Author/Editor		Stavrev, Pavel; Schinkel, Coleen; Stavreva, Nadia; Markov, Krassimir; Fallone, B Gino
Title		Analytical investigation of properties of the iso-NTCP envelope
Translated title		Analitična raziskava lastnosti izo-NTCP ovojnice
Type		članek
Source		Radiol Oncol
Vol. and No.		Letnik 41, št. 1
Publication year		2007
Volume		str. 41-7
Language		eng
Abstract		Background. A property of the integral dose-volume histogram (DVH) space is analytically investigated in this work. A curve called an alpha-iso-NTCP (normal tissue complication probability) envelope is constructed by connecting points belonging to step-like integral DVHs, each corresponding to homogeneous partial organ irradiation of a relative volume vk to dose Dk such that the resulting NTCP has, in all cases, a particular value alpha. The two subspaces into which the envelope divides the DVH space are analytically explored in terms of the equivalent uniform doses (EUDs) corresponding to the different DVHs. It is theoretically proven that any DVH, other than the step-like DVH, passing through a point (Dk1 vk) from the alpha-iso-NTCP envelope, will result in an NTCP > alpha. Conclusions. Thus, it is proven that any DVH that at least partially lies above the envelope results in an NTCP > alpha. 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 > alpha. However, it was numerically demonstrated elsewhere that there east DVHs lying entirely in the lower subspace that result in an NTCP < alpha. Therefore, one can conclude that since there is a chance that a DVH lying under the alpha-iso-NTCP envelope will result in NTCP < alpha, it would be preferable in the treatment optimization process to seek solutions for DVHs lying entirely under an iso-NTCP envelope and avoid solutions that have DVHs above an iso-NTCP envelope.
Summary		Izhodišča. V članku smo raziskali lastnost prostora integralnega dozno-volumskega histograma (DVH). Krivuljo enake verjetnosti poškodbe zdravega tkiva [alfa-izo-NTCP (normal tissue complication probability)] smo oblikovali s povezovanjem točk, ki pripadajo intervalom vk stopničastega integralnega DVH s pripadajočo dozo Dk in posledičnim NTCP z vrednostjo alfa. Podprostora, na katera krivulja razdeli DVH prostor, smo raziskali v smislu ekvivalentnih uniformnih doz (EUD), ki pripadajo različnim DVH-jem. Zaključki. Teoretično je dokazano, da ima vsak DVH, ki je različen od stopničastega DVH in ki gre skozi točko (Dk1 vk) alfa-izo-NTCP ovojnice, NTCP > alfa. Iz česar sledi, da vsakemu DVH, ki vsaj delno leži nad ovojnico, pripada NTCP > alfa. Nekaterim DVH, ki ležijo pod ovojnico, npr. se je dotikajo, prav tako pripada NTCP > alfa. Vendar je bilo numerično dokazano, da ima DVH, ki v celoti leži v spodnjem podprostoru, NTCP < alfa. Glede na slednje bi bilo v postopku optimizacije zdravljenja zaželeno iskati rešitve z DVH povsem pod izo-NTCP ovojnico in se izogibati tistim, ki ležijo nad njo.
Descriptors		DOSE-RESPONSE RELATIONSHIP, RADIATION MODELS, THEORETICAL