Determination and comparison of mechanical properties of articular cartilage using pro-hyper-viscoelastic models based on an unconfined stress relaxation

Document Type : Mechanics article

Authors

1 Islamic Azad University

2 Department of Biomedical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran

Abstract

Recently, the most common tool to compensate for various organ defects is tissue transplantation with several problems involved. These problems have led to the rapid growth of tissue engineering with a designed tissue approach or organ substitute in the last decade. For this purpose, it is important to determine the tissue mechanical properties. In this study, to obtain the cartilage structural parameters, isotropic Pro-Hyper-Viscoelastic Mooney-Rivlin and Neo-Hooke are used. These model coefficients are obtained by reverse engineering methods and using a coupled finite element-optimization algorithm utilized unconfined stress relaxation tests with root-mean-square error (RMSE)) less than 0.036, 0.033 for Neo-Hooke and Mooney-Rivlin respectively. Using Neo-Hooke and Mooney-Rivlin models, the modulus of elasticity was 0.47 MPa and 0.44 MPa, and the shear modulus was 0.188 MPa and 0.184 MPa, respectively. The predicted tissue mechanical response obtained by the finite element model showed that the Mooney-Rivlin model is more consistent with the stress relaxation experiments than Neo-Hooke one. The results showed that during the stress relaxation test, by applying a compressing load on the sample, initially the fluid pressurization in the matrix pores has the most contribution in the load-bearing (total stress). When time elapses, the fluid contribution in the load-bearing decreases, and the solid matrix contribution increases.

