Toward a quantitative formulation of Wolff's Law in trabecular bone

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Hayes, W. C.¹; Snyder, B.¹

Toward a quantitative formulation of Wolff's Law in trabecular bone

Mechanical Properties of Bone

Affiliations

¹Orthopaedic Biomechanics Laboratory, Charles A. Dana Research Institute, Beth Israel Hospital and Harvard Medical School, Boston, Massachusetts

²Orthopaedic Surgical Research, Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania
Abstract

It is widely assumed that trabecular architecture is related through Wolff's Law to functionally imposed stresses. However, quantitative formulations of this law are not available. The objective of this investigation is to provide correlations between stereological parameters describing patellar trabecular morphology and global stresses obtained using finite element analysis. Finite element models were developed based on microstructural analyses of the patellar geometry and literature values for loading and material properties. Special stereological analysis techniques were developed to quantitatively describe trabecular architecture. The stereologic techniques were assessed for accuracy using independent measurements and arrays of ellipses with known geometries Comparisons of predicted trabecular stresses and trabecular morphology exhibited highly significant positive correlations between von Mises effective stresses and trabecular areal density. Highly significant correlations between principal stress directions and trabecular orientation were also shown, a finding which supports the trajectorial theory of trabecular architecture. These two results taken together suggest that trabecular bone is most dense in regions of high shear stress and that the trabecular orientation is such to minimize bending deformations in individual trabeculae.

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