Skeletal Muscle Mechanics from Hill-Based Muscle Model to Computer Applications: State of the Art Review

Abstract

The first studies on muscle mechanics widely accepted in the literature have been known the macroscopic mechanical behavior of skeletal muscle since 1920’s. A. V. Hill and his associates used modern experimental equipment to understand muscle contraction. On the other hand, A. F. Huxley presented cross-bridge models to understand the mechanisms of molecular contraction level, thermodynamics and biochemical experiments on skeletal muscles in the 1950’s. By the 1990’s, computer applications have been used for analysis of muscle mechanics. In this way, somesoftware such as OpenSim, LifeModeler and AnyBody have been developed for only mechanical analysis of musculoskeletal system. In addition, some software developed for general analysis of dynamic systems such as MATLAB, ADAMS, COMSOL and ANSYS can be used for analysis of muscle mechanics. In this study, Hill-type muscle model and Huxley-type cross-bridge model have been explained and computer applications of muscle mechanics have been mentioned.

Keywords

• Muscle contraction
• muscle force
• joint moment
• simulation model
• finite element model

References

1. [1]Serbest, K., & Eldoğan, O. (2014). Structure and biomechanics of skeletal muscle. Academic Platform Journal of Engineering and Science, 2(3), 41-51.
2. [2]Hill, A. V. (1938). The heat of shortening and the dynamic constants of muscle.Proceedings of the Royal Society of London. Series B-Biological Sciences,126(843), 136-195.
3. [3]Hill, A. V. (1964). The effect of load on the heat of shortening of muscle.Proceedings of the Royal Society of London. Series B. Biological Sciences,159(975), 297-318.
4. [4]Huxley, A. F. (1957). Muscle structure and theories of contraction.Prog. Biophys. Biophys. Chem,7, 255-318.
5. [5]Huxley, A. F., & Simmons, R. M. (1971). Proposed mechanism of force generation in striated muscle.Nature,233(5321), 533-538.
6. [6]Feldman, A. G., Adamovich, S. V., Ostry, D. J., Flanagan, J. R., Winters, J., & Woo, S. L. Y. (1990). Multiple muscle systems: Biomechanics and movement organization.
7. [7]Chao, E. Y. S., Lynch, J. D., & Vanderploeg, M. J. (1993). Simulation and animation of musculoskeletal joint system.
8. [8]Johansson, T., Meier, P., & Blickhan, R. (2000). A finite-element model for the mechanical analysis of skeletal muscles.Journal of Theoretical Biology,206(1), 131-149.

