Fujifilm Measurements of Interfacial Contact Area and Stress in Articulating Joints

Biomechanical Measurement Error Can Be Caused by Fujifilm Thickness: A Theoretical, Experimental, and Computational Analysis

“…Third, prior Fujifilm tests on a single CoCr condyle of the Omnifit implant undergoing 335 N during 90° knee flexion generated line-type contact with W FC = 13.61 mm and W FS = 2.35 mm [ 6 ]. Fourth, recall that the Hertzian equation for cylinder-on-flat contact is [ 3 , 21 , 22 ] where W O is true contact width in the sagittal plane without Fujifilm (i.e., W S ), F is compressive force of 335 N, D cyl is CoCr condyle curvature diameter of 36.5 mm in the sagittal plane during 90° knee flexion [ 1 , 6 ], ν cyl and ν flat are CoCr and UHMWPE Poisson's ratios of 0.31 and 0.4 [ 22 ], E cyl and E flat are CoCr and UHMWPE elastic moduli of 210 and 0.9 GPa [ 24 ], and L cyl is W CONDYLE of 13.61 mm. This generates a W S = 1.46 mm.…”

“…Secondly, although only two loads were evaluated, they did simulate clinical loads for the single-legged stance phase of walking for a 75 kg person (i.e., 1x and 4x body weight) [ 23 , 46 , 47 ]. Thirdly, theoretical contact widths W O were orthogonal projections that ignored the slight curvature at the cylinder-on-flat interface caused by the cylinder, whereas experimental W F measurements were made by “unfolding” the Fujifilm squares which had followed the cylinder curvature during the indentation tests [ 3 ]. This might have exaggerated current values for Fujifilm measurement error in the lower test range (i.e., D < 10 mm) when contact width was comparable to cylinder diameter, which possibly indicates some minor plastic deformation [ 22 ].…”

“…Consequently, classic Hertzian contact mechanics theory was used for the case without Fujifilm ( Figure 1(a) ). Hertzian formulas are valid for quasi-static normal loads, nonconforming surfaces, smooth surfaces with frictionless contact, and small linear elastic deformations in which the contact width is much smaller than the cylinder diameter [ 3 , 21 , 22 ]. Hertzian analysis was applied under the following conditions.…”

“…Third, the material properties of elastic modulus and Poisson's ratio were based on steel, ultrahigh molecular weight polyethylene (UHMWPE), and artificial cortical bone, respectively, for MOM, MOP, and MOB configurations, to match later experiments. Finally, the Hertzian equation for cylinder-on-flat indentation was used in the following form: where W O is contact width without Fujifilm, F is compressive force (i.e., 750 or 3000 N), D cyl is cylinder diameter (i.e., 0 to 80 mm), L cyl is cylinder length that mimics later experiments (i.e., 75 mm of cylinder length was in contact for MOM tests, but 50 mm of cylinder length was in contact for MOP and MOB tests), ν cyl is Poisson's ratio for a steel cylinder (0.31), ν flat is Poisson's ratio for steel (0.31), UHMWPE (0.4), or artificial cortical bone (0.3) flat substrate, E cyl is elastic modulus for a steel cylinder (210 GPa), and E flat is elastic modulus for a steel (210 GPa), UHMWPE (0.9 GPa), or artificial cortical bone (16.7 GPa) flat substrate [ 3 , 21 , 22 , 24 , 25 ].…”

“…The boundary conditions of the FE models involved assigning different friction coefficients μ for Fujifilm contact with all other surfaces ( μ = 0) [ 15 , 16 ], MOM contact ( μ = 0.420) [ 26 ], MOP contact ( μ = 0.045) [ 27 , 28 ], and MOB contact ( μ = 0.080) [ 29 ]. The materials properties of the FE models were set for elastic modulus E and Poisson's ratio ν for steel ( E = 210 GPa, ν = 0.31), UHMWPE ( E = 0.9 GPa, ν = 0.4), and artificial cortical bone ( E = 16.7 GPa, ν = 0.3) as done above [ 3 , 21 , 22 , 24 , 25 ], as well as for Fujifilm ( E = 0.1 GPa, ν = 0.45) [ 14 – 16 ]. The constraints of the FE models were attributed to the cylinder to allow for deformation (i.e., no constraints in x , y , or z directions), the plate bottom to mimic resting on a rigid foundation (i.e., constrained in the x , y , and z directions), and the Fujifilm to simulate no crinkling or lift-off (i.e., constrained in the z direction at the edges only).…”