Avoiding toxicities in radiotherapy requires the knowledge of tolerable organ doses. For new, experimental fractionation schemes (e.g. hypofractionation) these are typically derived from traditional schedules using the Biologically Effective Dose (BED) model. In this report we investigate the difficulties of establishing mean dose tolerances that arise since the mean BED depends on the entire spatial dose distribution, rather than on the dose level alone. Methods: A formula has been derived to establish mean physical dose constraints such that they are mean BED equivalent to a reference treatment scheme. This formula constitutes a modified BED equation where the influence of the spatial dose distribution is summarized in a single parameter, the dose shape factor. To quantify effects we analyzed 24 liver cancer patients for whom both proton and photon IMRT treatment plans were available. Results: The results show that the standard BED equation - neglecting the spatial dose distribution - can overestimate mean dose tolerances for hypofractionated treatments by up to 20%. The shape difference between photon and proton dose distributions can cause 30-40% differences in mean physical dose for plans having identical mean BEDs. Converting hypofractionated, 5/15-fraction proton doses to mean BED equivalent photon doses in traditional 35-fraction regimens resulted in up to 10 Gy higher doses than applying the standard BED formula. Conclusions: The dose shape effect should be accounted for to avoid overestimation of mean dose tolerances, particularly when estimating constraints for hypofractionated regimens. Additionally, tolerances established for one treatment modality cannot necessarily be applied to other modalities with drastically different dose distributions, such as proton therapy. Last, protons may only allow marginal (5-10%) dose escalation if a fraction-size adjusted organ mean dose is constraining instead of a physical dose.