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Section: Research Program
Interaction models
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 instance, we have shown in [30] and [31] that complex interactions between a coil and aneurysm, or alternatively between a flexible needle and 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.
Coupled biophysical systems
Research dealing with interactive medical simulations is currently limited to (bio-)mechanical aspects. However, an important step needs to be done to capture more precisely the complex nature of human organs such as liver or heart: the liver can be regarded as a composite structure made of parenchyma, vessels and a capsule, while a complete simulation of heart requires a coupled electro-mechanical model. Moreover, computing the interactions (or coupling) between anatomical structures can be useful for a simulation of larger systems; for instance we are investigating the modeling of connective tissues. Since the solutions to the above-mentioned problems usually lead to very large systems of equations, our strategy is based on approach similar to that used in domain-decomposition: instead of solving the large system at once, we propose techniques where one system per model is solved in order to improve the efficiency of solution procedures.