N. Abolhassani, R. Patel, and M. Moallem, Needle insertion into soft tissue: A survey, Medical Engineering & Physics, vol.29, issue.4, pp.413-444, 2007.
DOI : 10.1016/j.medengphy.2006.07.003

A. Abosch, L. Timmermann, S. Bartley, H. G. Rietkerk, D. Whiting et al., An International Survey of Deep Brain Stimulation Procedural Steps, Stereotactic and Functional Neurosurgery, vol.91, issue.1, pp.1-11, 2013.
DOI : 10.1159/000343207

J. Allard, F. Faure, H. Courtecuisse, F. Falipou, C. Duriez et al., Volume contact constraints at arbitrary resolution, Proceedings of SIGGRAPH 2010), pp.1-10, 2010.
DOI : 10.1145/1778765.1778819

URL : https://hal.archives-ouvertes.fr/inria-00502446

R. Alterovitz, K. Goldberg, and A. Okamura, Planning for Steerable Bevel-tip Needle Insertion Through 2D Soft Tissue with Obstacles, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp.1640-1645, 2005.
DOI : 10.1109/ROBOT.2005.1570348

R. J. Anderson, M. A. Frye, O. Abulseoud, K. H. Lee, J. Mcgillivray et al., Deep brain stimulation for treatment-resistant depression: Efficacy, safety and mechanisms of action, Neuroscience & Biobehavioral Reviews, vol.36, issue.8, pp.1920-1953, 2012.
DOI : 10.1016/j.neubiorev.2012.06.001

B. S. Appleby, P. S. Duggan, A. Regenberg, R. , and P. V. , Psychiatric and neuropsychiatric adverse events associated with deep brain stimulation: A meta-analysis of ten years' experience, Movement Disorders, vol.63, issue.12, pp.1722-1730, 2007.
DOI : 10.1002/mds.21551

E. Arruda and M. Boyce, A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials, Journal of the Mechanics and Physics of Solids, vol.41, issue.2, 1993.
DOI : 10.1016/0022-5096(93)90013-6

URL : https://hal.archives-ouvertes.fr/hal-01390807

M. A. Audette, K. Siddiqi, F. P. Ferrie, and T. M. Peters, An integrated range-sensing, segmentation and registration framework for the characterization of intra-surgical brain deformations in image-guided surgery, Computer Vision and Image Understanding, vol.89, issue.2-3, pp.226-251, 2003.
DOI : 10.1016/S1077-3142(03)00004-3

G. H. Baltuch and M. B. Stern, Deep Brain Stimulation for Parkinson's Disease. Neurological Disease and Therapy, 2007.

P. V. Bayly, E. H. Clayton, and G. M. Genin, Quantitative imaging methods for the development and validation of brain biomechanics models. Annual review of biomedical engineering, pp.369-96, 2012.

A. Benabid, P. Pollak, A. Louveau, S. Henry, D. Rougemont et al., Combined (Thalamotomy and Stimulation) Stereotactic Surgery of the VIM Thalamic Nucleus for Bilateral Parkinson Disease, Stereotactic and Functional Neurosurgery, vol.50, issue.1-6, pp.1-6344, 1987.
DOI : 10.1159/000100803

S. Benzley, E. Perry, K. Merkley, C. , and B. , A comparison of all hexagonal and all tetrahedral finite element meshes for elastic and elasto-plastic analysis, International Meshing, 1995.

S. Bériault, F. A. Subaie, D. L. Collins, A. F. Sadikot, and G. B. Pike, A multi-modal approach to computer-assisted deep brain stimulation trajectory planning, International Journal of Computer Assisted Radiology and Surgery, vol.38, issue.6, pp.687-704, 2012.
DOI : 10.1007/s11548-012-0768-4

B. Berkels, I. Cabrilo, S. Haller, M. Rumpf, and K. Schaller, Co-registration of intra-operative brain surface photographs and pre-operative MR images, International Journal of Computer Assisted Radiology and Surgery, vol.16, issue.4, pp.387-400, 2014.
DOI : 10.1007/s11548-014-0979-y

A. Bilger, E. Bardinet, S. Fernandez-vidal, C. Duriez, P. Jannin et al., Intra-operative Registration for Deep Brain Stimulation Procedures based on a Full Physics Head Model, MICCAI 2014 Workshop on Deep Brain Stimulation Methodological Challenges, p.65, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01060304

A. Bilger, E. Bardinet, S. Fernandez-vidal, C. Duriez, P. Jannin et al., Intra-Operative Registration for Stereotactic Procedures Driven by a Combined Biomechanical Brain and CSF Model, ISBMS-International Symposium on Biomedical Simulation, 2014.
DOI : 10.1007/978-3-319-12057-7_9

URL : https://hal.archives-ouvertes.fr/hal-01058435

A. Bilger, J. Dequidt, C. Duriez, C. , and S. , Biomechanical Simulation of Electrode Migration for Deep Brain Stimulation, Proc. Medical Image Computing and Computer-Assisted Intervention, pp.339-346, 2011.
DOI : 10.1109/TBME.2010.2099733

URL : https://hal.archives-ouvertes.fr/hal-00685737

A. Bilger, C. Duriez, C. , and S. , Computation and visualization of risk assessment in deep brain stimulation planning, Studies in health technology and informatics, vol.196, issue.94, pp.29-35, 2014.

A. Bilger, C. Essert, C. Duriez, C. , and S. , Brain-shift aware risk map for Deep Brain Stimulation Planning, DBSMC -MICCAI 2012 Workshop on Deep Brain Stimulation Methodological Challenges, p.83, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00736773

L. E. Bilston, Linear viscoelastic properties of bovine brain tissue in shear, Biorheology, vol.34, issue.6, pp.377-385, 1997.
DOI : 10.1016/S0006-355X(98)00022-5

L. E. Bilston, Brain tissue mechanical properties, Biomechanics of the brain, pp.69-89, 2011.

P. Boris, F. Bundgaard, and A. Olsen, The CT (Hounsfield unit) number of brain tissue in healthy infants. Child's Nervous System, pp.175-177, 1987.

