W. Niessen and M. Viergever (Eds.): MICCAI 2001, LNCS 2208, pp. 1271-1272, 2001.  Springer-Verlag Berlin Heidelberg 2001 Non-linear Soft Tissue Deformations for the Simulation of Percutaneous Surgeries Jean-Marc Schwartz 1 , ¨ve Langelier 2 , Christian Moisan 3 , and Denis Laurendeau 1 1 Computer Vision and Systems Laboratory, Univ. Laval, QuØbec (Qc) G1K 7P4, Canada 2 Biomechanics Laboratory, Univ. Laval, QuØbec (Qc) G1K 7P4, Canada 3 iMRI Unit, Quebec City University Hospital, QuØbec (Qc) G1L 3L5, Canada Abstract. We introduce a non-linear extension of the tensor-mass method for real-time computation of biological soft tissue deformations. We aim at devel- oping a simulation tool for the planning of cryogenic surgical treatment of liver cancer. This therapy requires careful planning, therefore accurate modeling of the mechanical behavior of organs is required. Our method presently allows real-time computation of non-linear elastic tissue deformations, and further ex- tension towards viscoelasticity modeling is planned. 1 Introduction The development of surgery simulation systems requires fast algorithms to allow real- time computation of tissue deformations, as well as accurate modeling of soft tissue mechanical properties. We are currently developing a simulation tool for the planning of percutaneous image-guided cryosurgical treatment of liver cancer. This therapy consists in destroying tumor cells through successive application of freezing and pas- sive thawing cycles [3]. Careful planning is required to optimize the destruction of tumor cells vs. damage to healthy cells. In particular accurate modeling of the geomet- ric, thermal, and mechanical behavior of organs is required. Several methods have been reported for rapid calculation of linear elastic mechani- cal deformations, from relatively simple physical models such as the spring-mass model to models based of continuum mechanics such as the Finite Element Method [1]. However experimental characterizations suggest that linear elasticity is only a coarse approximation of real properties of biological soft tissues. Among other stud- ies, Miller et al. [2] identified a viscoelastic constitutive model as accurate for model- ing brain tissue deformations. 2 Non-linear Modeling The most promising approach towards real-time computation of non-linear viscoelas- ticity appeared to be the tensor-mass model introduced by Cotin et al. [1], as it is both time-efficient and physically accurate. It additionally allows local topological changes on mesh elements so that simulation of cutting or perforation is possible. As a first step we show that adequate real-time correction of linear elasticity parameters allows to model different types of non-linear elastic deformations. In our model, expression of force ) ( j T i F applied on vertex ) ( j T i P within a tetrahedral mesh element T i is: