A parametric study on the mechanical role of fibrillar rotations in an articular cartilage finite element model

Sajjadinia, S. S.; Haghpanahi, M.

doi:10.24200/sci.2020.51785.2362

A parametric study on the mechanical role of fibrillar rotations in an articular cartilage finite element model

Document Type : Research Note

Authors

S. S. Sajjadinia ¹
M. Haghpanahi ²

¹ Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bozen-Bolzano, Italy

² School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846, Iran

10.24200/sci.2020.51785.2362

Abstract

Collagen network is one of the articular cartilage (AC) vital components, which contributes to the depth-dependent and anisotropic response of the tissue. As it is computationally expensive to simulate all the structural details of the AC network, they were typically simplified in numerical analysis. In particular, the so-called arcade-like structure, which has been widely used in the previous complex simulations, does not capture the rotations of the fibrillar bundles. In this study, we investigate the role of such possible rotations in the AC mechanical response by a set of advanced, biphasic, and parametric finite element (FE) simulations of indentation tests. Our results unveil the influence of fibrillar rotation (FR) on the mechanical response by increasing the fibrillar stress while regionally affecting the stress in the upper layers of the AC tissue. On the contrary, the FR did not significantly alter the tissue elasticity, and consequently might be ignored safely in pure contact mechanical problems. It is concluded that the excessive FR might regionally increase the stress, which can have a degenerative effect on the collagen constituent, and therefore, should not be neglected in the corresponding future studies, in which the upper AC layers resist high permanent shear strains.

Keywords

20.1001.1.10263098.2021.28.2.20.5

References

1. Mow, V. C. and Huiskes, R. Basic orthopaedic biomechanics & mechano-biology. Lippincott Williams & Wilkins (2005).

2. Lories, R. J. and Luyten, F. P. “The bone–cartilage unit in osteoarthritis,” Nat. Rev. Rheumatol., vol. 7, no. 1, pp. 43–49, Jan. (2011).

3. Korhonen, R. K., Julkunen, P., Wilson, W., et al. “Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes,” J. Biomech. Eng., vol. 130, no. 2, p. 21003 (2008).

4. Taffetani, M., Griebel, M., Gastaldi, D., et al. “Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 32, pp. 17–30 (2014).

5. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.,” J. Biomech., vol. 37, no. 3, pp. 357–66 (2004).

6. Li, L. P. and Herzog, W. “The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation,” Biorheology, vol. 41, no. 3–4, pp. 181–194 (2004)

7. Ateshian, G. A., Rajan. V., Nadeen, O., et al. “Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena,” J. Biomech. Eng., vol. 131, no. 6, pp. 1–34 (2009).

8. Stender, M. E., Raub, C. B., Yamauchi, K. A., et al. “Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF-β1 and IGF-1 regulation of articular cartilage fiber modulus,” Biomech. Model. Mechanobiol., vol. 12, no. 6, pp. 1073–1088, (2012).

9. Klets, O., Mononen, M. E., Tanska, P., et al. “Comparison of different material models of articular cartilage in 3D computational modeling of the knee: Data from the Osteoarthritis Initiative (OAI),” J. Biomech., vol. 49, no. 16, pp. 3891–3900 (2016).

10. Stender, M. E., Regueiro, R. A., and Ferguson, V. L. “A poroelastic finite element model of the bone–cartilage unit to determine the effects of changes in permeability with osteoarthritis,” Comput. Methods Biomech. Biomed. Engin., pp. 1–13 (2016).

11. Stender, M. E., Carpenter, R. D., Regueiro, R. A., et al. “An evolutionary model of osteoarthritis including articular cartilage damage, and bone remodeling in a computational study,” J. Biomech., vol. 49, no. 14, pp. 3502–3508 (2016).

12. Wilson, W., Huyghe, J. M., and Van Donkelaar, C. C. “Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition,” Biomech. Model. Mechanobiol., vol. 6, no. 1–2, pp. 43–53 (2007).

13. Mononen, M. E., Julkunen, P., Töyräs, J., et al. “Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses,” Biomech. Model. Mechanobiol., vol. 10, no. 3, pp. 357–369 (2011).

14. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “A fibril-reinforced poroviscoelastic swelling model for articular cartilage,” J. Biomech., vol. 38, no. 6, pp. 1195–1204 (2005).

15. Matsui, Y., Kadoya, Y., Uehara, K., et al. “Rotational deformity in varus osteoarthritis of the knee: Analysis with computed tomography,” Clin. Orthop. Relat. Res., no. 433, pp. 147–151 (2005).

16. Shirazi, R., Shirazi-Adl, A., and Hurtig, M. “Role of cartilage collagen fibrils networks in knee joint biomechanics under compression,” J. Biomech., vol. 41, no. 16, pp. 3340–3348 (2008).

17. Hosseini, S. M., Wu, Y., Ito, K., et al. “The importance of superficial collagen fibrils for the function of articular cartilage,” Biomech. Model. Mechanobiol., vol. 13, no. 1, pp. 41–51 (2014).

18. Quiroga, J. M. P. P., Wilson, W., Ito, K., et al. “Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate,” Biomech. Model. Mechanobiol., vol. 16, no. 1, pp. 151–158 (2017).

19. Meng, Q., An, S., Damion, R.A., et al. “The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 65, pp. 439–453 (2016).

20. Mow, V. C., Kuei, S. C., Lai, W. M., et al. “Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments,” J. Biomech. Eng., vol. 102, no. 1, p. 73 (1980).

21. Sajjadinia, S. S., Haghpanahi, M., and Razi, M. “Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests,” Proc. Inst. Mech. Eng. Part H J. Eng. Med., vol. 233, no. 9, pp. 871–882 (2019).

22. Benninghoff, A. “Form und Bau der Gelenkknorpel in ihren Beziehungen zur Funktion,” Z. Anat. Entwicklungsgesch., vol. 76, no. 1–3, pp. 43–63 (1925).

23. Li, L. P., Cheung, J. T. M., and Herzog, W. “Three-dimensional fibril-reinforced finite element model of articular cartilage,” Med. Biol. Eng. Comput., vol. 47, no. 6, pp. 607–615 (2009).

24. Gupta, S., Lin, J., Ashby, P., et al. “A fiber reinforced poroelastic model of nanoindentation of porcine costal cartilage: A combined experimental and finite element approach,” J. Mech. Behav. Biomed. Mater., vol. 2, no. 4, pp. 326–338 (2009).

25. Lipshitz, H., Etheredge, R., and Glimcher, M. J. “In vitro wear of articular cartilage,” J. Bone Joint Surg. Am., vol. 57, no. 4, pp. 527–34 (1975).

26. Rieppo, J. “Poster: Spatial Determination of Water, Collagen and Proteogycan Content by Fourier Transform Infrared Imaging and Digital Densitometry,” 50th Annu. Meet. Orthop. Res. Soc., no. Evo 5173, p. Poster No: 1021 (2004).

27. Shapiro, E. M., Borthakur, A., Kaufman, J. H., et al. “Water distribution patterns inside bovine articular cartilage as visualized by 1H magnetic resonance imaging,” Osteoarthr. Cartil., vol. 9, no. 6, pp. 533–538 (2001).

28. Freutel, M., Schmidt, H., Dürselen, L., et al. “Finite element modeling of soft tissues: Material models, tissue interaction and challenges,” Clin. Biomech., vol. 29, no. 4, pp. 363–372 (2014).

29. Mononen, M. E., Tanska, P., Isaksson, H., et al. “A novel method to simulate the progression of collagen degeneration of cartilage in the knee: Data from the osteoarthritis initiative,” Sci. Rep., vol. 6, no. February, p. 21415 (2016).

30. Below, S., Arnoczky, S. P., Dodds, J., et al. “The split-line pattern of the distal femur: A consideration in the orientation of autologous cartilage grafts,” Arthroscopy, vol. 18, no. 6, pp. 613–617 (2002).

Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 830-836

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A parametric study on the mechanical role of fibrillar rotations in an articular cartilage finite element model

References

References

1. Mow, V. C. and Huiskes, R. Basic orthopaedic biomechanics & mechano-biology. Lippincott Williams & Wilkins (2005).

2. Lories, R. J. and Luyten, F. P. “The bone–cartilage unit in osteoarthritis,” Nat. Rev. Rheumatol., vol. 7, no. 1, pp. 43–49, Jan. (2011).