S. Breit, J. B. Schulz, and A. Benabid, Deep brain stimulation, Cell and Tissue Research, vol.64, issue.1, pp.275-88, 2004.
DOI : 10.1007/s00441-004-0936-0

E. J. Brunenberg, A. Vilanova, V. Visser-vandewalle, Y. Temel, L. Ackermans et al., Automatic Trajectory Planning for Deep Brain Stimulation: A Feasibility Study, Medical Image Computing and Computer-Assisted Intervention--MICCAI 2007, pp.584-92, 2007.
DOI : 10.1007/978-3-540-75757-3_71

M. Bucki, C. Lobos, and Y. Payan, Framework for a Low-Cost Intra-Operative Image-Guided Neuronavigator Including Brain Shift Compensation, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp.872-875, 2007.
DOI : 10.1109/IEMBS.2007.4352429

URL : https://hal.archives-ouvertes.fr/hal-00170005

C. R. Butson, S. E. Cooper, J. M. Henderson, and C. C. Mcintyre, Patient-specific analysis of the volume of tissue activated during deep brain stimulation, NeuroImage, vol.34, issue.2, pp.661-70, 2007.
DOI : 10.1016/j.neuroimage.2006.09.034

A. Castellano-smith, T. Hartkens, and J. Schnabel, Constructing Patient Specific Models for Correcting Intraoperative Brain Deformation, Image Computing, vol.60, issue.117, pp.1091-1098, 2001.
DOI : 10.1007/3-540-45468-3_130

S. Chatelin, A. Constantinesco, and R. Willinger, Fifty years of brain tissue mechanical testing: from in vitro to in vivo investigations, Biorheology, vol.47, issue.5-6, pp.255-76, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00799194

I. Chen, A. M. Coffey, S. Ding, P. Dumpuri, B. M. Dawant et al., Intraoperative Brain Shift Compensation: Accounting for Dural Septa, IEEE Transactions on Biomedical Engineering, vol.58, issue.3, pp.499-508, 2011.
DOI : 10.1109/TBME.2010.2093896

Z. Cho, H. Min, S. Oh, J. Han, C. Park et al., Direct visualization of deep brain stimulation targets in Parkinson disease with the use of 7-tesla magnetic resonance imaging, Journal of Neurosurgery, vol.113, issue.3, pp.639-647, 2010.
DOI : 10.3171/2010.3.JNS091385

D. B. Clarke, R. C. D-'arcy, S. Delorme, D. Laroche, G. Godin et al., Virtual Reality Simulator, Surgical Innovation, vol.8, issue.2, 2012.
DOI : 10.1016/S0140-6736(08)60878-8

O. Clatz, H. Delingette, E. Bardinet, and D. Dormont, Building a Specific Biomechanical Model of the Brain from Medical Image Analysis and Its Application to the Planning, Methods, 2004.

O. Clatz, H. Delingette, E. Bardinet, D. Dormont, and N. Ayache, Patient-Specific Biomechanical Model of the Brain: Application to Parkinson???s Disease Procedure, Proceedings of the 2003 international conference on Surgery simulation and soft tissue modeling, pp.321-331, 2003.
DOI : 10.1007/3-540-45015-7_31

R. J. Cloots, H. M. Gervaise, J. A. Van-dommelen, and M. G. Geers, Biomechanics of Traumatic Brain Injury: Influences of the Morphologic Heterogeneities of the Cerebral Cortex, Annals of Biomedical Engineering, vol.4, issue.7, pp.1203-1218, 2008.
DOI : 10.1007/s10439-008-9510-3

S. D. Conte and C. W. Boor, Elementary numerical analysis: an algorithmic approach, 1980.

J. B. Cooper and V. R. Taqueti, A brief history of the development of mannequin simulators for clinical education and training. Postgraduate medical journal, pp.563-70, 2008.

H. Courtecuisse, J. Allard, C. Duriez, C. , and S. , Asynchronous preconditioners for efficient solving of non-linear deformations. VRIPHYS-Virtual Reality Interaction and Physical Simulation, pp.59-68, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00688865

D. 'albis, T. Haegelen, C. Essert, C. Fernandez-vidal, S. Lalys et al., PyDBS : An automated image-processing workflow for planning and postoperative assessment of deep brain stimulation, International Journal of Computer Assisted Radiology and Surgery, vol.86, issue.120, p.74, 2014.

D. J. Debono, L. J. Hoeksema, and R. D. Hobbs, Caring for Patients With Chronic Pain: Pearls and Pitfalls, The Journal of the American Osteopathic Association, vol.113, issue.8, pp.620-627, 2013.
DOI : 10.7556/jaoa.2013.023

J. S. Denson and S. Abrahamson, A Computer-Controlled Patient Simulator, JAMA: The Journal of the American Medical Association, vol.208, issue.3, pp.504-508, 1969.
DOI : 10.1001/jama.1969.03160030078009

D. 'haese, P. Cetinkaya, E. Konrad, P. E. Kao, C. Dawant et al., Computer-aided placement of deep brain stimulators: from planningto intraoperative guidance, IEEE Transactions on Medical Imaging, vol.24, issue.11, pp.1469-78, 2005.
DOI : 10.1109/TMI.2005.856752

S. S. Dimaio and S. E. Salcudean, Needle Steering and Motion Planning in Soft Tissues, IEEE Transactions on Biomedical Engineering, vol.52, issue.6, pp.965-974, 2005.
DOI : 10.1109/TBME.2005.846734

