IEEE TRANSACTIONS ON MEDICAL IMAGING 1 Registration of 3D Intraoperative MR Images of the Brain Using a Finite Element Biomechanical Model Matthieu Ferrant , student Member, IEEE, Arya Nabavi , Benoˆ ıt Macq , Senior Member, IEEE, Ferenc A. Jolesz , Ron Kikinis , and Simon K. Warfield , Member, IEEE Abstract— We present a new algorithm for the non-rigid registration of 3D Magnetic Resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces of objects (cortical surface and the lateral ventricles) in the image sequence using a deformable sur- face matching algorithm. The volumetric deformation field of the objects is then inferred from the displacements at the boundary surfaces using a linear elastic biomechanical finite element model. Two experiments on syn- thetic image sequences are presented, as well as an initial experiment on intra-operative MR images showing brain shift. The results of the registra- tion algorithm show a good correlation of the internal brain structures after deformation, and a good capability of measuring surface as well as sub- surface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. Cortical surface shifts of up to 10mm and subsurface shifts of up to 6mm were re- covered with an accuracy of 1mm or less and 3mm or less respectively. 1 Keywords—Intraoperative image registration, brain modeling, finite ele- ment method, tetrahedral mesh generation. I. I NTRODUCTION A. Image-Guided Neurosurgery The development of image guided surgery systems has fos- tered significant improvements in minimally invasive surgery over the last decade. Such systems have been increasingly used in neurosurgery and have been shown to improve surgical vi- sualization and navigation, and to reduce the amount tumor re- maining after surgery [30], [32]. However, image-guided neurosurgery (IGNS) has brought to prominence the problem of brain shift, the shape deformations the brain undergoes during surgery. The main factors causing this deformation include the loss of cerebrospinal fluid (CSF), the injection of anaesthetic agents, and the actions of the neuro- surgeon (such as resection and retraction). These deformations can significantly diminish the accuracy of neuronavigation sys- tems ([6], [35], [43]), and it is therefore of great importance to be able to quantify and correct for these deformations by updat- ing pre-operative imaging during surgery. Corresponding Author. MF is now with General Electric Medical Systems, Buc, France. Communications and Remote Sensing Laboratory, Univer- sit´ e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. E-Mail: ferrant,macq @tele.ucl.ac.be Surgical Planning Laboratory, Department of Radiology, Brigham and Women’s Hospital and Harvard Medical School, Boston MA 02115, USA. E-Mail: arya,jolesz,kikinis,warfield @bwh.harvard.edu Department of Neurosurgery, University of Kiel, Germany. This paper appeared in IEEE Transactions on Medical Imaging, December 2001, Volume 20, Issue 12, pages 1384–1397. B. Non-Rigid Registration for IGNS Previous work that has been done for capturing non-rigid intraoperative volumetric deformations can be categorized by those using image-based models and those using biomechanical models. Image-based models are often used when intraoperative image acquisition is available. B.1 Image-based models Image-based models propose to locally satisfy an image simi- larity criterion under a given regularization constraint. The main assumption of such methods is constant intensity and small dis- placements between the images to be matched. If such algo- rithms are run in multiresolution and if noise and intensity vari- ation artifacts can be corrected for, good results can be obtained from a purely visual point of view (recent examples include [28], [13], [26], [29], [27]). However, such methods tend to only es- tablish correspondences between local image structures and ar- bitrarily interpolate between these, without accounting for prior knowledge one has about the imaged objects (such as inhomo- geneity and anisotropy). To cope with this issue, physical deformation models have been proposed to constrain a deformation field computed from image data using elastic (e.g. [5], [1], [20], [56], [11], [16]) and viscous fluid deformation models (e.g. [7], [4]). However, in these works the physical models were just used as a better regularization constraint on the image similarity criterion, with- out incorporating specific material properties (such as hard/soft parts, etc.). It is only recently that biomechanical models have been ex- plicitly proposed to constrain the registration of images (e.g. [33], [50], [25]) in the context of deformable brain registration. Peckar et al. [50] describe a framework for registering 3D im- ages given prescribed correspondences and an elastic deforma- tion model to infer a volumetric deformation field. Even though the algorithm was applied on 3D synthetic data, it was only tested in 2D on medical images. Following this work, Hage- mann et al. [25], [24] developed a 2D biomechanical model of the head to register brain images showing deformations due to neurosurgical operations. The model is deformed by enforcing correspondences between landmark contours manually or semi- automatically. The constitutive equations of the biomechanical model are discretized using finite elements (FE), and the basic elements of the mesh are the pixels of the image, which causes the computations to be particularly heavy. Kyriacou et al. [33] study the effect of tumor growth in brain images for doing atlas registration. They use a FE model and