Musculoskeletal biomechanical analysis of the three-dimensional gastrocnemius and soleus muscles_Journal of Biomedical Engineering

Authors：

TANG Zhihao ¹ , XU Jinghao ¹ , JIN Zhongmin ¹ ,  LI Junyan ^2,3

1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
2. College of Medical Instrumentation, Shanghai University of Medicine & Health Sciences, Shanghai 201318, P. R. China;
3. Shanghai Health Medical College Affiliated Zhoupu Hospital, Shanghai 200120, P. R. China;

Corresponding?author：

LI Junyan, Email: ljyjerry@gmail.com

Keywords：

Lower limb musculoskeletal system; Hybrid muscle model; Multibody dynamics; Inverse dynamics; Finite element; Hill-type muscle

DOI：

10.7507/1001-5515.202509045

Video：

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Musculoskeletal models based on multibody dynamics have been widely applied in human biomechanics research; however, conventional one-dimensional (1D) muscle models are limited in their ability to represent realistic muscle geometry and fiber architecture, resulting in restricted biomechanical predictions. Although three-dimensional (3D) finite element (FE) muscle models can provide more detailed mechanical information, high computational cost limits their application at the whole lower-limb scale. To address these limitations, this study develops a unilateral lower-limb musculoskeletal model with hybrid muscles based on the TLEM2.0 database, in which the soleus-gastrocnemius muscle group was represented using 3D FE models, while the remaining muscles were modeled using 1D Hill-type formulations. By coupling FE analysis with muscle recruitment optimization, muscle activation patterns of the right lower limb during the stance phase of level walking were obtained. Model predictions were validated against in vivo knee joint reaction forces and surface electromyography (sEMG) data. The results demonstrated good agreement between the predicted and experimentally measured knee joint reaction forces, and the predicted force patterns of the medial and lateral gastrocnemius muscles corresponded well with sEMG trends. In addition, the model enabled detailed observation of muscle deformation as well as internal tensile stress and strain distributions in the 3D muscles during gait. This hybrid musculoskeletal modeling framework achieves a balance between computational efficiency and biomechanical fidelity, providing an effective platform for investigating lower-limb muscle biomechanics.

Citation： TANG Zhihao, XU Jinghao, JIN Zhongmin, LI Junyan. Musculoskeletal biomechanical analysis of the three-dimensional gastrocnemius and soleus muscles. Journal of Biomedical Engineering, 2026, 43(2): 227-234. doi: 10.7507/1001-5515.202509045 Copy

