Indentation response of human patella with elastic modulus correlation to localized fractal dimension and bone mineral density

• Ten human cadaver patellae were tested in spherical indentation–relaxation.
• Small and large indenter response was fit to a viscoelastic Hertzian contact models.
• Bone mineral density and fractal dimension calculated at each test location.
• Bone mineral density had a low correlation to patella elastic modulus.
• Fractal dimension had a very high correlation to patella elastic modulus.

The goal of this study was to determine material properties for the anterior cortex and subcortical regions of human patellae and relate those properties to mineral density and fractal dimension of the bone. Ten human patellae were obtained from eight fresh frozen human cadavers and subjected to anteriorly-directed spherical indentation–relaxation experiments using two different sized indenters to two different indentation depths. Response data were fit to a three-mode viscoelastic model obtained through elastic–viscoelastic correspondence of the Hertzian contact relation for spherical indentation. A location-specific effective bone density measurement that more heavily weighted bone material close to the indentation site (by von Mises stress distribution) was determined from micro-computed tomography (38 µm resolution) data captured for each specimen. The same imagery data were used to compute location specific fractal dimension estimates for each indentation site. Individual and averaged patella material models verified the hypothesis that when the larger indenter and greater indentation depth is used to engage the surface and deeper (trabecular) bone, the bone exhibits a more compliant response than when only the surface (cortical) bone was engaged (instantaneous elastic modulus was 325 MPa vs. 207 MPa, p<0.05). Effective bone mineral density was shown to be a significant predictor of the elastic modulus for both small and large indentation types (p<0.05) despite relatively low correlations. Exponential regressions of fractal dimension on elastic modulus showed significant relationships with high correlation for both the small (R2=0.93) and large (R2=0.97) indentations.

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