Bone poroelasticity

Bone Mechanics Handbook, Second Edition

Volumn , Issue , 2001, Pages 23-1-23-31

  Cowin, Stephen C ^a  

^a CITY COLLEGE OF NEW YORK   (United States)

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EID: 85032851289     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (166)

1. Weinbaum, S., Cowin, S. C., and Zeng, Yu, A model for the fluid shear stress excitation of membrane ion channels in osteocytic processes due to bone strain, in 1991 Advances in Bioengineering, Vanderby, Jr., R., Ed., American Society of Mechanical Engineers, New York, 1991, 317-320.
2. Weinbaum, S., Cowin, S. C., and Zeng, Yu, A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses, J. Biomech., 27, 339-360, 1994.
3. Moss, M. L. and Cowin, S. C., Mechanosensory mechanisms in bone, in Textbook of Tissue Engineering, Lanza, R., Langer, R., and Chick, W., Eds., R.G. Landes, Austin, 1997, 645-659.
4. Burger, E. L., Klein Nulend, J., and Cowin, S. C., Mechanotransduction in bone, in Advances in Organ Biology, Zaidi, M., Ed., JAI Press, Stamford, CT, Vol. 5a, 1998, 107-118.
5. Biot, M. A., Le problème de la consolidation des matières argileuses sous une charge, Ann. Soc. Sci. Bruxelles, B55, 110-113, 1935.
6. Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys., 12, 155-164, 1941.
7. de Boer, R., Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory, Appl. Mech. Rev., 49, 201-262, 1996.
8. Li, G., Bronk, J. T., An, K. N., and Kelly, P. J., Permeability of cortical bone of canine tibiae, Microcirc. Res., 34, 302-310, 1987.
9. Miller, S. C. and Jee, W. S. S., Bone lining cells, in Bone, Vol. 4, Bone Metabolism and Mineralization, Hall, B. K., Ed., CRC Press, Boca Raton, FL, 1992, 1-19.
10. Chole, R. A. and Tinling, S. P., Incomplete coverage of mammalian bone cell matrix by lining cells, Ann. Otol. Rhinol. Laryngol., 102, 543-550, 1993.
11. Bernard, C., Leçons sur les phénomènes de la vie communs aux animaux et aux végétaux, Vol. 1, Ballière et Fils, Paris, 1878, 113.
12. Howard, J. E., Present knowledge of parathyroid function with especial emphasis on its limitations, in Bone Structure and Metabolism, Wolsternholme, G. E. W. and O’Connor, C. M., Eds., Little, Brown, Boston, 1959, 206-222.
13. Neuman, W. F., Fed. Proc. Fed. Am. Soc. Exp. Biol., 28, 1846, 1969.
14. Neuman, W. F. and Ramp, W. K., The concept of a bone membrane: Some implications, in Cellular Mechanisms for Calcium Transfer and Homeostasis, Academic Press, New york, 1971, 197-209.
15. Neuman, M. W., Bone blood equilibrium, Cal. Tissue Int., 34, 117-120, 1982.
16. Soares, A. M. V., Arana-Chavez, V. E., Reid, A. R., and Katchburian, B., Lanthanum tracer and freeze-fracture studies suggest that compartmentalization of early bone matrix may be related to initial mineralization, J. Anat., 181, 343-356, 1992.
17. Neuman, W. F. and Neuman, M. W., The Chemical Dynamics of Bone, University of Chicago Press, Chicago, 1958.
18. Hillsley, M. V. and Frangos, J. A., Osteoblast hydraulic conductivity is regulated by calcitonin and parathyroid hormone, J. Bone Miner. Res., 11, 114-124, 1996.
19. Zhang, D., Weinbaum, S., and Cowin, S. C., Estimates of the peak pressures in the bone pore water, J. Biomech. Eng., 120, 697-703, 1998.
20. Weinbaum, S., Private communication, 1998.
21. Seliger, W. G., Tissue fluid movement in compact bone, Anat. Rec., 166, 247-256, 1969.
22. Doty, S. D. and Schofield, B. H., Metabolic and structural changes within osteocytes of rat bone, in Calcium, Parathyroid Hormone and the Calcitonins, Talmage, B. V. and Munson, P. L., Eds, Excerpta Medica, Amsterdam, 1972, 353-364.