1.	Wakeling J M, Febrer-Nafría M, De Groote F. A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years. J Biomech, 2023, 155: 111657.
2.	Hicks J L, Uchida T K, Seth A, et al. Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement. J Biomech Eng, 2015, 137(2): 020905.
3.	Chen Z, Wang L, Liu Y, et al. Effect of component mal-rotation on knee loading in total knee arthroplasty using multi-body dynamics modeling under a simulated walking gait. J Orthop Res, 2015, 33(9): 1287-1296.
4.	Francis C A, Lenz A L, Lenhart R L, et al. The modulation of forward propulsion, vertical support, and center of pressure by the plantarflexors during human walking. Gait Posture, 2013, 38(4): 993-997.
5.	Hejazi S, Rouhi G, Rasmussen J. The effects of gastrocnemius-soleus muscle forces on ankle biomechanics during triple arthrodesis. Comput Methods Biomech Biomed Eng, 2017, 20(2): 130-141.
6.	Blemker S S, Pinsky P M, Delp S L. A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii. J Biomech, 2005, 38(4): 657-665.
7.	Yamamura N, Alves J L, Oda T, et al. Effect of tendon stiffness on the generated force at the Achilles tendon-3D finite element simulation of a human triceps surae muscle during isometric contraction. J Biomech Sci Eng, 2014, 9(3): 13-00294.
8.	Webb J D, Blemker S S, Delp S L. 3D finite element models of shoulder muscles for computing lines of actions and moment arms. Comput Methods Biomech Biomed Eng, 2014, 17(8): 829-837.
9.	Li J, Lu Y, Miller S C, et al. Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles. J Biomech, 2019, 94: 230-234.
10.	Arnold E M, Ward S R, Lieber R L, et al. A model of the lower limb for analysis of human movement. Ann Biomed Eng, 2010, 38(2): 269-279.
11.	Carbone V, Fluit R, Pellikaan P, et al. TLEM 2. 0 – A comprehensive musculoskeletal geometry dataset for subject-specific modeling of lower extremity. J Biomech, 2015, 48(5): 734-741.
12.	Hill A V. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci, 1938, 126(843): 136-195.
13.	Allinger T L, Epstein M, Herzog W. Stability of muscle fibers on the descending limb of the force-length relation. A theoretical consideration. J Biomech, 1996, 29(5): 627-633.
14.	Bahler A S. Series elastic component of mammalian skeletal muscle. Am J Physiol Leg Content, 1967, 213(6): 1560-1564.
15.	De Bruijn E, Van Der Helm F C T, Happee R. Analysis of isometric cervical strength with a nonlinear musculoskeletal model with 48 degrees of freedom. Multibody Syst Dyn, 2016, 36: 339-362.
16.	Walker S M, Schrodt G R. I segment lengths and thin filament periods in skeletal muscle fibers of the Rhesus monkey and the human. Anat Rec, 1974, 178(1): 63-81.
17.	Weiss J A, Maker B N, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng, 1996, 135(1-2): 107-128.
18.	Guccione J M, McCulloch A D. Mechanics of active contraction in cardiac muscle: part I—constitutive relations for fiber stress that describe deactivation. J Biomech Eng, 1993, 115(1): 72-81.
19.	Mo F, Li F, Behr M, et al. A lower limb-pelvis finite element model with 3D active muscles. Ann Biomed Eng, 2018, 46(1): 86-96.
20.	R?hrle O, Pullan A J. Three-dimensional finite element modelling of muscle forces during mastication. J Biomech, 2007, 40(15): 3363-3372.
21.	Teran J, Sifakis E, Blemker S S, et al. Creating and simulating skeletal muscle from the visible human data set. IEEE Trans Vis Comput Graph, 2005, 11(3): 317-328.
22.	Anderson F C, Pandy M G. Static and dynamic optimization solutions for gait are practically equivalent. J Biomech, 2001, 34(2): 153-161.
23.	Li J. Development and validation of a finite-element musculoskeletal model incorporating a deformable contact model of the hip joint during gait. J Mech Behav Biomed Mater, 2021, 113: 104136.
24.	Fregly B J, Besier T F, Lloyd D G, et al. Grand challenge competition to predict in vivo knee loads. J Orthop Res, 2012, 30(4): 503-513.
25.	Lund M E, Andersen M S, De Zee M, et al. Scaling of musculoskeletal models from static and dynamic trials. Int Biomech, 2015, 2(1): 1-11.
26.	Lin Y C, Fok L A, Schache A G, et al. Muscle coordination of support, progression and balance during stair ambulation. J Biomech, 2015, 48(2): 340-347.
27.	Thelen D G. Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J Biomech Eng, 2003, 125(1): 70-77.
28.	Zajac F E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng, 1989, 17(4): 359-411.
29.	Guo J, Sun Y, Hao Y, et al. A mass-flowing muscle model with shape restrictive soft tissues: correlation with sonoelastography. Biomech Model Mechanobiol, 2020, 19(3): 911-926.
30.	Azizi E, Brainerd E L, Roberts T J. Variable gearing in pennate muscles. Proc Natl Acad Sci U S A, 2008, 105(5): 1745-1750.
31.	Günther M, R?hrle O, Haeufle D F B, et al. Spreading out muscle mass within a hill-type model: a computer simulation study. Comput Math Methods Med, 2012, 2012: 848630.
32.	Delp S L, Loan J P, Hoy M G, et al. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng, 1990, 37(8): 757-767.
33.	Garner B A, Pandy M G. Estimation of musculotendon properties in the human upper limb. Ann Biomed Eng, 2003, 31(2): 207-220.
34.	Blemker S S, Delp S L. Three-dimensional representation of complex muscle architectures and geometries. Ann Biomed Eng, 2005, 33(5): 661-673.
35.	Lamberto G, Martelli S, Cappozzo A, et al. To what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts? J Biomech, 2017, 62: 68-76.
36.	Farris D J, Robertson B D, Sawicki G S. Elastic ankle exoskeletons reduce soleus muscle force but not work in human hopping. J Appl Physiol, 2013, 115(5): 579-585.
37.	Lee H S, Lee J H, Kim H S. Activities of ankle muscles during gait analyzed by simulation using the human musculoskeletal model. J Exerc Rehabil, 2019, 15(2): 229.
38.	Rajagopal A, Dembia C L, Demers M S, et al. Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans Biomed Eng, 2016, 63(10): 2068-2079.
39.	Simonsen E B, Alkj?r T, Raffalt P C. Reflex response and control of the human soleus and gastrocnemius muscles during walking and running at increasing velocity. Exp Brain Res, 2012, 219(2): 163-174.
40.	Di Nardo F, Ghetti G, Fioretti S. Assessment of the activation modalities of gastrocnemius lateralis and tibialis anterior during gait: a statistical analysis. J Electromyogr Kinesiol, 2013, 23(6): 1428-1433.
41.	Bouché R T, Johnson C H. Medial tibial stress syndrome (tibial fasciitis): a proposed pathomechanical model involving fascial traction. J Am Podiatr Med Assoc, 2007, 97(1): 31-36.
42.	Cheng H Y K, Lin C L, Wang H W, et al. Finite element analysis of plantar fascia under stretch—the relative contribution of windlass mechanism and Achilles tendon force. J Biomech, 2008, 41(9): 1937-1944.

