Osteonal Lamellar Kemikte Mineralize Kolajen Fibril Yönlenmesinin Mekanik Önemi Üzerine Teorik Çalışma

Abstract

Bu çalışmada, dehidrasyon-rehidrasyon sonrasında lameler kemik örneklerinden elde edilen veriler kullanılarak, mineralize kolajen fibril yönlenmesinin kemiğin mekanik özelliklerine olan etkisi incelenmiştir. Dehidrasyon-rehidrasyon sonrasında kemiğin osteonal eksenine paralel olan ve dik kesen yönlerde deneysel olarak gelişen çekme kullanılarak, kemiğin anizotropik özellikleri hesaplanmıştır. Sublameller kemik modelinde mineralize kolajen fibrilleri katmanlar halinde ve 5 derecelik açılarla rotasyon yapacak şekilde modellenmiştir. Bu modele göre, mineralize kolajen tabakaları, transformasyon matrisi kullanılarak ortogonal eksenlere 5° açı yapacak şekilde dönüştürülmüştür. Dehidrasyon sonucunda fibril çapı mineral doğrultusunda daralmış, çekmeye bağlı bir deplasman vektörü oluşturmuştur. Vektörlerin x, y ve z eksenlerindeki izdüşümleri, u, v ve w deplasmanları hesaplanarak, 0,15266-6,55054 aralığında anizotropi oranları bulunmuştur. Literatürdeki deneysel nanoindentasyon verileriyle kıyaslandığında, sonuçlar, sublamellerin yaklaşık 20 derecelik açılarla düzenlenmiş olabileceğini göstermiştir. Anizotropi deneylerinin bir unsuru olan lateral indentasyon farklı oranlarda u ve v deplasmanları içerebileceğinden, lateral indentasyon açısı modelin yapısal özellikleri bağlamında değerlendirilmiştir. Bu değerlendirmenin sonucunda, v deplasmanının lateral çekmeye u deplasmanından daha fazla katkıda bulunduğu görülmektedir. Bulgular, mineralize kolajen fibrillerinin sublamellar düzenlenmesinin kemiğin anizotropisine olan önemli katksını göstermektedir.

Keywords

• anizotropi oranları
• transformasyon matrisi
• büzülme vektörü
• mineralize kolajen fibrili yönlenmesi

A Theoretical Study on the Mechanical Significance of Mineralized Collagen Fibril Orientation in Osteonal Lamellar Bone

Abstract

In this study, the effect of orientation of mineralized collagen fibrils on bone mechanical properties relating to bone anisotropy was studied using data obtained from rehydrated lamellar bone samples. The dehydration-rehydration based and experimentally determined contraction, observed in orientations parallel and perpendicular to the osteonal axis was used to calculate bone anisotropy. The sublamellar bone model, with the layered mineralized collagen fibrils rotating at 5° was used. Following this model, the mineralized collagen layers were transformed at 5° relative to the orthogonal axes using a transform matrix. With dehydration, fibril diameter was reduced towards the mineral, forming contraction vectors. The x, y and z intercepts for these vectors were then calculated to give the u, v and w displacements, which gave anisotropy ratios ranging from 0.15266 to 6.55054. Compared with the experimental nanoindentation findings in the literature, there may be an indication of a correlation with the results of sublamellar arrangement at 20° angles. As the lateral indentation used in the anisotropy experiments may involve varying amounts of u and v displacements, the aspect angle of lateral indentation was evaluated in relation to the structural features of the model. This evaluation indicated the larger contribution of v displacement and thus relatively much smaller contribution of u displacement to lateral contraction. These findings indicate the significant effect of the mineralized collagen fibril arrangement on bone anisotropy.

Keywords

• contraction
• mineralized collagen fibril orientation
• anisotropy ratio
• transformation matrix

