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Technol Health Care. 2018;26(6):909-920. doi: 10.3233/THC-181267.

Improved Hill-type musculotendon models with activation-force-length coupling.



Hill-type musculotendon models are most commonly used in biomechanical simulations for their computational efficacy and efficiency. But these models are generally built for maximally-activated muscles and linearly scale muscle properties when applied to submaximal conditions. However, the precondition of this scaling, which is muscle activation and properties are independent each other, has been proven unreal in many studies. Actually, the maximal activation condition is not ubiquitous for muscles in vivo, so it is necessary to adapt the linear scaling approach to improve the model practicability.


This paper aimed at proposing two improved Hill-type musculotendon models that are better suited for submaximal conditions.


These two models were built by including the activation-force-length coupling and their biological accuracy and computation speed were evaluated by a series of benchmark simulations.


Compared to experimental measurements, the percent root mean square errors of forces calculated by the two AFLC models were less than 13.98% and 13.81% respectively. However, the average running time of the second AFLC model was nearly 17 times that of the first one with only a little improvement in accuracy.


The two AFLC models were validated more accurate than the common Hill-type model in submaximally activated conditions and the first one was recommended in the construction of upper-layer musculoskeletal models.


Hill-type model; activation force-length coupling; musculotendon model; submaximal activation

[Indexed for MEDLINE]

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