Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 861869, 10 pages
Research Article

A Probability Approach to the Study on Uncertainty Effects on Gamma Index Evaluations in Radiation Therapy

1Servicio de Medicina Nuclear, Hospital General Universitario Gregorio Marañón, Calle Doctor Esquerdo, 46, 28007 Madrid, Spain
2Laboratorio de Metrología de Radiaciones Ionizantes, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Avenida Complutense, 22, 28040 Madrid, Spain

Received 21 March 2010; Accepted 4 November 2010

Academic Editor: Sivabal Sivaloganathan

Copyright © 2011 Francisco Cutanda Henríquez and Silvia Vargas Castrillón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two datasets of points of known spatial positions and an associated absorbed dose value are often compared for quality assurance purposes in External Beam Radiation Therapy (EBRT). Some problems usually arise regarding the pass fail criterion to accept both datasets as close enough for practical purposes. Instances of this kind of comparisons are fluence or dose checks for intensity modulated radiation therapy, modelling of a treatment unit in a treatment planning system, and so forth. The gamma index is a figure of merit that can be obtained from both datasets; it is widely used, as well as other indices, as part of a comparison procedure. However, it is recognized that false negatives may take place (there are acceptable cases where a certain number of points do not pass the test) due in part to computation and experimental uncertainty. This work utilizes mathematical methods to analyse comparisons, so that uncertainty can be taken into account. Therefore, false rejections due to uncertainty do not take place and there is no need to expand tolerances to take uncertainty into account. The methods provided are based on the rules of uncertainty propagation and help obtain rigorous pass/fail criteria, based on experimental information.