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In radiation therapy tumor size, and thus also volume, has a significant impact on the local control of tumors. Moreover, tumor volume is a significant prognostic factor for modelling and predicting therapeutic outcomes in cancer treatment. In research, the distribution of tumor volumes in patient populations has so far remained widely unexplored. In this work, the frequency distributions of maximum diameter of tumors for various types of cancer was studied based on SEER data and it was explored if they can be modelled using Weibull distributions. Further, actual volume data were obtained directly from computer tomography (CT) datasets and the frequency distributions of tumor volumes and maximum diameters were explored and a link between them was found. In cancer research, tumors are often modelled as ellipsoids. In order to verify the appropriateness of using ellipsoids as a model, to the obtained three-dimensional data, ellipsoids were fitted and the resulting volumes and diameters analysed. Finally, NSCLC tumor diameters were Monte Carlo simulated using tumor growth and incidence models. A comparison of the simulated tumor diameter distributions with observed SEER data yielded the determination of tumor growth rates.

Purpose: In this modelling study we pursued two main goals. The first was to establish a new CTV-to-PTV expansion which considers the closest and most critical organ at risk (OAR). The second goal was to investigate the impact of the planning target volume (PTV) margin size on the tumor control probability (TCP) dependent on the geometrical setup uncertainties. The aim was to achieve a smaller margin expansion close to the OAR while allowing a moderately larger expansion in less critical areas further away from the OAR and most importantly while maintaining the TCP. Methods and Materials: Imaging data of radiation therapy (RT) plans from pet dogs which had undergone RT for brain tumor were used to estimate the clinic specific rotational setup uncertainties. A Monte-Carlo methodology used to quantify the implications of those uncertainties on the TCP. A computational CTV-to-PTV expansion method based on probability density was established. All required software modules were developed and integrated into a software package which directly interacts with the Varian Eclipse treatment planning system. Results: The rotational setup uncertainties were obtained from 44 dog patients. Their frequency distributions were analysed, and the mean values and standard deviations were determined. To investigate the impact on the TCP, several uniform and non-isotropic PTV targets were created. Standardized RT plans with equal optimization constraints were defined and automatically applied and calculated on these targets. The resulting TCPs were then evaluated and compared. Conclusion: The non-isotropic margins were found to result in larger TCPs with smaller margin excess volume. Further we have presented an additional application of the newly established CTV-to-PTV expansion method for radiation therapy of the spinal axis of human patients.

TCP models based on Poisson statistics are characterizing the distribution of the surviving clonogens. It enables the calculation of TCP for individuals. In order to describe clinically observed survival data of patient cohorts it is necessary to extend the model. This is typically done by either incorporating variations of various model parameters, or by using an empirical logistic model. The purpose of this work is the development of an analytical population TCP model by mechanistic extension of the Poisson model.The frequency distribution of GTVs is used to incorporate tumor volume variations into the TCP model. Additionally the tumor cell density variation is incorporated. Both versions of the population TCP model were fitted to clinical data and compared to literature. It was shown that clinically observed brain tumor volumes of dogs undergoing radiotherapy are exponentially distributed. The average GTV size was 3.37 cm$^3$. Fitting the population TCP model including the volume variation LQ and track-event model yielded $\alpha=0.36 ~Gy^{-1}$, $\beta=0.045~Gy^{-2}$, $a=0.9$, $T_D=5.0~d$ and $p = 0.36~Gy^{-1}$, $q=0.48~Gy^{-1}$, $a=0.80$, $T_D = 3.0~d$, respectively. Fitting the population TCP model including both the volume and cell density variation yields $\alpha=0.43~Gy^{-1}$, $\beta=0.0537~Gy^{-2}$, $a=2.0$, $T_D=3.0~d$, $\sigma=2.5$ and $p=0.43~ Gy^{-1}$, $q=0.55~Gy^{-1}$, $a=2.0$, $T_D=2.0~d$, $\sigma=3.0$ respectively. Two sets of radiobiological parameters were obtained which can be used for quantifying the TCP for radiation therapy of dog brain tumors. We established a mechanistic link between the poisson statistics based individual TCP model and the logistic TCP model. This link can be used to determine the radiobiological parameters of patient specific TCP models from published fits of logistic models to cohorts of patients.