Calculation of Muscle Coactivation

Previous studies have observed greater muscle coactivation during sloped walking (Lay et al., 2007; Franz and Kram, 2013), which may affect the amounts of muscle eccentric contractions. Therefore, the levels of muscle coactivations were assessed using moment-based coactivation indices (CI) for the multiple muscles across the hip, knee and ankle joints (Le et al., 2017). The flexion/extension muscle moments in one gait cycle for the muscles across the hip, knee and ankle were calculated as the product of the active force and the moment arm of one muscle with respect to the corresponding joint. The net joint moment was the sum of the moments of all muscles with respect to a given joint. Moments in the hip flexion, knee flexion and ankle plantarflexion directions were defined positively. At each time step, muscles were classified as agonists if they generated moments with the same sign as the net joint moment, and antagonists if they generated moments with the opposite sign of the net joint moment. The ratio of antagonists to agonists (b(t)) was defined as:

where agonist_i (t) is magnitude of the moment of the ith agonist, and antagonist_j (t) is the magnitude of the moment of the jth antagonist. The total absolute moments of agonists and antagonists across one joint (M_total) were calculated as:

No normalization was applied to the moments in Eqs 1 and 2. The moment-based coactivation index of a joint (CI_jnt) was then defined as the ratio of antagonists to agonists (b(t)) multiplied by the total absolute moment (M_total(t)) normalized by the maximum total absolute moment across all the trials and slopes for each participant (M_max):

The M_max was used so that CI_jnt could be compared across various walking conditions. The average of CI_jnt over the entire gait cycle was calculated to represent the level of coactivation at a joint during walking.