D. Dormont, D. Seidenwurm, D. Galanaud, P. Cornu, J. Yelnik et al., Neuroimaging and Deep Brain Stimulation, American Journal of Neuroradiology, vol.31, issue.1, pp.15-23, 2010.
DOI : 10.3174/ajnr.A1644

URL : https://hal.archives-ouvertes.fr/hal-00805431

V. Duay, T. K. Sinha, M. I. Miga, and B. M. Dawant, Non-rigid Registration of Serial Intra-operative Images for Automatic Brain Shift Estimation, pp.61-70, 2003.
DOI : 10.1007/978-3-540-39701-4_7

C. Duriez and S. Cotin, New approaches to catheter navigation for interventional radiology simulation, Computer Aided Surgery, vol.11, issue.6, pp.300-308, 2005.
DOI : 10.1016/S0045-7825(97)00137-0

URL : https://hal.archives-ouvertes.fr/hal-01386225

C. Duriez, S. Cotin, J. Lenoir, P. Neumann, D. et al., New approaches to catheter navigation for interventional radiology simulation, Medical Image Computing and Computer-Assisted Intervention--MICCAI 2005, pp.534-542, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01386225

C. Duriez, F. Dubois, A. Kheddar, and C. Andriot, Realistic haptic rendering of interacting deformable objects in virtual environments. Visualization and Computer Graphics, IEEE Transactions on, vol.12, issue.1, pp.1-12, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00269404

C. Duriez, C. Guébert, M. Marchal, S. Cotin, and L. Grisoni, Interactive Simulation of Flexible Needle Insertions Based on Constraint Models, Medical Image Computing and Computer-Assisted Intervention--MICCAI 2009, pp.291-300, 2009.
DOI : 10.1007/978-3-642-04271-3_36

URL : https://hal.archives-ouvertes.fr/inria-00540334

H. M. Duvernoy, S. Delon, and J. L. Vannson, Cortical blood vessels of the human brain, Brain Research Bulletin, vol.7, issue.5, pp.519-79, 1981.
DOI : 10.1016/0361-9230(81)90007-1

G. Echegaray, I. Herrera, I. Aguinaga, C. Buchart, and D. Borro, A Brain Surgery Simulator, IEEE Computer Graphics and Applications, vol.34, issue.3, pp.3412-3430, 2014.
DOI : 10.1109/MCG.2014.43

W. J. Elias, K. Fu, and R. C. Frysinger, Cortical and subcortical brain shift during stereotactic procedures, Journal of Neurosurgery, vol.107, issue.5, pp.983-991, 2007.
DOI : 10.3171/JNS-07/11/0983

. Ellabib and . Nachaoui, An iterative approach to the solution of an inverse problem in linear elasticity, Mathematics and Computers in Simulation, vol.77, issue.2-3, pp.189-201, 2008.
DOI : 10.1016/j.matcom.2007.08.014

URL : https://hal.archives-ouvertes.fr/hal-00139180

C. Essert, C. Haegelen, F. Lalys, A. Abadie, and P. Jannin, Automatic Computation of Electrodes Trajectory for Deep Brain Stimulation, pp.34-96, 2011.
DOI : 10.1007/978-3-642-15699-1_16

URL : https://hal.archives-ouvertes.fr/hal-00853972

P. Farnia, A. Ahmadian, T. Shabanian, N. D. Serej, and J. And-alirezaie, Brain-shift compensation by non-rigid registration of intra-operative ultrasound images with preoperative MR images based on residual complexity, International Journal of Computer Assisted Radiology and Surgery, vol.18, issue.5, 2014.
DOI : 10.1007/s11548-014-1098-5

F. Faure, C. Duriez, H. Delingette, J. Allard, B. Gilles et al., SOFA: A Multi-Model Framework for Interactive Physical Simulation, pp.1-39, 2012.
DOI : 10.1007/8415_2012_125

URL : https://hal.archives-ouvertes.fr/hal-00681539

M. Fava, Diagnosis and definition of treatment-resistant depression, Biological Psychiatry, vol.53, issue.8, pp.649-659, 2003.
DOI : 10.1016/S0006-3223(03)00231-2

C. Felippa and B. Haugen, A unified formulation of small-strain corotational finite elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.21-24, pp.2285-2335, 2005.
DOI : 10.1016/j.cma.2004.07.035

M. Fernandes, M. Pavithra, A. Jatti, . Of, . Brain et al., ESTIMATION, International Journal, vol.1, issue.5, pp.490-498, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00417566

M. Ferrant, A. Nabavi, B. Macq, P. M. Black, F. Jolesz et al., Serial registration of intraoperative MR images of the brain, Medical Image Analysis, vol.6, issue.4, pp.337-59, 2002.
DOI : 10.1016/S1361-8415(02)00060-9

M. Ferrant, A. Nabavi, B. Macq, F. Jolesz, R. Kikinis et al., Registration of 3-d intraoperative MR images of the brain using a finite-element biomechanical model, IEEE Transactions on Medical Imaging, vol.20, issue.12, pp.1384-97, 2001.
DOI : 10.1109/42.974933

N. Galoppo, M. A. Otaduy, P. Mecklenburg, M. Gross, and M. C. Lin, Fast simulation of deformable models in contact using dynamic deformation textures, Proceedings of the 2006 ACM SIG- GRAPH/Eurographics symposium on Computer animation, pp.73-83, 2006.

