Ion induced deformation of soft tissue
Identifieur interne : 001F78 ( Istex/Curation ); précédent : 001F77; suivant : 001F79Ion induced deformation of soft tissue
Auteurs : T. G. Myers [Royaume-Uni] ; G. K. Aldis [Australie] ; S. Naili [France]Source :
- Bulletin of Mathematical Biology [ 0092-8240 ] ; 1994.
English descriptors
- KwdEn :
- Absolute temperature, Activity coefficient, Articular, Articular cartilage, Behaviour, Boundary condition, Bovine articular cartilage, Cartilage, Charge density, Charge shielding, Chemical expansion stress, Chemical mass, Chemical potentials, Coefficient, Concentration condition, Concentration curves, Concentration equation, Cornea1 stroma, Deformation, Diarthrodial joints, Different values, Displacement equation, Displacement equations, Dominant term, Drag coefficient, Eisenberg, Elastic modulus, Equilibrium value, Experimental data, Exponential form, External bath, Final state, Final values, Fluid phase, Fluid pressure, Fluid stress, Free ions, Full system, Full theory, Good approximation, Grodzinsky, Hypertonic, Hypertonic bathing solution, Infinitesimal theory, Initial concentration, Initial displacement, Isometric tension states, Large times, Linear system, Material parameters, Myers, Numerical results, Osmotic coefficient, Parameter values, Phase velocities, Physiological concentrations, Physiological state, Physiological values, Present chemical expansion stress, Present theory, Present work, Pressure field, Previous section, Pure water, Pure water bath, Reference configuration, Reference state, Relative magnitude, Salt bath, Salt solution, Soft tissue, Soft tissues, Solid line, Solid matrix, Solid stress, Solution method, Spherical geometries, Spherical geometry, Spherical sample, Stress relaxation, Time course, Tissue water volume, Total stress, Triphasic, Triphasic theory, Volume fraction, Water phases.
- Teeft :
- Absolute temperature, Activity coefficient, Articular, Articular cartilage, Behaviour, Boundary condition, Bovine articular cartilage, Cartilage, Charge density, Charge shielding, Chemical expansion stress, Chemical mass, Chemical potentials, Coefficient, Concentration condition, Concentration curves, Concentration equation, Cornea1 stroma, Deformation, Diarthrodial joints, Different values, Displacement equation, Displacement equations, Dominant term, Drag coefficient, Eisenberg, Elastic modulus, Equilibrium value, Experimental data, Exponential form, External bath, Final state, Final values, Fluid phase, Fluid pressure, Fluid stress, Free ions, Full system, Full theory, Good approximation, Grodzinsky, Hypertonic, Hypertonic bathing solution, Infinitesimal theory, Initial concentration, Initial displacement, Isometric tension states, Large times, Linear system, Material parameters, Myers, Numerical results, Osmotic coefficient, Parameter values, Phase velocities, Physiological concentrations, Physiological state, Physiological values, Present chemical expansion stress, Present theory, Present work, Pressure field, Previous section, Pure water, Pure water bath, Reference configuration, Reference state, Relative magnitude, Salt bath, Salt solution, Soft tissue, Soft tissues, Solid line, Solid matrix, Solid stress, Solution method, Spherical geometries, Spherical geometry, Spherical sample, Stress relaxation, Time course, Tissue water volume, Total stress, Triphasic, Triphasic theory, Volume fraction, Water phases.
Abstract
In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.
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DOI: 10.1016/0092-8240(94)00025-8
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Aldis</name><affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia</mods:affiliation><country xml:lang="fr">Australie</country><wicri:regionArea>Department of Mathematics, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: g-aldis@adfa.edu.au</mods:affiliation><country wicri:rule="url">Australie</country></affiliation></author><author><name sortKey="Naili, S" sort="Naili, S" uniqKey="Naili S" first="S." last="Naili">S. Naili</name><affiliation wicri:level="1"><mods:affiliation>Universite de Paris, 12 Val de Marne, Laboratoire de Mecanique Physique, 94010 Creteil Cedex, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Universite de Paris, 12 Val de Marne, Laboratoire de Mecanique Physique, 94010 Creteil Cedex</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A70D648E38957BF3A43368A5F2E56A7037AC4E04</idno><date when="1994" year="1994">1994</date><idno type="doi">10.1016/0092-8240(94)00025-8</idno><idno type="url">https://api.istex.fr/document/A70D648E38957BF3A43368A5F2E56A7037AC4E04/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001F78</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001F78</idno><idno type="wicri:Area/Istex/Curation">001F78</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Ion induced deformation of soft tissue</title><author><name sortKey="Myers, T G" sort="Myers, T G" uniqKey="Myers T" first="T. G." last="Myers">T. G. Myers</name><affiliation wicri:level="1"><mods:affiliation>OCIAM, Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, U.K.