SU-E-T-429: Uncertainties of Cell Surviving Fractions Derived From Tumor-Volume Variation Curves




To evaluate uncertainties of cell surviving fraction reconstructed from tumor-volume variation curves during radiation therapy using sensitivity analysis based on linear perturbation theory.


The time dependent tumor-volume functions V(t) have been calculated using a twolevel cell population model which is based on the separation of entire tumor cell population in two subpopulations: oxygenated viable and lethally damaged cells. The sensitivity function is defined as S(t)=[δV(t)/V(t)]/[δx/x] where δV(t)/V(t) is the time dependent relative variation of the volume V(t) and δx/x is the relative variation of the radiobiological parameter x. The sensitivity analysis was performed using direct perturbation method where the radiobiological parameter x was changed by a certain error and the tumor-volume was recalculated to evaluate the corresponding tumor-volume variation. Tumor volume variation curves and sensitivity functions have been computed for different values of cell surviving fractions from the practically important interval S2=0.1-0.7 using the two-level cell population model.


The sensitivity functions of tumor-volume to cell surviving fractions achieved a relatively large value of 2.7 for S2=0.7 and then approached zero as S2 is approaching zero Assuming a systematic error of 3-4% we obtain that the relative error in S2 is less that 20% in the range S2=0.4-0.7. This Resultis important because the large values of S2 are associated with poor treatment outcome should be measured with relatively small uncertainties. For the very small values of S2<0.3, the relative error can be larger than 20%; however, the absolute error does not increase significantly.


Tumor-volume curves measured during radiotherapy can be used for evaluation of cell surviving fractions usually observed in radiation therapy with conventional fractionation.