- Email: [email protected]
Hydroxyapatite-Sheet Parallel Microstructure of Shinbone
Journal of Bionic Engineering Suppl. (2008) 9–13
Hydroxyapatite-Sheet Parallel Microstructure of Shinbone Bin Chen, Xiang-he Peng, Shi-tao Sun, Jing-hong Fan Department of Engineering Mechanics, College of Resource and Environment Science, Chongqing University, Chongqing 400044, P. R. China
Abstract Bone is a natural biomaterial. It behaves favorable strength, stiffness and fracture toughness, which are closely related to its eximious microstructure. Scanning Electron Microscope (SEM) observation on a shinbone showed that the bone is a bioceramic composite consisting of laminated hydroxyapatite and collagen matrix. The hydroxyapatite layers are parallel with the surface of the bone and consist of long and thin hydroxyapatite sheets. The observation also showed that the hydroxyapatite sheets in different hydroxyapatite layers also parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. It was shown that the long and thin shape of the hydroxyapatite sheets in the parallel microstructure is profitable to increase the maximum pullout energy and enhance the fracture toughness of the bone. Keywords: shinbone, hydroxyapatite sheets, parallel microstructure, maximum pullout energy, fracture toughness Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.
1 Introduction Animal bone, a kind of structural bioceramic composite in nature, possesses favorable strength, stiffness and fracture toughness, which are owed to its highly optimized microstructure formed from natural evolution over many centuries[13]. The research on the microstructures of bones may provide beneficial information for the development of new high-performance ceramic composites, especially those medical bioceramic composites to meet specific clinical requirements[4]. As a kind of natural bioceramic composite, bone has to bear static and dynamic mechanical loads applied by body weight and locomotion. In general, bone is composed of hydroxyapatite crystals and various collagen proteins[1,2]. The hydroxyapatite crystals occupy about 65 wt% and afford the high stiffness of bone[3]. In addition, the hydroxyapatite crystals also provide the most strength of bone as the reinforcement of bone[35]. Researches on the hydroxyapatite crystals showed that several typical microstructures of the material, including Corresponding author: Bin Chen E-mail: [email protected]
their morphology, dimension and distribution, markedly affect the mechanical properties of bone[6,7]. Understanding bone’s mechanical properties, through the analysis of various microstructures of the hydroxyapatite crystals, is essential for the assessment of bone diseases such as osteoporosis[8] and the developments of high-performance mimetic-bone composites or replaced-bone composites[9,10]. In this paper, the microstructural characteristics of a shinbone were observed with a SEM. It was shown that the bone is a bioceramic composite composed of hydroxyapatites and collagen proteins. The hydroxyapatites possess laminated microstructure and all hydroxyapatite layers are parallel with the surface of the bone. The observation also showed that each hydroxyapatite layer consists of long and thin hydroxyapatite sheets. The hydroxyapatite sheets in different hydroxyapatite layers are also parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. It showed that the long and thin shape of the hydroxyapatite sheets in the microstructure
10
Journal of Bionic Engineering (2008) Suppl.
is favorable to increase the maximum pullout energy and enhance the fracture toughness of the bone.
2 Materials and methods The microstructures of bones change with their species[7,8]. The bone used in this study is a shinbone. A SEM was used for the observation of its microstructures. The samples of the bone were prepared by the following procedure: removing the flesh from the bone, cleaning the surface of the bone with 95% alcohol, and then dividing the bone along different directions. The specimens were then placed on a metal tray using viscid fabric. A coat about 10nm gold-palladium was made using a sputter coater. These samples were then observed using a SEM (Amray KYKY-1000B) under a voltage about 20 kV and with magnifications ranged from 20 to 13 000.
Fig. 1 Parallel hydroxyapatite layers.
