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. 2022 Jul 7;12:9842. doi: 10.1038/s41598-022-13386-9

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Simulation of a gastrocnemius avoidance coordination pattern. Identical joint kinetics were simulated (n = 1) with a natural (Eq. 1) and a gastrocnemius (gastroc) avoidance (Eq. 2) static optimization objective function. During late stance, the muscles generate ankle plantarflexion, knee flexion, and hip flexion moments. The gastrocnemius avoidance coordination pattern requires increased soleus and hamstrings force to compensate for the ankle and knee moments normally generated by the gastrocnemius. The larger knee flexion moment arm (r) of the hamstrings compared to the gastrocnemius allows the hamstrings to generate the same moment with less force than the gastrocnemius, reducing knee contact force. A weighted average of the moment arms (hamstrings: biceps femoris long head and short head, semitendinosus, semimembranosus; gastrocnemius: medial and lateral heads) was computed at 75% of the stance phase, weighted by each muscle’s optimal force in the musculoskeletal model³⁶.