On cold spots in tumor subvolumes

Losses in tumor control are estimated for cold spots of various "sizes" and degrees of "cold dose." This question is important in the context of intensity modulated radiotherapy where differential dose-volume histograms (DVHs) for targets that abut a critical structure often exhibit a cold dose tail. This can be detrimental to tumor control probability (TCP) for fractions of cold volumes even as small as 1%, if the cold dose is lower than the prescribed dose by substantially more than 10%. The Niemierko-Goitein linear-quadratic algorithm with γ₅₀ slope 1-3 was used to study the effect of cold spots of various degrees (dose deficit below the prescription dose) and size (fractional volume of the cold dose). A two-bin model DVH has been constructed in which the cold dose bin is allowed to vary from a dose deficit of 1%-50% below prescription dose and to have volumes varying from 1% to 90%. In order to study and quantify the effect of a small volume of cold dose on TCP and effective uniform dose (EUD), a four-bin DVH model has been constructed in which the lowest dose bin, which has a fractional volume of 1%, is allowed to vary from 10% to 45% dose deficit below prescription dose. The highest dose bin represents a simultaneous boost. For fixed size of the cold spot the calculated values of TCP decreased rapidly with increasing degrees of cold dose for any size of the cold spot, even as small as 1% fractional volume. For the four-subvolume model, in which the highest dose bin has a fractional volume of 80% and is set at a boost dose of 10% above prescription dose, it is found that the loss in TCP and EUD is moderate as long as the cold 1% subvolume has a deficit less than approximately 20%. However, as the dose deficit in the 1% subvolume bin increases further it drives TCP and EUD rapidly down and can lead to a serious loss in TCP and EUD. Since a dose deficit to a 1% volume of the target that is larger than 20% of the prescription dose may lead to serious loss of TCP, even if 80% of the target receives a 10% boost, particular attention has to be paid to small-volume cold regions in the target. The effect of cold regions on TCP can be minimized if the EUD associated with the target DVH is constrained to be equal to or larger than the prescription dose.