# Program Information

## Uncertainties of Cell Surviving Fractions Derived From Tumor-Volume Variation Curves

### A Chvetsov*, University of Washington, Seattle, WA

## Presentations

**SU-E-T-429 Sunday 3:00PM - 6:00PM Room: Exhibit Hall**

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

Methods: The time dependent tumor-volume functions V(t) have been calculated using a two-level 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)=[Î´V(t)/V(t)]/[Î´x/x] where Î´V(t)/V(t) is the time dependent relative variation of the volume V(t) and Î´x/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 Sâ‚‚=0.1-0.7 using the two-level cell population model.

Results: The sensitivity functions of tumor-volume to cell surviving fractions achieved a relatively large value of 2.7 for Sâ‚‚=0.7 and then approached zero as Sâ‚‚ is approaching zero Assuming a systematic error of 3-4% we obtain that the relative error in Sâ‚‚ is less that 20% in the range S2=0.4-0.7. This result is important because the large values of Sâ‚‚ 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.

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

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