Quantifying the regional variations in the mechanical properties of cancellous bone of the tibia using indentation testing and quantitative computed tomographic imaging

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Abstract

Finite element models apply material properties using experimentally derived density–modulus equations and computed tomographic image data, yet numerous different equations exist in the literature. The purpose of this study was to experimentally evaluate the distribution of mechanical properties through the proximal tibia and compare with those predicted using existing density–modulus equations. Indentation testing was performed on five cadaveric tibiae, with four slices removed from the proximal epiphysis and metaphysis of each. Elastic modulus and yield strength were identified for each test and grouped into nine transverse regions. These regions were identified on computed tomographic scans, and four density–modulus equations from the literature applied. Errors between measured and predicted modulus were then calculated. Elastic modulus and yield strength varied regionally, with the bone located closest to the joint and in the condyles being strongest and the intercondylar region the weakest. The optimal relationship for predicting modulus varied depending on anatomical region, but generally was best predicted by the Goulet equation. The regions of high strength identified in this study (condyles and proximal regions) can serve as improved sites of attachment for orthopedic devices and should be preserved during surgery, if possible. The substantial regional variations observed herein (almost a threefold change in modulus across different regions) should be incorporated into finite element models and applied using the Goulet density–modulus equation.

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Relations of mechanical properties to density and CT numbers in human bone.

J.Y. Rho, M.C. Hobatho, R.B. Ashman (1995)

Mechanical properties of cortical and cancellous bone from eight human subjects were determined using an ultrasonic transmission technique. Raw computerized tomography (CT) values obtained from scans of the bones in water were corrected to Hounsfield units. The correlations between CT numbers and mechanical property estimated from cortical bone were found to be low (r2 0.6). These results suggest that CT values may be useful in predicting mechanical properties only for cancellous bone. Poor correlations were found between modulus in the radial or circumferential direction and modulus in the superior-inferior direction for cortical bone, whereas good correlations were found between modulus in the anterior-posterior direction or medial-lateral direction and modulus in the S-I direction for cancellous bone. These results indicate that modulus in the radial or circumferential direction could not be predicted from modulus in the S-I direction for cortical bone, but could be predicted for cancellous bone. The predictive capabilities of linear and power models evaluated for cancellous bone alone were approximately equal. However, the power function gives a better fit of data at the low and high density values. The specific relationships, depending on the types of bone, that predict elastic modulus from density and CT numbers were suggested for human cortical and cancellous bone. These specific correlations may help a number of researchers develop more accurate models; however, these hypotheses should be proven by further study.