Determination of mineral-organic bonding effectiveness in bone--theoretical considerations

It is postulated that the effectiveness of bonding between the mineral and organic phases could be an important influence on the behavior of bone with respect to its mechanical properties, metabolic activity, and aging effects associated with these factors. Changes in bonding effectiveness might also be related to the etiology of osteoporosis. If this hypothesis is correct, it would be of interest to determine the amount of debonding present in bone. An analysis that employs both macromechanical and micromechanical composite theory is performed to show how this quantity could be calculated. The approach taken is first to determine the elastic moduli of a characteristic volume from bulk elastic properties of bone and the mineral crystallite orientation distribution. Voigt and Reuss type averages are used to obtain upper and lower bounds. Modifications of the Halpin-Tsai equations that apply to chopped fiber composites are then used to calculate the amount of debonding between the phases in the characteristic volume. All of the parameters employed in the theory are measurable using established techniques. To apply the theory quantitatively the following information must be known: 1) the density and elastic moduli of the bone (and its phases), and 2) the mineral orientation distribution.