References

1. [1] R. Robinson and M. L. Watson, “Collagen-crystal relationships in bone as seen in the electron microscope.” Anat. Rec., vol. 114, no. 32, pp. 383–410, 1952, doi:10.1002/ar.1091140302.
2. [1] R. Robinson and M. L. Watson, “Collagen-crystal relationships in bone as seen in the electron microscope.” Anat. Rec., vol. 114, no. 32, pp. 383–410, 1952, doi:10.1002/ar.1091140302.
3. [2] A. Ascenzi and E. Bonucci, “The tensile properties of single osteons,” Anat. Rec., vol. 158, no. 4, pp. 375-386, 1967, doi: 10.1002/ar.1091580403.
4. [2] A. Ascenzi and E. Bonucci, “The tensile properties of single osteons,” Anat. Rec., vol. 158, no. 4, pp. 375-386, 1967, doi: 10.1002/ar.1091580403.
5. [3] S. Nomura, A. Hiltner, J. B. Lando, and E. Baer, “Interaction of water with native collagen,” Biopolymers, vol. 16, no. 2, pp. 231-246, 1977, doi: 10.1002/bip.1977.360160202.
6. [3] S. Nomura, A. Hiltner, J. B. Lando, and E. Baer, “Interaction of water with native collagen,” Biopolymers, vol. 16, no. 2, pp. 231-246, 1977, doi: 10.1002/bip.1977.360160202.
7. [4] S. Weiner and H. D. Wagner, “The material bone: Structure mechanical function relations,” Annu. Rev. Mater. Sci., vol. 28, pp. 271-298, 1998, doi: 10.1146/annurev.matsci.28.1.271.
8. [4] S. Weiner and H. D. Wagner, “The material bone: Structure mechanical function relations,” Annu. Rev. Mater. Sci., vol. 28, pp. 271-298, 1998, doi: 10.1146/annurev.matsci.28.1.271.

