Table 1.

Survey of tool-tissue interaction models for surgical simulation and robot-assisted surgery. Within each category, authors are listed alphabetically and simulators that provide haptic feedback are designated by †.

Operation		Model
		Linear elastic FE	Hyperelastic FE	Visco-hyperelastic FE	Other methods
Deformation (via indentation)	Simulation only	Basdogan et al. †	Y. Liu et al.	Puso and Weiss	LEM (2002LEM (2002) †
		Bro-Nielsen	X. Wu et al.		Mass- (1994; 1996; 1996)
		Cotin et al. †			spring- (2003 (1992)
		Frank, Twombly, Barth, and Smith			damper model (2000)
		Gladilin et al.			Thin-walled model (1999)
		Kühnapfel et al. †			PCMFS (2005) †and PAFF (2006) †
					BEM solution (2001)
					J-shaped function (1994)
	Real/Phantom tissue studies	Gosline et al. †	Carter et al.	Székely et al. †	Curve-fitting (2003)
		Kerdok et al.	Chui et al.		Green’s function (2002)
		Sedef et al.-	Davies et al.	Miller
		viscoelastic	Hu and Desai	Nava et al.
			Molinari et al.	Kim et al.
Rupture (via needle insertion)	Simulation only	Alterovitz et al.	Nienhuys and van der Stappen		Spring model (2004)
					Volume model (2001)
					3D chain mail (2004)
	Real/Phantom tissue studies	Crouch et al.			Resistive-(1997) †
		DiMaio and Salcudean †			force model (2000) †
		Hing et al.			Curve-fitting (2001)
					Friction model (2004)
Cutting (via blade/scissors)	Simulation only	Picinbono et al. †	Picinbono et al.		Hybrid model (2000)
		W. Wu and Heng
	Real/Phantom tissue studies	Chanthasopeephan et al.			Fracture mechanics (2001)
					Haptic Scissors (2003)