Fig 1.
Conceptual summary of ankle joint vs. muscle-tendon-unit (MTU) power.
Net ankle joint power (green, top row) can be computed from inverse dynamics by multiplying ankle joint moment, Mank, by ankle angular velocity, ωank (sagittal plane depicted). Due to assumptions in inverse dynamics, this ankle power may or may not correspond with net MTU power (second row), depending on the underlying MTU contributions (cartoon depicted in bottom row). (A) Ankle power is expected to reflect MTU power when MTUs are monoarticular (red, acting solely about the ankle). (B) Ankle power may not reflect power contributions from multiarticular MTUs (blue). In the extreme example depicted, the multiarticular MTU provides torque about both the ankle and MTP (toe) joints, but due to the simultaneous plantarflexion of the ankle and extension of the toes, the MTU does not change length. Thus the MTU behaves like a rigid cable and performs zero net power. However, inverse dynamics (joint-by-joint) analysis would indicate positive power about the ankle (Mank ∙ ωank), and equal offsetting negative power about the toe joints (MMTP ∙ ωmtp, inset). In this case, net ankle power would greatly overestimate net MTU power. (C) In actuality, both mono- and multi-articular MTUs contribute to human movement. However, it remains unclear if and by how much ankle power overestimates net MTU power. If multiarticular MTUs act isometrically (i.e., perform zero net power, as depicted here) or close to isometrically, then it is expected that ankle power magnitude will be larger than net MTU power.
Fig 2.
Simplified representation of ankle-foot musculoskeletal model.
This simplified model was used to investigate the ankle plantarflexor muscles during the Push-off phase of walking. (A) The main ankle plantarflexor MTUs were included in the model: triceps surae (soleus and gastrocnemius), the peroneus longus, and the flexor digitorum and hallucis longus (FDHL). See S1 Appendix for more details on muscles that were included/excluded. (B) Kinematic, anthropomorphic, and EMG data were used to estimate power contributions from each MTU. An example is depicted for the multiarticular FDHL MTUs. Anthropomorphic MTU moment arms about the ankle (rfdhl,ank) and MTP joints (rfdhl,mtp) were combined with kinematic estimates–angular velocities of the ankle (ωank) and MTP joints (ωmtp), and longitudinal arch length (larch)–to estimate time-varying MTU length changes. MTU force was estimated using an EMG-to-force mapping algorithm (see S1 Appendix for full details). Force was then multiplied by the rate of MTU length change to compute MTU power.
Fig 3.
EMG-driven musculoskeletal model was able to reproduce inverse dynamics sagittal plane ankle power.
Results are depicted for each individual subject at 1.25 m/s. The EMG-driven ankle joint power, , (red dashed line) correlated strongly with inverse dynamics ankle power, Pank, (blue solid line).
Table 1.
Electromechanical delay (EMD, τ) and scaling factor, C, for each speed, subject, and the overall study average.
Fig 4.
Average MTU contributions to at 1.25 m/s.
Estimated MTU contributions are shown for the triceps surae, flexor digitorum and hallucis longus (FDHL), and peroneus longus (N = 6).
Fig 5.
Net ankle power vs. minimum MTU power vs. MTU power during human walking at 1.25 m/s (N = 6).
Net ankle power overestimated MTU power and minimum MTU power by about 2% and 7%, respectively, due to multiarticular FDHL dynamics. Inset: Push-off work (area under the power curve within the shaded region) exhibited similar, relatively small differences.