ARTICLE IN PRESS JID: MDO [mUS5Gb;November 19, 2019;22:10] Medical Dosimetry xxx (xxxx) xxx Medical Dosimetry journal homepage: www.meddos.org The mean absolute dose deviation–A common metric for the evaluation of dose-volume histograms in radiation therapy Vincent Vinh-Hung, M.D., Ph.D. ∗,∗∗ , Nicolas Leduc, M.Sc., M.D. ∗ , Dirk Verellen, M.Sc., Ph.D. † , Claire Verschraegen, M.D. ‡ , Giovanna Dipasquale, M.Sc. § , Nam P. Nguyen, M.D. ¶ ∗ Radiation Oncology, University Hospital of Martinique, Fort-de-France 97200 Martinique, France † Medical Physics, Iridium Cancer Network, Wilrijk 2610, Belgium ‡ Medical Oncology, The Ohio State University Comprehensive Cancer Center, Columbus, OH 43210, USA § Medical Physics, University Hospitals of Geneva, Geneva 1205, Switzerland ¶ Howard University, Washington, DC 20060, USA a r t i c l e i n f o Article history: Received 21 June 2019 Revised 22 September 2019 Accepted 20 October 2019 Available online xxx Keywords: Radiation therapy Treatment planning Dose volume histogram Area between curves a b s t r a c t Radiation therapy needs to balance between delivering a high dose to targets and the lowest possible dose to the organs at risk. Dose-volume histograms (DVHs) summarize the distribution of radiation doses in the irradiated structures. The interpretation can however be a challenge when the number of struc- tures is high. We propose the use of a simple summary metric. We define the mean absolute dose devia- tion (MADD) as the average of absolute differences between a DVH and a reference dose. The properties are evaluated through numerical analysis. Calculus trivially shows the identity of the MADD and the area between curves, between DVH and reference dose. Computation of the MADD is the same regardless of structures’ designation, whether organ at risk or target, on the same dose scale. Basic calculus properties open the perspective of applying the MADD to the evaluation of treatment plans. © 2019 American Association of Medical Dosimetrists. Published by Elsevier Inc. All rights reserved. Background Dose-volume histograms (DVH) are routinely used in radiation therapy. The characteristics are well known. Briefly, a DVH is a graphical summary output from a radiation treatment planning that summarizes the distribution of the computed radiation doses delivered to a given structure. 1 The most frequently reported type of DVH is the cumulative DVH. Usually, by convention, the ordinate y-axis represents the percentage or the proportion of the volume irradiated and the abscissa x-axis represents the absolute dose, or can also represent the relative dose. The cumulative DVH plots the volume receiving a dose greater than or equal to the correspond- ing dose represented on the x-axis. The major utility of DVH is to assess whether a treatment plan would be associated with excess toxicity and/or with an inadequate dose to control a tumor. The comparison of DVH between different treatment plan alternatives is a cornerstone of the radiation treatment planning process. International recommendations specify selected ∗∗ Reprint requests to Vincent Vinh-Hung, CHU Martinique, Radiation Oncology, Site Clarac, Bld Pasteur, Fort-de-France 97200 Martinique, France. E-mail address: anhxang@gmail.com (V. Vinh-Hung). DVH points for reporting patients’ treatment plans, such as the D mean /D min /D max (i.e., the mean/minimum/maximum dose received by a structure, respectively) or the D 2% , D 50% , D 95% , D 98% (i.e., the dose received being 2%, 50%, 95%, 98% of the volume of the structure, respectively. 2 When the number of structures is high, the interpretation of the DVHs and the series of values can be a daunting task. The present communication presents a simple measure that might facilitate the evaluation of DVHs. Method: the mean absolute deviation of the dose The magnitude of the difference between a DVH curve and a reference dose, A, can be considered by calculating the area between curves (AbC), that is, the area between the actual DVH, and the reference dose A. We use the singular A in the same symbolic manner of the singular DVH, implying a set of multiple points. Using absolute deviations avoids generating negative area values. We will show later that the AbC is identical to the mean absolute dose deviation (MADD) between the DVH and the reference dose A, noted as M(A). For discrete DVH data points, M(A) can be formalized as: M(A) = n  i=1 |x i − a i | × δy i V 0 (1) where x i , y i , i = 1 ··· n are the n pairs of the DVH dose (x i ) - volume (y i ) data points outputted by the treatment planning for the structure of interest, δy i are the volume steps between successive points, V 0 is the structure’s volume (1 if relative proportion, 100 if percentage, or actual absolute volume according to the https://doi.org/10.1016/j.meddos.2019.10.004 0958-3947/© 2019 American Association of Medical Dosimetrists. Published by Elsevier Inc. All rights reserved.