A Novel Analytical Population Tumor Control Probability Model Includes Cell Density and Volume Variations: Application to Canine Brain Tumor

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