3 Observation results The SEM observation showed that the bone is a bioceramic composite consisting of hydroxyapatite and collagen matrix. The hydroxyapatite in the composite is of layered microstructure and all of the hydroxyapatite layers are parallel with the surface of the bone (Fig. 1), coincide with the direction of the maximum principal stress of the bone when subjected to an external load. The observation also showed that each hydroxyapatite layer consists of numerous hydroxyapatite sheets arranged perpendicular to the layer where they are located (Fig. 2). The perpendicular arrangement of the sheets may enhance the flexural rigidity of the bone, which will be discussed elsewhere. It was also seen that the hydroxyapatite sheets in the hydroxyapatite layers possess long and thin shape and are arranged compactly side by side, the thickness of which is about several dozen to several hundred nanometers. More careful observation showed that the hydroxyapatite sheets in different hydroxyapatite layers are of identical orientation, which composes a hydroxyapatite-sheet parallel microstructure (Fig. 2). The long and thin shape as well as the parallel arrangement of the hydroxyapatite sheets may be favorable to increase the maximum pullout energy of the sheets and enhance the fracture toughness of the bone, which will be analyzed in next section.
Fig. 2 Parallel sheets in hydroxyapatite layers.
4 Model analysis It is known that the fracture toughness of a composite is closely related to the maximum pullout energy of its reinforcing phase. In this section, the maximum pullout energy of the long and thin hydroxyapatite sheets in the parallel microstructure is analyzed based on a representative model. First, the maximum pullout energy of a single hydroxyapatite sheet, embedded in its matrix and in its pullout direction, as shown in Fig. 3, was analyzed. Suppose that the sheet has long and thin shape and its width, thickness and embedded length are b, h and l, respectively, and that the interfacial shearing stress between the sheet and its matrix is the function of the embedded depth x of the sheet, the pullout energy of
Chen et al.: Hydroxyapatite-Sheet Parallel Microstructure of Shinbone
Fig. 4 Model of parallel microstructure.
Fig. 3 Model of a single hydroxyapatite sheet.
a microsegment dx of the sheet can be estimated with dw 2(b h) xW ( x)dx ,
(1)
the total pullout energy of the sheet is W
l
2³ (b h) xW ( x)dx . 0
(2)
(b h)l 2W s .
(3)
The representative model of the parallel microstructure composed of the long and thin hydroxyapatite sheets is shown in Fig. 4. Suppose that the hydroxyapatite sheets in the model have the same width b, thickness h and embedded length l, and that the layer number of the hydroxyapatites and the sheet number in each hydroxyapatite layer are m and n, respectively, the total pullout energy of the hydroxyapatite sheets in the parallel microstructure can be given as W
l
2³ mn(b h) xW ( x)dx . 0
load and that the maximum applied load is reached when the interfacial shearing stress reaches the critical interfacial shearing strength s, the maximum pullout energy of the hydroxyapatite sheets in the parallel microstructure is mn(b h)l 2W s .
Wmax
Suppose the interfacial shearing stress increases continuously with the applied load, and the maximum applied load is reached when the interfacial shearing stress reaches the critical interfacial shearing strength s, the maximum pullout energy of the sheet can be expressed as Wmax
11
(4)
Similarly, suppose that the interfacial shearing stress increases continuously with the increment of the applied
(5)
Because the thickness b of the sheets is much less than their length l and width b, the maximum pullout energy Eq. (5) can be re-written as Wmax
mnbl 2W s .
(6)
Suppose the hydroxyapatite layers in the microstructure have identical width B, Eq. (6) can be written as Wmax
mBbl 2W s / h .
(7)
It can be seen from Eq. (7) that the maximum pullout energy is related to the number and width of the hydroxyapatite layers, and the width, thickness and embedded length of the hydroxyapatite sheets as well as the interfacial shearing strength. Fig. 5 shows that the relationship between the sheet thickness and the maximum pullout energy. It can be seen that the lesser the thickness, the larger the maximum pullout energy. This is the reason why the hydroxyapatite sheets in the bone take very small thickness size (nanometer scale). Fig. 6 shows that the relationship between the embedded length of the sheet and the maximum pullout energy. It can be seen
Journal of Bionic Engineering (2008) Suppl.
12
that the larger the embedded length of the hydroxyapatite sheets, the larger the maximum pullout energy. Specially, the maximum pullout energy increases with the embedded length by second power rule (Eq. (7) and Fig. 6). This is why the hydroxyapatite sheets in the bone take very large length size.
Fig. 5 Pullout energy W vs. sheet thickness h.