9. [5] S. C. Cowin, “Mechanosensation and fluid transport in living bone,” J Musculoskelet. Neuronal Interact., vol. 2, no. 3, pp. 256-260, 2002.
10. [5] S. C. Cowin, “Mechanosensation and fluid transport in living bone,” J Musculoskelet. Neuronal Interact., vol. 2, no. 3, pp. 256-260, 2002.
11. [6] V. Ziv, I. Sabanay, T. Arad, W. Traub, and S. Weiner, “Transitional structures in lamellar bone,” Microsc. Res. Techniq., vol. 33, no. 2, pp. 203-213, 1996.
12. [6] V. Ziv, I. Sabanay, T. Arad, W. Traub, and S. Weiner, “Transitional structures in lamellar bone,” Microsc. Res. Techniq., vol. 33, no. 2, pp. 203-213, 1996.
13. [7] P. Fratzl and R. Weinkamer, “Nature's hierarchical materials,” Prog. Mater. Sci., vol. 52, no. 8, pp. 1263-1334, 2007.
14. [7] P. Fratzl and R. Weinkamer, “Nature's hierarchical materials,” Prog. Mater. Sci., vol. 52, no. 8, pp. 1263-1334, 2007.
15. [8] F. S. Utku, E. Klein, H. Saybasili, C. A. Yucesoy, and S. Weiner, “Probing the role of water in lamellar bone by dehydration in the environmental scanning electron microscope,” J. Struct. Biol., vol. 162, no. 3, pp. 361-367, 2008, doi: 10.1016/j.jsb.2008.01.004.
16. [8] F. S. Utku, E. Klein, H. Saybasili, C. A. Yucesoy, and S. Weiner, “Probing the role of water in lamellar bone by dehydration in the environmental scanning electron microscope,” J. Struct. Biol., vol. 162, no. 3, pp. 361-367, 2008, doi: 10.1016/j.jsb.2008.01.004.
17. [9] N. Reznikov, R. Shahar, and S. Weiner, “Bone hierarchical structure in three dimensions,” Acta Biomater., vol. 10, no. 9, pp. 3815-s3826, 2014, doi: 10.1016/j.actbio.2014.05.024.
18. [9] N. Reznikov, R. Shahar, and S. Weiner, “Bone hierarchical structure in three dimensions,” Acta Biomater., vol. 10, no. 9, pp. 3815-s3826, 2014, doi: 10.1016/j.actbio.2014.05.024.
19. [10] A. Faingold, S. R. Cohen, R. Shahar, S. Weiner, L. Rapoport, and H. D. Wagner, “The effect of hydration on mechanical anisotropy. topography and fibril organization of the osteonal lamellae,” J Biomech., vol. 47, no. 2, pp. 367-372, 2014, doi: 10.1016/j.jbiomech.2013.11.022.
20. [10] A. Faingold, S. R. Cohen, R. Shahar, S. Weiner, L. Rapoport, and H. D. Wagner, “The effect of hydration on mechanical anisotropy. topography and fibril organization of the osteonal lamellae,” J Biomech., vol. 47, no. 2, pp. 367-372, 2014, doi: 10.1016/j.jbiomech.2013.11.022.
21. [11] M. M. Giraud-Guille, “Twisted plywood architecture of collagen fibrils in human compact-bone osteons,” Calcif. Tissue Int., vol. 42, no. 3, pp. 167-180, 1988, doi: 10.1007/BF02556330.
22. [11] M. M. Giraud-Guille, “Twisted plywood architecture of collagen fibrils in human compact-bone osteons,” Calcif. Tissue Int., vol. 42, no. 3, pp. 167-180, 1988, doi: 10.1007/BF02556330.
23. [12] S. Weiner and W. Traub, “Bone structure: from angstroms to microns,” FASEB J., vol. 6, no. 3, pp. 879-895, 1992.
24. [12] S. Weiner and W. Traub, “Bone structure: from angstroms to microns,” FASEB J., vol. 6, no. 3, pp. 879-895, 1992.
25. [13] W. Wagermaier, H. S. Gupta, A. Gourrier, M. Burghammer, P. Roschger, and P. Fratzl, “Spiral twisting of fiber orientation inside bone lamellae,” Biointerphases, vol. 1, no. 1, pp. 1-5, 2006, doi: 10.1116/1.2178386.
26. [13] W. Wagermaier, H. S. Gupta, A. Gourrier, M. Burghammer, P. Roschger, and P. Fratzl, “Spiral twisting of fiber orientation inside bone lamellae,” Biointerphases, vol. 1, no. 1, pp. 1-5, 2006, doi: 10.1116/1.2178386.
27. [14] G. Marotti, “A new theory of bone lamellation,” Calcif. Tissue Int., vol. 53, Suppl. 1, pp. S47-S56, 1993, doi: 10.1007/BF01673402.
28. [14] G. Marotti, “A new theory of bone lamellation,” Calcif. Tissue Int., vol. 53, Suppl. 1, pp. S47-S56, 1993, doi: 10.1007/BF01673402.
29. [15] J. D. Currey, “The Structure of Bone Tissue,” in Bones: Structure and Mechanics, 1st. ed. Princeton, NJ, USA: Princeton University Press, 2002, ch. 1, pp. 2- 25.
30. [15] J. D. Currey, “The Structure of Bone Tissue,” in Bones: Structure and Mechanics, 1st. ed. Princeton, NJ, USA: Princeton University Press, 2002, ch. 1, pp. 2- 25.
