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Background/Objectives: This study explores an optimization-based strategy for muscle force estimation by employing simplified cost functions integrated with physiologically relevant muscle models. Methods: Considering elbow flexion as a case study, we employ an inverse-dynamics approach to estimate muscle forces for the biceps brachii, brachialis, and brachioradialis, utilizing different combinations of cost functions and muscle constitutive models. Muscle force generation is modeled by accounting for active and passive contractile behavior to varying degrees using Hill-type models. In total, three separate cost functions (minimization of total muscle force, mechanical work, and muscle stress) are evaluated with each muscle force model to represent potential neuromuscular control strategies without relying on electromyography (EMG) data, thereby characterizing the interplay between muscle models and cost functions. Results: Among the evaluated models, the Hill-type muscle model that incorporates both active and passive properties, combined with the stress minimization cost function, provided the most accurate predictions of muscle activation and force production for all three arm flexor muscles. Our results, validated against existing biomechanical data, demonstrate that even simplified cost functions, when paired with detailed muscle models, can achieve high accuracy in predicting muscle forces. Conclusions: This approach offers a versatile, EMG-free alternative for estimating muscle recruitment and force production, providing a more accessible and adaptable tool for muscle force analysis. It has profound implications for enhancing rehabilitation protocols and athletic training, not only broadening the applicability of muscle force estimation in clinical and sports settings but also paving the way for future innovations in biomechanical research.
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This content will become publicly available on November 18, 2026
Neural networks estimate muscle force in dynamic conditions better than Hill-type muscle models
ABSTRACT Hill-type muscle models are widely used, even though they do not accurately represent the relationship between activation and force in dynamic contractions. We explored the use of neural networks as an alternative approach to capture features of dynamic muscle function, without a priori assumptions about force–length–velocity relationships. We trained neural networks using an existing dataset of two guinea fowl muscles to estimate muscle force from activation, fascicle length and velocity. Training data were recorded using sonomicrometry, electromyography and a tendon buckle. First, we compared the neural networks with Hill-type muscle models, using the same data for network training and model optimization. Second, we trained neural networks on larger datasets, in a more realistic machine learning scenario. We found that neural networks generally yielded higher coefficients of determination and lower errors than Hill-type muscle models. Neural networks performed better when estimating forces on the muscle used for training, but on another bird, than on a different muscle of the same bird, likely due to inaccuracies in activation and force scaling. We extracted force–length and force–velocity relationships from the trained neural networks and found that both effects were underestimated and the relationships were not well replicated outside the training data distribution. We discuss suggested experimental designs and the challenge of collecting suitable training data. Given a suitable training dataset, neural networks could provide a useful alternative to Hill-type muscle models, particularly for modeling muscle dynamics in faster movements; however, scaling of the training data should be comparable between muscles and animals.
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- Award ID(s):
- 2319710
- PAR ID:
- 10657296
- Publisher / Repository:
- The Company of Biologists
- Date Published:
- Journal Name:
- Journal of Experimental Biology
- Volume:
- 228
- Issue:
- 22
- ISSN:
- 0022-0949
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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