100 mm) in epoxy-resin matrix. The width and thickness of the fibers is 2 mm and 1 mm, respectively. One end of the fibers was remained outside the matrix for applying the pullout forces. The tests were performed on an Instron 1342 Material Testing System and the loads were applied to the ends of these fibers with special clamps. The experimental results are plotted in Fig. 6, from which it can be seen that the larger the embedded length of the fiber, the larger the maximum pullout energy, which is consistent with analytical results. In Fig. 6, the experimental results are slightly different from the predicted values, which can be attributed to the error of the parameters provided, for example, the interfacial shearing strength, and the experimental conditions that are different from the ideal ones used in the analyses. In addition, in the model analysis and experimental investigation, it was concluded that the larger the fiber length is, the more the maximum pullout energy will increase. But such increase will be limited by the strengths of the fiber and matrix. It is suggested that, for effective use of the fiber-parallel microstructure, the fiber, the matrix as well as the interfacial property of the fiber/matrix should be rationally designed.
6 Conclusions
Fig. 6 Pullout energy W vs. fiber length l.
5 Experimental verification In order to verify above model-analytical results, the tests of the maximum pullout energy of steel-thread fibers in the parallel structure were conducted. First, a set of specimens were fabricated by embedding steelthread fibers of different depth (40 mm, 60 mm, 80 mm,
SEM observation on a shinbone revealed that the bone is a natural bioceramic composite consisting of laminated hydroxyapatite and collagen matrix. All of the hydroxyapatite layers are parallel with the surface of the bone. The observation also showed that each hydroxyapatite layer consists of many long and thin hydroxyapatite sheets and that all hydroxyapatite sheets are parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. The investigated result showed that the long and thin shape of the sheets in the parallel microstructure is favorable to increase the maximum pullout energy of the sheets and enhance the fracture toughness of the bone.
Acknowledgement This work is financially supported by the Natural Science Foundation of China (Grant no. 10572157).
Chen et al.: Hydroxyapatite-Sheet Parallel Microstructure of Shinbone
References [1]
[6]
in calcified tissues – A comparative study by SAXS. Journal
M, Bass H, Stern R (eds), Handbook of Elastic Properties of ton, USA, 2000. [2]
Currey J D. The many adaptations of bone. Journal of Biomechanics, 2003, 36, 1487–1493.
[3]
of Bone and Mineral Research, 1992, 7, 329–334. [7] Lees S, Prostak K. The locus of mineral crystallites in bone. Connective Tissue Research, 1988, 18, 41–54. [8]
in bone. Journal of Materials Chemistry, 2004, 14, 2115–
Relating local bone stiffness and calcium content by comMRS Proceedings: Structure and Mechanical Behavior of Biological Materials, 2005, 847, 79–84. [4]
Glimcher M J. The nature of the mineral component of bone and the mechanisms of calcification. In: Coe F L, Favus M J (eds), Disorders of Bone and Mineral Metabolism, Raven Press, New York, USA, 1992, 265–286.
[5] Su X, Sun K, Cui F Z, Landis W J. Organization of apatite crystals in human woven bone. Bone, 2003, 32, 150–162.
Fratzl P, Gupta H S, Paschalis E P, Roschger P. Structure and mechanical quality of the collagen-mineral nano-composite
Weber M, Schoeberl T, Roschger P, Klaushofer K, Fratzl P. bined nanoindentation and backscattered electron imaging.
Fratzl P, Groschner M, Vogl G, Plenk H Jr, Eschberger J, Fratzl-Zelman N, Koller K, Klaushofer K. Mineral crystals
Vincent J F V. Ceramics from invertebrate animals. In: Levy Solids, Liquids and Gases, vol 3, Academic Press, Burling-
13
2123. [9]
Woesz A, Rumpler M, Stampfl J, Varga F, Fratzl, Roschger Z N, Klaushofer K, Fratzl P. Towards bone replacement materials from calcium phosphates via rapid prototyping and ceramic gelcasting. Materials Science and Engineering C, 2005, 25, 181–186.
[10] Weiner S, Wagner H D. The material bone: Structuremechanical function relations. Annual Review of Materials Science, 1998, 28, 271–298.
