An Invertible Mathematical Model of Cortical Bone's Adaptation to Mechanical Loading.

Determination of mechanical loading regimen that would induce a prescribed new bone formation rate and its site-specific distribution, may be desirable to treat some orthopaedic conditions such as bone loss due to muscle disuse, e.g. because of space flight, bed-rest, osteopenia etc. Site-specific new bone formation has been determined earlier experimentally and numerically for a given loading regimen; however these models are mostly non-invertible, which means that they cannot be easily inverted to predict loading parameters for a desired new bone formation. The present work proposes an invertible model of bone remodeling, which can predict loading parameters such as peak strain, or magnitude and direction of periodic forces for a desired or prescribed site-specific mineral apposition rate (MAR), and vice versa. This fast, mathematical model has a potential to be developed into an important aid for orthopaedic surgeons for prescribing exercise or exogenous loading of bone to treat bone-loss due to muscle disuse.