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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Fitting a Round Peg to a Square Hole

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Fitting a round peg to a square hole

A Method for Physical Validation of Finite Element Pressure Models

Fitting a Round Peg to a Square Hole

Janna Balling

and Andrew Anderson


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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