Page 405 - Biomedical Engineering and Design Handbook Volume 2, Applications

SURGICAL SIMULATION TECHNOLOGIES 383

used, and it is possible to perform extensive off-line calculations to significantly reduce the real-time
computational burden. However, linear models are based on the assumption of small deformation,
which is not valid for large manipulations of the soft tissue during parts of surgery.
These models cannot handle rigid motions either. Linear models lose their computational advan-
tage under topology changes, for example, as a result of cutting, as the off-line calculations cannot be
used. Nonlinear finite element models are highly accurate models, which take into account nonlinear
constitutive behaviors of the materials as well as large deformation effects. Nonlinear finite element
models have been used extensively in biomechanics literature to model tissue deformations with off-
line computations. 36 These models are computationally intensive, and therefore development of
suitable algorithms for their real-time simulation is required. 15,37–41 Hybrid modeling approaches
employing models of different types have also been proposed to address computational limitation
while taking advantage of the strength of each of the modeling approaches. For example, Delingette 42
proposed to use lumped element models locally where there is topological change (such as cutting)
and use a linear finite element model for the rest.
An important characteristic of the surgical manipulation is its topology changing nature. During
surgical manipulation, the soft tissue are routinely cut, punctured, sutured, etc. Such manipulations
bring significant modeling and computational challenges. These types of manipulations require mod-
els to include highly nonlinear and discontinuous deformable object behavior, such as, plasticity and
43
fractures. They also require online modification of the geometric models, and sometimes remesh-
ing of the object. 44 The mesh modifications typically increase the number of elements used in the
computation, increasing the computational complexity of the models. Furthermore, when geometric
models of objects are modified, most precomputations performed become invalid, increasing the
computational complexity even more.
The measurement of the tissue parameters for live tissue is a difficulty that is widely recognized
in the literature. Not only the mechanical characteristics of tissue are highly nonlinear and time depen-
dant, but also there is significant variability between different subjects. 45,46 However, it is important
to realize that, for a training simulator, it is only necessary to provide qualities of the tissue behavior
that the human operator can actually sense. Psychophysics studies on the haptic sensory-motor abil-
ities of the human operator 47–49 reveal that humans are haptically more sensitive in detecting changes
in mechanical impedances than they are in identifying the absolute values of these impedances.
These results coupled with the inherent variability of the actual tissue properties suggest that it would
be acceptable for a training simulator to use approximate tissue parameter values, such as those
available in the literature. 50,51 However, it is important to include the nonlinear shape of the consti-
tutive behavior of the tissue, as these characteristic nonlinearities yield the changes in the perceived
tissue impedance during manipulation that the humans are good at detecting, and they usually relate
to the damage occurring to the tissue that the trainees need to learn to identify. The time-dependent
biphasic behavior of the tissue 52–54 and the strain rate effects, such as creep, are critical for accurate
predictive modeling of surgical outcomes for surgical planning applications. However, such complex
behaviors of tissue are not critical when teaching trainees the advanced endoscopic navigation and
manipulation techniques, the steps of advanced endoscopic procedures, or strategies to avoid pitfalls.
Therefore, including these types of tissue behaviors in a training simulator is not essential.
Simulation of these tissue behaviors is also prohibitively computationally expensive for a real-time
interactive simulation.

13.3.3 Collision Detection and Response
The simulation of tool-tissue and tissue-tissue interactions require the detection of contact locations.
Collision detection is one of the most computationally intensive components of a surgical simula-
tion. Furthermore, surgical simulations require collision detection to be performed at interactive
speeds, at the update rates of the underlying physical models. Therefore, development of computa-
tionally efficient collision-detection algorithms is of great importance.
Collision-detection algorithms have been the focus of much research in the computer graphics lit-
erature (see Refs. 55 to 57 for review of general collision-detection algorithms). Most of these studies