Human running is a bouncing gait during which the body mass center slows and lowers during the first half of the stance phase;​ muscle forces then accelerate the mass center forward and upward in the second half of stance. Muscle-driven simulations of running allow us to determine how muscle forces give rise to the accelerations of the body mass center. Before this dissertation, it remained unclear how muscle forces modulate accelerations of the mass center at various running speeds as three-dimensional, muscle-driven simulations of running had yet been created or analyzed. Thus the goal of this dissertation was to better understand the functional role of muscles by generating the first three-dimensional, muscle-driven simulation of the running gait cycle and quantifying how muscles contribute to vertical and fore-aft accelerations of the body mass center over a range of running speeds.

Initially, I created a three-dimensional, muscle-driven simulation of a single subject running at a single speed and quantitatively described how individual muscles accelerated the subject’s body mass center. The simulation was generated with a musculoskeletal model driven by 92 musculotendon actuators of the lower extremities and torso. The model also included torque-driven arms, which allowed me to investigate the contributions of arm motion to running dynamics. This single simulation revealed that during the first half of the stance phase, quadriceps was the largest contributor to backward and upward accelerations of the mass center. During the second half of stance, the soleus and gastrocnemius muscles were the greatest contributors to forward and upward accelerations of the mass center.

To determine how individual muscle forces in these simulations acted to generate the ground reaction force, and the resulting accelerations of the body mass center, it is necessary to model ground contact. The accelerations computed in such simulation analyses are sensitive to the model used to represent contact between the foot and ground. To have confidence in our ability to interpret muscle function, a ground contact model should be able to reproduce experimentally measured ground reaction forces and moments. I show that a rolling constraint accurately reproduces the measured ground reaction forces and moments in an induced acceleration analysis of muscle-driven simulations for walking, running, and crouch gait. I also evaluated other contact models used in previous studies (e.g., point and weld constraints) to illustrate that these models can produce inaccurate reaction moments and lead to contradictory interpretations of muscle function, including the contribution of major muscles, like the vasti and soleus, to fore-aft and upward mass center accelerations.

To determine how muscles modulate ground reaction forces and mass center accelerations over a range of running speeds, I created muscle-driven simulations of ten subjects running at four speeds:​ 2 m/s, 3 m/s, 4 m/s, and 5 m/s. An induced acceleration analysis was used to determine the contribution of each muscle to body mass center accelerations. Analysis of the simulations revealed that soleus provides the greatest upward mass center acceleration at all running speeds, with a peak upward acceleration of 19.8 m/s² (i.e., the equivalent of approximately 2.0 body weights of ground reaction force) at 5.0 m/s. Soleus also provided the greatest contribution to forward mass center acceleration, with contributions increasing from 2.5 m/s² to 4.0 m/s² as running speed increased from at 2.0 m/s to 5.0 m/s. Quadriceps produced the largest backward mass center acceleration;​ at 5.0 m/s peak contribution from quadriceps was 80% of total peak backward acceleration. At higher running speeds, greater velocity of the legs produced larger vertical angular momentum about the mass center, while vertical angular momentum from arm swing simultaneously increased to counterbalance that of the legs.

The ability to reproduce the results of a study is an essential principle of the scientific method. However, reproducing results of simulation studies remains challenging because the software, models, and data used to create and analyze the simulations are generally not freely available. Thus, to promote the utilization and acceptance of simulations in movement science, I have provided open-access to the models, data, and subject-specific simulations developed for this dissertation at https://simtk.org/home/RunningSim and https://simtk.org/home/nmbl_running. The data and simulations can be visualized and results can be reproduced in OpenSim (http://opensim.stanford.edu), a freely-available biomechanics simulation package.