Hydroxyapatite-Sheet Parallel Microstructure of Shinbone Bin Chen, Xiang-he Peng, Shi-tao Sun, Jing-hong Fan Department of Engineering Mechanics, College of Resource and Environment Science, Chongqing University, Chongqing 400044, P. R. China
Abstract Bone is a natural biomaterial. It behaves favorable strength, stiffness and fracture toughness, which are closely related to its eximious microstructure. Scanning Electron Microscope (SEM) observation on a shinbone showed that the bone is a bioceramic composite consisting of laminated hydroxyapatite and collagen matrix. The hydroxyapatite layers are parallel with the surface of the bone and consist of long and thin hydroxyapatite sheets. The observation also showed that the hydroxyapatite sheets in different hydroxyapatite layers also parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. It was shown that the long and thin shape of the hydroxyapatite sheets in the parallel microstructure is profitable to increase the maximum pullout energy and enhance the fracture toughness of the bone. Keywords: shinbone, hydroxyapatite sheets, parallel microstructure, maximum pullout energy, fracture toughness Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.
1 Introduction Animal bone, a kind of structural bioceramic composite in nature, possesses favorable strength, stiffness and fracture toughness, which are owed to its highly optimized microstructure formed from natural evolution over many centuries[13]. The research on the microstructures of bones may provide beneficial information for the development of new high-performance ceramic composites, especially those medical bioceramic composites to meet specific clinical requirements[4]. As a kind of natural bioceramic composite, bone has to bear static and dynamic mechanical loads applied by body weight and locomotion. In general, bone is composed of hydroxyapatite crystals and various collagen proteins[1,2]. The hydroxyapatite crystals occupy about 65 wt% and afford the high stiffness of bone[3]. In addition, the hydroxyapatite crystals also provide the most strength of bone as the reinforcement of bone[35]. Researches on the hydroxyapatite crystals showed that several typical microstructures of the material, including Corresponding author: Bin Chen E-mail: [email protected]
their morphology, dimension and distribution, markedly affect the mechanical properties of bone[6,7]. Understanding bone’s mechanical properties, through the analysis of various microstructures of the hydroxyapatite crystals, is essential for the assessment of bone diseases such as osteoporosis[8] and the developments of high-performance mimetic-bone composites or replaced-bone composites[9,10]. In this paper, the microstructural characteristics of a shinbone were observed with a SEM. It was shown that the bone is a bioceramic composite composed of hydroxyapatites and collagen proteins. The hydroxyapatites possess laminated microstructure and all hydroxyapatite layers are parallel with the surface of the bone. The observation also showed that each hydroxyapatite layer consists of long and thin hydroxyapatite sheets. The hydroxyapatite sheets in different hydroxyapatite layers are also parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. It showed that the long and thin shape of the hydroxyapatite sheets in the microstructure
10
Journal of Bionic Engineering (2008) Suppl.
is favorable to increase the maximum pullout energy and enhance the fracture toughness of the bone.
2 Materials and methods The microstructures of bones change with their species[7,8]. The bone used in this study is a shinbone. A SEM was used for the observation of its microstructures. The samples of the bone were prepared by the following procedure: removing the flesh from the bone, cleaning the surface of the bone with 95% alcohol, and then dividing the bone along different directions. The specimens were then placed on a metal tray using viscid fabric. A coat about 10nm gold-palladium was made using a sputter coater. These samples were then observed using a SEM (Amray KYKY-1000B) under a voltage about 20 kV and with magnifications ranged from 20 to 13 000.
Fig. 1 Parallel hydroxyapatite layers.
