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Medical Simulation. Talk by Lisa Lyons. Surgery Simulation Requirements. Realistic visualization of internal organs Organs react realistically in real time to: User interactions Environmental restrictions

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medical simulation

Medical Simulation

Talk by Lisa Lyons

surgery simulation requirements
Surgery Simulation Requirements
  • Realistic visualization of internal organs
  • Organs react realistically in real time to:
    • User interactions
    • Environmental restrictions
  • Organs react to typical surgeon’s gestures through geometric and topological modifications
surgery simulation grouping
Surgery Simulation Grouping
  • First generation:
    • Only deal with geometric nature of human anatomy
  • Second generation:
    • + permit physical interactions with anatomy
    • Include needle-type, exploration-type, catheter installation-type simulators as well as simulators that permit training in only one task and full simulators
  • Third generation:
    • + consider functional nature of organs
outline
Outline
  • Physical Modeling
  • Reduction of Computing Time
  • Collision Detection
  • Example Systems
  • Results and Conclusion
anatomical model of the liver
Anatomical Model of the Liver
  • Data set consists of about 180 slices of frozen human tissue that has been put through CT scan
    • Enhance contrast
    • Apply edge detection
    • Semi-automatic deformable models → binary images
    • Stack images to form 3D binary image [Montagnat, 1997]
simplex meshes
Simplex Meshes
  • Better than marching cubes – avoids “staircase effects
  • Developed by Delingette to represent 3D objects [Delingette, 1994]
  • Adaptable (figure to right)
  • Working on a method to extract liver models from CT images
force feedback
Force Feedback
  • How physically realistic the model is correlated with how realistic force feedback is
  • Model deforms with surgeon’s motion
  • Contact force may be computed from deformation
  • Force generated back to surgeon through mechanical actuators
slide8
Method uses linear elasticity as an approximation for tissue deformation
  • Let the configuration of an elastic body be defined as Ω
  • A field of volumetric and surface forces f acts on the body so it has a new configuration Ω*
  • We want the displacement field u which associates the initial configuration of any particle with its final configuration
  • Use FEM – Lagrange elements of type P1 [Bathe, 1996]
  • Formulate the problem as a linear system
  • Where [K] is the 3n by 3n stiffness matrix and n is the number of mesh vertices (more on this in a minute)
slide9
Only thing we know is endoscope position
    • must use displacement not force constraints
  • Given some displacements between the surgical tool and the body, we can find
    • Force on end effecter
    • Global deformation
  • Now we use variational formulation and Lagrange multipliers to minimize
  • Include constraints u = u*
  • Solving for λi gives the opposite of the necessary forces to impose the displacement u*
  • See Appendix A [Cotin, 1999] for full derivation
slide10
Stiffness matrix containing

3X3 “mini-matrix” of stiffness information

for each node

Matrix composed of a 3X3 identity

matrix for each constrained segment (k)

Forces required to obtain

desired state

Desired displacements

of k nodes

linear representation
Linear Representation
  • In theory, this behavior is only physically correct for small displacements
  • Force feedback limits the range of deformations
    • Feedback force on surgeon’s hand will increase as deformation increases
quasi non linear representation
Quasi Non-Linear Representation
  • Mix of linear representation and empirical results using a cylindrical piece of brain tissue
  • [Chinsei, 1997] found that deformation depends on loading speed and is nonlinear
outline1
Outline
  • Physical Modeling
  • Reduction of Computing Time
  • Collision Detection
  • Example Systems
  • Results and Conclusion
computation time
Computation Time
  • Number of mesh vertices has high impact
    • Makes matrices larger
  • Must use speedups
    • Cannot make necessary calculations in real-time
pre computation algorithm
Pre-Computation Algorithm
  • Specify a set of nodes to remain fixed
    • Don’t have to set all three dof
  • For every “free” node k and degree of freedom on the surface, emplace an “elementary” displacement constraint (δ)
    • Denote this as
  • Compute the displacement of every free node n in the mesh with respect to every node k
    • Store as set of 3X3 tensors
  • Compute elementary force at each constrained node k
    • Store as 3X3 tensors
solving the linear system
Solving The Linear System
  • Must be solved 3m times where m is the total number of free nodes inside the tetrahedral mesh
  • Can take anywhere from a few minutes to several hours
linear elasticity
Linear Elasticity
  • For any n where k≠ n, the relation between n and k is
  • Superposition may be used to find the total displacement of a node but some modifications must be made
slide18
Use tensors of deformation found in preprocessing to generate a vector of modified constraints

