In spite of the computational load of FEM; it is still the most popular method to model physically realistic deformations for soft tissue. While it is easier to solve linear FEM equations in real-time; it is observed that soft tissues have non-linear behaviour; such that the linear deformation becomes un-realistic if the size of the deformation exceeds a threshold (typically 10% of the original tissue size). In addition to non-linearity; soft tissues may also have various complex behaviours like visco-elasticity and anisotropicity increasing the computational burden. If tissue cutting is also to be simulated; the model should be updated both physically and virtually; which makes the real time simulations even harder.
To reach a compromise between the necessity of high haptic refresh rates and the computational burden of the FEM; several optimization techniques such as condensation [Bro-Nielsen and Cotin 1996]; pre-computation [Cotin et al. 1999; Sedef et al. 2006; Sela et al. 2007]; level of detail [Debunne et al. 2001]; and exploitation of the sparse matrix structure have been introduced in simulations. Current simulators; however; still have to either sacrifice one property of real tissues such as non-linearity; anisotropicity or visco-elasticity; or apply force interpolation or extrapolation techniques to reach a sufficient haptic refresh rate (1 kHz). Therefore solution of large FEM systems in real-time to be used in soft-tissue deformations is still a challenge for which new solutions are being sought.
Keywords: Soft tissue deformation; surgery simulation; FEM