3 Observation results The SEM observation showed that the bone is a bioceramic composite consisting of hydroxyapatite and collagen matrix. The hydroxyapatite in the composite is of layered microstructure and all of the hydroxyapatite layers are parallel with the surface of the bone (Fig. 1), coincide with the direction of the maximum principal stress of the bone when subjected to an external load. The observation also showed that each hydroxyapatite layer consists of numerous hydroxyapatite sheets arranged perpendicular to the layer where they are located (Fig. 2). The perpendicular arrangement of the sheets may enhance the flexural rigidity of the bone, which will be discussed elsewhere. It was also seen that the hydroxyapatite sheets in the hydroxyapatite layers possess long and thin shape and are arranged compactly side by side, the thickness of which is about several dozen to several hundred nanometers. More careful observation showed that the hydroxyapatite sheets in different hydroxyapatite layers are of identical orientation, which composes a hydroxyapatite-sheet parallel microstructure (Fig. 2). The long and thin shape as well as the parallel arrangement of the hydroxyapatite sheets may be favorable to increase the maximum pullout energy of the sheets and enhance the fracture toughness of the bone, which will be analyzed in next section.
Fig. 2 Parallel sheets in hydroxyapatite layers.
4 Model analysis It is known that the fracture toughness of a composite is closely related to the maximum pullout energy of its reinforcing phase. In this section, the maximum pullout energy of the long and thin hydroxyapatite sheets in the parallel microstructure is analyzed based on a representative model. First, the maximum pullout energy of a single hydroxyapatite sheet, embedded in its matrix and in its pullout direction, as shown in Fig. 3, was analyzed. Suppose that the sheet has long and thin shape and its width, thickness and embedded length are b, h and l, respectively, and that the interfacial shearing stress between the sheet and its matrix is the function of the embedded depth x of the sheet, the pullout energy of
Chen et al.: Hydroxyapatite-Sheet Parallel Microstructure of Shinbone
Fig. 4 Model of parallel microstructure.
Fig. 3 Model of a single hydroxyapatite sheet.
a microsegment dx of the sheet can be estimated with dw 2(b h) xW ( x)dx ,
(1)
the total pullout energy of the sheet is W
l
2³ (b h) xW ( x)dx . 0
(2)
(b h)l 2W s .
(3)
The representative model of the parallel microstructure composed of the long and thin hydroxyapatite sheets is shown in Fig. 4. Suppose that the hydroxyapatite sheets in the model have the same width b, thickness h and embedded length l, and that the layer number of the hydroxyapatites and the sheet number in each hydroxyapatite layer are m and n, respectively, the total pullout energy of the hydroxyapatite sheets in the parallel microstructure can be given as W
l
2³ mn(b h) xW ( x)dx . 0
load and that the maximum applied load is reached when the interfacial shearing stress reaches the critical interfacial shearing strength s, the maximum pullout energy of the hydroxyapatite sheets in the parallel microstructure is mn(b h)l 2W s .
Wmax
Suppose the interfacial shearing stress increases continuously with the applied load, and the maximum applied load is reached when the interfacial shearing stress reaches the critical interfacial shearing strength s, the maximum pullout energy of the sheet can be expressed as Wmax
11
(4)
Similarly, suppose that the interfacial shearing stress increases continuously with the increment of the applied
(5)
Because the thickness b of the sheets is much less than their length l and width b, the maximum pullout energy Eq. (5) can be re-written as Wmax
mnbl 2W s .
(6)
Suppose the hydroxyapatite layers in the microstructure have identical width B, Eq. (6) can be written as Wmax
mBbl 2W s / h .
(7)
It can be seen from Eq. (7) that the maximum pullout energy is related to the number and width of the hydroxyapatite layers, and the width, thickness and embedded length of the hydroxyapatite sheets as well as the interfacial shearing strength. Fig. 5 shows that the relationship between the sheet thickness and the maximum pullout energy. It can be seen that the lesser the thickness, the larger the maximum pullout energy. This is the reason why the hydroxyapatite sheets in the bone take very small thickness size (nanometer scale). Fig. 6 shows that the relationship between the embedded length of the sheet and the maximum pullout energy. It can be seen
Journal of Bionic Engineering (2008) Suppl.
12
that the larger the embedded length of the hydroxyapatite sheets, the larger the maximum pullout energy. Specially, the maximum pullout energy increases with the embedded length by second power rule (Eq. (7) and Fig. 6). This is why the hydroxyapatite sheets in the bone take very large length size.
Fig. 5 Pullout energy W vs. sheet thickness h.
