Population TCP estimators in case of heterogeneous irradiation: a new discussion of an old problem.
OBJECTIVE
To investigate the capacity of two phenomenological expressions to describe the population tumor response in case of a heterogeneous irradiation of the tumor. The generalization of the individual tumor control probability (TCP) models to include the case of a heterogeneous irradiation is a trivial problem. However, an analytical solution that results in a closed form population TCP formula for the heterogeneous case is, unfortunately, a very complex mathematical problem. Therefore we applied a numerical approach to the problem.


METHODS
Pseudo-experimental data sets are constructed through the generation of dose distributions and population TCP data obtained by a numerical solution of a multi-dimensional integral over an individual TCP model. The capacity of the following two phenomenological - Poisson and equivalent uniform dose (EUD) based - TCP expressions: [Figure: see text] to describe the population tumor response in case of heterogeneous irradiation is investigated through their fitting to the psuedo-experimental data sets. RESULTS AND CONCLUSIONS. While both expressions produce statistically acceptable fits to the pseudo-experimental data within 2% TCP error band, the use of the second expression is preferable since it produces considerably better fits to the data sets.
Istituto Scientifico Romagnolo per lo Studio e la Cura dei Tumori, Meldola, FC, Italy. pavel.stavrev@gmail.com
Pavel
P
Stavrev
Colleen
C
Schinkel
Nadia
N
Stavreva
Brad
B
Warkentin
Marco
M
Carlone
B Gino
BG
Fallone
D004307:Dose-Response Relationship, Radiation; D006801:Humans; D008432:Mathematical Computing; D015233:Models, Statistical; D009369:Neoplasms / Q000532:radiotherapy; D011879:Radiotherapy Dosage