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Hamner SR and Delp SL. Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds. Journal of Biomechanics; 46(4), 780-7. (2013)
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Running is a bouncing gait in which the body mass center slows and lowers during the first half of the stance phase; the mass center is then accelerated forward and upward into flight during the second half of the stance phase. Muscle-driven simulations can be analyzed to determine how muscle forces accelerate the body mass center. However, muscle-driven simulations of running at different speeds have not been previously developed, and it remains unclear how muscle forces modulate mass center accelerations at different running speeds. Thus, to examine how muscles generate accelerations of the body mass center, we created three-dimensional muscle-driven simulations of ten subjects running at 2.0, 3.0, 4.0, and 5.0 m/s. An induced acceleration analysis determined the contribution of each muscle to mass center accelerations. Our simulations included arms, allowing us to investigate the contributions of arm motion to running dynamics. Analysis of the simulations revealed that soleus provides the greatest upward mass center acceleration at all running speeds; soleus generates a peak upward acceleration of 19.8 m/s/s (i.e., the equivalent of approximately 2.0 bodyweights of ground reaction force) at 5.0 m/s. Soleus also provided the greatest contribution to forward mass center acceleration, which increased from 2.5 m/s/s at 2.0 m/s to 4.0 m/s/s at 5.0 m/s. At faster running speeds, greater velocity of the legs produced larger angular momentum about the vertical axis passing through the body mass center; angular momentum about this vertical axis from arm swing simultaneously increased to counterbalance the legs. We provide open-access to data and simulations from this study for further analysis in OpenSim at simtk.org/home/nmbl_running, enabling muscle actions during running to be studied in unprecedented detail.


Repository of experimental data (i.e., motion capture, EMG, GRFs), subject-specific models, and muscle-driven simulation results of 10 male subject running across a range of speeds: 2 m/s, 3 m/s, 4 m/s, and 5 m/s.

License: Raw EMG Data, Subject 01, Subject 02, Subject 03, Subject 04, Subject 08, Subject 10, Subject 11, Subject 17, Subject 19, Subject 20

These simulations were created using OpenSim and the workflow included Scale, Inverse Kinematics (IK), Reduced Residual Algorithm (RRA), Computed Muscle Control (CMC), and Induced Acceleration Analysis (IAA). The following resources provide instructions for using these tools and information on how to generate and evaluate musculoskeletal simulations:

• OpenSim User's Guide | http://stanford.io/17cia3U

• OpenSim Support Webpage | http://stanford.io/17ciwrn

• Webinar on Simulations of Running | http://bit.ly/oDIUOa

Muscle contributions to fore-aft and vertical body mass center accelerations over a range of running speeds from Samuel Hamner on Vimeo.


The goal of this study was to determine how muscles and arm swing affect dynamics of the body at different running speeds. Specifically, we determined how muscles contribute to mass center accelerations during the stance phase of running, and how the arms act to counterbalance the motion of the legs. We achieved this goal by creating and analyzing muscle-driven, forward dynamic simulations of ten subjects running across a range of speeds: 2 m/s, 3 m/s, 4 m/s, and 5 m/s. An induced acceleration analysis determined the contribution of each muscle to mass center accelerations. Our simulations also included arm motion, allowing us to investigate the contributions of arm swing to running dynamics. These simulations use experimental data as inputs, so we also collected data to characterize joint angles, joint moments, and ground reaction forces at different running speeds.

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This project serves as a repository of experimental data (i.e., motion capture, EMG, GRFs), subject-specific models, and resulting muscle-driven simulation results for 10 male subjects running at multiple speeds: 2 m/s, 3 m/s, 4 m/s, and 5 m/s. Data was collected on an instrumented treadmill in the Human Performance Lab at Stanford University. All subjects were experienced runners, each reporting to run at least 30 miles per week.

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