K. Ganser, H. Dickhaus, R. Metzner, and C. R. Wirtz, A deformable digital brain atlas system according to Talairach and Tournoux, Medical Image Analysis, vol.8, issue.1, pp.3-22, 2004.
DOI : 10.1016/j.media.2003.06.001

D. T. Ginat, B. Swearingen, W. Curry, D. Cahill, J. Madsen et al., 3 Tesla intraoperative MRI for brain tumor surgery, Journal of Magnetic Resonance Imaging, vol.10, issue.Suppl, pp.1357-1365, 2014.
DOI : 10.1002/jmri.24380

D. G. Gobbi, <title>Correlation of pre-operative MRI and intra-operative 3D ultrasound to measure brain tissue shift</title>, Medical Imaging 2000: Ultrasonic Imaging and Signal Processing, pp.77-84, 2000.
DOI : 10.1117/12.382260

M. S. Gordon, Cardiology patient simulator, The American Journal of Cardiology, vol.34, issue.3, pp.350-355, 1974.
DOI : 10.1016/0002-9149(74)90038-1

R. Grant, B. Condon, I. Hart, and G. Teasdale, Changes in intracranial CSF volume after lumbar puncture and their relationship to post-LP headache., Journal of Neurology, Neurosurgery & Psychiatry, vol.54, issue.5, pp.440-443, 1991.
DOI : 10.1136/jnnp.54.5.440

R. E. Gross, P. Krack, M. C. Rodriguez-oroz, A. R. Rezai, and A. Benabid, Electrophysiological mapping for the implantation of deep brain stimulators for Parkinson's disease and tremor, Movement Disorders, vol.61, issue.S14, pp.259-83, 2006.
DOI : 10.1002/mds.20960

T. Guo, A. G. Parrent, and T. M. Peters, Automatic target and trajectory identification for deep brain stimulation (DBS) procedures. In Medical Image Computing and Computer-Assisted Intervention-MICCAI, pp.483-90, 2007.

A. Hagemann, K. Rohr, H. S. Stiehl, U. Spetzger, and J. M. Gilsbach, Biomechanical modeling of the human head for physically based, nonrigid image registration, IEEE Transactions on Medical Imaging, vol.18, issue.10, pp.875-84, 1999.
DOI : 10.1109/42.811267

N. Hamid, R. D. Mitchell, P. Mocroft, G. W. Westby, J. Milner et al., Targeting the subthalamic nucleus for deep brain stimulation: technical approach and fusion of pre- and postoperative MR images to define accuracy of lead placement, Journal of Neurology, Neurosurgery & Psychiatry, vol.76, issue.3, pp.409-423, 2005.
DOI : 10.1136/jnnp.2003.032029

H. Hamidian, H. Soltanian-zadeh, R. Faraji-dana, and M. Gity, Estimating Brain Deformation During Surgery Using Finite Element Method: Optimization and Comparison of Two Linear Models, Journal of Signal Processing Systems, vol.53, issue.10, pp.157-167, 2008.
DOI : 10.1007/s11265-008-0195-5

W. N. Hardy, C. D. Foster, M. J. Mason, K. H. Yang, A. I. King et al., Investigation of head injury mechanisms using neutral density technology and high-speed biplanar X-ray, 2001.

P. Hastreiter, Registration techniques for the analysis of the brain shift in neurosurgery, Computers & Graphics, vol.24, issue.3, pp.385-389, 2000.
DOI : 10.1016/S0097-8493(00)00034-0

S. Hemm, J. Coste, J. Gabrillargues, L. Ouchchane, L. Sarry et al., Contact position analysis of deep brain stimulation electrodes on post-operative CT images, Acta Neurochirurgica, vol.1, issue.7, pp.823-832, 2009.
DOI : 10.1007/s00701-009-0393-3

M. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Journal cf Research of the National Bureau of Standards, vol.49, issue.123, pp.81-85, 1952.

D. Hirtz, D. J. Thurman, K. Gwinn-hardy, M. Mohamed, . R. Chaudhuri et al., How common are the "common" neurologic disorders?, Neurology, vol.68, issue.5, pp.326-363, 2007.
DOI : 10.1212/01.wnl.0000252807.38124.a3

M. Hrapko, J. A. Van-dommelen, G. W. Peters, and J. S. Wismans, The Influence of Test Conditions on Characterization of the Mechanical Properties of Brain Tissue, Journal of Biomechanical Engineering, vol.130, issue.3, p.31003, 2008.
DOI : 10.1115/1.2907746

J. Hu, X. Jin, J. B. Lee, L. Zhang, V. Chaudhary et al., Intraoperative brain shift prediction using a 3D inhomogeneous patient-specific finite element model, Journal of Neurosurgery, vol.106, issue.1, pp.164-173, 2007.
DOI : 10.3171/jns.2007.106.1.164

O. O. Huston, R. E. Watson, M. A. Bernstein, K. P. Mcgee, S. M. Stead et al., Intraoperative magnetic resonance imaging findings during deep brain stimulation surgery, Journal of Neurosurgery, vol.115, issue.4, pp.852-857, 2011.
DOI : 10.3171/2011.5.JNS101457

Y. Ishiwata, K. Fujitsu, T. Sekino, H. Fujino, T. Kubokura et al., Subdural tension pneumocephalus following surgery for chronic subdural hematoma, Journal of Neurosurgery, vol.68, issue.1, pp.58-61, 1988.
DOI : 10.3171/jns.1988.68.1.0058

M. Jenkinson, P. Bannister, M. Brady, and S. Smith, Improved Optimization for the Robust and Accurate Linear Registration and Motion Correction of Brain Images, NeuroImage, vol.17, issue.2, pp.825-841, 2002.
DOI : 10.1006/nimg.2002.1132

M. Jenkinson and S. Smith, A global optimisation method for robust affine registration of brain images, Medical Image Analysis, vol.5, issue.2, pp.143-156, 2001.
DOI : 10.1016/S1361-8415(01)00036-6

C. Karachi, C. François, K. Parain, E. Bardinet, D. Tandé et al., Three-dimensional cartography of functional territories in the human striatopallidal complex by using calbindin immunoreactivity, Journal of Comparative Neurology, vol.332, issue.2, pp.26-31, 2002.
DOI : 10.1002/cne.10312

URL : https://hal.archives-ouvertes.fr/inria-00615628

M. Kass, A. Witkin, T. , and D. , Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

T. Kaster, I. Sack, and . Samani, Measurement of the hyperelastic properties of ex vivo brain tissue slices, Journal of Biomechanics, vol.44, issue.6, pp.1158-63, 2011.
DOI : 10.1016/j.jbiomech.2011.01.019

L. Kohn, J. Corrigan, and M. Donaldson, To Err Is Human:: Building a Safer Health System, National Academies Press, vol.627, 2000.

