Purpose The strain rate (SR) tensor measures the principal directions and magnitude of the instantaneous deformation; this study aims to track age related changes in the 2D SR tensor in the medial gastrocnemius during passive joint rotation and active isometric contraction. Methods SR tensors were derived from velocity encoded magnetic resonance phase-contrast images in nine young (28 yrs) and eight senior (78 yrs) women. Strain rates along and in the cross-section of the fiber were calculated from the SR tensor and used to derive the out-plane SR. Age related and regional differences in the SR eigenvalues, orientation, and the angle between the SR and muscle fiber (SR-fiber angle) were statistically analyzed. Results SR along the fiber was significantly different between the cohorts during isometric contraction with higher values in the young (P<0.05). The SR-fiber angle was larger in the young for both motion types but this difference was not statistically significant. Significant regional differences in the SR indices was seen in passive joint rotation (P<0.05) for both cohorts. Conclusion SR mapping reflects age related and regional differences during active and passive motion respectively; this may arise from differences in contractility (active motion) and elastic properties (active and passive motion).

In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements.

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