1. Wakeling J M, Febrer-Nafría M, De Groote F. A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years. J Biomech, 2023, 155: 111657.
2. Hicks J L, Uchida T K, Seth A, et al. Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement. J Biomech Eng, 2015, 137(2): 020905.
3. Chen Z, Wang L, Liu Y, et al. Effect of component mal-rotation on knee loading in total knee arthroplasty using multi-body dynamics modeling under a simulated walking gait. J Orthop Res, 2015, 33(9): 1287-1296.
4. Francis C A, Lenz A L, Lenhart R L, et al. The modulation of forward propulsion, vertical support, and center of pressure by the plantarflexors during human walking. Gait Posture, 2013, 38(4): 993-997.
5. Hejazi S, Rouhi G, Rasmussen J. The effects of gastrocnemius-soleus muscle forces on ankle biomechanics during triple arthrodesis. Comput Methods Biomech Biomed Eng, 2017, 20(2): 130-141.
6. Blemker S S, Pinsky P M, Delp S L. A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii. J Biomech, 2005, 38(4): 657-665.
7. Yamamura N, Alves J L, Oda T, et al. Effect of tendon stiffness on the generated force at the Achilles tendon-3D finite element simulation of a human triceps surae muscle during isometric contraction. J Biomech Sci Eng, 2014, 9(3): 13-00294.
8. Webb J D, Blemker S S, Delp S L. 3D finite element models of shoulder muscles for computing lines of actions and moment arms. Comput Methods Biomech Biomed Eng, 2014, 17(8): 829-837.
9. Li J, Lu Y, Miller S C, et al. Development of a finite element musculoskeletal model with the ability to predict contractions of three-dimensional muscles. J Biomech, 2019, 94: 230-234.
10. Arnold E M, Ward S R, Lieber R L, et al. A model of the lower limb for analysis of human movement. Ann Biomed Eng, 2010, 38(2): 269-279.
11. Carbone V, Fluit R, Pellikaan P, et al. TLEM 2. 0 – A comprehensive musculoskeletal geometry dataset for subject-specific modeling of lower extremity. J Biomech, 2015, 48(5): 734-741.
12. Hill A V. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci, 1938, 126(843): 136-195.
13. Allinger T L, Epstein M, Herzog W. Stability of muscle fibers on the descending limb of the force-length relation. A theoretical consideration. J Biomech, 1996, 29(5): 627-633.
14. Bahler A S. Series elastic component of mammalian skeletal muscle. Am J Physiol Leg Content, 1967, 213(6): 1560-1564.
15. De Bruijn E, Van Der Helm F C T, Happee R. Analysis of isometric cervical strength with a nonlinear musculoskeletal model with 48 degrees of freedom. Multibody Syst Dyn, 2016, 36: 339-362.
16. Walker S M, Schrodt G R. I segment lengths and thin filament periods in skeletal muscle fibers of the Rhesus monkey and the human. Anat Rec, 1974, 178(1): 63-81.
17. Weiss J A, Maker B N, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng, 1996, 135(1-2): 107-128.
18. Guccione J M, McCulloch A D. Mechanics of active contraction in cardiac muscle: part I—constitutive relations for fiber stress that describe deactivation. J Biomech Eng, 1993, 115(1): 72-81.
19. Mo F, Li F, Behr M, et al. A lower limb-pelvis finite element model with 3D active muscles. Ann Biomed Eng, 2018, 46(1): 86-96.
20. R?hrle O, Pullan A J. Three-dimensional finite element modelling of muscle forces during mastication. J Biomech, 2007, 40(15): 3363-3372.
21. Teran J, Sifakis E, Blemker S S, et al. Creating and simulating skeletal muscle from the visible human data set. IEEE Trans Vis Comput Graph, 2005, 11(3): 317-328.
