Chapter 6. Conclusion
6.2. Contributions
inability or extreme difficulty to control stiffness to characterize tissue elasticity due to the large number of parameters inherent to the system.
We tested a number of approaches which allow for a certain control over the objects elasticity, which is given by the material Young’s modulus. We finally propose an inter-active approach which ensures control of the linear part of the stress-strain relation for a given range of forces for arbitrary mass-spring meshes. Given the fact that the range of forces inside a joint is known and can be found in the literature of Biomechanics, our model guarantees an accurate enough tissue characterization for the intended medical applications.
6.2.3 Quasi-permanent contact model
Collision detection and collision avoidance are important research threads in Computer Graphics because they increase the realism of virtual environments. In a virtual phys-ical environment aimed at medphys-ical applications, however, the realism of the collision cannot be merely visual. Contact must provide information which can be used for medical decision making.
Contact management inside an articulation model is a specific situation with two opposed characteristics. On one hand, the permanent contact and pressure makes the problem more complex and difficult to optimize. On the other hand, the articulation is a somewhat closed system in which a number of assumptions can be done, for instance:
the topology does not change during physiological activity.
In this context, we bring two contributions. First, we detect collisions efficiently using a method which takes advantage of the known joint topology. Second, we avoid penetration at the collision loci without directly calculating response forces, relying on the propagation of strain provided by our soft tissues deformation model.
Our collision detection method, which we call sliding sphere, measures in constant time the signed distance to the closest point for each point of two meshes subject to collide. It makes use of a hash table to determine at any time which element of one mesh is the closest to any given element of the other mesh. The method has shown to be effective for contact between cartilage caps and for the hip ligaments. It may not be effective for the knee cruciate ligaments, for example, because they do not respect a layered topology.
Our penetration avoidance method consists in putting the two colliding elements aside geometrically such as they lie on each other instead of penetrating further. To increase stability for computer simulation, we also look one timestep forward at every simulation iteration and tune the velocities of potentially colliding elements one step further, in order for them to lie on each other in the next frame. These geometrical changes on the surface are then propagated throughout the tissue which physically reacts to the tension they impose on the springs closed to the surface.
The combination of the two methods has shown to be efficient and effective for the tested applications. It does not increase the numerical instability of the system; we demonstrated that the numerical errors we have with the deformation model are not
Chapter 6. Conclusion
negatively affected by our contact management model.
6.2.4 Biomechanics-based articulation model
The main contribution of this thesis, as foretold by its title, is an articulation model for medical applications. We combined the kinematical skeleton provided by our anatomy-based articulation model with our biomechanics-anatomy-based model of soft tissues, and with our contact management model to build up such as 3D articulation model.
The bones are rigid and move following kinematical rules controlled by the parame-ters of the anatomic joint model. Motion can be specified from patients motion capture, thus reproducing real motions, or specified by a specialist, which gives flexibility. On top of the bones, more specifically around the locus where they meet, virtual cartilages and ligaments deform under the constraints imposed by the bones motion. Physical parameters such as stress distribution along the soft tissues can then be evaluated.
The obtained articulation motion has shown to be visually realistic and the physical parameters calculated are meaningful for the intended applications. Nevertheless, the absence of global clinical validation is a main deficiency, even if some validation could be done involving clinically measured ranges of motions. Validating biological systems is a very hard task because in-vivo data are difficult to obtain. One possible approach for further work could be using dynamic MRI to compare deformations.
6.2.5 Force-feedback from deformable objects
Another contribution is the use of a haptic interface with deformable objects. Haptic interfaces are becoming popular in Virtual Reality applications. They can enrich the amount and the quality of the information perceived by a user. They can be valuable to medical applications. Consequently, we tested the compliance of our deformable model with such interfaces.
Haptic applications are realtime, and force feedback devices require high frequency updates (at least 400 Hz but usually 1000 Hz). It is for this reason that most haptic ap-plications involve rigid objects only. To achieve such performances with deformations, we created coarse resolution objects with our deformation model (27 mass elements).
We then presented uniformly shaped objects characterized by different elasticities to a group of users to try to identify them, classifying them in order of stiffness.
The perception test was successful, the users being able to recognize different elas-ticities despite the limitations of the force-feedback used. However, more complex objects, like the ones of the articulation model, cannot be simulated in realtime, which makes the use of haptics still inviable.
6.2.6 Medical applications
We also contributed by setting up a few applications exploiting our models in the fields of computer aided diagnosis and surgery planning. We built a model of the hip joint
6.2. Contributions
and developed the following four medical applications:
• Stress distribution for joint congruity assessment
Considering the loads provoked by bones motion, this application computes stress on the cartilage caps. It uses methods from scientific visualization, such as color mapping, to visualize the stress in non-photorealist rendering mode.
The application aids medical doctors to build a more accurate mental model of the patient case, correlating abnormal stress distribution with pain, for example.
• Range of motion estimation based on ligament constraint
This application aims at estimating the joint range of motion. Unlike most ex-isting approaches, which are based on bone contact to define range of motions, we impose an additional constraint by considering the presence of the ligaments.
Using information about the maximum stress a ligament can bare before rupture, we move our joints to extreme positions while we measure the current maximum stress on the ligament at each timestep. The positions in which the maximum measured stress is greater than the failure stress for the material are considered unreachable, defining joint limits.
• Ligament elasticity estimation from range of motion
This application uses the inverse approach to the previous one. Here, we use the range of motions measured by a clinician as input, and aim at estimating the ligament elasticity.
Knowing that for certain postures moving further than the limits of the range of motions causes ligament rupture, and knowing the average ligament rupture stress, which can be found in Biomechanics literature, we estimate the Young’s modulus of this tissue. We start simulating with a very soft ligament, and we drive the joint to an extreme position. At that point we start increasing the ligament stiffness at every timestep, always controlling the maximum stress, which will be consequently increasing as well. When the maximum measured stress reaches the rupture stress, we stop simulating, and consider that the current stiffness we have obtained corresponds to the actual ligament elasticity.
• Pre- and post-operative evaluation of stress distribution
Reorienting a malformed bone by osteotomy is a practice in orthopedical surgery.
However, planning such a surgery always involve unknown elements which can only be partially controlled, and only by an experienced surgeon. The Imh¨auser osteotomy, for instance, aims at reorienting the femoral head in order to improve the hip range of motions. It can be necessary, for example when a patient has
Chapter 6. Conclusion
part of the femoral head cartilage destroyed and contact with the acetabulum wants to be avoided.
We proposed an application allowing to simulate the effects of such a surgery.
Range of motions and stress distribution are first evaluated on the pre-operative model. Then, the bone is edited to provide a new joint configuration, analo-gously to what happens in a surgical procedure. Finally, the analysis of the post-operative virtual model allows for the assessment of the improvements ob-tained. In case it is not satisfactory, different femoral head orientations can be tested until the surgeon is satisfied with the result on the 3D model. They can then reproduce the same parameters in the real surgery with a better chance of success.