Page 406 - Biomedical Engineering and Design Handbook Volume 2, Applications

384 SURGERY

have focused on solving the collision-detection problem for rigid objects. Collision-detection algorithms
for rigid bodies heavily rely on precomputed data structures, such as bounding volume hierarchies.
However, these algorithms cannot be directly applied or do not necessarily result in efficient algorithm
for deformable objects, since the data structures used to improve collision-detection efficiency need
to be updated or reconstructed when the underlying object geometries change. Therefore, in surgical
simulations, it is necessary to employ algorithms specialized in collision detection for deformable
objects. 58–60
In order to improve computational efficiency, most collision-detection algorithms use a two-stage
approach. The first stage, which typically relies on forms of bounding volume hierarchies 60,61 or space
partitioning 62,63 , bounds the region of intersection. The second stage then determines the exact loca-
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tion of the collision, typically using ray-polygon 64,65 or polygon-polygon intersection algorithms.
13.3.4 Haptic Interaction with Simulated Deformable Objects
in Virtual Environments

The value of haptic interaction in surgical simulation applications has led to a great deal of research
interest in the challenges involved in providing haptic force-feedback in virtual environment simu-
lations with deformable surfaces. 67,68
Ensuring stability of the haptic interaction is a fundamental concern in haptic systems. Stability of
haptic systems, and the stability-performance trade-off has been subject to much research in the haptics
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literature 69,70 . The virtual coupling networks, and time domain passivity observer algorithms are
effective algorithms to guarantee stability of haptic interaction with virtual environments.
The human sense of touch is remarkably sensitive, and can distinguish between changes in force
into the range of hundreds of hertz. It is generally accepted that the update rate of the haptic inter-
face must be 10 to 20 times higher than the highest frequency event that is to be simulated. Therefore,
in order to render events in the 50 to 100 Hz range matching the capabilities of the PHANTOM or
similar haptic interfaces, 1 kHz is widely considered the minimum update rate for realistic haptic
feedback. On the other hand, the simulation of the deformable object models are typically linked to
the graphical update rates of 10 to 60 Hz because of computational limitations. This 2 order of mag-
nitudes difference between the physical model and haptic update rates is one of the major issues in
haptic interaction with deformable objects. One common method of bridging this gulf is through
multirate simulation. The core of the multirate simulation approaches is to divide the necessary com-
putational tasks into those that must be performed at the servo-loop update rate of the haptic inter-
face and those that can be performed at the same rate as the overall simulation. The algorithm is
divided into two basic blocks, as shown in Fig. 13.3a. The “global” simulation incorporates the entire
virtual environment and runs at the visual update rate in the order of magnitude of 10 Hz. A “local”
simulation runs at the haptic device update rate and simulates the behavior of a subset of the global
model (Fig. 13.3b). After each update of the global model, a low-order approximation model is gen-
erated and passed to a second simulation, running either in a separate process or thread in single-
computer operation, or running on a second computer in networked operation. This second simulation
uses the low-order approximation model to provide force output to the user and then sends the state
of the haptic instrument back to the global model, which then recomputes a new low-order approxi-
mation for the next cycle. 73,74

13.3.5 Realistic Graphical Rendering of Surgical Scenes
After the geometric model of the anatomy is constructed from medical diagnostic imaging data, it
needs to be incorporated into the virtual surgical environment and displayed in a realistic manner.
Therefore, the development of the virtual environment-based surgical simulators requires real-time
realistic rendering of the surgical scene. The visual realism of the virtual environment is critical for
a training simulator for several reasons. Teaching correct identification of critical structures and
anatomical landmarks to a nonexpert requires a visual model which is as faithful to the reality as
possible. Visual realism and availability of the visual cues used in depth perception in an endoscopic
view, which is monoscopic, is also important to teach minimally invasive navigation skills to a