100 mm) in epoxy-resin matrix. The width and thickness of the fibers is 2 mm and 1 mm, respectively. One end of the fibers was remained outside the matrix for applying the pullout forces. The tests were performed on an Instron 1342 Material Testing System and the loads were applied to the ends of these fibers with special clamps. The experimental results are plotted in Fig. 6, from which it can be seen that the larger the embedded length of the fiber, the larger the maximum pullout energy, which is consistent with analytical results. In Fig. 6, the experimental results are slightly different from the predicted values, which can be attributed to the error of the parameters provided, for example, the interfacial shearing strength, and the experimental conditions that are different from the ideal ones used in the analyses. In addition, in the model analysis and experimental investigation, it was concluded that the larger the fiber length is, the more the maximum pullout energy will increase. But such increase will be limited by the strengths of the fiber and matrix. It is suggested that, for effective use of the fiber-parallel microstructure, the fiber, the matrix as well as the interfacial property of the fiber/matrix should be rationally designed.
6 Conclusions
Fig. 6 Pullout energy W vs. fiber length l.
5 Experimental verification In order to verify above model-analytical results, the tests of the maximum pullout energy of steel-thread fibers in the parallel structure were conducted. First, a set of specimens were fabricated by embedding steelthread fibers of different depth (40 mm, 60 mm, 80 mm,
SEM observation on a shinbone revealed that the bone is a natural bioceramic composite consisting of laminated hydroxyapatite and collagen matrix. All of the hydroxyapatite layers are parallel with the surface of the bone. The observation also showed that each hydroxyapatite layer consists of many long and thin hydroxyapatite sheets and that all hydroxyapatite sheets are parallel with each other, which composes a hydroxyapatite-sheet parallel microstructure. The maximum pullout energy of the parallel microstructure was investigated based on its representative model. The investigated result showed that the long and thin shape of the sheets in the parallel microstructure is favorable to increase the maximum pullout energy of the sheets and enhance the fracture toughness of the bone.
Acknowledgement This work is financially supported by the Natural Science Foundation of China (Grant no. 10572157).
Chen et al.: Hydroxyapatite-Sheet Parallel Microstructure of Shinbone
References [1]
[6]
in calcified tissues – A comparative study by SAXS. Journal
M, Bass H, Stern R (eds), Handbook of Elastic Properties of ton, USA, 2000. [2]
Currey J D. The many adaptations of bone. Journal of Biomechanics, 2003, 36, 1487–1493.
[3]
of Bone and Mineral Research, 1992, 7, 329–334. [7] Lees S, Prostak K. The locus of mineral crystallites in bone. Connective Tissue Research, 1988, 18, 41–54. [8]
in bone. Journal of Materials Chemistry, 2004, 14, 2115–
Relating local bone stiffness and calcium content by comMRS Proceedings: Structure and Mechanical Behavior of Biological Materials, 2005, 847, 79–84. [4]
Glimcher M J. The nature of the mineral component of bone and the mechanisms of calcification. In: Coe F L, Favus M J (eds), Disorders of Bone and Mineral Metabolism, Raven Press, New York, USA, 1992, 265–286.
[5] Su X, Sun K, Cui F Z, Landis W J. Organization of apatite crystals in human woven bone. Bone, 2003, 32, 150–162.
Fratzl P, Gupta H S, Paschalis E P, Roschger P. Structure and mechanical quality of the collagen-mineral nano-composite
Weber M, Schoeberl T, Roschger P, Klaushofer K, Fratzl P. bined nanoindentation and backscattered electron imaging.
Fratzl P, Groschner M, Vogl G, Plenk H Jr, Eschberger J, Fratzl-Zelman N, Koller K, Klaushofer K. Mineral crystals
Vincent J F V. Ceramics from invertebrate animals. In: Levy Solids, Liquids and Gases, vol 3, Academic Press, Burling-
13
2123. [9]
Woesz A, Rumpler M, Stampfl J, Varga F, Fratzl, Roschger Z N, Klaushofer K, Fratzl P. Towards bone replacement materials from calcium phosphates via rapid prototyping and ceramic gelcasting. Materials Science and Engineering C, 2005, 25, 181–186.
[10] Weiner S, Wagner H D. The material bone: Structuremechanical function relations. Annual Review of Materials Science, 1998, 28, 271–298.