Application of multidimensional interpolation on nonhomogeneous cancellous bone

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Abstract

Bone, especially cancellous bone, has been demonstrated to be nonhomogeneous. When applied to bone study, it raises the following question: How should the material properties of the bone from the available experimental data be interpolated?

In this study, the finite element model of the femur has been built and the nonhomogeneous material properties of the femur have been assigned from the computed tomography (CT) data. These results have been applied to assess some common interpolation algorithms on the bone study, such as Linear Multivariate, Radial Basis, and Nearest Neighbor. It was found that among 3 tested algorithms, the RBAS algorithm has more points with errors from 0% to 15% than in the other 2 algorithms. When the supporting points jump from 160 to 288, the interpolation results significantly improve. When the finite element model reduces the element number from 38,230 to 13,424, all 3 algorithms have slightly better results.

The interpolation of bone material properties should use 2 different approaches. The bone interpolation should be applied only to the bone with uniform structure. For the area with dramatic change of structure, the material properties can be defined directly. Among 3 tested algorithms, the Radial Basis algorithm performs best in the statistic study and should be the first choice in the bone study. In addition, the Radial Basis algorithm can be introduced into other methods to smooth the distribution of material properties. Also, with more supporting points (experimental data), the interpolation error becomes less. The interpolation approach offers a significant advantage in the finite element analysis: only 1 material ID needs to define the material interpolated from experimental data, unlike the several hundred material IDs defined for the elements derived from CT data that take material inhomogeneity into account.

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