Accuracy-dependent dose-constraints and dose-based safety margins for organs-at-risk in radiotherapy

Abstract

Background and purpose

Geometrical uncertainties in radiotherapy are generally accounted for by margins for tumors, but their effect on organs-at-risk (OARs) is often ignored. We developed a model that incorporates dose- and geometry-based uncertainties in OAR planning using dose constraints.

Materials and methods

Radiotherapy uncertainties cause real dose-volume histograms (DVHs) to spread around the planned DVH. With a published OAR dose constraint D(V_crit) < D_crit such that complication probability < Y%, real differences from planned D_crit can be described by mean- (MD_Dcrit) and standard deviations (SD_Dcrit). Assuming complications are associated with the worst DVHs, New dose constraints that maintain complication probability can be derived for new treatments:D_crit,New = D_crit,publ + Φ⁻¹(1 - Y%) * (SD_Dcrit,publ - SD_Dcrit,New) + (MD_Dcrit,publ - MD_Dcrit,New),with Φ⁻¹(x) the inverse cumulative normal distribution function. Setting SD_Dcrit,New = MD_Dcrit,New = 0 in the recipe yields the “True” critical dose, and D_crit,True - D_crit,publ can be considered a dose-based safety margin (DSM).

As hypothetical example, we estimated MD_Dcrit and SD_Dcrit values by simulating geometric errors in our clinical treatment plans and adding dose-based uncertainty. Over 1000 OARs with 108 different regular- and hypo-fractionation constraints were simulated. We assumed accuracy SDs to change from 2.5mm/3% to 1.5mm/2%.

Results

Results varied per OAR, fractionation, and constraint-type. If our 2.5mm/3% MD_Dcrit and SD_Dcrit values approximated dose-constraint studies, on average the DSM would be 4.5 Gy (18%) and our dose constraints would increase with 1.2 Gy (5%).

Conclusions

We introduced a first model relating dose constraints and complication probabilities with treatment uncertainties and safety margins for OARs. Among other things, it quantified how higher constraints can be applied with increasing radiotherapy accuracy.