Materials Science and Nanotechnology

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Short Communication - Materials Science and Nanotechnology (2018) Volume 2, Issue 1

Some properties of bones at different nanostructural microstrucral and mesostructural levels.

Fae`q AA Radwan*

Faculty of Engineering, Near East University, Turkey

Corresponding Author:
Fae`q AA Radwan
Faculty of Engineering, Near East University
Turkey
E-mail: faeq.radwan@neu.edu.tr

Accepted date: March 14, 2018

Citation: Radwan FAA. Some properties of bones at different nanostructural microstrucral and mesostructural levels. Mater Sci Nanotechnol. 2018;2(1):13-14.

Abstract

The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of bones at different nanostructural, microstrucral and mesostructural levels are calculated. The relation of the scalar parts norm and the other parts norms and the anisotropy of bones at different nanostructural, microstrucral and mesostructural levels are presented. The norm ratios are used to study anisotropy of bones at different nanostructural, microstrucral and mesostructural levels and the relationship of their structural properties and other properties with their anisotropy are given.

Keywords

Mineralized collagen, Microfibril, Fibril, Fiber, Lamella, Canaliculi, Lacunae, Osteous, Cortical bone Nanostructrctural level, Nanostructrctural level, Mesostructural level, Norm, Anisotropy, Elastic constants.

Introduction

The decomposition procedure and the decomposition (Elastic constant tensor can be decomposed into two scalar parts, two deviator parts and one nonor part) of elastic constant tensor is given [1,2] also the definition of norm concept and the norm ratios and the relationship between the anisotropy and the norm ratios are given [1,2]. As the ratio (Norm of the scalar part of the elastic constant tensor/Norm of the elastic constant tensor) becomes close to one the material becomes more isotropic, and as the ratio (Norm of the nonor part of the elastic constant tensor/Norm of the elastic constant tensor) becomes close to one the material becomes more anisotropic is explained [1,2].

Calculations

By using and the decomposition of the elastic constant tensor, we have calculated the norms and the norm ratios as shown in Tables 1 and 2.

Bone c11 c22 c33 c12 c13 c23 c44 c55 c66
Mineralized collagen, microfibril, Nanostructrctural level 1.07 1.07 1.07 0.434 0.434 0.434 0.632 0.632 0.632
Mineralized collagen, fibril, Nanostructrctural level 1.133 1.185 1.226 0.468 0.468 0.474 0.787 0.787 0.787
Mineralized collagen, fiber, Nanostructrctural level 16.144 16.144 16.11 6.233 6.233 6.237 9.928 9.928 9.928
Lamella, microstrucral level 16.08 16.08 16.07 6.21 6.21 6.22 9.88 9.88 9.88
Lamellae with canaliculi, microstrucral level 16.18 16.18 16.14 6.24 6.24 6.25 9.96 9.96 9.96
LRC Lamellae, microstrucral level 21.57 21.57 21.51 8.32 8.32 8.33 13.28 13.28 13.3
Lamellae with lacunae, microstrucral level 19.44 20.34 32.2 8.24 8.25 8.25 14.02 12.33 12.54
Osteous, mesostructural level  19.44 20.34 32.3 8.24 8.25 8.25 13.17 13.16 13.18
Cortical bone, mesostructural level 21.96 23 26.04 8.24 10.19 8.25 6.89 6.12 6.45

Table 1: Elastic constants (GPa) [3].

Bone Ns Nd Nn N NS/N Nd/N Nn/N
Mineralized collagen, microfibril, Nanostructrctural level 2.56451 0 0.57557 2.62830 0.97573 0 0.21899
Mineralized collagen, fibril, Nanostructrctural level 2.94165 0.06102 0.79082 3.04671 0.96552 0.02003 0.25956
Mineralized collagen, fiber, Nanostructrctural level 38.8703 0.02427 9.12636 39.9273 0.97353 0.00061 0.22857
Lamella, microstrucral level 38.7178 0.01024 9.07045 39.7661 0.97364 0.00026 0.22810
Lamellae with canaliculi, microstrucral level 38.9629 0.02862 9.16211 40.0257 0.97345 0.00072 0.22891
LRC Lamellae, microstrucral level 51.9518 0.05348 12.2324 53.3725 0.97338 0.00100 0.22919
Lamellae with lacunae, microstrucral level 54.3382 9.34852 9.67607 55.9791 0.97069 0.167 0.17285
Osteous, mesostructural level 54.65294 9.05628 10.10629 56.31249 0.97053 0.16082 0.17947
Cortical bone, mesostructural level 47.26546 3.61626 1.72146 47.43485 0.99643 0.07624 0.03629

Table 2: The norms and norm ratios.

Results and Conclusion

From Table 2 and the Graphs 1-3 and analysing the ratio equation

Figure

Graph 1: Isotropy degree.

Figure

Graph 2: Anisotropy degree.

Figure

Graph 3: Elastically strong.

we can conclude that Cortical bone, mesostructural level is the most isotropic bone which has the largest value (0.99643) and

has the smallest value of equation, (0.03629) and small value of equation, (0.07624) and Mineralized collagen, fibril, Nanostructrctural level is the least isotropic bone which has the smallest value (0.96552) of equation and has the largest value (0.25956) of equation and has large value (0.02003) of equation, so we can say that Mineralized collagen, fibril, Nanostructrctural level is the most anisotropic bone. Also we can make the comparison in the same structural level, in the case of Nanostructrctural level the most isotropic bone is Mineralized collagen, microfibril, and the most anisotropic bone is Mineralized collagen, fibril, and in the case of microstrucral level, the most isotropic bone is Lamella, and Lamellae with lacunae is the most anisotropic bone, and in the case of mesostructural level the most isotropic bone is Cortical bone and the most anisotropic bone is Osteous.

Also we can notice by considering the value of N that this value is the highest (56.31249) in the case of Osteous, mesostructural level so we can say that Osteous, mesostructural level elastically is the strongest bone, and the in the case Mineralized collagen, microfibril, Nanostructrctural level (2.62830) which is its value of N is the smallest so we can say that Mineralized collagen, microfibril, Nanostructrctural level elastically is the least strong bone among the bones in the table.

References

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