Keywords

References

[1] Williams RJ, editor, Cartilage Repair Strategies, Humana Press, 2007, Available from: http://dx.doi.org/10.1007/978-1-59745-343-1.
[2] W. Wilson, C.C. V. Donkelaar, B. V. Rietbergen, and R. Huiskes, "The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage", Medical Engineering and Physics, Vol. 27, No. 10, 2005, pp. 810-826.
[3] T. Guo, L. Yu, C. G. Lim, A. S. Goodley, X. Xiao, J. K. Placone, K. M. Ferlin, B. N. B. Nguyen, A. H. Hsieh, and J. P. Fisher, "Effect of Dynamic Culture and Periodic Compression on Human Mesenchymal Stem Cell Proliferation and Chondrogenesis", Annals of Biomedical Engineering, Vol. 44, No. 7, 2016, pp. 2103-2113.
[4] E. Masaeli, F. Karamali, S. H. Loghmani, M. B. Eslaminejad, and M. H. Nasr-Esfahani, "Bio-engineered Electrospun Nanofibrous Membranes Using Cartilage Extracellular Matrix Particles", Journal of Materials Chemistry B, Vol. 1, 2017, pp. 1-10.
[5] H. Lipshitz, R. 3rd. Etheredge, and M. J. Glimcher, "In vitro wear of articular cartilage", Journal of Bone and Joint Surgery, Vol. 57, No. 4, 1975, pp. 527-534.
[6] V. C. Mow, M. H. Holmes, and W. M. Lai, "Fluid transport and mechanical properties of articular cartilage: a review", Journal of Biomechanics, Vol. 17, No. 5, 1984, pp. 377-394.
[7] M. A. Cremer, E. F. Rosloniec, and A. H. Kang, "The cartilage collagens: a review of their structure, organization, and role in the pathogenesis of experimental arthritis in animals and in human rheumatic disease", Journal of Molecular Medicine  (Berl), Vol. 76, No. 3-4, 1988, pp. 275-288.
[8] E. M. Hasler, W. Herzog, J. Z. Wu, W. Muller, and U. Wyss, "Articular cartilage biomechanics: theoretical models, material properties, and biosynthetic response", Critical Reviews in Biomedical Engineering, Vol. 27, No. 6, 1999, pp. 415-488.
[9] S. Saarakkala, P. Julkunen, P. Kiviranta, J. M. Akitalo, J. S. Jurvelin and R. K. Korhonen, "Depth-wise progression of osteoarthritis in human articular cartilage: investigation of composition, structure and biomechanics", Osteoarthritis and Cartilage, Vol. 18, No. 1, 2010, pp. 73-81.
[10] J. A. Buckwalter, and H. J. Mankin, Instructional Course Lectures, "The American Academy of Orthopaedic Surgeons Articular Cartilage. Part II: Degeneration and Osteoarthrosis, Repair, Regeneration, and Transplantation", Journal of Bone and Joint Surgery, Vol. 79, No. 4, 1997, pp. 612-32.
[11] N. D. Broom, "The collagenous architecture of articular cartilage a synthesis of ultrastructure and mechanical function", Journal of Rheumatology, Vol. 13, No. 1, 1986, pp. 142-52.
[12] X. Bi, X. Yang, M. P. G. Bostrom, and N. P. Camacho, "Fourier transform infrared imaging spectroscopy investigations in the pathogenesis and repair of cartilage", Biochimica et Biophysica Acta (BBA) - Biomembranes, Vol. 1758, No. 7, 2006, pp. 934-941.
[13] X. Bi, G. Li, S. B. Doty, and N. P. Camacho, "A novel method for determination of collagen orientation in cartilage by Fourier transform infrared imaging spectroscopy (FT-IRIS)", Osteoarthritis and Cartilage, Vol. 13, NO. 12, 2005, pp. 1050-1058.
[14] H. E. Panula, M. M. Hyttinen, and J. P. A. Arokoski, "Articular cartilage superficial zone collagen birefringence reduced and cartilage thickness increased before surface fibrillation in experimental osteoarthritis", Annals of the Rheumatic Diseases, Vol. 57, No. 4, 1998, pp. 237-45.
[15] A. J. Sutherland, G. L. Converse, R. A. Hopkins, and M.S. Detamore, "The bioactivity of cartilage extracellular matrix in articular cartilage regeneration", Advanced Healthcare Materials, Vol. 4, No. 1, 2015, pp. 29-39.
[16] D. B. Saris, J. Vanlauwe, J. Victor, K. F. Almqvist, R. Verdonk, J. Bellemans, and F. P. Luyten, , "Treatment of symptomatic cartilage defects of the knee: characterized chondrocyte implantation results in better clinical outcome at 36 months in a randomized trial compared to microfracture", American Journal of Sports Medicine, Vol. 37, Suppl 1, 2009, pp. 10s-19s.
[17] E. A. Makris, A. H. Gomoll, K. N. Malizos, J. C. Hu, and K. A. Athanasiou, "Repair and tissue engineering techniques for articular cartilage", Nature reviews rheumatology, Vol. 11, No.1, 2015, pp. 21-34.
