A concept of equivalent-volume concordance coefficient for comparing target volumes in radiotherapy

The significant limitation of simple volume analyses for target volumes is that they disregard the spatial distribution of non-overlapping volumes and the surrounding dose gradient.

To present a concept of equivalent-volume concordance coefficient (CC_EV) for comparing target volumes in radiotherapy, which takes into account the dose coverage requirement and the spatial relationship between the standard volume (V_Std) and the reference volume (V_Ref).

By using uniform expansion and Boolean operations, the non-overlapped volumes were segmented by a certain spatial distance (d) from the margin of V_Std or V_Ref. The volume of V_Std-I and V_Ref-I were defined as V_Std and V_Ref minus their intersection volume (V_I), respectively. The equivalent volume (EV) increased with d (EV_Std-I = ∑V_{Std-I_ i}(d_i/d_r)ⁿ; EV_Ref-I = ∑V_{Ref-I_ i}(d_i/d_r)ⁿ). The dose-volume histograms (DVHs) of whole body were exported in 20 volumetric modulated arc therapy (VMAT) plans. The radius (R) of the equivalent sphere for V_PCT (the volume covered by a percentage dose (PCT)) was calculated (R_PCT = (3V_PCT/4π)^1/3), and the mean dose fall-off distance (d_PCT) from V_PCT to V_100% was calculated by the equation: d_PCT = R_PCT-R_100%. The distance-penalty parameter n was determined by the exponential relationship between PCT and d_PCT. The CC_EV was evaluated via the Jaccard coefficient (JC) and dice similarity coefficient (DSC) and was compared against traditional indices in an illustrative case and two sets of volumes delineated at different time points.

The DVH could be divided into prescription dose region, rapid fall-off region, slow fall-off region and low-dose region according to dose gradients of 20 plans. The volume of V_48% minus V_100% was contained in the rapid dose fall-off region, where the mean d_48% was 2.03 cm (1.75-2.40 cm), and PCT was linearly correlated with d_PCT (all R²≥0.987, P < 0.001), leading to the setting of reference distance (d_r) = 1 cm and n = 1. CC_EV distinguished different intersection conditions and yielded reasonable results. The mean JC_EV and DSC_EV of two volume sets were 0.929 and 0.963, respectively.

A reference penalty distance of 1 cm and a distance-penalty parameter of 1 are recommended for CC_EV in clinical practice. CC_EV effectively incorporates the spatial location of non-overlapped volumes and key radiotherapy requirements.