S. Kruse, G. H. Rose, K. J. Glaser, A. Manduca, J. P. Felmlee et al., Magnetic resonance elastography of the brain, NeuroImage, vol.39, issue.1, pp.231-238, 2008.
DOI : 10.1016/j.neuroimage.2007.08.030

R. Kumar, A. M. Lozano, Y. J. Kim, W. D. Hutchison, E. Sime et al., Double-blind evaluation of subthalamic nucleus deep brain stimulation in advanced Parkinson's disease, Neurology, vol.51, issue.3, pp.850-855, 1998.
DOI : 10.1212/WNL.51.3.850

K. Laksari, M. Shafieian, and K. Darvish, Constitutive model for brain tissue under finite compression, Journal of Biomechanics, vol.45, issue.4, pp.642-648, 2012.
DOI : 10.1016/j.jbiomech.2011.12.023

F. Lalys, C. Haegelen, T. Jannin, and P. , Analysis of electrode deformations in deep brain stimulation surgery, International Journal of Computer Assisted Radiology and Surgery, vol.24, issue.1, p.129, 2013.
DOI : 10.1007/s11548-013-0911-x

URL : https://hal.archives-ouvertes.fr/inserm-00836932

F. Lalys, C. Haegelen, J. Ferre, O. El-ganaoui, and P. Jannin, Construction and assessment of a 3-T MRI brain template, NeuroImage, vol.49, issue.1, pp.345-54, 2010.
DOI : 10.1016/j.neuroimage.2009.08.007

URL : https://hal.archives-ouvertes.fr/inserm-00546487

F. Lalys, C. Maumet, C. Haegelen, and P. Jannin, Analysis of Electrode placement and deformation in deep brain stimulation from medical images, Brain, pp.3-6, 2011.

T. Larsson and T. Akenine-möller, Collision detection for continuously deforming bodies, Eurographics, pp.325-333, 2001.

J. Lenoir, P. Meseure, L. Grisoni, and C. Chaillou, Surgical thread simulation, ESAIM: Proceedings, pp.102-107, 2002.
DOI : 10.1051/proc:2002017

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

P. Limousin and P. Krack, Electrical Stimulation of the Subthalamic Nucleus in Advanced Parkinson's Disease, New England Journal of Medicine, vol.339, issue.16, pp.1105-1111, 1998.
DOI : 10.1056/NEJM199810153391603

P. Limousin, P. Pollak, and A. Benazzouz, Effect on parkinsonian signs and symptoms of bilateral subthalamic nucleus stimulation. The Lancet, pp.91-95, 1995.

E. L. Lin, D. K. Park, P. G. Whang, H. S. An, and F. M. Phillips, O-Arm Surgical Imaging System, Seminars in Spine Surgery, vol.20, issue.3, pp.209-213, 2008.
DOI : 10.1053/j.semss.2008.06.008

S. A. Lippert, E. M. Rang, and M. J. Grimm, The high frequency properties of brain tissue, Biorheology, vol.41, issue.6, pp.681-691, 2004.

C. Lurig, P. Hastreiter, C. Nimsky, and T. Ertl, Analysis and Visualization of the Brain Shift Phenomenon in Neurosurgery, TCVG Symposium on Visualization (VisSym), pp.285-290, 1999.
DOI : 10.1007/978-3-7091-6803-5_28

J. Marescaux, J. M. Clément, V. Tassetti, C. Koehl, S. Cotin et al., Virtual Reality Applied to Hepatic Surgery Simulation: The Next Revolution, Annals of Surgery, vol.228, issue.5, pp.627-661, 1998.
DOI : 10.1097/00000658-199811000-00001

URL : https://hal.archives-ouvertes.fr/inria-00615079

H. S. Mayberg, A. M. Lozano, V. Voon, H. E. Mcneely, D. Seminowicz et al., Deep Brain Stimulation for Treatment-Resistant Depression, Neuron, vol.45, issue.5, pp.651-60, 2005.
DOI : 10.1016/j.neuron.2005.02.014

S. Mehdizadeh, M. Khoshgoftar, S. Najarian, F. Farmanzad, and S. A. Ahmadi, Comparison between Brain Tissue Gray and White Matters in Tension Including Necking Phenomenon, American Journal of Applied Sciences, vol.5, issue.12, pp.1701-1706, 2008.
DOI : 10.3844/ajassp.2008.1701.1706

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949.
DOI : 10.1080/01621459.1949.10483310

M. I. Miga, K. D. Paulsen, P. J. Hoopes, F. E. Kennedy, . Hartov et al., In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery, IEEE Transactions on Biomedical Engineering, vol.47, issue.2, pp.266-73, 2000.
DOI : 10.1109/10.821778

M. I. Miga, K. D. Paulsen, P. J. Hoopes, K. Jr, F. E. Hartov et al., In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery, IEEE Transactions on Biomedical Engineering, vol.47, issue.2, pp.266-273, 2000.
DOI : 10.1109/10.821778

M. I. Miga, K. D. Paulsen, J. M. Lemery, S. D. Eisner, . Hartov et al., Model-updated image guidance: initial clinical experiences with gravity-induced brain deformation, IEEE Transactions on Medical Imaging, vol.18, issue.10, pp.866-74, 1999.
DOI : 10.1109/42.811265

K. Miller and K. Chinzei, Mechanical properties of brain tissue in tension, Journal of Biomechanics, vol.35, issue.4, pp.483-490, 2002.
DOI : 10.1016/S0021-9290(01)00234-2

