Mathematical osteon model for examining poroelastic behaviors
An extended and reasonable stress boundary condition at an osteon exte- rior wall is presented to solve the model proposed by Remond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. （i） Both...
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| Published in | Applied mathematics and mechanics Vol. 34; no. 4; pp. 405 - 416 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Shanghai University
01.04.2013
College of Mechanics, Taiyuan University of Technology,Taiyuan 030024, P.R.China%College of Mathematics, Taiyuan University of Technology,Taiyuan 030024, P.R.China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0253-4827 1573-2754 |
| DOI | 10.1007/s10483-013-1680-x |
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| Abstract | An extended and reasonable stress boundary condition at an osteon exte- rior wall is presented to solve the model proposed by Remond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. （i） Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. （ii） In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. （iii） At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not. |
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| AbstractList | An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by Rémond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. (i) Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. (ii) In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. (iii) At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not. An extended and reasonable stress boundary condition at an osteon exte- rior wall is presented to solve the model proposed by Remond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. （i） Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. （ii） In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. （iii） At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not. An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by RACOmond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. (i) Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. (ii) In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. (iii) At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not. |
| Author | 武晓刚 陈维毅 王旦霞 |
| AuthorAffiliation | College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China |
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| Cites_doi | 10.1063/1.1721956 10.1016/j.medengphy.2010.02.001 10.1016/j.jbiomech.2005.08.005 10.1163/157361109789017005 10.1016/S0021-9290(99)00210-9 10.1007/s10237-011-0287-1 10.1016/S0020-7683(98)00105-X 10.1016/j.mechrescom.2004.10.003 10.1016/S8756-3282(98)00118-5 10.1007/s10237-007-0111-0 10.1016/j.crme.2009.06.033 10.1016/S0020-7683(98)00101-2 10.1007/BF02368235 |
| ClassificationCodes | R318.01 |
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| Copyright | Shanghai University and Springer-Verlag Berlin Heidelberg 2013 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | osteon bone fluid flow 92C10 transverse isotropy R318.01 poroelasticity pressure 74L15 |
| Language | English |
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| Notes | 31-1650/O1 osteon, poroelasticity, transverse isotropy, bone fluid flow, pressure Xiao-gang WU , Wei-yi CHEN , Dan-xia WANG （1 2. College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China; College of Mathematics, Taiyuan University of Technology Taiyuan 030024, P. R. China） An extended and reasonable stress boundary condition at an osteon exte- rior wall is presented to solve the model proposed by Remond and Naili. The obtained pressure and fluid velocity solutions are used to investigate the osteonal poroelastic behaviors. The following results are obtained. （i） Both the fluid pressure and the velocity amplitudes are proportional to the strain amplitude and the loading frequency. （ii） In the physiological loading state, the key role governing the poroelastic behaviors of the osteon is the strain rate. （iii） At the osteon scale, the pressure is strongly affected by the permeability variations, whereas the fluid velocity is not. ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| PublicationTitle | Applied mathematics and mechanics |