3. Korhonen, R. K., Julkunen, P., Wilson, W., et al. “Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes,” J. Biomech. Eng., vol. 130, no. 2, p. 21003 (2008).

4. Taffetani, M., Griebel, M., Gastaldi, D., et al. “Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 32, pp. 17–30 (2014).

5. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.,” J. Biomech., vol. 37, no. 3, pp. 357–66 (2004).

6. Li, L. P. and Herzog, W. “The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation,” Biorheology, vol. 41, no. 3–4, pp. 181–194 (2004)

7. Ateshian, G. A., Rajan. V., Nadeen, O., et al. “Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena,” J. Biomech. Eng., vol. 131, no. 6, pp. 1–34 (2009).

9. Klets, O., Mononen, M. E., Tanska, P., et al. “Comparison of different material models of articular cartilage in 3D computational modeling of the knee: Data from the Osteoarthritis Initiative (OAI),” J. Biomech., vol. 49, no. 16, pp. 3891–3900 (2016).

10. Stender, M. E., Regueiro, R. A., and Ferguson, V. L. “A poroelastic finite element model of the bone–cartilage unit to determine the effects of changes in permeability with osteoarthritis,” Comput. Methods Biomech. Biomed. Engin., pp. 1–13 (2016).

11. Stender, M. E., Carpenter, R. D., Regueiro, R. A., et al. “An evolutionary model of osteoarthritis including articular cartilage damage, and bone remodeling in a computational study,” J. Biomech., vol. 49, no. 14, pp. 3502–3508 (2016).

12. Wilson, W., Huyghe, J. M., and Van Donkelaar, C. C. “Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition,” Biomech. Model. Mechanobiol., vol. 6, no. 1–2, pp. 43–53 (2007).

13. Mononen, M. E., Julkunen, P., Töyräs, J., et al. “Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses,” Biomech. Model. Mechanobiol., vol. 10, no. 3, pp. 357–369 (2011).

14. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “A fibril-reinforced poroviscoelastic swelling model for articular cartilage,” J. Biomech., vol. 38, no. 6, pp. 1195–1204 (2005).

15. Matsui, Y., Kadoya, Y., Uehara, K., et al. “Rotational deformity in varus osteoarthritis of the knee: Analysis with computed tomography,” Clin. Orthop. Relat. Res., no. 433, pp. 147–151 (2005).

16. Shirazi, R., Shirazi-Adl, A., and Hurtig, M. “Role of cartilage collagen fibrils networks in knee joint biomechanics under compression,” J. Biomech., vol. 41, no. 16, pp. 3340–3348 (2008).

17. Hosseini, S. M., Wu, Y., Ito, K., et al. “The importance of superficial collagen fibrils for the function of articular cartilage,” Biomech. Model. Mechanobiol., vol. 13, no. 1, pp. 41–51 (2014).

18. Quiroga, J. M. P. P., Wilson, W., Ito, K., et al. “Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate,” Biomech. Model. Mechanobiol., vol. 16, no. 1, pp. 151–158 (2017).

19. Meng, Q., An, S., Damion, R.A., et al. “The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 65, pp. 439–453 (2016).

20. Mow, V. C., Kuei, S. C., Lai, W. M., et al. “Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments,” J. Biomech. Eng., vol. 102, no. 1, p. 73 (1980).

21. Sajjadinia, S. S., Haghpanahi, M., and Razi, M. “Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests,” Proc. Inst. Mech. Eng. Part H J. Eng. Med., vol. 233, no. 9, pp. 871–882 (2019).

22. Benninghoff, A. “Form und Bau der Gelenkknorpel in ihren Beziehungen zur Funktion,” Z. Anat. Entwicklungsgesch., vol. 76, no. 1–3, pp. 43–63 (1925).

23. Li, L. P., Cheung, J. T. M., and Herzog, W. “Three-dimensional fibril-reinforced finite element model of articular cartilage,” Med. Biol. Eng. Comput., vol. 47, no. 6, pp. 607–615 (2009).

