Quantifying Uncertainties for Prostate Image-Guided Radiotherapy: A 3D Organ Reconstruction and Registration Method

Ximo Gual-Arnau*, 1, Rubén Masó1, Françoise Lliso2, Juan López-Tarjuelo3
1 Department of Mathematics, Universitat Jaume I, 12071-Castelló, Spain
2 Servicio de Oncología Radioterápica, Hospital Universitario La Fe, Valencia, Spain
3 Servicio de Radiofísica y Protección Radiológica, Instituto Oncológico, C.H. Provincial de Castellón, Castellón, Spain

© 2009 Gual-Arnau et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics, Universitat Jaume I, 12071-Castelló, Spain; E-mail:


The purpose of this paper is to present a method for volumetric reconstruction, registration and margin assignation applicable to both conventional CT scans and on board CT imaging. This method does not depend on the shape of the organs, the bony anatomy or the use of markers, and we apply it to prostate and bladder. 3D reconstructions are performed by means of spline surfaces and the 3D reconstructed surfaces are registered to a planning surface, using a multidimensional alignment from the Euclidean distance transform and the Levenberg-Marquardt optimization algorithm. Once the reconstructed surfaces are registered, we define a mean surface and obtain the corresponding variances from this mean surface. The method works properly and demonstrates that once translations are insulated by registration, residual uncertainties can be handled with the margin assigned for delineation variation and organ deformation.

Keywords: Geometrical uncertainties, image-guided radiotherapy, interobserver variability, organ motion, registration, shape variation, stereology, volumetric reconstruction.