1. Fitting a Round Peg to a Square Hole Janna Balling and Andrew Anderson A Method for Physical Validation of Finite Element Pressure Models

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

3. Introduction Pressure sensitive film 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 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 Given d={x,y,z} for n points Least-Squares Fit Least-Squares FitWhere Loop Loop r (a,b,c) a= -0.000422081 b= 0.000270402 c= 0.146251 r= 20.5007 only 317 iterations a o -a ≈ 0 b-b ≈0 c-c≈0 a o -a ≈ 0 b o -b ≈ 0 c o -c≈ 0 else a=a b=b c=c else a o =a b o =b c o =c 0 approximation = 2.2204460492503131e-016 origin: radius:

6. Transform to Sphere Coordinates Given Given d={x,y,z} origin=(a,b,c) radius=r Surface Point along vector to origin Surface Point along vector to origin (x,y,z) (a,b,c) (x’,y’,z’) (0,0,0) x y r x’-a x-a L x’ r

7. top center origin Transform to Femur Coordinates Given Given d={x,y,z} origin=(a,b,c) radius=r center=(cx,cy,cz) top=(tx,ty,tz) Find Coordinate Transform to origin Find Coordinate Transform to origin Apply To Each Point Apply To Each Point y -z origin top

8. Transform to Plane Coordinates Given Givend={x,y,z}origin=(a,b,c)radius=rcenter=(0,0,0)top=(tx,ty,tz) Preserve arc length and x-y orientation Preserve arc length and x-y orientation. d (0,0,0) (x,y,z) r L σ x z y (0,0,0) (x,y,z) x β (tx,ty,tz) (0,0,0) (x’,y’) d x’ y’ (tx,ty,tz) β

9. Map Plane to JPEG Given Given d={x,y} pressure={p(x,y)} resolution=(xres,yres) Determine Bins and Sample Determine Bins and Sample bwx = dx/xres bwy= dy/yres Pressure = average of 3 nearest nodes bwx bwy dy dx

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