[18] H. Kwon, L. Sun, D. M. Cairns, R. S. Rainbow, R. C. Preda, D. L. Kaplan, and L. Zeng, "The influence of scaffold material on chondrocytes under inflammatory conditions", Acta Biomaterialia, Vol. 9, No. 5, 2013, pp. 6563-6575.
[19] S. Zahiri, E. Masaeli, E. Poorazizi, and M. H. Nasr Esfahani, "Chondrogenic response in presence of cartilage extracellular matrix nanoparticles",  Journal of Biomedical Materials Research Part A, Vol. 106, No. 9, 2018, pp. 2463-2471.
[20] K. Terzaghi, "Theoretical Soil Mechanics", John Wiley and Sons, 1951.
[21] M. A. Biot, "Mechanics of deformation and  acoustic propagation in porous media", Journal of Applied Physics, Vol. 33, 1962, pp.1482-1498.
[22] V. C. Mow, S. C. Kuei, W. M. Lai, and C. G. Armstrong, "Biphasic creep and stress relaxation of articular cartilage in compression:Theory and experiments", Journal of Biomechanical Engineering, Vol. 102, No.1, 1980, pp. 73-84.
[23] A. F. Mak, "Unconfined compression of hydrated viscoelastic tissues: a biphasic poroviscoelastic analysis", Biorheology, Vol.23, NO.4, 1986, pp. 371-383.
[24] J. K. F. Suh, and S. Bai, "Biphasic Poroviscoelastic Behaviour of Articular Cartilage in Creep Indentation Test", Transactions of the 43rd Annual Meeting of the Orthopedic Research Society, 1977, pp. 823.
[25] J. Soulhat, M.D. Buschmann, and A. Shirazi-Adl, "A fibril-network-reinforced biphasic model of cartilage in unconfined compression", Journal of Biomechanical Engineering, Vol. 121, N. 3, 1999, pp. 340-347.
[26] W. Wilson, C. C. van Donkelaar, C. van Rietbergen, K. Ito, and R. Huiskes, "Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study", Journal of Biomechanics, Vol. 37. No.3, 2004, pp. 357-366.
[27] L. P. Li, J. Soulhat, M. D. Buschmann, and A. Shirazi-Adl, "Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model", Clinical Biomechanics (Bristol, Avon), Vol. 14, No. 9, 1999, pp. 673-682.
[28] L. P. Li, M. D. Buschmann and A. Shirazi-Adl, "Strain-rate dependent stiffness of articular cartilage in unconfined compression", Journal of Biomechanical Engineering, Vol. 125, No. 2, 2003, pp. 161-168.
[29] F. Lei, and A. Z. Szeri, "Inverse analysis of constitutive models: Biological soft tissues", Journal of Biomechanics, Vol. 40, No. 4, 2007, pp. 936-940.
[30] L. Cao, I. Youn Inchan, F. Guilak, and L. A. Setton, "Compressive properties of mouse articular cartilage determined in a novel micro-indentation test method and biphasic finite element model", Journal of Biomechanical Engineering, Vol. 128, No. 5, 2006, pp. 766-772.
[31] D. L. Robinson, M. E. Kersh, N. C. Walsh, D. C. Ackland, R. N. DeSteiger, and M. G. Pandy, "Mechanical properties of normal and osteoarthritic human articular cartilage", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 61, 2016, pp. 96-109.
[32] L. V. Burgin, L. Edelsten, and R. M. Aspden, "The mechanical and material properties of elderly human articular cartilage subject to impact and slow loading", Medical Engineering and Physics, Vol. 36, Issue 2, 2014,pp. 226-232.
[33] A. Seifzadeh, D. Oguamanam, N. Trutiak, M. Hurtig, and M. Papini, "Determination of nonlinear fibre-reinforced biphasic poroviscoelastic constitutive parameters of articular cartilage using stress relaxation indentation testing and an optimizing finite element analysis", Computer Methods and Programs in Biomedicine, Vol. 107, No. 2, 2012, pp. 315-326.
[34] N. Sasaki, Y. Nakayama, M. Yoshikawa, and A. Enyo, "Stress relaxation function of bone and bone collagen", Journal of Biomechanics, Vol. 26, No. 12, 1993, pp. 1369-1376.
[35] T. Iyo, Y. Maki, N. Sasaki, and M. Nakata, "Anisotropic viscoelastic properties of cortical bone", Journal of Biomechanics, Vol. 37, No. 9, 2004, pp. 1433-1437.
[36] T. Iyo, N. Sasaki, Y. Maki, and M. Nakata, "Mathematical description of stress relaxation of bovine femoral cortical bone", Biorheology, Vol. 43, No. 2, 2006, pp. 117-132.
[37] R. S. Lakes, and J. L. Katz, "Viscoelastic properties of wet cortical bone—III. A non-linear constitutive equation", Journal of Biomechanics, Vol. 12, No. 9, 1979, pp. 689-698.
 
