Analytical investigation of the possibility of parameter invariant TCP-based radiation therapy plan ranking

To analytically investigate the possibility of a parameter invariant ranking of radiotherapy (RT) plans based on comparing the tumor control probabilities (TCPs) produced by the competing plans for different values of the radiobiological model parameters determining the radiation response.Individual TCP models based on the Single hit model of cell kill and on the linear-quadratic (LQ) model of cell damage, with and without repopulation, are considered. The tumor dose distributions in case of heterogeneous dose irradiation are described by a Gaussian distribution function on the basis of which a TCP expression is derived depending only on the mean dose to the tumor and its standard deviation and the TCP model parameters.It is shown that in case of homogeneous dose to the tumor the plan ranking in terms of TCP is parameter invariant. In case of heterogeneous dose to the tumor there are cases when the plan ranking is parameter invariant and cases when the parameter invariance is violated. An interesting dependence of the extent of the parameter invariance violation on the model of cell kill as well as on the size and repopulation rate of the tumor is noted.We conclude that in many cases RT plan ranking in terms of TCP is parameter invariant. However, since there exist cases where the parameter invariance is lost an investigation of the specific plans to be ranked should be performed applying the proposed approach.