31. [16] H. D. Wagner and S. Weiner, “On the relationship between the microstructure of bone and its mechanical stiffness,” J Biomech., vol. 25, no. 11, pp. 1311-1320, 1992, doi: 10.1016/0021-9290(92)90286-a.
32. [16] H. D. Wagner and S. Weiner, “On the relationship between the microstructure of bone and its mechanical stiffness,” J Biomech., vol. 25, no. 11, pp. 1311-1320, 1992, doi: 10.1016/0021-9290(92)90286-a.
33. [17] C. J. Newcomb, R. Bitton, Y. S. Velichko, M. L. Snead, and S. I. Stupp, “The role of nanoscale architecture in supramolecular templating of biomimetic hydroxyapatite mineralization,” Small, vol. 8, no. 14, pp. 2195-2202, 2012, doi: 10.1002/smll.201102150.
34. [17] C. J. Newcomb, R. Bitton, Y. S. Velichko, M. L. Snead, and S. I. Stupp, “The role of nanoscale architecture in supramolecular templating of biomimetic hydroxyapatite mineralization,” Small, vol. 8, no. 14, pp. 2195-2202, 2012, doi: 10.1002/smll.201102150.
35. [18] N. Reznikov, R. Shahar, and S. Weiner, “Three-dimensional structure of human lamellar bone: the presence of two different materials and new insights into the hierarchical organization,” Bone, vol. 59, pp. 93-104, 2014, doi: 10.1016/j.bone.2013.10.023.
36. [18] N. Reznikov, R. Shahar, and S. Weiner, “Three-dimensional structure of human lamellar bone: the presence of two different materials and new insights into the hierarchical organization,” Bone, vol. 59, pp. 93-104, 2014, doi: 10.1016/j.bone.2013.10.023.
37. [19] N. Reznikov, J. A. M. Steele, P. Fratzl, and M. M. Stevens, “A materials science vision of extracellular matrix mineralization,” Nat. Rev. Mater., vol. 1, Art. no. 16041, 2016, doi: 10.1038/natrevmats.2016.41.
38. [19] N. Reznikov, J. A. M. Steele, P. Fratzl, and M. M. Stevens, “A materials science vision of extracellular matrix mineralization,” Nat. Rev. Mater., vol. 1, Art. no. 16041, 2016, doi: 10.1038/natrevmats.2016.41.
39. [20] E. E. Wilson, A. Awonusi, M. D. Morris, D. H. Kohn, M. M. Tecklenburg, and L. W. Beck, “Three structural roles for water in bone observed by solid-state NMR,” Biophys. J., vol. 90, no. 10, pp. 3722-3731, 2006, doi: 10.1529/biophysj.105.070243.
40. [20] E. E. Wilson, A. Awonusi, M. D. Morris, D. H. Kohn, M. M. Tecklenburg, and L. W. Beck, “Three structural roles for water in bone observed by solid-state NMR,” Biophys. J., vol. 90, no. 10, pp. 3722-3731, 2006, doi: 10.1529/biophysj.105.070243.
41. [21] W. J. Landis, M. J. Song, A. Leith, L. McEwen, and B. F. McEwen, “Mineral and organic matrix interaction in normally calcifying tendon visualized in 3 dimensions by high-voltage electron-microscopic tomography and graphic image-reconstruction,” J. Struct. Biol., vol. 110, no. 1, pp. 39-54, 1993, doi: 10.1006/jsbi.1993.1003.
42. [21] W. J. Landis, M. J. Song, A. Leith, L. McEwen, and B. F. McEwen, “Mineral and organic matrix interaction in normally calcifying tendon visualized in 3 dimensions by high-voltage electron-microscopic tomography and graphic image-reconstruction,” J. Struct. Biol., vol. 110, no. 1, pp. 39-54, 1993, doi: 10.1006/jsbi.1993.1003.
43. [22] E. D. Eanes, D. R. Lundy, and G. N. Martin, “X-Ray diffraction study of the mineralization of turkey leg tendon,” Calcif. Tissue Res., vol. 6, no. 3, pp. 239-248, 1970, doi: 10.1007/BF02196204.
44. [22] E. D. Eanes, D. R. Lundy, and G. N. Martin, “X-Ray diffraction study of the mineralization of turkey leg tendon,” Calcif. Tissue Res., vol. 6, no. 3, pp. 239-248, 1970, doi: 10.1007/BF02196204.
45. [23] E. D. Eanes, G. N. Martin, and D. R. Lundy, “The distribution of water in calcified turkey leg tendon,” Calcif. Tissue Res., vol. 20, no. 3, pp. 313-316, 1976, doi: 10.1007/BF02546418.
46. [23] E. D. Eanes, G. N. Martin, and D. R. Lundy, “The distribution of water in calcified turkey leg tendon,” Calcif. Tissue Res., vol. 20, no. 3, pp. 313-316, 1976, doi: 10.1007/BF02546418.
47. [24] L. C. Bonar, S. Mook, and H. A. Lees, “Neutron-diffraction studies of collagen in fully mineralized bone,” J. Mol. Biol., vol. 181, no. 2, pp. 265-270, 1985, doi: 10.1016/0022-2836(85)90090-7.