[38] D.D. Deligianni, A. Maris, and Y.F. Missirlis, "Stress relaxation behaviour of trabecular bone specimens", Journal of Biomechanics, Vol. 27, No. 12, 1994, pp. 1469-1476.
[39] R. M. Guedes, J. A. Simões, and J. L. Morais, "Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate", Journal of Biomechanics, Vol. 39, No. 1, 2006, pp. 49-60.
[40] V. Quaglini, V. L. Russa, and S. Corneo, "Nonlinear stress relaxation of trabecular bone", Mechanics Research Communications, Vol. 36, No. 3, 2009, pp. 275-283.
[41] L. Li, X. Yang, L. Yang, K. Zhang, J. Shi, L. Zhu, H. Liang, X. Wang, and Q. Jiang, "Biomechanical analysis of the effect of medial meniscus degenerative and traumatic lesions on the knee joint", American Journal of Translational Research, Vol. 11. No. 2, 2019, pp. 542-556.
[42] Y. T. Men, Y. Jiang, L. Chen, C. Zhang, and J.D. Ye, "On mechanical mechanism of damage evolution in articular cartilage", Materials Science and Engineering: C Materials for Biological Applications, Vol. 8, 2017, pp. 79-87.
[43] S. Park, C. T. Hung, and G. A. Ateshian, "Mechanical response of bovine articular cartilage under dynamic unconfined compression loading at physiological stress levels", Osteoarthritis Cartilage, Vol. 12, No. 1, 2004, pp. 65-73.
[44] S. Chokhandre, and A. Erdemir, "A comprehensive testing protocol for macro-scale mechanical characterization of knee articular cartilage with documented experimental repeatability", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 112, 2020, pp.104025.
[45] M. Hossain, H. Noori-Dokht, S. Karnik, N. Alyafei, A. Joukar, and B. Stephen, "Anisotropic properties of articular cartilage in an accelerated in vitro wear test", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 109, 2020, pp. 103834.
 [46]محمد رضا سلطانی صدرآبادی  ، بهمن وحیدی و روزبه ریاضی"تحلیل جریان خون در حلقه ی ویلیس مغزی با استفاده از تصاویر سی تی اسکن و روش برهمکنش سیال-سازه"، نشریه مدل‌سازی در مهندسی، دوره 17، شماره  57 تابستان 1398صفحه  285- 294.
[47] I. Koksal, Biomaterials in Orthopedics.: Springer Berlin Heidelberg, 2014.
[48] W. M. Lai, V. C. Mow, and V. Roth, "Effects of nonlinear strain-dependent permeability and rate of compression on the stress behavior of articular cartilage", Journal of Biomechanical Engineering, Vol. 103, No. 2, 1981, pp. 61-6.
[49] R. W. Ogden, "Large deformation isotropic elasticity–on the correlation of theory and experiment for incompressible rubberlike solids", Proceedings of  the Royal Society A, Vol. 326, No. 1567, 1972, pp. 565-584.
[50] J. C. Simo, and R. L. Taylor, "Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms", Computer methods in applied mechanics and engineering, Vol. 85, No. 3, 1991, pp. 273-310.
[51] W. M. Lai, and V. C. Mow, "Drag-induced compression of articular cartilage during a permeation experiment", Biorheology, Vol. 17, No. 1-2, 1980, pp. 111-123.
[52] فرشاد حکیم پور، سیامک طلعت اهری و ابوالفضل رنجبر،" ارزیابی و مقایسه الگوریتم های بهینه سازی ژنتیک، شبیه سازی تبرید و فاخته ها در مکان یابی رقابتی تسهیلات (مطالعه موردی: بانکها)"، نشریه مدل‌سازی در مهندسی، دوره 15، شماره 48، بهار 1396، صفحه  231- 246.
[53] سید حسین فلاح و محمدصادق ولی پور،"مدل‌سازی و بهینه سازی نیروگاه دودکش خورشیدی با الگوریتم‌های SA و PSO"، نشریه مدل‌سازی در مهندسی، دوره 16، شماره 53، تابستان 1397 ، صفحه75-87.
[54] امین رضایی پناه، علی مبارکی و  سعید بحرانی خادمی، "بهینه سازی شبکه عصبی MLP با استفاده از الگوریتم ژنتیک موازی  FinGrain  برای تشخیص سرطان سینه "، نشریه مدل‌سازی در مهندسی، دوره 17، شماره 57، تابستان 1398، صفحه 173- 186.
[55] S. Budday, G. Sommer , C. Birkl, C. Langkammer , J. Haybaeck , J. Kohnert , M. Bauer , F. Paulsen , P. Steinmann , E. Kuhl , and G. A Holzapfel, "Mechanical characterization of human brain tissue", Acta biomaterialia, Vol. 48, 2017, pp. 319-340.
[56] S. K. Kyriacou, A. Mohamed, K. Miller, and  S. Neff , "Brain mechanics for neurosurgery: modeling issues", Biomechanics and modeling in mechanobiology, Vol. 1, No. 2, 2002, pp. 151-164.
[57] L. Treloar, "Stress-strain data for vulcanized rubber under various types of deformation", Rubber Chemistry and Technology, Vol. 17, No. 4, 1944, pp. 813-825.
[58] Y. C. Fung, Biomechanics, Springer New York, 1993, Available from: http://dx.doi.org/10.1007/978-1-4757-2257-4
[59] J. V. Garcia Sestafe, J. M. GarcíA Paez, A. Carrera san Martín, E. Jorge Herrero, R. Navidad, I. Candela, and J. L. Castillo Olivares, "Description of the mathematical law that defines the relaxation of bovine pericardium subjected to stress",  Journal of Biomedical Materials Research , Vol. 28, No. 6, 1994, pp. 755-760.
 
Journal of Modeling in Engineering
Volume 19, Issue 66
September 2021
Pages 95-106

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  • Receive Date: 28 February 2021
  • Revise Date: 24 May 2021
  • Accept Date: 12 June 2021

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