Implicit Representations of the Human Intestines for Surgery Simulations

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, FranceiMAGIS-GRAVIR, Grenoble, France

2

Context

Laparoscopic Surgery

3

Context

Laparoscopic Surgery

Medical Simulator XitactTM

original

virtual

4

Context

Surgical technique: Clearing stage, by pulling & folding

the intestines

Challenges for the simulation: Large displacements Numerous contacts and self-collisions

5

Outline

3-component Model for the Intestines Mechanical Model Collision/Self-collision Model Skinning Model

New Skinning Methods, with Implicit Surfaces Using Point-Skeletons Generated by a Convolution Surface

Conclusion

6

Model of Intestines

Mechanical Model Motion computation

Collision Model Interaction computation

Skinning Model Object representation

Mechanical Mechanical ModelModel

Collision Collision ModelModel

Geometrical Geometrical ModelModel

7

Mechanical + Collision Models

Mechanical Model• Intestines’ axis: A cubic Catmull-Rom spline

• Motion computed by dynamic resolution of Lagrange equations applied to splines

Collision/Self-collision Model• Approximation of all objects by spheres for collision • If collision, computation of a penalty force proportional

to the penetration

n

kkk sbtqtsP

0

)()(),(q2

q0q1

q3q4

q5

qi: control pointsbi: basis functions

Self-collision

Neighbor spheres

8

Skinning Model: Previous Method

Parametric surface [VRIC’02]• A generalized cylinder with a spline skeleton

associated to a circular section of varying radius

qi

qj

ks-ds

bs-dsts-ds

ks

bs ts

sss

dssss

tbk

ktb

9

Skinning Model: New methods

Basis: Implicit surfaces Definition

• Examples:

Advantages• Straightforward detection of object’s interior/exterior • Simplification of the collision detection between objects

ePfPS )(f: field functione: iso-valueP: points

10

Distance surfacesEvaluation of the field function f for any point P

• From its distance to its closest point on the skeleton

Method using Point-Skeletons (1)

PS

x

x

s

f(S,P)

11

Method using Point-Skeletons (2)

Application to the IntestinesGeometric Model:

• Implicit surface generated by discrete point-skeletons positioned along the spline curve

Animation: • 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

Visualization• Use of a marching cubes algorithm (real-time

implementation)

x xx x

12

Method using Point-Skeletons (3)

Results: Video

13

Results: Blending of several skeletons contributions = sum of their

field valuesSuppression of surface folds at the joint of skeletons => Continuous shape for the intestines model

Potential creation of bulgesDifficulty 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 graphBlending control not at a sufficient rate due to marching

cube method

Method using Point-Skeletons (4)

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Method generated by a Convolution Surface (1)

Definition:

• Shape = set of connected convolution segment-skeletons

For 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:

),(

sinsin)(

221

HPdPf

P

H

d(P,H)

x

15

Method generated by a Convolution Surface (2)

Display 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

Unwanted blending managed by local convolution

Di

Dj

Pi

ui

Pjuj

16

Method generated by a Convolution Surface (3)

Results: Video

17

Method generated by a Convolution Surface (4)

ResultsAvoidance 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

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Conclusion

Two implicit solutions to improve the Skinning of the Intestines

• Using Point-Skeletons + Generated by a Convolution Surface

Advantages• 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

Improvement of: Dynamic adaptation of the discretization of

the skeleton • According to the varying curvature

Addition of contact surfaces • To better handle contact

More precise detection of self-collisions • By taking into account the information provided by the

implicit surface