## Step 14 Collision Detection and Deformation

A crucial element of virtual reality simulation is determining when a surgical tool has collided with tissue structures or other tools.

In addition, tool contact can force one tissue structure into other tissue structures, which in turn could lead to even more collisions. Determining if and where collisions take place can be very computationally expensive. As discussed in step 8, models are typically rendered in terms of polygons. The objective is to determine if a point on the surface of one object has crossed the face of a polygon on another object. There can be tens of thousands of nodes (the corners of the surface polygons) on the tools and tissue structures in a scene that must be tested against tens of thousands of polygons.

A variety of techniques have been created to avoid the necessity to test every point against every polygon. The objective is to cull all the model polygons into smaller sets of "probable" collision polygons. Finding collisions with rigid objects is relatively straightforward. This is because all the polygons on an object stay in relative position to each other. For this reason, it is possible to sort surface polygons into a number of bounding volumes, such as a sphere, cube, or cylinder that can help collision algorithms zero in on polygons of probable collision. By first testing a point to see which bounding volume it is in, it becomes possible to reduce the total number of polygons that might come into collision. This is one reason why implicit solid models (as discussed in step 8) can offer tremendous performance advantages when it comes to collision detection. It is also possible to put bounding volumes within bounding volumes to further subdivide a model into probable collision polygons. This type of architecture is often referred to as a voxel tree.

Specific hardware is often added to the computer platform just to accommodate collision detection. As mentioned in step 6, multiprocessor computers are sometimes used in simulation. Often the reason is so that one of the processors can be dedicated to collision detection. Graphics cards can also be converted to collision detection systems.

The difficulty with surgery simulation is that there are usually a number of deformable object in the scene.

eSensable Technologies, Woburn, MA. fMimic Technologies, Seattle, WA.

Soft tissue is an extremely complex material and very difficult to accurately model. Not only does soft tissue contain three phases (solid, liquid, and gas) but also material properties vary significantly from person to person, tissue structure to tissue structure, and even within the same tissue body.

While finite element models are more accurate than spring models in terms of stability, deformation, and force feedback, the method still has its limitations.

Once an object deforms, techniques such as using a voxel tree, become ineffective because polygons are likely to stray out of their original bounding volumes. For this reason, a tremendous amount of research has been dedicated to methodologies for reducing the computational cost of collision detection when using deformable models. This is a complex issue that routinely receives a lot of focus at conferences such as MM virtual reality and SIGGRAPH.

After collision takes place, another difficult problem is determining how a model should deform. This often requires even more computation than collision detection.

Soft tissue is an extremely complex material and very difficult to accurately model. Not only does soft tissue contain three phases (solid, liquid, and gas) but also material properties vary significantly from person to person, tissue structure to tissue structure, and even within the same tissue body.

While continuum mechanical-based methods have been demonstrated to accurately model tissue structures such as cartilage, the majority of soft tissue types have yet to be modeled. More importantly, the methodologies that exist are so computationally intensive that it can take hours, or even days, just to model a single scenario for tissue deformation. This hardly applies to virtual reality where a new solution must sometimes be found a thousand times a second.

There is definitely a long way to go before modeling tissue deformation in surgery simulation becomes highly precise. However, as long as the deformation modeling is realistic enough to promote learning, it might be deemed "good enough." Most simulators actually employ "video game-like" techniques that completely ignore the tissue material properties. Spring models are most commonly used. Techniques vary, but many simply place a linear representation of a spring on the edge of every tetrahedron in a volumetric element model (step 8). Moving a node on a model compresses a set of springs that then in turn push into other nodes. Iterating through all the springs will result in a global deformation. One example of a spring-based model is the LapMentor simulator sold by Simbionix.

Beyond the problem of the inherent instability that often makes spring models appear to "flutter," spring models are also very difficult to calibrate. Determining an appropriate stiffness for every spring to approximate realistic deformation can be extremely difficult and labor intensive. Also, a spring model does not maintain its overall volume as is natural for most materials. Just the same, the trade-off is fast performance for limited accuracy.

A number of new techniques based on continuum mechanics have started to emerge. Finite element modeling is the industry standard for modeling stress, strain, and deformation in objects such as bridges, mechanical parts, car frames, cell phones, prosthetics, and more. Unfortunately, this methodology in its raw form does not lend itself to real-time applications. Fortunately, some versions of the technique have been recently adapted for application to surgery simulation. Now it is possible to measure a subject's soft tissue material properties and plug them in to a finite element model. Examples of finite element modeling-based simulators include the suturing simulator developed at the University of Washington and the robotic prostatectomy simulator currently under development at Mimic Technologies, Seattle, Washington, U.S.A.

While finite element models are more accurate than spring models in terms of stability, deformation, and force feedback, the method still has its limitations.

In particular, a lot of computation is required to build the mathematical representation of a finite element mesh. When the mesh is altered, such as when cutting through skin, the mathematical representation of the mesh must be updated. Significant mesh updates can be difficult to accommodate in real time. This limits the use of finite element models to certain surgery scenarios.

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