Premium
SU‐FF‐T‐370: Properties of the Iso‐NTCP Envelope
Author(s) -
Stavrev P,
Schinkel C,
Stavreva N,
Markov K,
Fallone B G
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2241288
Subject(s) - envelope (radar) , linear subspace , mathematics , monotonic function , homogeneous , dosimetry , nuclear medicine , mathematical analysis , pure mathematics , computer science , combinatorics , medicine , telecommunications , radar
Purpose: To analytically investigate a property of the integral dose‐volume histogram (DVH) space. Method and Materials: A curve called an α‐iso‐NTCP envelope is constructed by connecting points belonging to step‐like integral DVHs each corresponding to partial organ homogeneous irradiation of relative volumes ν α to dose levels D α such that the resulting NTCP is in all cases α %. The two subspaces into which the envelope divides the DVH space are analytically explored through comparing the values of the equivalent uniform doses (EUDs) corresponding to the different DVHs and using the fact that NTCP is a monotonic function of EUD as well as the monotonic nature of the integral DVH itself. Results: It is theoretically proven that any DVH passing through a point ( D α , ν α ) from the α‐iso‐NTCP envelope, i.e. any DVH that crosses or is tangential to the envelope, will result in an NTCP ⩾α%, the equality being valid only for the step‐like DVH corresponding to the partial organ homogeneous irradiation of ν α to D α, . Thus, it is proven that any DVH that at least partially lies above the envelope result in NTCP >α%. For some of the DVHs lying under the envelope, e.g. those that are tangential to the envelope, it is also true that the resulting NTCP >α%. However, it was numerically demonstrated elsewhere that there exist DVHs lying entirely in the lower subspace that result in NTCP <α%. Conclusion: Since there is a chance that a DVH lying under the α‐iso‐NTCP envelope will result in NTCP <α%, it would therefore be preferable in the treatment optimization process to seek solutions for DVHs lying entirely under an iso‐NTCP envelope.