Video Driven Finite Element Deformation Models for Surgical Simulation

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					           Video Driven Finite Element Deformation Models for
                           Surgical Simulation
        Adrian Chung, Fani Deligianni, Pallav Shah, Athol Wells, and Guang-Zhong Yang
                       Royal Society/Wolfson Foundation MIC Laboratory, Department of Computing

                                                                                    a                                       b
The effectiveness of computer simulation for training specialists in
minimally invasive surgical techniques, relies heavily on the level of
realism achieved by the simulated environment. An important aspect of
this realism is the realtime behaviour of the anatomical model in response
to trainee interactions [1]. This may include grabbing, prodding, and
cutting with tools. Additionally, the simulated anatomy must also react to
time varying forces that arise from within the patient model due to
respiration, cardiac motion, and peristalsis. Much progress in this area has
been achieved through the use of finite element modelling [2], however
many simplifications have had to be made in order to achieve interactivity
at the expense of physical accuracy. Furthermore, the straightforward
application of forces acquired through accurate in vivo measurments, on
these less accurate, interactive deformation models may have unintended
consequences, yielding unnatural motions.         This paper proposes a
framework by which physical realism may be re-introduced into an                        (a) Voronoi regions constructed over bronchial surface topology and
interactive simulation model by analysing in vivo video of tissue                       (b) the dual Delaunay triangulation on which FEM model is based
deformation and then deriving a model of the external forces to achieve
similar behaviour in the deformable model.                                        Force estimation
                                                                                  For the purposes of optimisation the FEM system needs to evaluate
Method                                                                            deformations given a large set of possible trial boundary forces. Only for the
                                                                                  most simple of models can a solution be found using a straight forward
Bronchoscope video was captured from a bronchoscope (Olympus BF                   minimisation technique within a practical time scale. With larger and more
type 120º field of view) held reasonably stationary while viewing the             complex finite element models solving for the boundary conditions through
caronus of the bronchial airway, an area subject to cyclic deformation            optimisation will in general be intractable. This is due to the high
forces due to the close proximity of the beating heart. A CT Scan                 dimensional solution space over which boundary forces can vary. If one
(Siemens Somaton Volume Zoom 4-Channel Multidetector CT, 3mm slice                assumes that deformations are small, simplifications can be applied that
thickness, 1mm in-plane resolution) of this same patient was also acquired        reduce the dimensionality of the parameter space and hence expand the
in order to reconstruct a 3D polygonal surface model of the area that was         range of FEM models that can be solved. This was achieved by grouping
captured on video. A decimated version of this model was used to build a          similar local deformations together and estimating the force profile for the
finite element mesh (FEM) for the deformable simulation model. By                 each group.
applying 2D/3D registration to a single reference frame of video and the
reconstructed surface, the 3D position of the bronchoscope was                     a                                        b
determined. Virtual landmarks were tracked through the video sequence
via image feature tracking which yielded correspondences between
frames. The bronchoscope pose was corrected for any rigid motion
between frames by minimising the distances between pairs of
correspondence points. Any correspondence pairs with a greater than
average separation distance after applying pose correction, were assumed
to be due to non-rigid deformation.

a                            b                           c

                                                                                        (a) and (b) represents the changing forces applied to the bronchial
                                                                                        model at two different instances recovered from the recorded
                                                                                        video sequence.

    The virtual landmarks have been applied to reference video frame (a)
    which were tracked through to a later frame (b) in the video sequence         Deriving nodal forces from non-rigid displacements amounts to inverting the
    using image feature tracking. The landmark motion vectors are a
    combination of rigid motion and deformation. (c) After correcting for rigid   FEM equations which are generally ill-posed. The problem is made more
    motion, any remaining motion vectors are assumed to be due to non-rigid       difficult by the fact that there is only one camera view. This paper presents a
    deformation.                                                                  new approach in the development of realistic interactive finite element
                                                                                  models using normal endoscopy video. The issue of validation will be
                                                                                  handled through subjective visual assessment of physically based
Finite Element Model                                                              animations of virtual endoscopy sequences in comparison with real
Standard CT based surface reconstruction methods often are not of the             endoscopy video. A complete error analysis of the linear approximation of
quality required for accurate finite element analysis and may be too large        FEM systems undergoing small deformations is also being conducted.
for interactive simulation. A new method was developed for surface
simplification that extends 2D Voronoi partitioning methods to arbitrary          References
surface topologies so that models can be constructed for the wide variety
of shapes in which deformable tissues occur. The FEM model was                    1. “Endoscopic surgery training using virtual reality and deformable tissue
                                                                                     simulation”, U. Kühnapfel, H.K. Çakmak, H. Maaß, Computers & Graphics
constructed from the dual Delaunay triangulation. The technique maintains
a mapping between the lower resolution FEM model and the high                     2. ”Real-time volumetric deformable models for surgery simulation using finite
resolution surface reconstruction to facilitate deformation without loss of          elements and condensation”, M. Bro-Nielsen, S. Cotin, Computer Graphics
visual details.                                                                      Forum, 1996, 15(3), pp. 57-66

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