Real time simulation of nonlinear tissue response in virtual surgery using the point collocation-based method of finite spheres

The point collocation-based method of finite spheres (PCMFS) was introduced as a meshfree technique for real time simulation of surgical processes. While real time graphical rendering requires an update rate of about 30 Hz, a much higher update rate of 1 kHz is necessary for smooth haptic (touch) feedback. The requirement of real time performance is crucial to these simulations and is highly demanding in terms of computational efficiency. In this paper we extend the PCMFS technique to tissue deformations that are geometrically nonlinear. The technique is based on a novel combination of multiresolution approach coupled with a fast reanalysis scheme in which the response predicted by an underlying linear PCMFS model is enhanced in the local neighborhood of the surgical tool-tip by a nonlinear model. We present performance comparisons of PCMFS with traditional finite element models.