The new modalities of medical images enable to obtain high resolution anatomical and functional 3D images of the human body. It is common to use these images for the planning of surgical interventions and to guide the surgeon during the surgery. Also, to have surgical interventions as invasive as possible is desirable, tending to use preferably images for the operation and avoiding the need of a line of direct vision. This reduces the impact for the patient. Systems to obtain 3D images inside the surgical pavilion exist, for example, CT (computer tomography) [5] and of RM (Magnetic Resonance [1][11][12], but both are very expensive and they have disadvantages. The CT systems deliver ionizing radiation and do not produce good images of soft tissues. The systems of RM are incompatible with the conventional instruments because of the high magnetic fields that they generate. On the other hand, the preoperative images have many advantages, including that they are available in a routine way. The preoperative images have better quality, since the restrictions of the surgical pavilion do not exist when they are acquired. For example, the acquisition times can be longest, increasing the signal to noise ratio, this is particularly important for the MRI. Also, sufficient time to analyze carefully the images and to plan the operation exists, without using time during the surgery, which increases its costs.



To use a preoperative image as reliable guide during the surgery, it is necessary to realize a registration between the image and the position of the patient, in others words, to put the patient and the image in the same reference system so that the anatomical structures coincide. Methods to align the preoperative images with the position of the patient in the operating room exist. The neurosurgery is one of the first areas where these methods were used, with the use of the stereotactic frame [6]. With the stereotactic frame it is possible to fix a reference system in the operating room and relate it to the reference system of the image. After the stereotactic frame, other methods have appeared, for example, optical location by means of cameras, recognition of reflecting marks, infrared diodes fixed to a rigid body, recognition of marks attaches to the bones or to the skin of the patient. These methods do not need a frame attached to the patient’s head and can be used in other parts of the body



The registration can be a rigid transformation. But in many cases, the tissue is soft and an elastic transformation is necessary to adapt the image to the patient position during the surgery, for example, images of abdomen, lungs, etc. Also, these tissues can suffer distortions during the surgery, caused by the intervention or by processes as breathing. This distortion causes loss of accuracy. Because of these distortions it is necessary to carry out an adjustment of the registration during the intervention. A solution is to make a model of the tissue. Having a model of the tissue, it is possible to predict his distortion submitting the model to the restrictions derived from the intra-operative measurements. With this prediction, the preoperative images can be updated. To predict his behavior, these models must take into account the biomechanical characteristics of the tissue. Different way to constructing tissue models exist [7]. The models can be classified basically in three types: ad oc heuristic methods, simplifications of continuum-mechanical models, and hybrid methods. Some heuristic methods are: deformable splines, spring-mass mode, linked volumes, and mass-tensor model. These methods, in general, are fasters and simpler of using, but they are alternative representations of the tissue mechanics and therefore they can be less accurate. The finite element methods or the FFE (Fast finite elements) are simplifications of continuum-mechanical modes. These methods need to realize more calculations but they can deliver more accurate results. Finally, the hybrid models combine characteristics of both.



To direct properly the deformation of the model, it is necessary to acquire information during the surgery. In many cases these measurements are incomplete and of lower resolution than the image, therefore it is needed to realize an interpolation or extrapolation. This information can be the position of particular points or images that could be obtained easily, for example, US images or video. To using this information it is possible to obtain the position of some structure and update the model.



The Brain-Shift will be modeling on this study. The “Brain-Shift” [2][3] is the distortions of the brain into a surgery. For the brain good results can be obtained using a rigid transformation for the initial registration, but it has been seen that distortions of the brain exist during the surgery, which can be of up to 2.4cm [8][9]. Then, to realize an adjustment of the record during the intervention is necessary. On this work a segmentation method for MRI [10] of the brain will be implemented, and a model of the distortions produced during the surgery will be developed. To update the model during the surgery, US 2.5D [4] images and the location of points in the cortex, acquired by means of an optical localizer, will be used.