Treatment plan comparison using equivalent uniform biologically effective dose (EUBED)

With the continuing improvement in computer speed, dose distributions can be calculated quickly with confidence. However, the resulting biological effect is known with much less certainty, despite its critical importance when assessing treatment plans. To assess plans accurately, biologically based methods of ranking plans are necessary. Many authors have suggested the use of dose volume histograms with reduction schemes and Niemierko has recently introduced another method based on the cell kill occurring in the tumour. This study presents an investigation into this value and suggests a use in prescribing dose. Equivalent uniform dose (EUD) can obviously be used for assessing treatment plans, although in its current form it is not adequate for assessing normal tissues; however, it can also be used to adjust the prescription dose ensuring all plans deliver the same EUD to the tumour. Once this is performed, plans can more easily be assessed on the effects to the normal tissues. In calculating the EUD another concept is introduced--the equivalent uniform biologically effective dose (EUBED). This value considers the distribution of dose and dose per fraction when comparing plans. Reduced dose per fraction at the edge of the target volume will exacerbate the effect of reduced dose on cell kill. Two methods are suggested for calculating the necessary prescription dose: one using an iterative method and one using the gradient of the EUBED function. A comparison was made for a series of stereotactic cases using different collimator sizes. Interestingly, using this method, although the maximum doses were different, the dose volume histograms (DVHs) for the brainstem were similar in all cases.