9. [9]Zhao, J., & Narwani, G. (2005, June). Development of a human body finite element model for restraint system R&D applications. InThe19th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Paper(No. 05-0399).
10. [10]Martinek, J., Stickler, Y., Reichel, M., Mayr, W., & Rattay, F. (2008). A Novel Approach to Simulate Hodgkin–Huxley‐like Excitation With COMSOL Multiphysics. Artificial Organs, 32(8), 614-619.
11. [11]Bai, X., Wei, G., Ye, M., Wang, D., Hu, Y., Liu, Z., ... & Wang, C. (2008, May). Finite element musculoskeletal modeling of mechanical virtual human of China. In2008 2nd International Conference on Bioinformatics and Biomedical Engineering(pp. 1847-1850). IEEE.
12. [12]Lu, Y. T., Zhu, H. X., Richmond, S., & Middleton, J. (2010). A visco-hyperelastic model for skeletal muscle tissue under high strain rates. Journal of Biomechanics,43(13), 2629-2632.
13. [13]Kocbach, J., Folgerø, K., Mohn, L., & Brix, O. (2011). A simulation approach to optimizing performance of equipment for thermostimulation of muscle tissue using COMSOL multiphysics. Biophysics and Bioengineering Letters,4(2), 9-33.
14. [14]Trinler, U., & Baker, R. (2018). Estimated landmark calibration of biomechanical models for inverse kinematics.Medical Engineering & Physics,51, 79-83.
15. [15]Lieber, R. L., Fazeli, B. M., & Botte, M. J. (1990). Architecture of selected wrist flexor and extensor muscles. The Journal of Hand Surgery,15(2), 244-250.
16. [16]Lieber, R. L., Loren, G. J., & Fridén, J. (1994). In vivo measurement of human wrist extensor muscle sarcomere length changes. Journal of Neurophysiology,71(3), 874-881
17. [17]Rotter, N., Tobias, G., Lebl, M., Roy, A. K., Hansen, M. C., Vacanti, C. A., & Bonassar, L. J. (2002). Age-related changes in the composition and mechanical properties of human nasal cartilage.Archives of Biochemistry and Biophysics,403(1), 132-140.
18. [18]Lehtinen, J., Tingart, M., Apreleva, M., Zurakowski, D., Palmer, W., &Warner, J. (2003). Practical assessment of rotator cuff muscle volumes using shoulder MRI. Acta Orthopaedica Scandinavica,74(6), 722-729.
19. [19]Mochizuki, T., Sugaya, H., Uomizu, M., Maeda, K., Matsuki, K., Sekiya, I., ... & Akita, K. (2008). Humeral insertionof the supraspinatus and infraspinatus: new anatomical findings regarding the footprint of the rotator cuff. JBJS, 90(5), 962-969.
20. [20]Li, K., Wei, N., Cheng, M., Hou, X., & Song, J. (2018). Dynamical coordination of hand intrinsic muscles for precision grip in diabetes mellitus. Scientific Reports, 8(1), 1-13.
21. [21]Zilov, V. G., Khadartsev, A. A., Ilyashenko, L. K., Eskov, V. V., & Minenko, I. A. (2018). Experimental analysis of the chaotic dynamics of muscle biopotentials under various static loads. Bulletin of Experimental Biology and Medicine,165(4), 415-418.
22. [22]Zhang, N., Wei, N., & Li, K. (2020, July). Dynamic Analysis of Muscle Coordination at Different Force Levels during Grip and Pinch with Multiplex Recurrence Network. In2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC)(pp. 3788-3791). IEEE.
23. [23]Lieber, R. L. (1993). Skeletal muscle architecture: implications for muscle function and surgical tendon transfer.Journal of Hand Therapy,6(2), 105-113.
24. [24]Lee, T. Y.,Sum, Y. N., Lin, Y. C., Lin, L., & Lee, C. (1999). Three-dimensional facial model reconstruction and plastic surgery simulation. IEEE Transactions on Information Technology in Biomedicine,3(3), 214-220.
25. [25]Teran, J., Sifakis, E., Blemker, S. S., Ng-Thow-Hing, V., Lau, C., & Fedkiw, R. (2005). Creating and simulating skeletal muscle from the visible human data set.IEEE Transactions on Visualization and Computer Graphics,11(3), 317-328.
26. [26]Holzbaur, K. R., Murray, W. M., & Delp, S. L. (2005). A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Annals of Biomedical Engineering,33(6), 829-840.
27. [27]Blemker, S. S., Pinsky, P. M., & Delp, S. L. (2005). A 3D model of muscle reveals the causes of nonuniform strainsin the biceps brachii. Journal of Biomechanics,38(4), 657-665.
28. [28]Rehorn, M. R., & Blemker, S. S. (2010). The effects of aponeurosis geometry on strain injury susceptibility explored with a 3D muscle model.Journal of Biomechanics,43(13), 2574-2581.
29. [29]Silva,M. T., Pereira, A. F., Martins, J. M., & Biomechatronics Research Group. (2011). An efficient muscle fatigue model for forward and inverse dynamic analysis of human movements. Procedia IUTAM,2, 262-274.
