Age-dependent mathematical models of ligaments and tendons
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Abstract
Understanding the internal structure and the underlying physical mechanisms governing the mechanical properties of ligaments and tendons, particularly the elastic modulus, across different stages of life is critical for enhancing tissue strength during growth, maturation, and aging. This knowledge is essential not only for preventing tissue failure in older adults but also for advancing the development of biomaterials that can substitute or augment ligament and tendon function across all age groups. Despite the significance of this area, a comprehensive, mechanistic understanding of the relationship between structural changes and mechanical properties over time remains largely unexplored. To date, there is a lack of detailed studies that elucidate the physical mechanisms involved in these age-related changes. The absence of such mechanistic insights highlights a significant gap in the literature, necessitating further investigation. Therefore, this research delves into the age-dependent structural and mechanical property changes in ligaments and tendons, emphasizing both growth and mature phases. Utilizing a comprehensive approach, we have developed new mathematical models that directly correlate the growth of collagen in fibrils with the increasing elastic modulus in the fibers of ligaments and tendons over time. By integrating experimental data from mouse tail tendons in published work and conducting simulations, we have observed that the cross-sectional area of collagen in fibrils and the elastic modulus of a collagen fiber increase rapidly during the growth phase and stabilize during the mature phase. Our proposed models effectively describe the trends in collagen growth and the elastic modulus of fibers in ligaments and tendons over different ages, exhibiting consistency with experimental data. Through detailed analysis, we elucidate the mechanistic relationship between collagen growth and the elastic modulus of fibers as they age. This comprehensive approach significantly enhances our understanding of the age-related structural and mechanical property changes in connective tissues, providing a robust framework for future investigations.
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References
Ning C, Li P, Gao C, Fu L, Liao Z, Tian G, et al. Recent advances in tendon tissue engineering strategy. Front Bioeng Biotechnol. 2023;11:1115312.
Burgio V, Casari S, Milizia M, Sanna F, Spezia G, Civera M, et al. Mechanical properties of animal ligaments: a review and comparative study for the identification of the most suitable human ligament surrogates. Biomech Model Mechanobiol. 2023;22(5):1645-83.
Fang F, Lake SP. Modelling approaches for evaluating multiscale tendon mechanics. Interface Focus. 2016;6(1):1-13.
Theodossiou SK, Schiele NR. Models of tendon development and injury. BMC Biomed Eng 2019;1(32):1-24.
Thompson MS, Bajuri MN, Khayyeri H, Isaksson H. Mechanobiological modelling of tendons: Review and future opportunities. Proc Inst Mech Eng H. 2017;231(5):369-77.
Korcari A, Przybelski SJ, Gingery A, Loiselle AE. Impact of aging on tendon homeostasis, tendinopathy development, and impaired healing. Connect Tissue Res. 2023;64(1):1-13.
Freedman BR, Knecht RS, Tinguely Y, Eskibozkurt GE, Wang CS, Mooney D. Aging and matrix viscoelasticity affect multiscale tendon properties and tendon derived cell behavior. Acta Biomater. 2022;143:63-71.
Ellingson AJ, Pancheri NM, Schiele, NR. Regulators of collagen crosslinking in developing and adult tendons. Eur Cell Mater. 2022;43:130-52.
Thornton GM, Lemmex DB, Ono Y, Beach CJ, Reno CR, Hart DA, et al. Aging affects mechanical properties and lubricin/PRG4 gene expression in normal ligaments. J Biomech. 2015;48(12):3306-11.
Vafek EC, Plate JF, Friedman E, Mannava S, Scott AT, Danelson KA. The effect of strain and age on the mechanical properties of rat Achilles tendons. Muscles Ligaments Tendons J. 2018;7(3):548-53.
Waugh CM, Blazevich AJ, Fath F, Korff T. Age-related changes in mechanical properties of Achilles tendon. J Anat. 2012;220(2):144-55.
Gulick LV, Saby C, Jaisson S, Okwieka A, Gillery P, Dervin E, et al. An integrated approach to investigate age-related modifications of morphological, mechanical and structural properties of type I collagen. Acta Biomater. 2022;137:64-78.
Karathanasopoulos N, Ganghoffer JF. Investigating the effect of aging on the viscosity of tendon fascicles and fibers. Front Bioeng Biotechnol. 2019;7:107.
Hudson DM, Archer M, Rai J, Weis MA, Fernandes RJ, Eyre DR. Age-related type I collagen modifications reveal tissue-defining differences between ligament and tendon. Matrix Biol Plus. 2021;12:1-14.
Magnusson SP, Beyer N, Abrahamsen H, Aagaard P, Neergaard K, Kjaer M. Increased cross-sectional area and reduced tensile stress of the Achilles tendon in elderly compared with young woman. J Gerontol A Biol Sci Med Sci. 2003;58(2):123-7.
Delabastita T, Bogaerts S, Vanwanseele B. Age-related changes in Achilles tendon stiffness and impact on functional activities: A systematic review and meta-analysis. J Aging Phys Act. 2018;27(1):1-40.
Goh KL, Holmes DF, Lu YH, Kadler KE, Purslow PP. Age-related dataset on the mechanical properties and collagen fibril structure of tendons from a murine model. Sci Data. 2018;5(1):180140.
Stammers M, Ivanova IM, Niewczas IS, Segonds-Pichon A, Streeter M, Spiegel DA, et al. Age-related changes in the physical properties, cross-linking, and glycation of collagen from mouse tail tendon. J Biol Chem. 2020;295(31):10562-71.
Kwan KYC, Ng KWK, Rao Y, Zhu C, Qi S, Tuan RS, et al. Effect of aging on tendon biology, biomechanics and implications for treatment approaches. Int J Mol Sci. 2023;24(20):15183.
Peters AE, Geraghty B, Bates KT, Akhtar R, Readioff R, Comerford E. Ligament mechanics of aging and osteoarthritic human knees. Front Bioeng Biotechnol. 2022;10:954837.