Estimation of the deformations induced by articulated bodies: Registration of the spinal column Aloys du Bois d’Aische a,b, * , Mathieu De Craene a,b , Xavier Geets c , Vincent Gre ´goire c , Benoit Macq a , Simon K. Warfield d a Communications and Remote Sensing Laboratory, Universite ´ catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium b Computational Radiology Laboratory, Department of Radiology, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA 02115, USA c Imagerie Mole ´culaire et Re ´sonance Expe ´rimentale, Cliniques Saint-Luc, Universite ´ catholique de Louvain, B-1150 Bruxelles, Belgium d Computational Radiology Laboratory, Children’s Hospital and Brigham and Women’s Hospital, Harvard Medical School, Boston, MA 02115, USA Received 23 December 2006; received in revised form 12 March 2007; accepted 12 March 2007 Available online 4 May 2007 Abstract We present a new non-rigid registration algorithm estimating the displacement field generated by articulated bodies. Indeed the bony structures between different patient images may rigidly move while other tissues may deform in a more complex way. Our algorithm tracks the displacement induced in the column by a movement of the patient between two acquisitions. The volumetric deformation field in the whole body is then inferred from those displacements using a linear elastic biomechanical finite element model. We demonstrate in this paper that this method provides accurate results on 3D sets of computed tomography (CT), MR and positron emission tomography (PET) images and that the results of the registration algorithm show significant decreases in the mean, min and max errors. # 2007 Elsevier Ltd. All rights reserved. Keywords: Articulation; Vertebrae; Registration 1. Introduction 1.1. Image guided radiotherapy In radiation oncology, the development of new algorithms for three-dimensional dose calculation along with computer driven linear accelerators able to deliver intensity modulated radiation beams have made it possible to sculpt the radiation dose precisely to target volumes of almost any shape (see Webb [1]). Improvement in the physical dose distribution obtained by the procedure referred to as intensity-modulated radiation therapy (IMRT) has raised the critical issues of the adequacy and accuracy of the selection and delineation of the target volumes on a 3D-basis. In this context more delineations of the tumor and of the different organs should be taken into account to improve patient therapy. Unfortunately, tumors boundaries in the neck area are differently defined on each imaging modality (anatomical images such as the computed tomography (CT) scan, magnetic resonance imaging (MRI) or functional images such as the positron emission tomography (PET) scan). The patient’s treatment follow-up would be enhanced if previous delineations could be transferred onto new images to take account of previous radiation doses for subsequent scheduling. Furthermore it would save time to avoid completely new manual segmentations for the following radiation sessions and to enable the user to restart his delineations from previous segmentations. For these reasons, registration methods are increasingly important in clinical routine to transfer informa- tion between images and modalities. In the neck area, registration methods need to take rigid structures into account. Very few methods able to deal with multimodal images, volumetric registration and multiple elasticities have been proposed, and not for the neck area. In this work, the multimodal images of the neck to be processed induce different choices of deformation models. Indeed the following features have to be taken into account:  The methods registering the surfaces need smooth surfaces, but vertebrae have complex shapes. Furthermore, these www.elsevier.com/locate/bspc Biomedical Signal Processing and Control 2 (2007) 16–24 * Corresponding author. E-mail address: duboisda@tele.ucl.ac.be (A. du Bois d’Aische). 1746-8094/$ – see front matter # 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2007.03.002