30. [30]Stäubli, H. U., Schatzmann, L., Brunner, P., Rincón, L., & Nolte, L. P. (1999). Mechanical tensile properties of the quadriceps tendon and patellar ligament in young adults. The American Journal of Sports Medicine,27(1), 27-34.
31. [31]Bayraktar, H. H., Morgan, E. F., Niebur, G. L., Morris, G. E., Wong, E. K., & Keaveny, T. M. (2004). Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue.Journal of Biomechanics,37(1), 27-35.
32. [32]Ward, S. R., Eng, C. M., Smallwood, L. H., & Lieber, R. L. (2009). Are current measurements of lower extremity muscle architecture accurate?. Clinical Orthopaedics and Related Research,467(4), 1074-1082.
33. [33]Alexander, N., & Schwameder, H. (2016). Lower limb joint forces during walking on the level and slopes at different inclinations. Gait & Posture,45, 137-142.
34. [34]Alexander, N., & Schwameder, H. (2016). Effect of sloped walking on lower limb muscle forces.Gait & Posture,47, 62-67.
35. [35]Trinler, U., Schwameder, H., Baker, R., & Alexander, N. (2019). Muscle force estimation in clinical gait analysis using AnyBody and OpenSim.Journal of biomechanics,86, 55-63.
36. [36]Brekelmans, W. A. M., Poort, H. W., & Slooff, T. J. J. H. (1972). A new method to analyse the mechanical behaviour of skeletal parts.Acta Orthopaedica Scandinavica,43(5), 301-317.
37. [37]Delp, S. L., Ringwelski, D. A., & Carroll, N. C. (1994). Transfer of the rectus femoris: effects of transfer site on moment arms about the knee and hip.Journal of Biomechanics,27(10), 1201-1211.
38. [38]Anderson, D. L. (1996, March). Role of rapid prototyping in preoperative planning and patient-specific implant generation. InProceedings of the 1996 Fifteenth Southern Biomedical Engineering Conference(pp. 558-559). IEEE.
39. [39]Godest, A. C., Beaugonin, M., Haug, E., Taylor, M., & Gregson, P. J. (2002). Simulation of a knee joint replacement during a gait cycle using explicit finite element analysis.Journal of Biomechanics,35(2), 267-275.
40. [40]Helwig, P., Faust, G., Hindenlang, U., Kröplin, B., & Eingartner, C. (2006). Finite element analysis of a bone-implant system with the proximalfemur nail. Technology and Health Care, 14(4-5), 411-419.
41. [41]Cilingir, A. C., Ucar, V., & Kazan, R. (2007). Three-dimensional anatomic finite element modelling of hemi-arthroplasty of human hip joint. Trends Biomater Artif Organs, 21(1), 63-72.
42. [42]Linder-Ganz, E., Shabshin, N., Itzchak, Y., & Gefen, A. (2007). Assessment of mechanical conditions in sub-dermal tissues during sitting: a combined experimental-MRI and finite element approach. Journal of Biomechanics,40(7), 1443-1454.
43. [43]Carbone, V., van der Krogt, M. M., Koopman, H. F., & Verdonschot, N. (2016). Sensitivity of subject-specific models to Hill muscle–tendon model parameters in simulations of gait. Journal of Biomechanics,49(9), 1953-1960.
44. [44]Żuk, M., Syczewska, M., & Pezowicz, C. (2018). Influence of uncertainty in selected musculoskeletal model parameters on muscle forces estimated in inverse dynamics-based static optimization and hybrid approach.Journal of Biomechanical Engineering,140(12).
45. [45]Lieber, R. L., & Friden, J. (1993). Muscle damage is not a function of muscle force but active muscle strain. Journal of Applied Physiology,74(2), 520-526.
46. [46]Van Donkelaar, C. C., Willems, P. J. B., Muijtjens, A. M. M., & Drost, M. R. (1999). Skeletal muscle transverse strain during isometric contraction at different lengths. Journal of Biomechanics, 32(8), 755-762.
47. [47]Felder, A., Ward, S. R., & Lieber, R. L. (2005). Sarcomere length measurement permits high resolution normalization of muscle fiber length in architectural studies. Journal of Experimental Biology,208(17), 3275-3279.
48. [48]Zuurbier, C. J., Everard, A. J., van der Wees, P., & Huijing, P. A. (1994). Length-force characteristics of the aponeurosis in the passive and active muscle condition and in the isolated condition. Journal of Biomechanics,27(4), 445-453.
49. [49]Shue, G. H., & Crago, P. E. (1998). Muscle–tendon model with length history-dependent activation–velocity coupling.Annals of Biomedical Engineering,26(3), 369-380.
50. [50]Bourne, B. C., & van der Meulen, M. C. (2004). Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation.Journal of Biomechanics,37(5), 613-621.
51. [51]Loerakker, S., Stekelenburg, A., Strijkers, G. J., Rijpkema, J. J. M., Baaijens, F. P. T., Bader, D. L.,... & Oomens, C. W. J. (2010). Temporal effects of mechanical loading on deformation-induced damage in skeletal muscle tissue. Annals of Biomedical Engineering,38(8), 2577-2587