The generation of multimodal virtual environments for surgical training is complicated by the necessity to develop heterogeneous scenarios involving the interaction of surgical tools with soft biological tissues in real time with complex outcomes such as surgical incision, cauterization, bleeding and smoke generation. While several techniques ranging from rapid but nonphysical geometry-based procedures to complex but tardy finite element (FE) techiniques have been proposed, none is uniquely suited to solve the virtual surgery problem.
In this paper we present a promising new technique, the point-associated finite field (PAFF) approach, for real time surgery simulation. PAFF is a specialized version of a meshfree discretization scheme known as the method of finite spheres  in which partial differential equations may be solved on geometrically complex domains discretized using a scattered distribution of points. Unlike traditional mesh-based FE techniques, large tissue deformations, including surgical cutting, are particularly straightforward to handle using PAFF since interpolation functions are compactly supported on spherical subdomains which may intersect and overlap and are not constrained to abut each other as in the FEM.
We will present several specializations of this scheme having various operational complexities. The accuracy and efficiency of this technique will be compared with solutions using traditional finite element methods.
 S. De, and K. J. Bathe, "The Method of Finite Spheres," Computational Mechanics, v. 25, p. 329-345, 2000.
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