Fitting%20a%20Round%20Peg%20to%20a%20Square%20Hole

1
Fitting a Round Peg to a Square Hole
A Method for Physical Validation of Finite
Element Pressure Models

• Janna Balling
• and Andrew Anderson

2
Introduction

• Validate subject-specific FE models of the hip
  using experimental data
• Single-leg-stance and stair-climbing
• Cartilage contact stress measured using pressure
  sensitive film

3
Introduction

• Pressure sensitive film
• Cut into rosette pattern
• Fit to femoral head
• Film scanned in 2D
• Calibrated
• Color intensity is proportional to applied
  pressure

4
Objective

• Validate FE model predictions of contact stress
  with pressure film measurements
• Convert 3D FE model pressure plot into a 2D
  synthetic image
• Compare synthetic image with pressure film image

5
Fit A Sphere

• Given
• dx,y,z for n points
• Least-Squares Fit
• Where
• Loop

origin
(a,b,c)
r
a -0.000422081 b 0.000270402 c 0.146251 r
20.5007 only 317 iterations
radius
ao-a 0 bo-b 0 co-c 0 else aoa
bob coc 0 approximation 2.2204460492503131e-
016
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Transform to Sphere Coordinates

• Given
• dx,y,z origin(a,b,c) radiusr
• Surface Point along vector to origin

(x,y,z)
L
(x,y,z)
r
r
x
x-a
(a,b,c)
x-a
(0,0,0)
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Transform to Femur Coordinates

• Given
• dx,y,z origin(a,b,c) radiusr
• center(cx,cy,cz) top(tx,ty,tz)
• Find Coordinate Transform to origin
• Apply To Each Point

8
Transform to Plane Coordinates

• Given
• dx,y,z
• origin(a,b,c)
• radiusr
• center(0,0,0)
• top(tx,ty,tz)
• Preserve arc length and x-y orientation
• .

9
Map Plane to JPEG

• Given
• dx,y pressurep(x,y)
• resolution(xres,yres)
• Determine Bins and Sample

bwx dx/xres bwy dy/yres Pressure
average of 3 nearest nodes
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Future Work

• JPEG Bin assignment
• 3 node average
• all nodes average
• average of 4 corners
• transfer function/smoothing
• Comparison of JPEG values to film JPEG
• bitwise
• region
• Real Femur FE Mesh
• increased complexity
• sphere fitting