A novel analytical population tumor control probability model includes cell density and volume variations: application to canine brain tumor

Abstract

Purpose: Tumor control probability (TCP) models based on Poisson statistics characterize the distribution of surviving clonogens. Thus enabling the calculation of TCP for individuals. To mathematically describe clinically observed survival data of patient cohorts it is necessary to extend the Poisson TCP model. This is typically done by either incorporating variations of 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 Possion model. Methods and materials: The frequency distribution of gross tumor volumes was used to incorporate tumor volume variations into the TCP model. Additionally the tumor cell density variation was incorporated. Both versions of the population TCP model were fitted to clinical data and compared to existing literature. Results: It was shown that clinically observed brain tumor volumes of dogs undergoing radiotherapy are distributed according to an exponential distribution. The average gross tumor volume size was 3.37 cm3. Fitting the population TCP model including the volume variation using linear-quadratic and track-event model yieldedα=0.36Gy--1a, β=0.045Gy--2, a=0.9yr--1, TD=5.0d,and p=.36Gy--1, q=0.48Gy--1, a=0.80yr--1, TD=3.0d, respectively. Fitting the population TCP model including both the volume and cell density variation yielded α=0.43Gy--1, β=0.0537Gy--2, a=2.0yr--1, TD=3.0d, σ=2.5,and p=.43Gy--1, q=0.55Gy--1, a=2.0yr--1, TD=2.0d, σ=3.0,respectively. Conclusions: Two sets of radiobiological parameters were obtained which can be used for quantifying the TCP for radiation therapy of brain tumors in dogs. 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.