24. Gupta, S., Lin, J., Ashby, P., et al. “A fiber reinforced poroelastic model of nanoindentation of porcine costal cartilage: A combined experimental and finite element approach,” J. Mech. Behav. Biomed. Mater., vol. 2, no. 4, pp. 326–338 (2009).

25. Lipshitz, H., Etheredge, R., and Glimcher, M. J. “In vitro wear of articular cartilage,” J. Bone Joint Surg. Am., vol. 57, no. 4, pp. 527–34 (1975).

26. Rieppo, J. “Poster: Spatial Determination of Water, Collagen and Proteogycan Content by Fourier Transform Infrared Imaging and Digital Densitometry,” 50th Annu. Meet. Orthop. Res. Soc., no. Evo 5173, p. Poster No: 1021 (2004).

27. Shapiro, E. M., Borthakur, A., Kaufman, J. H., et al. “Water distribution patterns inside bovine articular cartilage as visualized by 1H magnetic resonance imaging,” Osteoarthr. Cartil., vol. 9, no. 6, pp. 533–538 (2001).

28. Freutel, M., Schmidt, H., Dürselen, L., et al. “Finite element modeling of soft tissues: Material models, tissue interaction and challenges,” Clin. Biomech., vol. 29, no. 4, pp. 363–372 (2014).

29. Mononen, M. E., Tanska, P., Isaksson, H., et al. “A novel method to simulate the progression of collagen degeneration of cartilage in the knee: Data from the osteoarthritis initiative,” Sci. Rep., vol. 6, no. February, p. 21415 (2016).

30. Below, S., Arnoczky, S. P., Dodds, J., et al. “The split-line pattern of the distal femur: A consideration in the orientation of autologous cartilage grafts,” Arthroscopy, vol. 18, no. 6, pp. 613–617 (2002).

Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 830-836

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A parametric study on the mechanical role of fibrillar rotations in an articular cartilage finite element model

References

References

1. Mow, V. C. and Huiskes, R. Basic orthopaedic biomechanics & mechano-biology. Lippincott Williams & Wilkins (2005).

2. Lories, R. J. and Luyten, F. P. “The bone–cartilage unit in osteoarthritis,” Nat. Rev. Rheumatol., vol. 7, no. 1, pp. 43–49, Jan. (2011).

3. Korhonen, R. K., Julkunen, P., Wilson, W., et al. “Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes,” J. Biomech. Eng., vol. 130, no. 2, p. 21003 (2008).

4. Taffetani, M., Griebel, M., Gastaldi, D., et al. “Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 32, pp. 17–30 (2014).

5. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.,” J. Biomech., vol. 37, no. 3, pp. 357–66 (2004).

6. Li, L. P. and Herzog, W. “The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation,” Biorheology, vol. 41, no. 3–4, pp. 181–194 (2004)

7. Ateshian, G. A., Rajan. V., Nadeen, O., et al. “Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena,” J. Biomech. Eng., vol. 131, no. 6, pp. 1–34 (2009).

9. Klets, O., Mononen, M. E., Tanska, P., et al. “Comparison of different material models of articular cartilage in 3D computational modeling of the knee: Data from the Osteoarthritis Initiative (OAI),” J. Biomech., vol. 49, no. 16, pp. 3891–3900 (2016).

10. Stender, M. E., Regueiro, R. A., and Ferguson, V. L. “A poroelastic finite element model of the bone–cartilage unit to determine the effects of changes in permeability with osteoarthritis,” Comput. Methods Biomech. Biomed. Engin., pp. 1–13 (2016).

11. Stender, M. E., Carpenter, R. D., Regueiro, R. A., et al. “An evolutionary model of osteoarthritis including articular cartilage damage, and bone remodeling in a computational study,” J. Biomech., vol. 49, no. 14, pp. 3502–3508 (2016).

12. Wilson, W., Huyghe, J. M., and Van Donkelaar, C. C. “Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition,” Biomech. Model. Mechanobiol., vol. 6, no. 1–2, pp. 43–53 (2007).

13. Mononen, M. E., Julkunen, P., Töyräs, J., et al. “Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses,” Biomech. Model. Mechanobiol., vol. 10, no. 3, pp. 357–369 (2011).

