Reconstruction of bone loading conditions from in vivo strain measurements

A method is described whereby bone loading conditions can be reconstructed from in vivo strain measurements. The method uses ex vivo calibration measurements to find the relationship between the strain data and the loads applied to the bone. Using singular value decomposition, a transformation matrix is determined which provides the best linear relationship available between the measured strain data and the measured loading components in the calibration measurements. The transformation matrix can then be used to calculate the loads which correspond best with any given strain data set made with that specific bone and strain gages. In this manner, the applied loads of earlier performed in vivo strain measurements can be reconstructed. The method was tested for the reconstruction of the loads on a tibia of a goat. After determining the transformation matrix from a set of calibration measurements, the transformation matrix was used to reconstruct all loading components (three forces and three moments) of a set of test measurements whereby the applied loads were measured. It was found that the axial force and the torsional moment on the bone could be reproduced very accurately, showing a root mean square error (RMSE) of only 2% of the maximal load in the test. The reconstruction of the bending moments was slightly worse, showing a RMSE of 5-8% of the maximal moments. The reconstruction of the transverse force components proved less accurate and a RMSE up to 24% of the maximum was found. Accuracy can be improved by using weight factors for the loading conditions and a more accurate measurement of the location of the loads during the calibration measurements.