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| PublicationYear | 2013 |
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| References | Biot (CR1) 1955; 26 Rémond, Naili (CR4) 2005; 32 Beno, Yoon, Cowin, Fritton (CR13) 2006; 39 Nguyen, Lemaire, Naili (CR8) 2010; 32 Nguyen, Lemaire, Naili (CR15) 2011; 10 Nguyen, Lemaire, Naili (CR6) 2009; 337 Zeng, Cowin, Weinbaum (CR2) 1994; 22 Zhang, Weinbaum, Cowin (CR3) 1998; 35 Cowin (CR11) 2002; 2 Nguyen, Lemaire, Naili (CR7) 2009; 5 Fritton, Kenneth, Rubin (CR10) 2000; 33 Rémond, Naili, Lemaire (CR5) 2008; 7 Abousleiman, Cui (CR9) 1998; 35 Turner (CR12) 1998; 23 Nguyen, Lemaire, Naili (CR14) 2009; 5 T Beno (1680_CR13) 2006; 39 Y Zeng (1680_CR2) 1994; 22 S P Fritton (1680_CR10) 2000; 33 V H Nguyen (1680_CR7) 2009; 5 Y Abousleiman (1680_CR9) 1998; 35 V H Nguyen (1680_CR14) 2009; 5 D Zhang (1680_CR3) 1998; 35 A Rémond (1680_CR5) 2008; 7 V H Nguyen (1680_CR6) 2009; 337 V H Nguyen (1680_CR15) 2011; 10 C H Turner (1680_CR12) 1998; 23 V H Nguyen (1680_CR8) 2010; 32 M A Biot (1680_CR1) 1955; 26 S C Cowin (1680_CR11) 2002; 2 A Rémond (1680_CR4) 2005; 32 |
| References_xml | – volume: 26 start-page: 182 year: 1955 end-page: 185 ident: CR1 article-title: Theory of elasticity and consolidation for a porous anisotropic solid publication-title: Journal of Applied Physics doi: 10.1063/1.1721956 – volume: 32 start-page: 384 year: 2010 end-page: 390 ident: CR8 article-title: Poroelastic behavior of cortical bone under harmonic axial loading: a finite element study at the osteonal scale publication-title: Medical Engineering & Physics doi: 10.1016/j.medengphy.2010.02.001 – volume: 2 start-page: 256 issue: 3 year: 2002 end-page: 260 ident: CR11 article-title: Mechanosensation and fluid transport in living bone publication-title: Journal of Musculoskeletal and Neuronal Interactions – volume: 39 start-page: 2378 year: 2006 end-page: 2387 ident: CR13 article-title: Estimation of bone permeability using accurate microstructural measurements publication-title: Journal of Biomechanics doi: 10.1016/j.jbiomech.2005.08.005 – volume: 5 start-page: 205 year: 2009 end-page: 222 ident: CR7 article-title: Anisotropic poroelastic hollow cylinders with damaged periphery under harmonically axial loadings: relevance to bone osteons publication-title: Multidiscipline Modeling in Materials and Structures doi: 10.1163/157361109789017005 – volume: 5 start-page: 205 year: 2009 end-page: 222 ident: CR14 article-title: Anisotropic poroelastic hollow cylinders with damaged periphery under harmonically axial loadings: relevance to bone osteons publication-title: Multidiscipline Modeling in Materials and Structures doi: 10.1163/157361109789017005 – volume: 33 start-page: 317 year: 2000 end-page: 325 ident: CR10 article-title: Quantifying the strain history of bone: spatial uniformity and self-similarity of low magnitude strains publication-title: Journal of Biomechanics doi: 10.1016/S0021-9290(99)00210-9 – volume: 10 start-page: 963 year: 2011 end-page: 972 ident: CR15 article-title: Influence of interstitial bone microcracks on strain-induced fluid flow publication-title: Biomechanics and Modeling in Mechanobiology doi: 10.1007/s10237-011-0287-1 – volume: 35 start-page: 4981 issue: 34–35 year: 1998 end-page: 4997 ident: CR3 article-title: On the calculation of bone pore water pressure due to mechanical loading publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(98)00105-X – volume: 32 start-page: 645 year: 2005 end-page: 651 ident: CR4 article-title: Transverse isotropic poroelastic osteon model under cyclic loading publication-title: Mechanics Research Communications doi: 10.1016/j.mechrescom.2004.10.003 – volume: 23 start-page: 399 year: 1998 end-page: 407 ident: CR12 article-title: Three rules for bone adaptation to mechanical stimuli publication-title: Bone doi: 