Medical simulation
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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

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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



  • 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

Medical simulation

  • 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)

Medical simulation

  • 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

Medical simulation

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



  • 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

Medical simulation

  • Use tensors of deformation found in preprocessing to generate a vector of modified constraints



Medical simulation

  • 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:



  • 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



  • 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

Results and demo video

Results and Demo Video



  • Physical Modeling

  • Reduction of Computing Time

  • Collision Detection

  • Example Systems

  • Results and Conclusion



  • 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



  • Use 450 MHz Pentium III with 256 MB memory

  • Computational Costs:

User interface for laproscopy

User Interface for Laproscopy



  • 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



  • 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





  • Physical Modeling

  • Reduction of Computing Time

  • Collision Detection

  • Example Systems

  • Results and Conclusion

Medical simulation

Surgical device with

force feedback simulation

Visual feedback

Medical simulation

Where is the future?

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:



  • 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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