The musculoskeletal model was then imported into OpenSim (opensim.stanford.edu) software in order to take advantage of the programme’s established analysis capabilities. OpenSim uses the ‘virtual work’ method (change of muscle–tendon unit length per unit joint rotation) explained by Delp & Loan (1995) (link), Delp & Loan (2000) (link) and Pandy (1999) (link) to compute muscular moment arms over a range of motion. Maximal muscular moments then can be estimated using muscle Fmax and potentially (see above and Zajac, 1989 (link)).
To test whether ostrich muscle moment-generating capacity is optimized to match peak loads during walking and running (our Question 1), we compared the results from estimated maximal muscle moments to experimentally-calculated internal and external moments (Rubenson et al., 2011 (link)), addressed in the Discussion. First, each muscle’s maximal isometric muscle force (Fmax) was multiplied by the flexor/extensor moment arm calculated by OpenSim (i.e., from the individual trials’ limb joint angle input data and the model’s resulting moment arm output data), for each pose adopted throughout the representative walking and running gait cycle trials (every 1% of gait cycle) to obtain the relationship between locomotor kinematics and isometric muscle moments. Second, OpenSim was used to calculate individual muscle moments directly, taking into account muscle force–length relationships (set as dimensionless in a Hill model as per Zajac, 1989 (link)), in order to provide a more realistic estimate of the variation of maximal moment-generating capacity throughout the same gait cycles. Both approaches were static, ignoring time/history-dependent influences on muscles. The second approach allowed non-isometric muscle action to be represented, but did not incorporate force–velocity effects, which would require a more dynamic simulation to resolve. Total extensor and flexor maximal moments were calculated in OpenSim as well as the net (extensor + flexor) maximal moment.
To determine if ostrich limb muscle moment arms peak at extended limb orientations or at mid-stance of locomotion (our Question 2), we used the model to calculate the mean moment arm of all extensor or flexor muscles across the full range of motion of each joint (estimated from osteological joint congruency as in Bates & Schachner (2012) (link)) in flexion/extension (set at constant values for mid-stance of running in other degrees of freedom), summed these mean moment arms, and divided that sum by the summed maximal moment arms for each muscle across the same range of motion (as in Hutchinson et al., 2005 (link)). We then inspected whether our representative mid-stance poses in walking or running matched maximal or minimal averaged moment arms corresponding to those poses.
To compare the degree of matching between muscle moment arms in our model and the experimental data of Smith et al. (2007) (link) and Bates & Schachner (2012) (link) (our Question 3), we obtained the published experimental and modelling data (KT Bates, provided by request), transformed their joint angle definitions to be consistent with our model definitions, and plotted the muscle moment arms vs. each joint angle with our moment arm data (also seeFigs. S1 –S4 ), restricting the other studies’ ranges of motion to those presented in the original studies. For the knee and joints distal to it, in this study we focus only on flexor/extensor moment arms for simplicity and because the importance of long-axis and ab/adduction muscle (vs. passive tissue) moments at these distal joints is unclear, although our model could be adjusted to calculate those non-sagittal moment arms and moments.
To test whether ostrich muscle moment-generating capacity is optimized to match peak loads during walking and running (our Question 1), we compared the results from estimated maximal muscle moments to experimentally-calculated internal and external moments (Rubenson et al., 2011 (link)), addressed in the Discussion. First, each muscle’s maximal isometric muscle force (Fmax) was multiplied by the flexor/extensor moment arm calculated by OpenSim (i.e., from the individual trials’ limb joint angle input data and the model’s resulting moment arm output data), for each pose adopted throughout the representative walking and running gait cycle trials (every 1% of gait cycle) to obtain the relationship between locomotor kinematics and isometric muscle moments. Second, OpenSim was used to calculate individual muscle moments directly, taking into account muscle force–length relationships (set as dimensionless in a Hill model as per Zajac, 1989 (link)), in order to provide a more realistic estimate of the variation of maximal moment-generating capacity throughout the same gait cycles. Both approaches were static, ignoring time/history-dependent influences on muscles. The second approach allowed non-isometric muscle action to be represented, but did not incorporate force–velocity effects, which would require a more dynamic simulation to resolve. Total extensor and flexor maximal moments were calculated in OpenSim as well as the net (extensor + flexor) maximal moment.
To determine if ostrich limb muscle moment arms peak at extended limb orientations or at mid-stance of locomotion (our Question 2), we used the model to calculate the mean moment arm of all extensor or flexor muscles across the full range of motion of each joint (estimated from osteological joint congruency as in Bates & Schachner (2012) (link)) in flexion/extension (set at constant values for mid-stance of running in other degrees of freedom), summed these mean moment arms, and divided that sum by the summed maximal moment arms for each muscle across the same range of motion (as in Hutchinson et al., 2005 (link)). We then inspected whether our representative mid-stance poses in walking or running matched maximal or minimal averaged moment arms corresponding to those poses.
To compare the degree of matching between muscle moment arms in our model and the experimental data of Smith et al. (2007) (link) and Bates & Schachner (2012) (link) (our Question 3), we obtained the published experimental and modelling data (KT Bates, provided by request), transformed their joint angle definitions to be consistent with our model definitions, and plotted the muscle moment arms vs. each joint angle with our moment arm data (also see
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