The influence of bone volume fraction and ash fraction on bone strength and modulus

Although bone strength and modulus are known to be influenced by both volum e fraction and mineral content (ash fraction), the relative influence of th ese two parameters remains unknown. Single-parameter power law functions ar e used widely to relate bone volume or ash fraction to bone strength and el astic modulus. In this study we evaluate the potential for predicting bone mechanical properties with two-parameter power law functions of bone volume fraction (BV/TV) and ash fraction (a) of the form y = a(BV/TV)(b) alpha (c ), (where y is either ultimate strength or elastic modulus). We derived an expression for bone volume fraction as a function of apparent density and a sh fraction to perform a new analysis of data presented by Keller in 1994. Exponents b and c for the prediction of bone strength were found to be 1.92 +/- 0.02 and 2.79 +/- 0.09 (mean +/- SE), respectively, with r(2) = 0.97. The value of b was found to be consistent with that found previously, where as the value of c was lower than values previously reported. For the predic tion of elastic modulus we found b and c to be 2.58 +/- 0.02 and 2.74 +/- 0 .13, respectively, with r2 = 0.97. The exponent related to ash fraction was typically larger than that associated with bone volume fraction, suggestin g that a change in mineral content will, in general, generate a larger chan ge in bone strength and stiffness than a similar change in bone volume frac tion. These findings are important for interpreting the results of antireso rptive drug treatments that can cause changes in both ash and bone volume f raction. (C) 2001 by Elsevier Science Inc. All rights reserved.