23. Morris, M. A., Lopez-Curato, J. A., Hughes, S. P. F., An, K. N., Bassingthwaighte, J. B. and Kelly, P. J., Fluid spaces in canine bone and marrow, Microvasc. Res., 23, 188-200, 1982.
24. Dillaman, R. M., Movement of ferritin in the 2 day-old chick femur, Anat. Rec., 209, 445-453, 1984.
25. Tanaka, T. and Sakano, A., Differences in permeability of microperoxidase and horseradish peroxidase into the alveolar bone of developing rats, J. Dent. Res., 64, 870-876, 1985.
26. Simonet, W. T., Bronk, J. T., Pinto, M. R., Williams, E. A., Meadows, T. H., and Kelly, P. J., Cortical and cancellous bone: age-related changes in morphological features, fluid spaces, and calcium homeostasis in dogs, Mayo Clin. Proc., 63, 154-160, 1988.
27. Doty, S. D., Private communication, 1997.
28. Knothe Tate, M. L., Niederer, P., and Knothe, U., In vivo tracer transport through the lacunocanal-icular system of rat bone in an environment devoid of mechanical loading, Bone, 22, 107-117, 1998.
29. Asasaka, N., Kondo, T., Goto, T., Kido, M. A., Nagata, E., and Tanaka, T., Differences in the transport systems between cementocytes and osteocytes in rats using microperoxidase as a tracer, Arch. Oral Biol., 37, 363-368, 1992.
30. Montgomery, R. J., Sutker, B. D., Bronk, J. T., Smith, S. R., and Kelly, P. J., Interstitial fluid flow in cortical bone, Microvasc. Res., 23, 188-200, 1988.
31. Williams, S. M. and McCarthy, I. D., Distributed model of blood-bone exchange, J. Biomed. Eng., 8, 235-243, 1986.
32. McCarthy, I. D. and Yang, L., A distributed model of exchange processes within the osteon, J. Biomech., 25, 441-450, 1992.
33. Martin, B., Mathematical model for the mineralization of bone, J. Orthop. Res., 12, 375-383, 1994.
34. Haines, R. W., Mehta, L., and Mohiuddin, A., Nutrition of interstitial lamellae of bone, Anat. Anz.(Jena), 154, 233-236, 1982.
35. Curtis, T. A., Ashrafti, S. H., and Weber, D. F., Canalicular communication in the cortices of human long bone, Anat. Rec., 212, 336-344, 1985.
36. Qiu, S.-J., Boyce, T. M., and Schaffler, M. B., Osteocyte loss and microdamage in aging human compact bone, Trans. Orthop. Res. Soc., 22, 88, 1997.
37. Cowin, S. C., Weinbaum, S., and Zeng, Yu, A case for bone canaliculi as the anatomical site of strain-generated potentials, J. Biomech., 28, 1281-1296, 1995.
38. Neuman, W. F., Toribara, T. Y., and Mulrvan, B. J., The surface chemistry of bone. VII, The hydration shell, J. Am. Chem. Soc., 75, 4239-4242, 1953.
39. Glimcher, M. J., The nature of the mineral phase in bone: biological and clinical implications, in Metabolic Bone Disease, Academic Press, New York, 23-50, 1998.
40. Bryant, J. D., The effect of impact on the marrow pressure in long bones, J. Biomech., 16, 659-665, 1983.
41. Bryant, J. D., On the mechanical function of marrow in long bones, Eng. Med., 17, 55-58, 1988.
42. Sobokova, E., Hubra, A., Kiefman, J., and Sobotka, Z., Rheological behavior of bone marrow, Rheol. Acta, 26 (Suppl.), 467-469, 1988.
43. Arramon, Y. P. and Cowin, S. C., Hydraulic stiffening of cancellous bone, FORMA, 12, 209-221, 1997.
44. Hashin, Z. and Shtrikman, S., Note on the variational approach to the theory of composite elastic materials, J. Franklin Inst., 271, 336-341, 1961.
45. Hill, R., Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids, 11, 357-372, 1963.
46. Christensen, R. M., Mechanics of Composite Materials, Wiley, New York, 1979.