10.1016/S8756-3282(98)00118-5 – volume: 7 start-page: 487 year: 2008 end-page: 495 ident: CR5 article-title: Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study publication-title: Biomechanics and Modeling in Mechanobiology doi: 10.1007/s10237-007-0111-0 – volume: 337 start-page: 268 year: 2009 end-page: 276 ident: CR6 article-title: Numerical study of deformation induced fluid flows in periodic osteonal matrix under harmonic axial loading publication-title: Comptes Rendus Mécanique doi: 10.1016/j.crme.2009.06.033 – volume: 35 start-page: 4905 year: 1998 end-page: 4929 ident: CR9 article-title: Poroelastic solutions in transversely isotropic media for wellbore and cylinder publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(98)00101-2 – volume: 22 start-page: 280 issue: 3 year: 1994 end-page: 292 ident: CR2 article-title: A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon publication-title: Annals of Biomedical Engineering doi: 10.1007/BF02368235 – volume: 337 start-page: 268 year: 2009 ident: 1680_CR6 publication-title: Comptes Rendus Mécanique doi: 10.1016/j.crme.2009.06.033 – volume: 5 start-page: 205 year: 2009 ident: 1680_CR7 publication-title: Multidiscipline Modeling in Materials and Structures doi: 10.1163/157361109789017005 – volume: 23 start-page: 399 year: 1998 ident: 1680_CR12 publication-title: Bone doi: 10.1016/S8756-3282(98)00118-5 – volume: 22 start-page: 280 issue: 3 year: 1994 ident: 1680_CR2 publication-title: Annals of Biomedical Engineering doi: 10.1007/BF02368235 – volume: 35 start-page: 4905 year: 1998 ident: 1680_CR9 publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(98)00101-2 – volume: 32 start-page: 645 year: 2005 ident: 1680_CR4 publication-title: Mechanics Research Communications doi: 10.1016/j.mechrescom.2004.10.003 – volume: 39 start-page: 2378 year: 2006 ident: 1680_CR13 publication-title: Journal of Biomechanics doi: 10.1016/j.jbiomech.2005.08.005 – volume: 26 start-page: 182 year: 1955 ident: 1680_CR1 publication-title: Journal of Applied Physics doi: 10.1063/1.1721956 – volume: 32 start-page: 384 year: 2010 ident: 1680_CR8 publication-title: Medical Engineering & Physics doi: 10.1016/j.medengphy.2010.02.001 – volume: 10 start-page: 963 year: 2011 ident: 1680_CR15 publication-title: Biomechanics and Modeling in Mechanobiology doi: 10.1007/s10237-011-0287-1 – volume: 35 start-page: 4981 issue: 34–35 year: 1998 ident: 1680_CR3 publication-title: International Journal of Solids and Structures doi: 10.1016/S0020-7683(98)00105-X – volume: 33 start-page: 317 year: 2000 ident: 1680_CR10 publication-title: Journal of Biomechanics doi: 10.1016/S0021-9290(99)00210-9 – volume: 7 start-page: 487 year: 2008 ident: 1680_CR5 publication-title: Biomechanics and Modeling in Mechanobiology doi: 10.1007/s10237-007-0111-0 – volume: 2 start-page: 256 issue: 3 year: 2002 ident: 1680_CR11 publication-title: Journal of Musculoskeletal and Neuronal Interactions – volume: 5 start-page: 205 year: 2009 ident: 1680_CR14 publication-title: Multidiscipline 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| Snippet | An extended and reasonable stress boundary condition at an osteon exte- rior wall is presented to solve the model proposed by Remond and Naili. The obtained... An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by Rémond and Naili. The obtained... An extended and reasonable stress boundary condition at an osteon exterior wall is presented to solve the model proposed by RACOmond and Naili. The obtained... |
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| SubjectTerms | Amplitudes Applications of Mathematics Biocompatibility Biomedical materials Classical Mechanics Computational fluid dynamics Fluid flow Fluid- and Aerodynamics Fluids Mathematical Modeling and Industrial Mathematics Mathematical models Mathematics Mathematics and Statistics Partial Differential Equations Walls 单位 孔隙 应力边界条件 弹性行为 数学模型 检查 流体压力 流体速度 |
| Title | Mathematical osteon model for examining poroelastic behaviors |
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