SOFA (Simulation Open Framework Architecture) is an open-source C++ library primarily targeted at interactive computational medical simulation. SOFA facilitates collaborations between specialists from various domains, by decomposing complex simulators into components designed independently and organized in a scenegraph data structure. Each component encapsulates one of the aspects of a simulation, such as the degrees of freedom, the forces and constraints, the differential equations, the main loop algorithms, the linear solvers, the collision detection al- Authors Suppressed Due to Excessive Length gorithms or the interaction devices. The simulated objects can be represented using several models, each of them optimized for a different task such as the computation of internal forces, collision detection, haptics or visual display. These models are synchronized during the simulation using a mapping mechanism. CPU and GPU implementations can be transparently combined to exploit the computational power of modern hardware architectures. Thanks to this flexible yet efficient architecture, SOFA can be used as a test-bed to compare models and algorithms, or as a basis for the development of complex, high-performance simulators.

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and other topological changes. We provide an integrated methodology able to deal both with the ill-conditioning issues associated with material heterogeneities, contact boundary conditions which are one of the main sources of inaccuracies, and cutting which is one of the most challenging issues in interactive simulations. Our approach is based on an implicit time integration of a non-linear finite element model. To enable real-time computations, we propose a new preconditioning technique, based on an asynchronous update at low frequency. The preconditioner is not only used to improve the computation of the deformation of the tissues, but also to simulate the contact response of homogeneous and heterogeneous bodies with the same accuracy. We also address the problem of cutting the heterogeneous structures and propose a method to update the preconditioner according to the topological modifications. Finally, we apply our approach to three challenging demonstrators: i) a simulation of cataract surgery ii) a simulation of laparoscopic hepatectomy iii) a brain tumor surgery.

This article describes a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, this article presents results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions described in this article share a common underlying model of deformation and rely on GPU implementations to significantly improve computation times. This consistency in the modelling technique and computational approach ensures coherent results as well as efficient, robust and flexible solutions.

Figure 1: Left: A stack of tori, with the intersection volumes and normals on the GPU. Right: intersection volume constraints allow us to resolve frictional contact in challenging scenarios.

In this paper, a new constraint-based biomechanical simulation method is proposed to compensate for craniotomy-induced brain-shift. While being efficient to correct this deformation, the method is fully integrable in a clinical process.

Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.

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Virtual cutting of deformable objects is at the core of many applications in interactive simulation and especially in computational medicine. The ability to simulate surgical cuts, dissection, soft tissue tearing or micro-fractures, is essential for augmenting the capabilities of existing or future simulation systems. To support such features, we combine a new remeshing algorithm with a fast finite element approach. The proposed method is generic enough to support a large variety of applications. We show the benefits of our approach evaluating the impact of cuts on the number of nodes and the numerical quality of the mesh. These points are crucial to ensure accurate and stable realtime simulations.