K. Miller, . Horton, G. R. Joldes, and . Wittek, Beyond finite elements: A comprehensive, patient-specific neurosurgical simulation utilizing a meshless method, Journal of Biomechanics, vol.45, issue.15, pp.2698-701, 2012.
DOI : 10.1016/j.jbiomech.2012.07.031

K. Miller and J. Lu, On the prospect of patient-specific biomechanics without patient-specific properties of tissues, Journal of the Mechanical Behavior of Biomedical Materials, vol.27, issue.62, p.58, 2013.
DOI : 10.1016/j.jmbbm.2013.01.013

K. Miller, A. Wittek, J. , and G. , Biomechanics of the brain for computer-integrated surgery, 2002.

K. Miller, A. Wittek, J. , and G. , Biomechanical Modeling of the Brain for Computer-Assisted Neurosurgery, Biomechanics of the Brain, pp.111-136, 2011.
DOI : 10.1007/978-1-4419-9997-9_6

M. Mooney, A Theory of Large Elastic Deformation, Journal of Applied Physics, vol.11, issue.9, p.582, 1940.
DOI : 10.1063/1.1712836

R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca et al., Magnetic resonance elastography by direct visualization of propagating acoustic strain waves, Science, vol.269, issue.5232, pp.2691854-1857, 1995.
DOI : 10.1126/science.7569924

A. Myronenko and X. Song, Intensity-Based Image Registration by Minimizing Residual Complexity, IEEE Transactions on Medical Imaging, vol.29, issue.11, pp.1882-1891, 2010.
DOI : 10.1109/TMI.2010.2053043

N. Nakano, M. Taneda, A. Watanabe, and A. Kato, Computed Three-Dimensional Atlas of Subthalamic Nucleus and Its Adjacent Structures for Deep Brain Stimulation in Parkinson's Disease, ISRN Neurology, vol.123, issue.10, p.592678, 2012.
DOI : 10.1136/jnnp.2003.016485

J. M. Nazzaro, K. E. Lyons, R. Honea, M. S. Mayo, G. Cook-wiens et al., Head positioning and risk of pneumocephalus, air embolism, and hemorrhage during subthalamic deep brain stimulation surgery, Acta Neurochirurgica, vol.77, issue.12, pp.2047-52, 2010.
DOI : 10.1007/s00701-010-0776-5

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-3105, 1965.
DOI : 10.1093/comjnl/7.4.308

R. V. Noort, M. Black, T. Martin, and S. Meanley, A study of the uniaxial mechanical properties of human dura mater preserved in glycerol, Biomaterials, issue.2, 1981.

W. L. Nowinski and C. Chui, Simulation of interventional neuroradiology procedures, Proceedings International Workshop on Medical Imaging and Augmented Reality, pp.87-94, 2001.
DOI : 10.1109/MIAR.2001.930269

R. Ogden, Large Deformation Isotropic Elasticity - On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.326, issue.1567, pp.565-584, 1567.
DOI : 10.1098/rspa.1972.0026

A. Ommaya, Mechanical properties of tissues of the nervous system, Journal of Biomechanics, vol.1, issue.2, pp.127-138, 1967.
DOI : 10.1016/0021-9290(68)90015-8

P. , L. Mauro, A. Raczkowsky, J. , A. et al., Virtual model of the human brain for neurosurgical simulation. Studies in health technology and informatics, pp.811-815, 2009.

K. D. Paulsen, M. I. Miga, F. E. Kennedy, P. J. Hoopes, . Hartov et al., A computational model for tracking subsurface tissue deformation during stereotactic neurosurgery, IEEE Transactions on Biomedical Engineering, vol.46, issue.2, pp.213-238, 1999.
DOI : 10.1109/10.740884

X. Pennec, N. Ayache, . Roche, and P. Cachier, Non-rigid MR/US registration for tracking brain deformations, Proceedings International Workshop on Medical Imaging and Augmented Reality, pp.79-86, 2005.
DOI : 10.1109/MIAR.2001.930268

URL : https://hal.archives-ouvertes.fr/inria-00615898

P. Perozzo, M. Rizzone, B. Bergamasco, L. Castelli, M. Lanotte et al., Deep brain stimulation of the subthalamic nucleus in Parkinson's disease: comparison of pre- and postoperative neuropsychological evaluation, Journal of the Neurological Sciences, vol.192, issue.1-2, pp.9-15, 2001.
DOI : 10.1016/S0022-510X(01)00575-5

I. Peterí-ik, C. Duriez, C. , and S. , Modeling and real-time simulation of a vascularized liver tissue, Medical Image Computing and Computer-Assisted Intervention--MICCAI 2012, pp.50-57, 2012.

P. Pollak, A. Benabid, C. Gross, D. M. Gao, A. Laurent et al., Effects of the stimulation of the subthalamic nucleus in Parkinson disease, Revue neurologique, vol.149, issue.17, pp.175-176, 1992.

C. Pollo, J. Villemure, F. Vingerhoets, J. Ghika, P. Maeder et al., Magnetic resonance artifact induced by the electrode Activa 3389: an in vitro and in vivo study, Acta Neurochirurgica, vol.146, issue.2, pp.161-165, 2004.
DOI : 10.1007/s00701-003-0181-4

F. Ponce and A. M. Lozano, Erratum: Highly cited works in neurosurgery. Part II: the citation classics, Journal of Neurosurgery, vol.120, issue.5, pp.1252-1259, 2014.
DOI : 10.3171/2014.2.JNS14358a

D. C. Popescu and M. Compton, A model for efficient and accurate interaction with elastic objects in haptic virtual environments, Proceedings of the 1st international conference on Computer graphics and interactive techniques in Austalasia and South East Asia , GRAPHITE '03, pp.245-250, 2003.
DOI : 10.1145/604471.604518

M. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives. The computer journal, 1964.