where

and

slide19
From this, we can find the displacement of any node
  • The force that must be applied to each node k to produce these displacements is
quasi non linear elastic deformations
Quasi Non-Linear Elastic Deformations
  • Computing times for a realistic looking liver model:
outline2
Outline
  • Physical Modeling
  • Reduction of Computing Time
  • Collision Detection
  • Example Systems
  • Results and Conclusion
collision detection
Collision Detection
  • Work discussed so far uses bounding boxes with a hash table
  • We know about these so lets move on to a new problem – simulating the folds of the intestines
simulating intestines
Simulating Intestines
  • Goal is simulator to allow doctors to practice a surgery that involves pulling and folding the intestines [Raghupathi L. et. al., 2003]
  • Real problem here is self-collsions
  • Complicated by tissue called mesentery
    • Connects small intestine and blood vessels
model
Model
  • Resting position:
    • Intestines look like folded curves lying in a cylinder
    • Mesentery is defined as line segments connecting folded intestine to the axis of the cylinder
  • Mechanical model uses masses and springs
collisions between intestines
Collisions Between Intestines
  • Model intestines like cylinders
  • Find distance between their principle axes
  • “Active pairs”
    • Local minima satisfying certain distance threshold
    • Updated every time step
  • N additional random pairs of segments also generated every time step
    • These are tested and thrown out if they are over the threshold or already represent a minimal pair
mesentery collisions
Mesentery Collisions
  • Complexity would be too high for real-time without approximation
  • Don’t consider mesentery-mesentery interactions
  • Adaptive convergence
    • Replace segment S1 by closest neighbor S to S2 and then replace S2 with neighbor closest to S
  • When collision occurs, recursive search begins across neighbors
outline3
Outline
  • Physical Modeling
  • Reduction of Computing Time
  • Collision Detection
  • Example Systems
  • Results and Conclusion
gertiss
GeRTiSS
  • The Generic Real Time Surgery Simulator [Monserrat et al., 2003]
scene generator
Scene Generator
  • Allows user to select tools and organs needed
  • Systems contains modeling parameters for a variety of organs
    • Mass-spring model
    • Boundary element based model (BEM)
scene generator1
Scene Generator
  • Tools:
    • Loading organs
    • Establishing input points for instruments
    • Associating different physical properties with organs
    • Establishing boundary conditions
    • Linking tissues
    • Adding special tissues
    • Associating textures to organs
surgery simulator
Surgery Simulator
  • Takes a scene and allows user to train
  • User can have interaction with organs:
    • Cut
    • Cauterize
    • Drag
    • Clip
  • User can exchange instruments
  • User is assessed at the end based on how many incorrect actions were taken
results
Results
  • Use 450 MHz Pentium III with 256 MB memory
  • Computational Costs:
haptics
Haptics
  • For good visual image 15Hz refresh rate
  • For good haptic stimulus 500 Hz refresh rate
  • Use a PC cluster to solve this
  • Cost of force feedback devices makes simulator 4X more expensive than without
cataract surgery simulation
Cataract Surgery Simulation
  • Surgery aims to extract cataract and replace it with intraocular lens [Agus et al., 2006]
  • Training is important
  • Simulation allows:
    • Flexibility
    • Gradual increase in difficulty
    • Exposure to rare events
    • Quantification of performance
the procedure
The Procedure
  • Phacoemulsification: breaking hardened lens into fragments and removing them with a small sucker using the phacoemulsificator
  • Create z-shaped corneal tunnel
  • Capsulorhexis: removing the anterior capsule to uncover the upper surface of the crystalline
methods
Methods
  • Decoupled simulation:
    • Fast subsystem for surgical instrument tracking and slower one for visual feedback
    • Slow subsystem does global simulation and interaction of devices and eye
    • Slow subsystem can be further broken into individual visual effects
  • Force feedback is useless in this surgery
    • Must use eye globe visualization
    • Conjugate gradient to minimize energy constraints gives equilibrium position
    • Rotate to reduce deformation
capsulorhexis simulation
Capsulorhexis Simulation
  • Use triangular mesh with a mass-spring network mapped over it
  • Mass particles may be anchored, scripted or free
  • Gravity, viscosity and springs contribute to acceleration
  • Weak springs simulate sticking effects
  • Solve ODE using semi FSAL (First Same as Last)
  • Velocity found using implicit method and feedback on position is computed explicitly
  • Correction routine applied after each step to correct position and velocity as required by constraints
  • Tearing – breaking overextended springs
phacoemulsification simulation
Phacoemulsification Simulation
  • Lens as collection of simplices
    • Tetrahedron mesh with particles placed at barycenters
    • Links connecting particles maintained for rendering and determining independent particles
  • Photoemulsificator modeled by eroding particles in a zone of influence
  • Employ Russian roulette scheme to decide which particles to erode
  • When particles are removed, simplicial mesh is updated
  • Idea is to replace energies by geometric constraints and forces by distance from current position to goal
  • Each connected subset of points is associated with a point cloud
    • Shape matching with undeformed rest state to determine goal positions
outline4
Outline
  • Physical Modeling
  • Reduction of Computing Time
  • Collision Detection
  • Example Systems
  • Results and Conclusion
slide43
Surgical device with