14. Wilson, W., van Donkelaar, C. C., van Rietbergen, B., et al. “A fibril-reinforced poroviscoelastic swelling model for articular cartilage,” J. Biomech., vol. 38, no. 6, pp. 1195–1204 (2005).

15. Matsui, Y., Kadoya, Y., Uehara, K., et al. “Rotational deformity in varus osteoarthritis of the knee: Analysis with computed tomography,” Clin. Orthop. Relat. Res., no. 433, pp. 147–151 (2005).

16. Shirazi, R., Shirazi-Adl, A., and Hurtig, M. “Role of cartilage collagen fibrils networks in knee joint biomechanics under compression,” J. Biomech., vol. 41, no. 16, pp. 3340–3348 (2008).

17. Hosseini, S. M., Wu, Y., Ito, K., et al. “The importance of superficial collagen fibrils for the function of articular cartilage,” Biomech. Model. Mechanobiol., vol. 13, no. 1, pp. 41–51 (2014).

18. Quiroga, J. M. P. P., Wilson, W., Ito, K., et al. “Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate,” Biomech. Model. Mechanobiol., vol. 16, no. 1, pp. 151–158 (2017).

19. Meng, Q., An, S., Damion, R.A., et al. “The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage,” J. Mech. Behav. Biomed. Mater., vol. 65, pp. 439–453 (2016).

20. Mow, V. C., Kuei, S. C., Lai, W. M., et al. “Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments,” J. Biomech. Eng., vol. 102, no. 1, p. 73 (1980).

21. Sajjadinia, S. S., Haghpanahi, M., and Razi, M. “Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests,” Proc. Inst. Mech. Eng. Part H J. Eng. Med., vol. 233, no. 9, pp. 871–882 (2019).

22. Benninghoff, A. “Form und Bau der Gelenkknorpel in ihren Beziehungen zur Funktion,” Z. Anat. Entwicklungsgesch., vol. 76, no. 1–3, pp. 43–63 (1925).

23. Li, L. P., Cheung, J. T. M., and Herzog, W. “Three-dimensional fibril-reinforced finite element model of articular cartilage,” Med. Biol. Eng. Comput., vol. 47, no. 6, pp. 607–615 (2009).

24. Gupta, S., Lin, J., Ashby, P., et al. “A fiber reinforced poroelastic model of nanoindentation of porcine costal cartilage: A combined experimental and finite element approach,” J. Mech. Behav. Biomed. Mater., vol. 2, no. 4, pp. 326–338 (2009).

25. Lipshitz, H., Etheredge, R., and Glimcher, M. J. “In vitro wear of articular cartilage,” J. Bone Joint Surg. Am., vol. 57, no. 4, pp. 527–34 (1975).

26. Rieppo, J. “Poster: Spatial Determination of Water, Collagen and Proteogycan Content by Fourier Transform Infrared Imaging and Digital Densitometry,” 50th Annu. Meet. Orthop. Res. Soc., no. Evo 5173, p. Poster No: 1021 (2004).

27. Shapiro, E. M., Borthakur, A., Kaufman, J. H., et al. “Water distribution patterns inside bovine articular cartilage as visualized by 1H magnetic resonance imaging,” Osteoarthr. Cartil., vol. 9, no. 6, pp. 533–538 (2001).

28. Freutel, M., Schmidt, H., Dürselen, L., et al. “Finite element modeling of soft tissues: Material models, tissue interaction and challenges,” Clin. Biomech., vol. 29, no. 4, pp. 363–372 (2014).

29. Mononen, M. E., Tanska, P., Isaksson, H., et al. “A novel method to simulate the progression of collagen degeneration of cartilage in the knee: Data from the osteoarthritis initiative,” Sci. Rep., vol. 6, no. February, p. 21415 (2016).

30. Below, S., Arnoczky, S. P., Dodds, J., et al. “The split-line pattern of the distal femur: A consideration in the orientation of autologous cartilage grafts,” Arthroscopy, vol. 18, no. 6, pp. 613–617 (2002).

Volume 28, Issue 2 Transactions on Mechanical Engineering (B)March and April 2021Pages 830-836

Files

Share

How to cite

Statistics

Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 830-836