J. S. Przemieniecki, Theory of matrix structural analysis, Courier Dover Publications, 1985.

R. H. Pudenz and C. H. Shelden, The Lucite Calvarium???A Method for Direct Observation of the Brain, Journal of Neurosurgery, vol.3, issue.6, pp.487-505, 1946.
DOI : 10.3171/jns.1946.3.6.0487

L. Raghupathi, L. Grisoni, F. Faure, D. Marchall, M. Cani et al., An intestinal surgery simulator: real-time collision processing and visualization, IEEE, pp.708-718, 2004.
DOI : 10.1109/TVCG.2004.36

URL : https://hal.archives-ouvertes.fr/inria-00537466

V. Rajagopal and J. C. Chung, Determining the finite elasticity reference state from a loaded configuration, International Journal for Numerical Methods in Engineering, vol.242, issue.12, pp.1434-1451, 2007.
DOI : 10.1002/nme.2045

V. Rajagopal, J. C. Chung, P. M. Nielsen, and M. P. Nash, Finite element modelling of breast biomechanics: finding a reference state, 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, pp.3268-71, 2005.
DOI : 10.1109/IEMBS.2005.1617174

V. Rajagopal, J. C. Chung, P. M. Nielsen, and M. P. Nash, Finite Element Modelling of Breast Biomechanics: Directly Calculating the Reference State, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society, pp.420-423, 2006.
DOI : 10.1109/IEMBS.2006.260047

D. Rasche, P. Rinaldi, R. Young, and V. Tronnier, Deep brain stimulation for the treatment of various chronic pain syndromes, Neurosurgical Focus, vol.21, issue.6, pp.1-8, 2006.
DOI : 10.3171/foc.2006.21.6.10

J. Reddy, An introduction to continuum mechanics, 2007.
DOI : 10.1017/CBO9780511800894

I. Reinertsen, M. Descoteaux, K. Siddiqi, C. , and D. L. , Validation of vessel-based registration for correction of brain shift, Medical Image Analysis, vol.11, issue.4, pp.374-88, 2007.
DOI : 10.1016/j.media.2007.04.002

I. Reinertsen, F. Lindseth, C. Askeland, D. H. Iversen, and G. Unsgå-rd, Intra-operative correction of brain-shift, Acta Neurochirurgica, vol.14, issue.7, 2014.
DOI : 10.1007/s00701-014-2052-6

R. S. Rivlin, Large Elastic Deformations of Isotropic Materials. I. Fundamental Concepts, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.240, issue.822, pp.459-490, 1948.
DOI : 10.1098/rsta.1948.0002

G. Schaltenbrand, W. Wahren, and R. Hassler, Atlas for Stereotaxy of the Human Brain, Thieme, 1977.

P. Schiavone, F. Chassat, T. Boudou, E. Promayon, F. Valdivia et al., In vivo measurement of human brain elasticity using a light aspiration device, Medical Image Analysis, vol.13, issue.4, pp.673-681, 2009.
DOI : 10.1016/j.media.2009.04.001

URL : https://hal.archives-ouvertes.fr/hal-00374101

M. Schulder and P. W. Carmel, Intraoperative magnetic resonance imaging: impact on brain tumor surgery, Cancer control : journal of the Moffitt Cancer Center, vol.10, issue.2, pp.115-139, 2003.

M. Sellier, An iterative method for the inverse elasto-static problem, Journal of Fluids and Structures, vol.27, issue.8, pp.1461-1470, 2011.
DOI : 10.1016/j.jfluidstructs.2011.08.002

C. Senft, A. Bink, K. Franz, H. Vatter, T. Gasser et al., Intraoperative MRI guidance and extent of resection in glioma surgery: a randomised, controlled trial, The Lancet Oncology, vol.12, issue.11, pp.997-1003, 2011.
DOI : 10.1016/S1470-2045(11)70196-6

R. R. Shamir, I. Tamir, E. Dabool, L. Joskowicz, and Y. Shoshan, A method for planning safe trajectories in image-guided keyhole neurosurgery. Medical Image Computing and Computer-Assisted Intervention--MICCAI, pp.1-8, 2010.

O. Skrinjar, A. Nabavi, D. , and J. S. , Model-driven brain shift compensation, Medical Image Analysis, vol.6, issue.4, pp.361-73, 2002.
DOI : 10.1016/S1361-8415(02)00062-2

P. J. Slotty, M. A. Kamp, C. Wille, T. M. Kinfe, H. J. Steiger et al., The impact of brain shift in deep brain stimulation surgery: observation and obviation, Acta Neurochirurgica, vol.76, issue.11, pp.2063-2071, 2012.
DOI : 10.1007/s00701-012-1478-y

P. A. Starr, C. W. Christine, P. V. Theodosopoulos, N. Lindsey, D. Byrd et al., Implantation of deep brain stimulators into subthalmic nucleus: technical approach and magnetic imaging???verified electrode locations, Journal of Neurosurgery, vol.97, issue.2, 2002.
DOI : 10.3171/jns.2002.97.2.0370

H. Takizawa and K. Sugiura, Analysis of Intracerebral Hematoma Shapes by Numerical Computer Simulation Using the Finite Element Method, Neurologia medico-chirurgica, vol.34, issue.2, 1994.
DOI : 10.2176/nmc.34.65

J. Talairach and P. Tournoux, Co-planar stereotaxic atlas of the human brain. 3-Dimensional proportional system: an approach to cerebral imaging, 1988.