force feedback simulation

Visual feedback

appendix a collision response
Appendix A – Collision Response
  • Tried penalty and constraint methods but stability of the system was reduced
  • Instead alter displacement velocities to avoid penetration
appendix a cont
Appendix A (cont.)
  • Interpolating:
  • Need force f’ = f so we have:
  • New velocities are:
  • Substituting we get:
appendix a cont1
Appendix A (cont)
  • Solving for f gives:
  • Condition for avoiding penetration takes radii into account:
  • The force required to change the positions of the endpoints to satisfy these conditions is:
references
References
  • Marco Agus, Enrico Gobbetti, Giovanni Pintore, Gianluigi Zanetti, and Antonio Zorcolo. Real-time Cataract Surgery Simulation for Training. In Eurographics Italian Chapter Conference. Eurographics Association, 2006.
  • K.-J. Bathe, Finite Element Procedures. Prentice Hall, 1996.
  • K. Chinsei and K. Miller, “Compression of Swine Brain Tissue Experiment In Vitro,” J. Mechanical Eng. Laboratory, pp. 106-115, 1997.
  • S. Cotin, H. Delingette, and N. Ayache. “A Hybrid Elastic Model allowing Real-Time Cutting, Deformations and Force-Feedback for Surgery Training and Simulation.” The Visual Computer, 16(8):437-452, 2000.
  • Cotin, S.; Delingette, H.; Ayache, N., "Real-time elastic deformations of soft tissues for surgery simulation," Visualization and Computer Graphics, IEEE Transactions on , vol.5, no.1, pp.62-73, Jan-Mar 1999
  • H. Delingette, ”Simplex Meshes: A General Representation for 3D Shape Reconstruction,” Technical Report 2214, INRIA, Mar. 1994.
  • Y.C. Fung, Biomechanics-Mechanical Properties of Living Tissues, second ed. Springer-Verlag, 1993.
  • Carlos Monserrat, Oscar López, Ullrich Meier, Mariano Alcañiz Raya, M. Carmen Juan Lizandra, Vicente Grau: GeRTiSS: A Generic Multi-model Surgery Simulator. IS4TH 2003: 59-66
  • J. Montagnat and H. Delingette, “Volumetric Medical Images Segmentation Using Shape Constrained Deformable Models,” Proc. First Joint Con5 CVRMed-MRCAS ’97, J. Troccaz, E. Grimson, and R. Mosges, eds. Mar. 1997.
  • M. Moore and J. Wilhelms, “Collision Detection and Response for Computer Animation,” Computer Graphics (SIGGRAPH ’88), vol. 22, pp. 289-298, Aug. 1988.
  •   Laks Raghupathi, Laurent Grisoni, Fran?ois Faure, Damien Marchal, Marie-Paule Cani, Christophe Chaillou, "An Intestinal Surgery Simulator: Real-Time Collision Processing and Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 6, pp. 708-718, November/December, 2004.
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