Effects of Aponeurosis and Fiber Alignment on The Force and Stability During Isometric Contraction of Frog Gastrocnemius

Öz

The aim of this study is to analyze the contractile behavior of frog gastrocnemius muscle (also known as plantaris longus) via a computational model based on the finite element method (FEM). Therefore, a physical reality simulation scenario which is based on the finite element method has been generated. The finite element model developed within the scenario uses the theory of distributed-moments in order to study the effect of the angular alignment of the aponeurosis sheet covering the muscle on the total contractile force. By the way, in order to investigate the effect of fiber alignment, fibers have been typified two distinct fiber architectures, as the uniaxial and fusiform ones and the effect of different architecture type on the developed force and convergence was studied. The physical reality simulation outputs have been compared with the real frog muscle force responses that has been obtained in the laboratory condition. Results indicate that both the choice of fiber architecture as well as the aponeurosis alignment and position have important consequences in terms of the computed muscle force as well was the numerical stability of the model and the muscle model used in this work is compatible to use for three-dimensional muscle modelling.

Anahtar Kelimeler

• Finite element method
• contractile mechanics
• aponeurosis
• fiber architecture
• fiber-reinforced composites

KURBAĞA BALDIRININ İZOMETRİK KASILMASINDA APONEVROZ VE LİF YÖNELİMİNİN KUVVET VE SAYISAL KARARLIK ÜZERİNDEKİ ETKİLERİ

Öz

Bu çalışmada, kurbağa gastrocnemius (plantaris longus olarak da bilinmektedir) kasının sayısal modelini oluşturarak sonlu elemanlar yöntemi (SEY) ile kasılma davranışı incelenmiştir. Bu amaçla sonlu elemanlar yöntemi ile çalışan bir fiziksel gerçeklik benzetim senaryosu oluşturulmuştur. Bu senaryo dahilinde, çapraz-bağ kinetik modelini dağıtık-moment yaklaşımını kullanarak çözen sonlu elemanlar yöntemi ile oluşturulmuş kas modeli, kas üzerinde ince bir zar şeklinde bulunan aponevroz örtüsünün açısal yerleşiminin, kasılma sonucunda oluşan toplam çekme kuvveti üzerindeki etkisini incelemek üzere kullanılmıştır. Bununla birlikte, kas modelinde lif yöneliminin etkisinin incelenmesi amacıyla yönelim eksenel (sabit eksen yönünde) ve fusiform (kas geometrisini takip eden) olarak iki tipte örneklenerek üretilen çekme kuvveti ve yakınsama üzerindeki etkileri değerlendirilmiştir. Ayrıca, elde edilen veriler, gerçek bir kurbağa kasından laboratuvar ortamında elde edilmiş verilerle karşılaştırılmıştır. Sonuç olarak, aponevroz örtüsünün şeklinin ve lif yöneliminin kas modeli üzerinde üretilen çekme kuvveti ve yakınsama özellikleri bakımından ayırt edici ve önemli etkileri olduğu deneyimlenmiş, kullanılan modelin 3 boyutlu kas modellemesine uygun olabileceği görülmüştür.

Anahtar Kelimeler

• Sonlu elemanlar yöntemi
• kasılma mekaniği
• aponevroz
• lif mimarisi
• lif-takviyeli kompozit

Kaynakça

1. 1. Azizi, E., Brainerd, E. L., and Roberts, T. J. (2008). Variable gearing in pennate muscles. Proceedings of the National Academy of Sciences, 105(5), 1745–1750. doi:10.1073/pnas.0709212105
2. 2. Cooke, R., and Holmes, K. C. (1986). The Mechanism of Muscle Contractio. Critical Reviews in Biochemistry, 21(1), 53–118. doi:10.3109/10409238609113609
3. 3. Ebashi, S., Endo, M., and Ohtsuki, I. (1969). Control of muscle contraction. Quarterly Reviews of Biophysics, 2(4), 351–384. doi:10.1017/s0033583500001190
4. 4. Gans, C., and Bock, W. J. (1965). The functional significance of muscle architecture--a theoretical analysis. Ergebnisse der Anatomie und Entwicklungsgeschichte, 38, 115–142. PMID: 5319094
5. 5. Gielen, A. W. J, (2000). A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction. Computer Methods in Biomechanics and Biomedical Engineering, 3(3), 231–244. doi:10.1080/10255840008915267
6. 6. Gordon, A. M., Huxley, A. F., and Julian, F. J. (1966). The variation in isometric tension with sarcomere length in vertebrate muscle fibres. The Journal of Physiology, 184(1), 170–192. doi:10.1113/jphysiol.1966.sp007909
7. 7. Holzapfel, G. (2000) Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Wiley.
8. 8. Holzapfel, G. A., and Ogden, R. W. (2010). Constitutive modelling of arteries. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2118), 1551–1597. doi:10.1098/rspa.2010.0058

