Author: Carlo Greco, Joep Stroom, Sandra Vieira ðšâð¬
Affiliation: Champalimaud Center for the Unknown ð
Purpose: RTP safety margins are generally based on geometrical uncertainties alone and not directly on clinical outcome. Here we use clinical dose-constraint data to generate dosimetric margins for OARs including radio-sensitivity uncertainties.
Methods: Considering a group of equal OARs all planned to a dose constraint Dp, the OARs actually receiving the most damaging treatment will be developing the NTCP% complications associated with Dp. Assuming that treatment effects Ep are normally distributed due to geometric, dosimetric, and biological uncertainties, we can derive a fixed threshold effect, Et, that separates cases with and without toxicity:
Et = Ep + Ί-1(1-NTCP) * SD(Ep),
with Ί-1 the inverse cumulative normal distribution. To obtain practical doses D, we used the LQ-model for E to derive threshold dose Dt as function of Dp, SD(Dp), NTCP, α/β, and radio-sensitivity variations SD(α). It can then be shown that Dt equals the dose giving 50% complication probability (D50), and is independent of treatment uncertainties. Finally, the difference
MD = Dt â Dp,
is our desired dosimetric safety margin for all treatment uncertainties (SD(Dp), SD(α)), that depends on clinical outcome data (NTCPs).
We estimated SD(Dp) by simulating dosimetric (3%) and geometric (2.5mm) variations in our treatment plans. We then fitted SD(α) to published dose constraints and D50 values for 24 OARs. We subsequently calculated margin MD for situations with and without SD(α) and determined margin and constraint changes when accuracy improves 1%/1mm.
Results: Average SD(Dp) for >1000 simulated OARs were about 9%, yielding an average SD(α) of 15%. Average MD is larger with SD(α) (22%ÃDp) than without (15%ÃDp), but mean Dp-increments on 1%/1mm improvement are smaller (2.4% vs 4.5%) because radio-sensitivity variations will downplay the effect of dosimetric and geometric variations.
Conclusion: We introduced NTCP-validated, dosimetric OAR safety margins taking into account the interplay between dosimetric, geometric, and radio-sensitivity variations.