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Section: Research Program
Numerical Methods for Complex Interactions
Dynamic topological changes
As mentioned previously, assisting the surgeon by providing either pre-operative planning or per-operative guidance assumes to increase the level of complexity and accuracy of our models, thus making the simulation more computationally-demanding. Innovative numerical methods must therefore be investigated. For instance, efforts are made to couple SOFA with CGoGN. CGoGN is a library based on combinatorial maps theory, specialized for representing and manipulating meshes. It is able to represent consistently objects of different dimensions composed of arbitrary cells (polygonal faces, polyhedral volumes). It provides an efficient way to explore the cells and their neighborhood; it allows to store data with the cells (both at execution time and compile time) and to efficiently modify the connectivity of the mesh even in highly dynamic cases. Adaptive meshing and efficient topological algorithm are thus available in SOFA.
Constraint models and boundary conditions
To simulate soft-tissue deformations accurately, the modeling technique must account for the intrinsic behavior of the modeled organ as well as for its biomechanical interactions with surrounding tissues or medical devices. While the biomechanical behavior of important organs (such as the brain or liver) has been studied extensively in the past, only few works exist dealing with the mechanical interactions between the anatomical structures. For tissue–tool interactions, most techniques rely on simple contact models, whereas advanced phenomena such as friction are rarely taken into account. While simplifications can produce plausible results in the case of interaction between the manipulator of a laparoscopic instrument and the surface of an organ, it is generally an insufficient approximation. As we move towards the simulations for planning or rehearsal, accurate modeling of contacts is playing an increasingly important role. For example, we have shown in [36] and [37] that complex interactions between a coil and an aneurysm, or alternatively between a flexible needle and a soft-tissue can be computed in real-time. In laparoscopic surgery, the main challenge is represented by modeling of interactions between anatomical structures rather than only between the instruments and the surface of the organ. Consequently, our objective was to model accurately the contacts with friction and other type on non-smooth interactions in a heterogeneous environment and to allow for stable haptic rendering. When different time integration strategies are used, another challenge is to compute the contact forces in such a way that integrity and stability of the overall simulation are maintained. Our objective was to propose a unified definition of such various boundary conditions and develop new numerical methods for simulations of heterogeneous objects.