Surgical simulators are valuable tools for surgical planning and training, and their usability is improving dramatically due to advancements in hardware and simulation techniques. One of the main challenges in this domain is the modeling of deformable objects. Precise methods for modeling deformable objects that are based on Continuum Mechanics cannot be implemented on a CPU in real time for a high number of polygonal meshes. Faster methods like Mass-Spring systems are not realistic enough and additional constraints are required for better simulation which makes them computationally expensive. Moreover, pre-computed methods which are faster and capable of modeling large deformations, are unable to model a wide range of object interactions which are essential for surgery simulation. Fortunately, NVIDIA's CUDA is an affordable technology enabling users to take advantage of GPU's parallel processing capability. We have developed a framework which uses meshfree methods for modeling deformable objects and uses CUDA to accelerate its calculation. By using the CUDA technology we were able to achieve up to 20 times speed up for large meshes, and provide real-time animation to support surgical planning and guidance. We have compared the accuracy of these methods with experimental data and provided guidelines for choosing a simulation method based on the application. In addition, we have developed a new method for modeling deformable objects called Local Shape Matching which is fast and stable.;Needle insertion is a common task within many different medical procedures. Therefore, the simulation of needle insertion can provide a tool for multiple purposes such as training, planning and the guidance of biopsies, endoscopic or robot-assisted interventions. Modeling of soft tissue plays an important role in needle insertion simulation, but the use of mesh based methods such as the Finite Element Method is frustrated by the need for remeshing in the neighborhood of the needle tip. We have developed a novel method that uses a meshfree formulation for the tissue deformation model. In this method, new tissue nodes are added on the needle shaft as the needle is inserted into the tissue. Our results showed that using our approach meshfree methods can be efficiently used for needle insertion simulation.
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