Ii.a.3 | Muscle Forces -bone Deformations -a Novel Approach to Determine Muscle Forces -corresponding to Measured Tibia Deformations (#107)

Content Introduction Bone deformation induced by muscle contractions are thought to play an important role for adaption of bones. Past simulation studies to determine bone forces during locomotion focused on an inverse dynamics approach, mostly without consideration of these deformations. However, latest studies have shown that both muscle forces and corresponding deformation of the bone are required for maintenance of bone [Ducos M., 2013]. A recently completed study at DLR produced in vivo data of tibia deformation during various activities (e.g. walking, running, hopping) [Yang P.-F., 2013]. Utilizing this data, we have begun the development of a computer program which inversely calculates the muscle forces corresponding to tibia deformation. Methods The basic concept is the combination of an operating software (MATLAB) forwarding input to a Finite Element model (ANSYS) and processing the results with an optimization algorithm. A 3D geometry (CAD) of the tibia and the muscle attachments has been created and the directions of the forces are defined on basis of the muscles’ anatomical location. Based on the superposition principle, the displacements for n forces can be summed up to form one equation: ∑i=1 ( fi * fmpi) * Di = ucalc (1) where f is the directional vector, fmp the magnitude, D the deformation matrix and ucalc the calculated displacement vector (fig. 1). Hence, the deformation matrix for each muscle force is determined via FEM. The now calculable displacements are compared to the measured ones and the difference is minimized by a constrained nonlinear optimization algorithm: | ucalc umeas | (2) Results The optimization algorithm, is searching for a fitting solution for the under-determined muscle force equation. In a regular FEM simulation the displacement induced by 10 forces has been calculated. Our program was then able to reconstruct the displacement with a precision of 10mm. Discussion The program can reconstruct muscle contraction patterns for given deformations. Future work will make them comparable to realistic patterns measured with EMG. Yet, the results are biased due to the simplified material properties implemented in the CAD model. Also, only the displacement of one point is taken into consideration, whereas the in vivo data provides three, enabling a more realistic deformation. Enhancing the program will bring further insight in the biomechanics of human locomotion and the mechanisms triggering bone remodelling.