Bone remodeling of diaphyseal surfaces by torsional loads: theoretical predictions

A theory of surface bone remodeling is extended to include the effects of shearing strains as well as normal strains. It is shown that the surface velocity can only depend upon the square of shearing strains, but that it can be linear as well as quadratic in the normal strains. The theory is applied to predict the surface bone remodeling in the diaphysis of a long bone under combined axial and torsional loading. In the general case the diaphysis of the long bone is modeled as a hollow thin-walled cylinder of arbitrary cross-section and, in a special case, as a right circular thin-walled tube. It is shown here that if a thin-walled right circular cylinder capable of surface remodeling is subjected to an axial compressive load and a twisting torque, then the effect of increasing the torque is the same as the effect of decreasing the axial compressive load, namely the mean radius of the cross-section increases and the wall width thins. Conversely, the effect of reducing the torque is the same as the effect of increasing the axial compressive load, namely the mean radius of the cross-section decreases and the wall width thickens.