An Architecture for RealTime Vertebrae Drilling Simulation

1
An Architecture for Real-Time Vertebrae Drilling
Simulation
2
Virtual WHAT?

• When a patient ruptures a disc, it has to be
  removed and the surrounding vertebrae are fused
  together using a piece of bone
• Pedicle screws are inserted into the vertebrae
  to stabilize it during fusion

Pictures from www.spine-health.com
3
Why simulate this?

• Pedicle screw insertion is inherently dangerous,
  so its difficult to get experience
• Training options are poor
• Simulation is cheap!

Haptic drill may in fact not be cheap
4
How to simulate Spinal Drilling

• Make a Virtual Vertebrae
• Make a Virtual Drill
• Virtually Drill the Virtual Drill into the
  Virtual Vertebrae
• (Its virtually that simple)

5
Step 2 A Virtual Drill

• Only the drill bit actually drills
• The drill bit is a cylinder with a conical end
  cap
• we ignore the threads on the drill bit

6
Step 3 Virtual Drilling

• General problem We have a volume we want to
  decimate with our Virtual Drill Bit
• General Solution Fill the volume with volume
  elements and throw them away when they
  intersect with the Virtual Drill Bit

7
A note about speed

• We are using haptic feedback devices
• Need high feedback rates (300Hz-10000Hz)
• This implies the intersection test has to be very
  fast
• Volume element with the fastest intersection
  test Points!
• Fast geometric test w/cylinder and cone
• Small memory footprint

8
Just how many points?

• That depends on the haptic drill
• Our guess (so far) 0.1mm between points
• Vertebrae volume is 100,000mm3
• we cant fill the whole thing
• We can cheat because surgeons are meticulous
• They plan surgeries before-hand
• We know where the drill is going!

9
Where do we put the points?

• Bad Idea voxels
• Good Idea cylindrical point volume
• Drill bit is a cylinder, so fill a bigger
  cylinder with points, and align it with the
  planned path
• Where in the cylinder?
• Structure can speed up collision algorithm

10
The Cylinder/Disc/Ring Paradigm
11
Off-Path Drilling

• Simple algorithm rewards on-path drilling
• Can avoid this by traversing ring in both
  directions

12
Testing the System

• No haptic drill!
• Try to simulate haptic drill input
• Drill input should be asynchronous
• Very difficult, Linux is not an RTOS
• Fallback method
• Move drill, test for collisions, move drill, test
  for collisions, etc

13
Simulation Results
14
Step 1 A Virtual Vertebrae

• Point inside/outside test
• Implicit surfaces are good for this
• Smooth, accurate polygonized surface
• Implicits work well here, too
• Reconstruction from CT slices
• People have been using Radial Basis Functions
  with good results

15
Computed Tomography

• AKA CT or CAT Scanning
• Greyscale slices of biological volume
• Isolating surface contours
• Segmenting is done by hand

16
Ugly Contours
17
Radial Basis Functions

• Radial Basis Function a continuous function
  that interpolates through an (almost)
  arbitrary set of data points
• The RBFs we are interested in are classified as
  the smoothest interpolants they minimize
  surface curvature
• In pictures.

18
An RBF takes these points
19
And gives you this surface
20
Definition of an RBF
21
Finding the coefficients

• We specify a set of N point/value pairs (xi,fi)
• s(xi) fi (these are called centers of
  the RBF)
• By plugging the xis back into the general form,
  we get a linear system of equations in N
  variables
• The coefficients of P go in there too, so
  actually N4
• Solving this system is O(N3) w/ O(N2) memory, and
  evaluation is O(N)
• Thats too slow to be practical, but Fast
  Multipole Methods reduce evaluation to O(1), with
  an O(NlogN) setup time, so iterative solving is
  O(NlogN)

22
Hole Filling Property

• The biharmonic has non-compact support, it can be
  used for mesh repair or to fill holes
• Vertebrae point set has two large holes

23
Off Surface Points

• For 3D biharmonic RBFs, specify a set of surface
  points with value f 0
• Also need inside and outside points with positive
  and negative values
• Trivial solution s 0 if we only specify surface
  points
• The distance between surface and off-surface
  points has a large effect on smoothness of the
  final surface

24
Why does OSP distance matter?

• When the distance is small, thesurface is
  restricted
• As the distance increases, there is more
  freedom
• This is why the pixel-basedfitting method failed

25
Center Reduction

• RBF center reduction throws away redundant
  centers that the RBF willinterpolate anyway
• Reduces N, which makesevaluation faster

26
RBF Smoothing

• Introduce smoothing factor into RBF
• Reduces solution accuracy at the expense of
  increased smoothness
• Can set smoothness foreach center individually

27
Dangers of RBF Smoothing

• A High smoothing factor can cause serious volume
  change

28
FastRBF

• FastRBF from FarFieldTechnology
• FMM, reduction, smoothing, automatic normal
  generation, optimized triangle polygonizer
• www.fastrbf.com

29
Vertebrae Model Results
30
Rendering the Point Volume
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
Questions?