A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

The origins of C4 grasslands: integrating evolutionary and ecosystem science.

The evolution of grasses using C4 photosynthesis and their sudden rise to ecological dominance 3 to 8 million years ago is among the most dramatic examples of biome assembly in the geological record. A growing body of work suggests that the patterns and drivers of C4 grassland expansion were considerably more complex than originally assumed. Previous research has benefited substantially from dialog between geologists and ecologists, but current research must now integrate fully with phylogenetics. A synthesis of grass evolutionary biology with grassland ecosystem science will further our knowledge of the evolution of traits that promote dominance in grassland systems and will provide a new context in which to evaluate the relative importance of C4 photosynthesis in transforming ecosystems across large regions of Earth.