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Optimization by visualization of indices

Optimierung durch Visualisierung von Indizes

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Background and purpose

Physical 3D treatment planning provides a pool of parameters describing dose distributions. It is often useful to define conformal indices to enable quicker evaluation. However, the application of individual indices is controversial and not always effective. The aim of this study was to design a quick check of dose distributions based on several indices detecting underdosages within planning target volumes (PTVs) and overdosages in normal tissue.

Materials and methods

Dose distributions of 215 cancer patients were considered. Treatment modalities used were three-dimensional conformal radiotherapy (3DCRT), radiosurgery, intensity-modulated radiotherapy (IMRT), intensity-modulated arc therapy (IMAT) and tomotherapy. The volumes recommended in ICRU 50 and 83 were used for planning and six conformation and homogeneity indices were selected: CI, CN, CICRU, COV, C, and HI. These were based on the PTV, the partial volume covered by the prescribed isodose (PI; PTVPI), the treated volume (TVPI), near maximum D2 and near minimum D98. Results were presented as a hexagon—the corners of which represent the values of the indices—and a modified test function F (Rosenbrock’s function) was calculated. Results refer to clinical examples and mean values, in order to allow evaluation of the power of F and hexagon-based decision support procedures in detail and in general.


IMAT and tomotherapy showed the best values for the indices and the lowest standard deviation followed by static IMRT. DCRT and radiosurgery (e.g. CN: IMAT 0.85 ± 0.06; tomotherapy 0.84 ± 0.06; IMRT 0.83 ± 0.07; 3DCRT 0.65 ± 0.08; radiosurgery 0.64 ± 0.11). In extreme situations, not all indices reflected the situation correctly. Over- and underdosing of PTV and normal tissue could be qualitatively assessed from the distortion of the hexagon in graphic analysis. Tomotherapy, IMRT, IMAT, 3DCRT and radiosurgery showed increasingly distorted hexagons, the type of distortion indicating exposure of normal tissue volumes. The calculated F values correlated with these observations.


An evaluation of dose distributions cannot be based on a single conformal index. A solution could be the use of several indices presented as a hexagonal graphic and/or as a test function.



Die physikalische 3-D-Bestrahlungsplanung liefert eine Fülle an Parametern zur Beschreibung der Dosisverteilung. Um zu einer schnellen Evaluation zu kommen, kann es sinnvoll sein, Konformationsindizes zu verwenden. Allerdings ist deren Anwendung umstritten und nicht immer effektiv. Es ist das Ziel dieser Studie, einen Quick-Check zu entwickeln, um Unterdosierungen im Zielvolumen (PTVs) und Überdosierungen im Normalgewebe zu detektieren.

Material und Methode

Von 215 Patienten wurden die Dosisverteilungen betrachtet. Therapiemodalitäten waren die 3-dimensionale konformale Strahlentherapie (3D-CRT), Radiochirurgie, die intensitätsmodulierte Strahlentherapie (IMRT), die intensitätsmodulierte Arc-Therapie (IMAT) und die Tomotherapie. Für die Planung wurden die in ICRU 50 und 83 vorgeschlagenen Volumen verwendet und entsprechend einer Literaturanalyse 6 Konformations- und Homogenitätsindizes ausgewählt (CI, CN, CICRU, COV, C, and HI), deren Definitionen auf dem PTV, dem Behandlungsvolumen (TVPI), dem Partialvolumen (PI, PTVPI), dem Maximum D2 und dem Minimum D98 basieren. Die Ergebnisse werden in Form eines Hexagons präsentiert, deren Ecken die Werte der Indizes repräsentieren, zusätzlich werden die Werte einer modifizierten Test-Funktion F (Rosenbrock-Funktion) berechnet. Im Rahmen dieser Arbeit werden klinische Beispiele und Mittelwerte betrachtet, um die Möglichkeiten der hier vorgestellten Evaluation im Detail und allgemein betrachten zu können.


IMAT und Tomotherapie zeigen die besten Mittelwerte gefolgt von der IMRT. 3DCRT und Radiochirurgie (Z. B. CN: IMAT 0,85 ± 0,06; Tomotherapie 0,84 ± 0,06; IMRT 0,83 ± 0,07; 3DCRT 0,65 ± 0,08; Radiochirurgie 0,64 ± 0,11). Zu beachten ist, dass nicht alle Indizes in Extremsituation zielführende Werte annehmen. Die graphische Analyse erfolgte über ein Hexagon; Über- und Unterdosierungen konnten qualitativ aus der Verzerrung ermittelt werden. Die Tomotherapie, IMRT, IMAT, 3D-CRT und Radiochirurgie zeigten zunehmend verzerrte Hexagone. Die Art der Verzerrung lässt auf eine Exposition des Normalgewebes schließen. Die ermittelten F-Werte korrelieren mit diesen Beobachtungen.


Die Evaluierung einer Dosisverteilung kann nicht mit einem Index erfolgen. Die Lösung kann eine graphische Analyse mehrerer Indizes sein und/oder die Bestimmung von Werten einer Testfunktion.

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Conflict of interest

U. Haverkamp, D. Norkus, J. Kriz, M. Müller Minai, F.-J. Prott, and H.T. Eich state that there are no conflicts of interest. The accompanying manuscript does not include studies on humans or animals.

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Correspondence to Uwe Haverkamp.

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Haverkamp, U., Norkus, D., Kriz, J. et al. Optimization by visualization of indices. Strahlenther Onkol 190, 1053–1059 (2014).

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