H. Talbot, F. Spadoni, C. Duriez, M. Sermesant, S. Cotin et al., Interactive Training System for Interventional Electrocardiology Procedures, Biomedical Simulation, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01338346

M. Tang, S. Curtis, S. Yoon, and D. Manocha, ICCD: Interactive Continuous Collision Detection between Deformable Models Using Connectivity-Based Culling, IEEE Transactions on Visualization and Computer Graphics, vol.15, issue.4, pp.544-57, 2009.
DOI : 10.1109/TVCG.2009.12

L. Thines, F. Lemarchand, and J. Francke, Atlas interactif de neuroanatomie clinique: Atlas photographique, p.18, 2008.

F. Tong, A. Ramirez-zamora, L. Gee, and J. Pilitsis, Unusual complications of deep brain stimulation, Neurosurgical Review, vol.110, issue.Suppl 2, 2014.
DOI : 10.1007/s10143-014-0588-9

R. Toro, M. Perron, B. Pike, L. Richer, S. Veillette et al., Brain Size and Folding of the Human Cerebral Cortex, Cerebral Cortex, vol.18, issue.10, pp.182352-182359, 1991.
DOI : 10.1093/cercor/bhm261

A. Valencia, B. Blas, and J. H. Ortega, Modeling of Brain Shift Phenomenon for Different Craniotomies and Solid Models, Journal of Applied Mathematics, vol.24, issue.5, pp.1-20, 2012.
DOI : 10.1016/S1053-8119(02)00017-4

P. Van-den-munckhof, M. F. Contarino, L. J. Bour, J. D. Speelman, R. M. De-bie et al., Postoperative Curving and Upward Displacement of Deep Brain Stimulation Electrodes Caused by Brain Shift, Neurosurgery, vol.67, issue.1, pp.49-53, 2010.
DOI : 10.1227/01.NEU.0000370597.44524.6D

N. L. Van-essen, I. Anderson, P. J. Hunter, J. Carman, R. D. Clarke et al., Anatomically Based Modelling of the Human Skull and Jaw, Cells Tissues Organs, vol.180, issue.1, pp.44-53, 2005.
DOI : 10.1159/000086198

M. Viceconti and F. Taddei, Automatic Generation of Finite Element Meshes from Computed Tomography Data, Critical Reviews in Biomedical Engineering, vol.31, issue.1-2, p.31, 2003.
DOI : 10.1615/CritRevBiomedEng.v31.i12.20

L. M. Vigneron, L. Noels, S. K. Warfield, J. G. Verly, and P. And-robe, Serial FEM/XFEM-Based Update of Preoperative Brain Images Using Intraoperative MRI, International Journal of Biomedical Imaging, vol.2, issue.11, pp.872783-60, 2012.
DOI : 10.1002/nme.1291

V. Visser-vandewalle, D. Huys, I. Neuner, L. Zrinzo, M. S. Okun et al., Deep Brain Stimulation for Tourette syndrome: The Current State of the Field, Journal of Obsessive-Compulsive and Related Disorders, vol.3, issue.4, pp.1-6, 2014.
DOI : 10.1016/j.jocrd.2014.06.005

?. Skrinjar, O. Spencer, D. , D. , and J. S. , Brain shift modeling for use in neurosurgery. Medical Image Computing and Computer-Assisted Interventation ? MICCAI'98, p.58, 1998.

D. Wang, L. Shi, W. C. Chu, J. C. Cheng, and P. A. Heng, Segmentation of human skull in MRI using statistical shape information from CT data, Journal of Magnetic Resonance Imaging, vol.2, issue.3, pp.490-498, 2009.
DOI : 10.1002/jmri.21864

E. Wang, T. Nelson, and R. Rauch, Back to elements-tetrahedra vs. hexahedra, Proceedings of the 2004 International ANSYS Conference. [Cited on page 65, 2004.

P. Wang, . Becker, I. Jones, . T. Glover, S. D. Benford et al., A virtual reality surgery simulation of cutting and retraction in neurosurgery with force-feedback. Computer methods and programs in biomedicine, pp.11-19, 2006.

S. W. Winchell and P. Safar, Teachin and Testing Lay and Paramedical Personnel in Cardiopulmonary Resuscitation, Anesthesia & Analgesia, vol.45, pp.441-449, 1966.

A. Wittek, G. Joldes, and K. Miller, Algorithms for Computational Biomechanics of the Brain, Biomechanics of the Brain, pp.189-219, 2011.
DOI : 10.1007/978-1-4419-9997-9_9

A. Wittek, K. Miller, R. Kikinis, and S. K. Warfield, Patient-specific model of brain deformation: Application to medical image registration, Journal of Biomechanics, vol.40, issue.4, pp.919-948, 2007.
DOI : 10.1016/j.jbiomech.2006.02.021

J. Yelnik, E. Bardinet, D. Dormont, G. Malandain, S. Ourselin et al., A three-dimensional, histological and deformable atlas of the human basal ganglia. I. Atlas construction based on immunohistochemical and MRI data, NeuroImage, vol.34, issue.2, pp.618-656, 2007.
DOI : 10.1016/j.neuroimage.2006.09.026

URL : https://hal.archives-ouvertes.fr/inria-00616029

H. Yousefi, A. Ahmadian, and D. Khodadad, An Optimised Linear Mechanical Model for Estimating Brain Shift Caused by Meningioma Tumours, International Journal of Biomedical Science and Engineering, vol.1, issue.1, pp.1-9, 2013.
DOI : 10.11648/j.ijbse.20130101.11

C. Zhang, M. Wang, and Z. Song, A Brain-Deformation Framework Based on a Linear Elastic Model and Evaluation Using Clinical Data, IEEE Transactions on Biomedical Engineering, vol.58, issue.1, pp.191-200, 2011.
DOI : 10.1109/TBME.2010.2070503

L. Zrinzo, A. L. Van-hulzen, A. Gorgulho, P. Limousin, M. J. Staal et al., Avoiding the ventricle: a simple step to improve accuracy of anatomical targeting during deep brain stimulation, Journal of Neurosurgery, vol.110, issue.6, pp.1283-90, 2009.
DOI : 10.3171/2008.12.JNS08885