Implicit Representations of the Human Intestines for Surgery Simulations L. France A. Angelidis P. Meseure M-P. Cani J. Lenoir F. Faure C. Chaillou LIFL, Lille, France iMAGIS-GRAVIR, Grenoble, France

2 Context zLaparoscopic Surgery

3 Context zLaparoscopic Surgeryz Medical Simulator Xitact TM original virtual

4 Context zSurgical technique: yClearing stage, by pulling & folding the intestines zChallenges for the simulation: yLarge displacements yNumerous contacts and self-collisions

5 Outline z3-component Model for the Intestines yMechanical Model yCollision/Self-collision Model ySkinning Model zNew Skinning Methods, with Implicit Surfaces yUsing Point-Skeletons yGenerated by a Convolution Surface zConclusion

6 Model of Intestines zMechanical Model  Motion computation zCollision Model  Interaction computation zSkinning Model  Object representation Mechanical Model Collision Model Geometrical Model

7 Mechanical + Collision Models yMechanical Model Intestines’ axis: A cubic Catmull-Rom spline Motion computed by dynamic resolution of Lagrange equations applied to splines yCollision/Self-collision Model Approximation of all objects by spheres for collision If collision, computation of a penalty force proportional to the penetration q2q2 q0q0 q1q1 q3q3 q4q4 q5q5 q i : control points b i : basis functions Self-collision Neighbor spheres

8 Skinning Model: Previous Method yParametric surface [VRIC’02] A generalized cylinder with a spline skeleton associated to a circular section of varying radius qiqi qjqj k s-ds b s-ds t s-ds ksks bsbs tsts

9 Skinning Model: New methods zBasis: Implicit surfaces yDefinition Examples: yAdvantages Straightforward detection of object’s interior/exterior Simplification of the collision detection between objects f: field function e: iso-value P: points

10 yDistance surfaces xEvaluation of the field function f for any point P From its distance to its closest point on the skeleton Method using Point-Skeletons (1) P S x x s f(S,P)

11 Method using Point-Skeletons (2) yApplication to the Intestines xGeometric Model: Implicit surface generated by discrete point-skeletons positioned along the spline curve xAnimation: Variation of the skeleton shape according to the movement of the spline points To avoid topology changes during the simulation: Adaptive positioning of spheres along the curve at regular intervals xVisualization Use of a marching cubes algorithm (real-time implementation) x x x x

12 Method using Point-Skeletons (3) yResults: Video

13 yResults : Blending of several skeletons contributions = sum of their field values Suppression of surface folds at the joint of skeletons => Continuous shape for the intestines model Potential creation of bulges Difficulty to provide a constant radius: Variation of the number of skeletons => Fluctuations of the geometry Avoidance of blending between non-consecutive parts => Requirement of blending graph Blending control not at a sufficient rate due to marching cube method Method using Point-Skeletons (4)

14 Method generated by a Convolution Surface (1) yDefinition: Shape = set of connected convolution segment-skeletons yFor a single convolution segment-skeleton: Field value at a point P = sum of the contribution of all the point-skeletons along the segment Closed-form solution of this integral for various point-skeleton kernel functions Fastest solution: P H   d(P,H) x

15 Method generated by a Convolution Surface (2) yDisplay of the surface at interactive rate Use of seed-based method which takes benefit from the temporal coherence Surface rendered at different levels of detail by adapting the discretization of the surface triangulation yUnwanted blending managed by local convolution DiDi DjDj PiPi uiui PjPj ujuj

16 Method generated by a Convolution Surface (3) zResults: Video

17 Method generated by a Convolution Surface (4) zResults Avoidance of bulges on the surface that coats the segments Possible changes of the number of segments at each time step without creating jumps on the implicit surface geometry Visual rendering of the intestines satisfying: No blending and no bulges created Computation time still too slow if a fine discretization of the surface object is wanted

18 Conclusion yTwo implicit solutions to improve the Skinning of the Intestines Using Point-Skeletons + Generated by a Convolution Surface yAdvantages Good visual results for the movements and deformations of the intestines Adaptive implicit surfaces based on convolution => Animation possibly displayed at different levels of detail Simulation at interactive rate of the intestines in the abdominal cavity

19 Future Work zImprovement of: yDynamic adaptation of the discretization of the skeleton According to the varying curvature yAddition of contact surfaces To better handle contact yMore precise detection of self-collisions By taking into account the information provided by the implicit surface