</mods:affiliation><country xml:lang="fr">Royaume-Uni</country><wicri:regionArea>OCIAM, Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB</wicri:regionArea></affiliation></author><author><name sortKey="Aldis, G K" sort="Aldis, G K" uniqKey="Aldis G" first="G. K." last="Aldis">G. K. Aldis</name><affiliation wicri:level="1"><mods:affiliation>Department of Mathematics, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia</mods:affiliation><country xml:lang="fr">Australie</country><wicri:regionArea>Department of Mathematics, University College, University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600</wicri:regionArea></affiliation><affiliation wicri:level="1"><mods:affiliation>E-mail: g-aldis@adfa.edu.au</mods:affiliation><country wicri:rule="url">Australie</country></affiliation></author><author><name sortKey="Naili, S" sort="Naili, S" uniqKey="Naili S" first="S." last="Naili">S. Naili</name><affiliation wicri:level="1"><mods:affiliation>Universite de Paris, 12 Val de Marne, Laboratoire de Mecanique Physique, 94010 Creteil Cedex, France</mods:affiliation><country xml:lang="fr">France</country><wicri:regionArea>Universite de Paris, 12 Val de Marne, Laboratoire de Mecanique Physique, 94010 Creteil Cedex</wicri:regionArea></affiliation></author></analytic><monogr></monogr><series><title level="j">Bulletin of Mathematical Biology</title><title level="j" type="abbrev">YBULM</title><idno type="ISSN">0092-8240</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1994">1994</date><biblScope unit="volume">57</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="77">77</biblScope><biblScope unit="page" to="98">98</biblScope></imprint><idno type="ISSN">0092-8240</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0092-8240</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Absolute temperature</term><term>Activity coefficient</term><term>Articular</term><term>Articular cartilage</term><term>Behaviour</term><term>Boundary condition</term><term>Bovine articular cartilage</term><term>Cartilage</term><term>Charge density</term><term>Charge shielding</term><term>Chemical expansion stress</term><term>Chemical mass</term><term>Chemical potentials</term><term>Coefficient</term><term>Concentration condition</term><term>Concentration curves</term><term>Concentration equation</term><term>Cornea1 stroma</term><term>Deformation</term><term>Diarthrodial joints</term><term>Different values</term><term>Displacement equation</term><term>Displacement equations</term><term>Dominant term</term><term>Drag coefficient</term><term>Eisenberg</term><term>Elastic modulus</term><term>Equilibrium value</term><term>Experimental data</term><term>Exponential form</term><term>External bath</term><term>Final state</term><term>Final values</term><term>Fluid phase</term><term>Fluid pressure</term><term>Fluid stress</term><term>Free ions</term><term>Full system</term><term>Full theory</term><term>Good approximation</term><term>Grodzinsky</term><term>Hypertonic</term><term>Hypertonic bathing solution</term><term>Infinitesimal theory</term><term>Initial concentration</term><term>Initial displacement</term><term>Isometric tension states</term><term>Large times</term><term>Linear system</term><term>Material parameters</term><term>Myers</term><term>Numerical results</term><term>Osmotic coefficient</term><term>Parameter values</term><term>Phase velocities</term><term>Physiological concentrations</term><term>Physiological state</term><term>Physiological values</term><term>Present chemical expansion stress</term><term>Present theory</term><term>Present work</term><term>Pressure field</term><term>Previous section</term><term>Pure water</term><term>Pure water bath</term><term>Reference configuration</term><term>Reference state</term><term>Relative magnitude</term><term>Salt bath</term><term>Salt solution</term><term>Soft tissue</term><term>Soft tissues</term><term>Solid line</term><term>Solid matrix</term><term>Solid stress</term><term>Solution method</term><term>Spherical geometries</term><term>Spherical geometry</term><term>Spherical sample</term><term>Stress relaxation</term><term>Time course</term><term>Tissue water volume</term><term>Total stress</term><term>Triphasic</term><term>Triphasic theory</term><term>Volume fraction</term><term>Water phases</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Absolute temperature</term><term>Activity coefficient</term><term>Articular</term><term>Articular cartilage</term><term>Behaviour</term><term>Boundary condition</term><term>Bovine articular cartilage</term><term>Cartilage</term><term>Charge density</term><term>Charge shielding</term><term>Chemical expansion stress</term><term>Chemical mass</term><term>Chemical potentials</term><term>Coefficient</term><term>Concentration condition</term><term>Concentration curves</term><term>Concentration equation</term><term>Cornea1 stroma</term><term>Deformation</term><term>Diarthrodial joints</term><term>Different values</term><term>Displacement equation</term><term>Displacement equations</term><term>Dominant term</term><term>Drag coefficient</term><term>Eisenberg</term><term>Elastic modulus</term><term>Equilibrium value</term><term>Experimental data</term><term>Exponential form</term><term>External bath</term><term>Final state</term><term>Final values</term><term>Fluid phase</term><term>Fluid pressure</term><term>Fluid stress</term><term>Free ions</term><term>Full system</term><term>Full theory</term><term>Good approximation</term><term>Grodzinsky</term><term>Hypertonic</term><term>Hypertonic bathing solution</term><term>Infinitesimal theory</term><term>Initial concentration</term><term>Initial displacement</term><term>Isometric tension states</term><term>Large times</term><term>Linear system</term><term>Material parameters</term><term>Myers</term><term>Numerical results</term><term>Osmotic coefficient</term><term>Parameter values</term><term>Phase velocities</term><term>Physiological concentrations</term><term>Physiological state</term><term>Physiological values</term><term>Present chemical expansion stress</term><term>Present theory</term><term>Present work</term><term>Pressure field</term><term>Previous section</term><term>Pure water</term><term>Pure water bath</term><term>Reference configuration</term><term>Reference state</term><term>Relative magnitude</term><term>Salt bath</term><term>Salt solution</term><term>Soft tissue</term><term>Soft tissues</term><term>Solid line</term><term>Solid matrix</term><term>Solid stress</term><term>Solution method</term><term>Spherical geometries</term><term>Spherical geometry</term><term>Spherical sample</term><term>Stress relaxation</term><term>Time course</term><term>Tissue water volume</term><term>Total stress</term><term>Triphasic</term><term>Triphasic theory</term><term>Volume fraction</term><term>Water phases</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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