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# Fitting a Round Peg to a Square Hole - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Fitting a Round Peg to a Square Hole' - janus

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### Fitting a Round Peg to a Square Hole

Janna Balling

and Andrew Anderson

Introduction Models

• 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

Introduction Models

• Pressure sensitive film

• Cut into rosette pattern

• Film scanned in 2D

• Calibrated

• Color intensity is proportional to applied pressure

? Models

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 Models

• 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

• ao-a ≈ 0 bo-b ≈0 co-c≈0

• else ao=a bo=b co=c

• 0 approximation = 2.2204460492503131e-016

y Models

x

Transform to Sphere Coordinates

• Given

• 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)

origin Models

center

y

top

top

origin

-z

Transform to Femur Coordinates

• Given

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

• Find Coordinate Transform to origin

• Apply To Each Point

(0,0,0) Models

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)

center=(0,0,0)

top=(tx,ty,tz)

• Preserve arc length and x-y orientation

.

dx Models

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 Models

• 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