9. 9. Huijing, P. A., and Ettema, G. J. (1988). Length-force characteristics of aponeurosis in passive muscle and during isometric and slow dynamic contractions of rat gastrocnemius muscle. Acta morphologica Neerlando-Scandinavica, 26(1), 51–62. PMID:3247879
10. 10. Huijing, P.A., Woittiez, R.D. (1984) The effect of architecture on skeletal muscle performance: a simple planimetric model. Netherlands Journal of Zoology 34(1), 21–32 ISBN: 0-7360-3966-X
11. 11. Huxley, A. F. (1974). Muscular contraction. The Journal of Physiology, 243(1), 1–43. doi:10.1113/jphysiol.1974.sp010740
12. 12. Ma, S., and Zahalak, G. I. (1991). A distribution-moment model of energetics in skeletal muscle. Journal of Biomechanics, 24(1), 21–35. doi:10.1016/0021-9290(91)90323-f
13. 13. Muramatsu, T., Muraoka, T., Takeshita, D., Kawakami, Y., Hirano, Y., and Fukunaga, T. (2001). Mechanical properties of tendon and aponeurosis of human gastrocnemius muscle in vivo. Journal of Applied Physiology, 90(5), 1671–1678. doi:10.1152/jappl.2001.90.5.1671
14. 14. Ogden, R. (2013) Non-Linear Elastic Deformations, Dover Civil and Mechanical Engineering, Dover Publications
15. 15. Okyar, F., Karadag, V., Akgun, M., and Ciblak, N. (2019). Leveraging artificial neural networks to mesh frog gastrocnemius muscle from digital photography. Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization, 8(2), 143–151. doi:10.1080/21681163.2019.1627677
16. 16. Richards, C. T. (2011). Building a robotic link between muscle dynamics and hydrodynamics. Journal of Experimental Biology, 214(14), 2381–2389. doi:10.1242/jeb.056671
17. 17. Scott, S. H., and Winter, D. A. (1991). A comparison of three muscle pennation assumptions and their effect on isometric and isotonic force. Journal of Biomechanics, 24(2), 163–167. doi:10.1016/0021-9290(91)90361-p
18. 18. Serbest, K., and Eldoğan O. (2014). Structure and biomechanics of skeletal muscle. Academic Platform Journal of Engineering and Science, 2(3), 41–51. doi:10.5505/apjes.2014.70299
19. 19. Shan, X., Otsuka, S., Yakura, T., Naito, M., Nakano, T., and Kawakami, Y. (2019). Morphological and mechanical properties of the human triceps surae aponeuroses taken from elderly cadavers: Implications for muscle-tendon interactions. PLOS ONE, 14(2), doi:10.1371/journal.pone.0211485
20. 20. A.V. Hill, The heat of shortening and the dynamic constants of muscle. (1938). Proceedings of the Royal Society of London. Series B- Biological Sciences, 126(843), 136–195. doi:10.1098/rspb.1938.0050
21. 21. Tözeren, A. (1985). Continuum rheology of muscle contraction and its application to cardiac contractility. Biophysical Journal, 47(3), 303–309. doi:10.1016/s0006-3495(85)83920-5
22. 22. University of California, (2014). FEAP-Finite Element Analysis Program. Erişim Adresi: http://www.ce.berkeley/feap. (Erişim Tarihi:10.10.2019)
23. 23. Waugh Anne, and Grant Allison, (2014) The Nervous System. Ross and Wilson Anatomy and Physiology. Elsevier, s.144-177
24. 24. Zahalak, G. I., and Ma, S.-P. (1990). Muscle Activation and Contraction: Constitutive Relations Based Directly on Cross-Bridge Kinetics. Journal of Biomechanical Engineering, 112(1), 52–62. doi:10.1115/1.2891126