Progressive Cutting with Minimal New Element Creation of Soft Tissue Models for Interactive ...

139 Pages·2001·1.54 MB·English

Progressive Cutting with
Minimal New Element Creation
of Soft Tissue Models for
Interactive Surgical Simulation
Andrew B. Mor
CMU-RI-TR-01-29
The Robotics Institute
Carnegie Mellon University
Pittsburgh, PA 15213
October 11, 2001
Thesis Committee
Takeo Kanade, Chair
Omar Ghattas
Branislav Jaramaz
Sarah F. Frisken
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Robotics
Copyright © 2001 Andrew B. Mor
November 29, 2001 DRAFT
November 29, 2001 DRAFT
for Maria, Euler, and Archimedes
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November 29, 2001 DRAFT
Abstract
This thesis deals with the modification of finite element models
used in surgical simulation.
Surgicalsimulationoffersthepromiseofenhancedmedicaltraining
and education. It can provide a more realistic learning environment
than many of the methodologies employed today while reducing costs.
It also increases the variability of pathologies presented to the student,
and can be used for continuing medical education. Simulators can also
gain a place in the medical practice, to rehearse difficult or uncommon
procedures.Whileagooddealofworkhasbeendoneontheunderlying
soft tissue simulation, cutting and interacting with the model has been
relatively ignored.
In this thesis, we present a method for simulating cutting of soft
tissue within a physically based surgical simulator. The technique
works on subdividing tetrahedral meshes while impacting model and
simulator efficiency as little as possible. Model stability is addresses so
that the new, cut, model does not cause the simulation to become
unstable. Also, within the framework the interactive simulator
demonstrated, the user is able to palpate, grasp, and puncture the
model.
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Acknowledgements
Thanks to my advisor Takeo Kanade, for helping and encouraging
me throughout the years working on this research in the Robotics
Institute.Also,thankstomythesiscommitteemembers,OmarGhattas,
Branislav Jaramaz and Sarah Frisken.
I would also like to thank the many members of the Institute who
have helped me reach this milestone, and some of my classmates over
the years: Zack Butler, Sundar Vedula, Patrick Rowe and Terry Fong.
Lastly, I would like to thank my family for helping to get me here.
Most of all, thanks to Maria (and Euler and Archimedes) for putting up
with me these many years.
November 29, 2001 DRAFT
November 29, 2001 DRAFT
November 29, 2001 DRAFT
Table of Contents
1 Introduction 11
2 Motivation and Background 15
2.1 Difficulties of an Interactive Surgical Simulator . . . . . . . . . . . . . . . . .15
2.2 Cutting as an Integral Part of Surgery . . . . . . . . . . . . . . . . . . . . . . . . .17
3 Previous Related Work 19
3.1 Model Modification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
3.2 Deformable Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
3.2.1 Surface-Based Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
3.2.2 Volume-Based Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
3.3 Haptic Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
4 Experimental Simulator Overview 27
5 Cutting 31
5.1 General Cutting Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
5.2 Minimal New Element Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
5.2.1 Element Subdivision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
5.2.2 Generation of the Minimal Set. . . . . . . . . . . . . . . . . . . . . . . . .33
5.2.3 Comparison of Minimal Sets to General Subdivision. . . . . . .35
5.2.4 Intersection Detection and Propagation. . . . . . . . . . . . . . . . . .35
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2 TABLE OF CONTENTS
5.2.5 Intersection Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
5.2.6 Intersection Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
5.3 Progressive Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
5.3.1 Progressive Cutting Between Elements. . . . . . . . . . . . . . . . . .38
5.3.2 Progressive Cutting with Temporary Subdivisions . . . . . . . . .41
5.3.3 Different Possible Cases for Temporary Progressive Cuts . . .42
5.3.4 Progressive Cutting: Cutting Tip Within Model . . . . . . . . . . .43
5.3.5 Progressive Cutting: Topology Change. . . . . . . . . . . . . . . . . .44
5.4 Stable Cutting With Snapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
5.4.1 General Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
5.4.2 Geometry Test for Element Stability. . . . . . . . . . . . . . . . . . . .46
5.4.3 Where Intersection Points Snap. . . . . . . . . . . . . . . . . . . . . . . .47
5.4.4 Ordering of Possible Cases to Find Stable Subdivision. . . . . .49
5.4.5 New Vertex Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
5.4.6 Paired Vertex Above or Below the Plane. . . . . . . . . . . . . . . . .52
5.4.7 Different Possible Cases For Snapped Cuts. . . . . . . . . . . . . . .56
6 Soft Tissue Modeling 61
6.1 Tensor Mass System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
6.1.1 Element Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
6.1.2 Nodal and Edge Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . .63
6.2 Position Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
6.2.1 Nodal Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
6.2.2 Euler Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
6.2.3 Runge-Kutta Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
6.2.4 Verlet Integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
6.2.5 Element Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
6.2.6 Computational Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
7 Object Interaction 73
7.1 Palpation of Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
7.1.1 Implicit Sphere - Node Interaction . . . . . . . . . . . . . . . . . . . . .74
November 29, 2001 DRAFT