48. [24] L. C. Bonar, S. Mook, and H. A. Lees, “Neutron-diffraction studies of collagen in fully mineralized bone,” J. Mol. Biol., vol. 181, no. 2, pp. 265-270, 1985, doi: 10.1016/0022-2836(85)90090-7.
49. [25] D. Magne, P. Weiss, J. M. Bouler, O. Laboux, and G. Daculsi, “Study of the maturation of the organic (Type I collagen) and mineral (nonstoichiometric apatite) constituents of a calcified tissue (dentin) as a function of location: A Fourier transform infrared microspectroscopic investigation,” J. Bone Miner. Res., vol. 6, no. 4, pp. 750-757, 2001, doi: 10.1359/jbmr.2001.16.4.750.
50. [25] D. Magne, P. Weiss, J. M. Bouler, O. Laboux, and G. Daculsi, “Study of the maturation of the organic (Type I collagen) and mineral (nonstoichiometric apatite) constituents of a calcified tissue (dentin) as a function of location: A Fourier transform infrared microspectroscopic investigation,” J. Bone Miner. Res., vol. 6, no. 4, pp. 750-757, 2001, doi: 10.1359/jbmr.2001.16.4.750.
51. [26] W. J. Landis, “The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix,” Bone, vol. 16, no. 5, pp. 533-544, 1995, doi: 10.1016/8756-3282(95)00076-p.
52. [26] W. J. Landis, “The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix,” Bone, vol. 16, no. 5, pp. 533-544, 1995, doi: 10.1016/8756-3282(95)00076-p.
53. [27] M. Fois, A. Lamure, M. J. Fauran, and C. Lacabanne, “Study of human cortical bone and demineralized human cortical bone viscoelasticity,” J. Appl. Polym. Sci., vol. 79, no. 14, pp. 2527-2533, 2001, doi: 10.1002/1097-4628(20010401)79:14<2527.
54. [27] M. Fois, A. Lamure, M. J. Fauran, and C. Lacabanne, “Study of human cortical bone and demineralized human cortical bone viscoelasticity,” J. Appl. Polym. Sci., vol. 79, no. 14, pp. 2527-2533, 2001, doi: 10.1002/1097-4628(20010401)79:14<2527.
55. [28] D. Liu, H. D. Wagner, and S. Weiner, “Bending and fracture of compact circumferential and osteonal lamellar bone of the baboon tibia,” J Mater. Sci. Mater. Med., vol. 11, no. 1, pp. 49-60, 2000, doi: 10.1023/a:1008989719560.
56. [28] D. Liu, H. D. Wagner, and S. Weiner, “Bending and fracture of compact circumferential and osteonal lamellar bone of the baboon tibia,” J Mater. Sci. Mater. Med., vol. 11, no. 1, pp. 49-60, 2000, doi: 10.1023/a:1008989719560.
57. [29] Z. Fan, J. G. Swadener, J. Y. Rho, M. E. Roy, and G. M. Pharr, “Anisotropic properties of human tibial cortical bone as measured by nanoindentation,” J Orthop. Res., vol. 20, no. 4, pp. 806-810, 2002, doi: 10.1016/S0736-0266(01)00186-3.
58. [29] Z. Fan, J. G. Swadener, J. Y. Rho, M. E. Roy, and G. M. Pharr, “Anisotropic properties of human tibial cortical bone as measured by nanoindentation,” J Orthop. Res., vol. 20, no. 4, pp. 806-810, 2002, doi: 10.1016/S0736-0266(01)00186-3.
59. [30] P. E. Riches, N. M. Everitt, A. R. Heggie, and D. S. McNally, “Microhardness anisotropy of lamellar bone,” J Biomech., vol. 30, no. 10, pp. 1059-1061, 1997, doi: 10.1016/s0021-9290(97)00075-4.
60. [30] P. E. Riches, N. M. Everitt, A. R. Heggie, and D. S. McNally, “Microhardness anisotropy of lamellar bone,” J Biomech., vol. 30, no. 10, pp. 1059-1061, 1997, doi: 10.1016/s0021-9290(97)00075-4.
61. [31] A. Faingold, S. R. Cohen, N. Reznikov, and H. D. Wagner, “Osteonal lamellae elementary units: Lamellar microstructure. curvature and mechanical properties,” Acta Biomater., vol. 9, no. 4, pp. 5956-5962, 2013, doi: 10.1016/j.actbio.2012.11.032.
62. [31] A. Faingold, S. R. Cohen, N. Reznikov, and H. D. Wagner, “Osteonal lamellae elementary units: Lamellar microstructure. curvature and mechanical properties,” Acta Biomater., vol. 9, no. 4, pp. 5956-5962, 2013, doi: 10.1016/j.actbio.2012.11.032.
63. [32] M-G. Ascenzi, “A first estimation of prestress in so-called circularly fibered osteonic lamellae,” J Biomech., vol. 32, no. 9, pp. 935-942, 1999, doi:10.1016/s0021-9290(99)00080-9.
64. [32] M-G. Ascenzi, “A first estimation of prestress in so-called circularly fibered osteonic lamellae,” J Biomech., vol. 32, no. 9, pp. 935-942, 1999, doi:10.1016/s0021-9290(99)00080-9.