Computational load estimation of the femur

The density distribution and, thus, mechanical properties of long bones such as the femur are dependent on their loading. Many bone tissue adaptation theories are proposed to describe the density distribution that results from a given set of loading parameters. It is relatively easy to measure the density distribution of long bones, for example, using Computed Tomography (CT). However, there is no easy non-invasive method for in-vivo measurement of musculoskeletal loads. It is therefore interesting to investigate whether or not it is possible to predict the musculoskeletal loads that have resulted in a certain measured density distribution using bone tissue adaptation models. An inverse problem has to be solved for that purpose. In this paper, we use Artificial Neural Networks (ANNs) to solve the associated inverse problem and estimate the loading parameters that have resulted in the CT-measured three-dimensional density distribution of a proximal femur. An ANN is trained using a dataset generated by solving the forward tissue adaptation model for a large number of loading parameters. Before training the ANN with the generated training dataset, a Gaussian noise component is added to the density distribution. This improves the robustness of the trained ANN against deviations of the measured density distribution from the predictions of the forward bone tissue adaptation model. It is shown that the proposed technique is capable of predicting loading parameters that result in a density distribution close to the measured density distribution.