{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T21:38:09Z","timestamp":1777585089921,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Estimation of vivo muscle forces during human motion is important for understanding human motion control mechanisms and joint mechanics. This paper combined the advantages of the convolutional neural network (CNN) and long-short-term memory (LSTM) and proposed a novel muscle force estimation method based on CNN\u2013LSTM. A wearable sensor system was also developed to collect the angles and angular velocities of the hip, knee, and ankle joints in the sagittal plane during walking, and the collected kinematic data were used as the input for the neural network model. In this paper, the muscle forces calculated using OpenSim based on the Static Optimization (SO) method were used as the standard value to train the neural network model. Four lower limb muscles of the left leg, including gluteus maximus (GM), rectus femoris (RF), gastrocnemius (GAST), and soleus (SOL), were selected as the studying objects in this paper. The experiment results showed that compared to the standard CNN and the standard LSTM, the CNN\u2013LSTM performed better in muscle forces estimation under slow (1.2 m\/s), medium (1.5 m\/s), and fast walking speeds (1.8 m\/s). The average correlation coefficients between true and estimated values of four muscle forces under slow, medium, and fast walking speeds were 0.9801, 0.9829, and 0.9809, respectively. The average correlation coefficients had smaller fluctuations under different walking speeds, which indicated that the model had good robustness. The external testing experiment showed that the CNN\u2013LSTM also had good generalization. The model performed well when the estimated object was not included in the training sample. This article proposed a convenient method for estimating muscle forces, which could provide theoretical assistance for the quantitative analysis of human motion and muscle injury. The method has established the relationship between joint kinematic signals and muscle forces during walking based on a neural network model; compared to the SO method to calculate muscle forces in OpenSim, it is more convenient and efficient in clinical analysis or engineering applications.<\/jats:p>","DOI":"10.3390\/s24031032","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T08:41:43Z","timestamp":1707122503000},"page":"1032","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Estimation of Muscle Forces of Lower Limbs Based on CNN\u2013LSTM Neural Network and Wearable Sensor System"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1869-9369","authenticated-orcid":false,"given":"Kun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, China"}]},{"given":"Yong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, China"}]},{"given":"Shuo","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, China"}]},{"given":"Chi","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, China"}]},{"given":"Jun","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130000, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Harrington, M.S., and Burkhart, T.A. (2023). Validation of a musculoskeletal model to investigate hip joint mechanics in response to dynamic multiplanar tasks. J. Biomech., 158.","DOI":"10.1016\/j.jbiomech.2023.111767"},{"key":"ref_2","first-page":"91","article-title":"Temporal Structure of Muscle Synergy of Human Stepping Leg During Sit-to-Walk Motion","volume":"531","author":"An","year":"2017","journal-title":"Intell. Auton. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1161\/01.STR.0000054630.33395.E2","article-title":"Stroke recovery and rehabilitation","volume":"34","author":"Teasell","year":"2003","journal-title":"Stroke"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sicherer, S.T., Venkatarama, R.S., and Grasman, J.M. (2020). Recent Trends in Injury Models to Study Skeletal Muscle Regeneration and Repair. Bioengineering, 7.","DOI":"10.3390\/bioengineering7030076"},{"key":"ref_5","first-page":"6","article-title":"Energy-Efficient Actuator Design Principles for Robotic Leg Prostheses and Exoskeletons: A Review of Series Elasticity and Backdrivability","volume":"18","author":"Laschowski","year":"2023","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2802","DOI":"10.1109\/TNSRE.2022.3209337","article-title":"Biomechanical and Physiological Evaluation of Biologically-inspired Hip Assistance with Belt-type Soft Exosuits","volume":"30","author":"Chen","year":"2022","journal-title":"IEEE Trans. Neural. Syst. Rehabil. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"104308","DOI":"10.1016\/j.robot.2022.104308","article-title":"Evaluation of safety-related performance of wearable lower limb exoskeleton robot (WLLER): A systematic review","volume":"160","author":"Wang","year":"2023","journal-title":"Rob. Auton. Syst."},{"key":"ref_8","first-page":"1","article-title":"Soft robotic exosuit augmented high intensity gait training on stroke survivors: A pilot study","volume":"19","author":"Sung","year":"2022","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.datak.2015.04.001","article-title":"Multimodal medical imaging (CT and dynamic MRI) data and computer-graphics multi-physical model for the estimation of patient specific lumbar spine muscle forces","volume":"96","author":"Dao","year":"2015","journal-title":"Data Knowl. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1249\/MSS.0000000000003175","article-title":"Muscle Contributions to Take-Off Velocity in the Long Jump","volume":"55","author":"Yang","year":"2023","journal-title":"Med. Sci. Sports Exerc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.medengphy.2018.02.002","article-title":"A computational framework for simultaneous estimation of muscle and joint contact forces and body motion using optimization and surrogate modeling","volume":"54","author":"Eskinazi","year":"2018","journal-title":"Med. Eng. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/10255842.2010.522187","article-title":"A hybrid static optimisation method to estimate muscle forces during muscle co-activation","volume":"15","author":"Son","year":"2012","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1109\/TNSRE.2021.3072771","article-title":"A model-based analysis of supraspinal mechanisms of inter-leg coordination in human gait: Toward modelinformed robot-assisted rehabilitation","volume":"29","author":"Chambers","year":"2021","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1016\/j.jbiomech.2008.07.031","article-title":"Muscle contributions to support and progression over a range of walking speeds","volume":"41","author":"Liu","year":"2008","journal-title":"J. Biomech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1109\/TBME.2007.901024","article-title":"OpenSim: Opensource software to create and analyze dynamic simulations of movement","volume":"54","author":"Delp","year":"2007","journal-title":"IEEE. Trans. Biomed. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.1007\/s13762-014-0662-4","article-title":"Kinetic model selection and the Hill model in geochemistry","volume":"12","author":"Turner","year":"2015","journal-title":"Int. J. Environ. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1109\/10.634654","article-title":"Relating agonist-antagonist electromyograms to joint torque during isometric, quasi-isotonic, nonfatiguing contractions","volume":"44","author":"Clancy","year":"1997","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1109\/TNSRE.2016.2515087","article-title":"Force Modelling of Upper Limb Biomechanics Using Ensemble Fast Orthogonal Search on High-Density Electromyography","volume":"24","author":"Johns","year":"2017","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/TNSRE.2014.2325713","article-title":"Enhanced Dynamic EMG-Force Estimation Through Calibration and PCI Modeling","volume":"23","author":"Hashemi","year":"2015","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1007\/s40747-021-00338-5","article-title":"A novel sEMG-based force estimation method using deep-learning algorithm","volume":"8","author":"Hua","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xu, L.F., Chen, X., Cao, S., Zhang, X., and Chen, X. (2018). Feasibility Study of Advanced Neural Networks Applied to sEMG-Based Force Estimation. Sensors, 18.","DOI":"10.3390\/s18103226"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.medengphy.2010.04.004","article-title":"Real-time pinch force estimation by surface electromyography using an artificial neural network","volume":"32","author":"Choi","year":"2010","journal-title":"Med. Eng. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Peng, L., Hou, Z.-G., Peng, L., Hu, J., and Wang, W. (2015, January 27\u201329). An sEMG-driven musculoskeletal model of shoulder and elbow based on neural networks. Proceedings of the 7th International Conference on Advanced Computational Intelligence, Wuyi, China.","DOI":"10.1109\/ICACI.2015.7184732"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1109\/TNSRE.2022.3226860","article-title":"Physics-Informed Deep Learning for Musculoskeletal Modeling: Predicting Muscle Forces and Joint Kinematics From Surface EMG","volume":"31","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1109\/TNSRE.2022.3166764","article-title":"A novel myoelectric control scheme supporting synchronous gesture recognition and muscle force estimation","volume":"30","author":"Hu","year":"2022","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"103118","DOI":"10.1016\/j.micpro.2020.103118","article-title":"Analyzing gait symmetry with automatically synchronized wearable sensors in daily life","volume":"77","author":"Tobias","year":"2020","journal-title":"Microprocess. Microsyst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Huang, D.B., Wu, C., Wang, Y.W., and Zhang, Z.Y. (2024). Episode-level prediction of freezing of gait based on wearable inertial signals using a deep neural network model. Biomed. Signal Process. Control., 88.","DOI":"10.1016\/j.bspc.2023.105613"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.jtv.2023.10.002","article-title":"Wearable sensors-based postural analysis and fall risk assessment among patients with diabetic foot neuropathy","volume":"32","author":"Lorenzo","year":"2023","journal-title":"J. Tissue Viability"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"065013","DOI":"10.1088\/1361-665X\/accf6f","article-title":"Investigation of a wearable piezoelectric-IMU multi-modal sensing system for real-time muscle force estimation","volume":"32","author":"Lu","year":"2023","journal-title":"Smart Mater. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1007\/s11517-018-1940-y","article-title":"From deep learning to transfer learning for the prediction of skeletal muscle forces","volume":"57","author":"Dao","year":"2019","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_31","first-page":"6747921","article-title":"Estimation of Individual Muscular Forces of the Lower Limb during Walking Using a Wearable Sensor System","volume":"2017","author":"Suin","year":"2017","journal-title":"J. Sens."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, K., Liu, Y., Ji, S., Gao, C., and Zhang, S.Z. (2023). A Novel Gait Phase Recognition Method Based on DPF-LSTM-CNN using Wearable inertial sensors. Sensors, 23.","DOI":"10.3390\/s23135905"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liu, K., Ji, S., Liu, Y., Gao, C., Zhang, S.Z., Fu, J., and Dai, L. (2023). Analysis of Ankle Muscle Dynamics during the STS Process Based on Wearable Sensors. Sensors, 23.","DOI":"10.3390\/s23146607"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0021-9290(02)00432-3","article-title":"Generating dynamic simulations of movement using computed muscle control","volume":"36","author":"Thelen","year":"2003","journal-title":"J. Biomech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3173","DOI":"10.1007\/s11831-023-09899-9","article-title":"On the Analyses of Medical Images Using Traditional Machine Learning Techniques and Convolutional Neural Networks","volume":"30","author":"Iqbal","year":"2023","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Aysa, Z., Ablimit, M., and Hamdulla, A. (2023). Multi-Scale Feature Learning for Language Identification of Overlapped Speech. Appl. Sci., 13.","DOI":"10.3390\/app13074235"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Alzahrani, N., and Al-Baity, H.H. (2023). Object Recognition System for the Visually Impaired: A Deep Learning Approach using Arabic Annotation. Electronics, 12.","DOI":"10.3390\/electronics12030541"},{"key":"ref_38","first-page":"1","article-title":"Design of Max Pooling Operation Circuit for Binarized Neural Networks Using Single-Flux-Quantum Circuit","volume":"33","author":"Han","year":"2023","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8892636","DOI":"10.1155\/2021\/8892636","article-title":"An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem","volume":"2021","author":"Su","year":"2021","journal-title":"J. Math."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/3\/1032\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:55:14Z","timestamp":1760104514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/3\/1032"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,5]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["s24031032"],"URL":"https:\/\/doi.org\/10.3390\/s24031032","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,5]]}}}