Surgery Simulation and Planning

Transcription

1 Surgery Simulation and Planning S. H. Martin Roth Dr. Rolf M. Koch Daniel Bielser Prof. Dr. Markus Gross Facial surgery project in collaboration with Prof. Dr. Dr. H. Sailer, University Hospital Zurich, currently at Sailer Clinic, Zurich

2 Overview Surgery Planning Cranio maxillofacial surgery Physics based tissue representation Emphasis on accuracy Surgery Simulation Surgical training Physics based tissue representation Emphasis on real time processing Arbitrary topology Haptics S. H. Martin Roth 2

3 Introduction & Motivation Simulation of cranio-maxillofacial surgical procedures 3-d Physically based tissue model Adapted to individual anatomy S. H. Martin Roth 3

4 Introduction & Motivation Conventional planning Computerassisted planning S. H. Martin Roth 4

5 Simulator Goals Evaluation of Mathematical model Custom-built finite element implementation Different finite elements Post-simulate actual surgery Compare simulation and real outcome Automatic registration Automatic determination of jaw movements S. H. Martin Roth 5

6 Prerequisites Volume data (CT) Pre-surgical Post-surgical Surface data (LR) Pre-surgical Post-surgical S. H. Martin Roth 6

7 Linear Elasticity & FEM Tissue as an elastic body Linear stress-strain relation τ = Cε Pure displacement based formulation Mixed formulation Pressure as an additional variable (Near) incompressible situations S. H. Martin Roth 7

8 Two Kinds of Elements Prism-shaped Hermite elements C 1 continuous surface C 0 continuous inside Displacements Derivative in u Derivative in v Pressure Tetrahedral Bézier elements C 0 linear, quadratic, and cubic C 1 cubic (Clough-Tocher split) S. H. Martin Roth 8

9 Model Build up read data pre-surgical LR pre-surgical CT mesh reduction marching cubes reduced LR CT isosurface mesh reduction reduced iso ICP registration skull extraction facial surface skull surface meshing FE mesh S. H. Martin Roth 9

10 Jaw Cutting & Displacement pre-surgical CT read data post-surgical CT CT registration registered post. CT pre-surgical skull surface cutting surface cutting upper jaw lower jaw ICP registration ICP registration displacements S. H. Martin Roth 10

11 Iterative Closest Points Besl & McKay 1992, Horn 1987 Registration used for Model build up Computation of displacement fields Objective Align two surfaces into a common coordinate frame Keep rotation orthonormal Find optimal solution in a least squares sense Problems Surfaces are not identical Outliers S. H. Martin Roth 11

12 ICP Objective Function Notation Surfaces Registration vector Objective function to minimize i= 1 R ( p ) q Refer coordinates to centroids y i = y i n f ( q) = n i= 1 y n 1 µ, µ = y Y Y {, i =1 m} X = xi.. i i q o R p i i = o q = [ q R q T ] p i T Y = yi, i =1.. n P = pi.. 2 n 1 µ, µ = p P { } {, i =1 n} P n i= 1 i S. H. Martin Roth 12

13 ICP Optimal Transformation Optimal translation f (q) minimal for Optimal rotation Equal scaling Centroid coordinates coincide f (q) minimal for maximal Represent rotation with unit quaternions Maximize qt = µ Y R o q (µ P ) o o Eigenvector to max. eigenvalue of N q = e 1 R n i= 1 o y i o q R o p i o R q n i= 1 y i R o T R q R q o R (p ) o Nq R i S. H. Martin Roth 13

14 ICP Algorithm Absolute translation and rotation We need corresponding point sets Iterative Closest Points: Find closest points Y of P (data) on X (model) Compute optimal translation and rotation Transform P Compute total distance d If d below threshold end, else iterate Search for closest points is expensive Spatial data structure needed S. H. Martin Roth 14

15 ICP Results Registration of LR scan to CT isosurface Region of interest Registration mask Initial registration Cross section Resulting registration S. H. Martin Roth 15

16 Image Registration Thévenaz, Ruttimann, Unser, Automatic subpixel registration algorithm Minimization Intensity difference by transformation Modified Levenberg Marquardt nonlinear leastsquare optimization 2-d and 3-d Transformation Affine or rigid-body Optional adjustment of image contrast Multiresolution spline representation S. H. Martin Roth 16

17 Image Registration Results 2-d image registration 3-d CT registration S. H. Martin Roth 17

18 Jaw Displacement Fields Jaw cutting Paint cut lines Jaw alignment Manual rough alignment Surface registration Cut geometry S. H. Martin Roth 18

19 Results Evaluation procedure Register post-surgical LR scan to pre-surgical situation Profile lines Error maps pre-surgical simulation post-surgical S. H. Martin Roth 19

20 Results C 0 Linear Profile lines pre-surgical simulation post-surgical tetrahedral elements x matrix (0.490%) displacement dofs 51 conjugent gradient iterations 1.3 seconds assembly 3.4 seconds solving S. H. Martin Roth 20

21 Results C 0 Linear Error maps pre-surgical simulation post-surgical % mean square error (with respect to bounding box) S. H. Martin Roth 21

22 Results C 0 Quadratic Profile lines pre-surgical simulation post-surgical tetrahedral elements x matrix (0.143%) displacement dofs 942 conjugent gradient iterations 4 seconds assembly 9 minutes 12 seconds solving S. H. Martin Roth 22

23 Results C 0 Quadratic Error maps pre-surgical simulation post-surgical % mean square error (with respect to bounding box) S. H. Martin Roth 23

24 Video Facial Surgery Today & Tomorrow

25 Conclusions & Future Work Conclusion Less emphasis on models More emphasis on simulator design and user interfaces Future work Data acquisition Simulator design User interfaces More complex surgical procedures S. H. Martin Roth 25

26 Goals Surgery Simulation Real time surgery simulation Physics based tissue representation Fast collision detection algorithms Parallel relaxation scheme with adaptive time steps Surgery training Arbitrary topology (cutting) Realistic force feed back Realistic rendering S. H. Martin Roth 26

27 Tissue Model Unstructured tetrahedral meshes Mass spring system for deformation modeling S. H. Martin Roth 27

28 Parallel Tasks in Simulation > 1 khz Collision Detection Haptics Geometry Update TCP/IP > 25 frames/s Rendering Relaxation S. H. Martin Roth 28

29 5 Topologically Different Cases S. H. Martin Roth 29

30 Permitted Face Subdivisions Face subdivision restricted to three cases Only cut edges are subdivided undivided one edge intersected completely split S. H. Martin Roth 30

31 Subdivision Patterns 1 edge cut 2 edges cut 3 edges cut 3 edges cut 4 edges cut partially cut completely split S. H. Martin Roth 31

32 Scheduling Algorithm scheduler node lists t 0 movenodedown t 1 schedulenodelist t 2 movenodeup t n threads insertnewnode S. H. Martin Roth 32

33 Example of an Interactive Cut Cut sequence in a knee model consisting of 1400 tetrahedra Rendered with 3D textures Wireframe representation S. H. Martin Roth 33

34 Example of a Crossing Cut 3000 tetrahedra S. H. Martin Roth 34

35 Conclusions & Future Work Conclusions Accurate and consistent subdivision Efficient and stable parallel relaxation scheme supporting adaptive time steps Hierarchical and local collision detection Realistic haptic model for scalpel forces Future work Visual discontinuities (popping artifacts) More accurate relaxation scheme: Volume preservation (tensor mass system) S. H. Martin Roth 35

36 Visit Us at... S. H. Martin Roth 36