22. Anderson F C, Pandy M G. Static and dynamic optimization solutions for gait are practically equivalent. J Biomech, 2001, 34(2): 153-161.
23. Li J. Development and validation of a finite-element musculoskeletal model incorporating a deformable contact model of the hip joint during gait. J Mech Behav Biomed Mater, 2021, 113: 104136.
24. Fregly B J, Besier T F, Lloyd D G, et al. Grand challenge competition to predict in vivo knee loads. J Orthop Res, 2012, 30(4): 503-513.
25. Lund M E, Andersen M S, De Zee M, et al. Scaling of musculoskeletal models from static and dynamic trials. Int Biomech, 2015, 2(1): 1-11.
26. Lin Y C, Fok L A, Schache A G, et al. Muscle coordination of support, progression and balance during stair ambulation. J Biomech, 2015, 48(2): 340-347.
27. Thelen D G. Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults. J Biomech Eng, 2003, 125(1): 70-77.
28. Zajac F E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng, 1989, 17(4): 359-411.
29. Guo J, Sun Y, Hao Y, et al. A mass-flowing muscle model with shape restrictive soft tissues: correlation with sonoelastography. Biomech Model Mechanobiol, 2020, 19(3): 911-926.
30. Azizi E, Brainerd E L, Roberts T J. Variable gearing in pennate muscles. Proc Natl Acad Sci U S A, 2008, 105(5): 1745-1750.
31. Günther M, R?hrle O, Haeufle D F B, et al. Spreading out muscle mass within a hill-type model: a computer simulation study. Comput Math Methods Med, 2012, 2012: 848630.
32. Delp S L, Loan J P, Hoy M G, et al. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans Biomed Eng, 1990, 37(8): 757-767.
33. Garner B A, Pandy M G. Estimation of musculotendon properties in the human upper limb. Ann Biomed Eng, 2003, 31(2): 207-220.
34. Blemker S S, Delp S L. Three-dimensional representation of complex muscle architectures and geometries. Ann Biomed Eng, 2005, 33(5): 661-673.
35. Lamberto G, Martelli S, Cappozzo A, et al. To what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts? J Biomech, 2017, 62: 68-76.
36. Farris D J, Robertson B D, Sawicki G S. Elastic ankle exoskeletons reduce soleus muscle force but not work in human hopping. J Appl Physiol, 2013, 115(5): 579-585.
37. Lee H S, Lee J H, Kim H S. Activities of ankle muscles during gait analyzed by simulation using the human musculoskeletal model. J Exerc Rehabil, 2019, 15(2): 229.
38. Rajagopal A, Dembia C L, Demers M S, et al. Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans Biomed Eng, 2016, 63(10): 2068-2079.
39. Simonsen E B, Alkj?r T, Raffalt P C. Reflex response and control of the human soleus and gastrocnemius muscles during walking and running at increasing velocity. Exp Brain Res, 2012, 219(2): 163-174.
40. Di Nardo F, Ghetti G, Fioretti S. Assessment of the activation modalities of gastrocnemius lateralis and tibialis anterior during gait: a statistical analysis. J Electromyogr Kinesiol, 2013, 23(6): 1428-1433.
41. Bouché R T, Johnson C H. Medial tibial stress syndrome (tibial fasciitis): a proposed pathomechanical model involving fascial traction. J Am Podiatr Med Assoc, 2007, 97(1): 31-36.
42. Cheng H Y K, Lin C L, Wang H W, et al. Finite element analysis of plantar fascia under stretch—the relative contribution of windlass mechanism and Achilles tendon force. J Biomech, 2008, 41(9): 1937-1944.

Journal of Biomedical Engineering

Musculoskeletal biomechanical analysis of the three-dimensional gastrocnemius and soleus muscles

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