effect could be accurately modelled using the linear Poisson model. The derived response parameters can be introduced into the clinical routine with the calculated accuracy assuming the same methodology in target definition and delineation. The known volume dependence of AVM radiosensitivity was confirmed. Moreover, a trend relating AVM location with its radiosensitivity was observed.

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.

This work provides a description of a new interaction, cross-section-based model for radiation-induced cellular inactivation, sublethal damage, DNA repair and cell survival, with the ability to more accurately elucidate different radiation-response phenomena. The principal goal of this work is to describe the damage-induction cross sections, as well as repair and survival, as Poisson processes with two main types of damage: mild damage that can be rapidly handled by the most basic repair processes; and more complex damage requiring longer repair times and the high-fidelity homologous recombination (HR) repair process to ensure accuracy and safety in the survival. This work is unique in its use of Poisson statistics to quantify the main repairable cell compartments that are exposed to simple and more complex sublethal hits, the cross section of which determines what is homologically and non-homologically repairable. The new method is applied to central radiation damage and survival data, such as in vitro cellular repair and survival with key DNA repair genes knocked out, low-dose hypersensitivity (LDHS), change in survival over the cell cycle, and variation with linear energy transfer (LET) for densely ionizing ions, all results supporting our basic assumptions. Among the results, it was shown that less than 1% of the simple DSBs are lethal at approximately 2 Gy and below for sparsely ionizing radiations, but their δ-electron track ends of between 1.5 and 0.5 keV can deliver 0.5 MGy to a few hundred nm3 volumes, mainly due to multiple scatter detours and multiple secondary electrons. They can cause dual double-strand breaks (DSBs) on the periphery of nucleosomes that are the most common multiply damaged sites, with an average of 1–2 δ-electron track ends per cell nucleus at 2 Gy. LDHS is most likely due to the normal lack of fast, efficient repair of sublethal damage below approximately 0.5 Gy, and requires largely intact key DNA repair genes to achieve significant repair recovery at higher doses. The new repair model describes this phenomenon quite accurately. Cells with key non-homologous end joining (NHEJ) genes knocked-out, lose LDHS but provoke HR repair, and cells with HR genes knocked out may lose some LDHS, but provoke NHEJ repair. The DNA duplication during the S phase results in a direct doubling as well of the total and sublethal hit cross sections. For the lowest LET carbon ions, NHEJ is reduced to where it is almost eliminated at maximum relative biological effectiveness (RBE), while HR is induced more than by X rays, due to complex damage and misrepair of DSBs produced by numerous δ electrons. The use of a lower LET such as electrons or photons during the final week of radiation treatment may potentially maximize complication-free cure. Optimally-designed weekly fractionation schedules are proposed to maximize the DNA repair potential in normal tissues. Additionally, the optimal therapeutic ion species, LET, apoptosis and permanent growth arrest/senescence window is identified with helium, lithium and boron ions and LETs at approximately 15–55 eV/nm, to maximize these quantities in the tumor and minimize them in the normal tissues, resulting in a very high probability of complication-free cure.