fitting a round peg to a square hole
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A Method for Physical Validation of Finite Element Pressure Models. Fitting a Round Peg to a Square Hole. Janna Balling and Andrew Anderson. Introduction. Validate subject-specific FE models of the hip using experimental data Single-leg-stance and stair-climbing

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Presentation Transcript
introduction
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
introduction1
Introduction
  • Pressure sensitive film
    • Cut into rosette pattern
    • Fit to femoral head
    • Film scanned in 2D
    • Calibrated
    • Color intensity is proportional to applied pressure
objective

?

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
fit a sphere
Fit A Sphere
  • Given

d={x,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 ao=a bo=b co=c
  • 0 approximation = 2.2204460492503131e-016
transform to sphere coordinates

y

x

Transform to Sphere Coordinates
  • Given

d={x,y,z} origin=(a,b,c) radius=r

  • 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)

transform to femur coordinates

origin

center

y

top

top

origin

-z

Transform to Femur Coordinates
  • Given

d={x,y,z} origin=(a,b,c) radius=r

center=(cx,cy,cz) top=(tx,ty,tz)

  • Find Coordinate Transform to origin
  • Apply To Each Point
transform to plane coordinates

(0,0,0)

d

x

L

(x,y,z)

r

σ

z

y

(tx,ty,tz)

(x,y,z)

β

x

(0,0,0)

y’

(tx,ty,tz)

(x’,y’)

d

β

x’

(0,0,0)

Transform to Plane Coordinates
  • Given

d={x,y,z}

origin=(a,b,c)

radius=r

center=(0,0,0)

top=(tx,ty,tz)

  • Preserve arc length and x-y orientation

.

map plane to jpeg

dx

dy

bwy

bwx

Map Plane to JPEG
  • Given

d={x,y} pressure={p(x,y)}

resolution=(xres,yres)

  • Determine Bins and Sample

bwx = dx/xres bwy= dy/yres

Pressure = average of 3 nearest nodes

future work
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
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