47. Nemat-Nasser, S. and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials, North-Holland, Amsterdam, 1993.
48. Nur, A. and Byerlee, J. D., An exact effective stress-strain law for elastic deformation of rock with fluids, J. Geophys. Res., 76, 6414-6419, 1971.
49. Rice, J. R. and Cleary, M. P., Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents, Rev. Geophys. Space Phys., 14, 227-241, 1976.
50. Carroll, M. M., An effective stress-strain law for anisotropic elastic deformation, J. Geophys. Res., 84, 7510-7512, 1979.
51. Rudnicki, J. W., Effect of pore fluid diffusion on deformation and failure of rock, in Mechanics of Geomaterials, Bazant, Z., Ed., Wiley, New York, 1985, 315-347.
52. Thompson, M. and Willis, J. R., A reformation of the equations of anisotropic poroelasticity, J. Appl. Mech., 58, 612-616, 1991.
53. Kenyon, D. E., Consolidation in compressible mixtures, J. Appl. Mech., 45, 727-732, 1978.
54. Kenyon, D. E., Consolidation in transversely isotropic solids, J. Appl. Mech., 46, 65-70, 1979.
55. Kenyon, D. E., A mathematical model of water flux through aortic tissue, Bull. Math. Biol., 41, 79-90, 1979.
56. Simon, B. R., Wu, J. S. S., Carlton, M. W., Kazarian, L. E., France, E. P., Evans, J. H., and Zienkiewicz, O. C., Poroelastic dynamic structural models of rhesus spinal motion segments, Spine, 10, 494-507, 1985.
57. Truesdell, C. A. and Toupin, R. A., The classical field theories, in Handbuch der Physik, Flugge, S., Ed., Springer Verlag, Berlin, 1960.
58. Truesdell, C. A., Sulle basi della termomeccania, Rend. Lincei, 22, 33-38, 1158-1166, 1957.
59. Bowen, R. M., Toward a thermodynamics and mechanics of mixtures, Arch. Ration. Mech. Anal., 24, 370-403, 1967.
60. Atkin, R. J. and Craine, R. E., Continuum theories of mixtures: basic theory and historical development, Q. J. Mech. Appl. Math., 29, 209-244, 1976.
61. Atkin, R. J. and Craine, R. E., Continuum theories of mixtures: applications, J. Inst. Math. Appl., 17, 153-207, 1976.
62. Bowen, R. M., Theory of mixtures, in Continuum Physics, Vol. III, Mixtures and EM Field Theories, Academic Press, New York, 1-127, 1976.
63. Bowen, R. M., Incompressible porous media models by use of the theory of mixtures, Int. J. Eng. Sci., 18, 1129-1148, 1980.
64. Bowen, R. M., Compressible porous media models by use of the theory of mixtures, Int. J. Eng. Sci., 20, 697-735, 1982.
65. Müller, I., A thermodynamic theory of mixtures, Arch. Ration. Mech. Anal., 28, 1-39, 1968.
66. Müller, I., Thermodynamics, Pitman, Boston, 1985.
67. Lai, W. M., Hou, J. S., and Mow, V. C., A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Eng., 113, 245-258, 1991.
68. Gu, W. Y., Lai, W. M., and Mow, V. C., Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage, J. Biomech., 26, 709-723, 1993.
69. Lanir, Y., Biorheology and fluid flux in swelling tissues, I: Bicomponent theory for small deformations, including concentration effects, Biorheology, 24, 173-187, 1987.
70. Mak, A. F. T., Huang, L., and Wang, Q., A biphasic poroelastic analysis of the flow-dependent subcutaneous tissue pressure and compaction due to epidermal loadings: issues in pressure sores, J. Biomech. Eng., 116, 421-429, 1994.
71. Frijns, A. J. H., Huyghe, J. M., and Jannsen, J. D., A validation of the quadriphasic mixture theory for intervertebral disc tissue, Int. J. Eng. Sci., 35, 1419-1429, 1997.
72. Vankan, W. J., Huyghe, J. M., Janssen, J. D., and Huson, A., Poroelasticity of saturated solids with an application to blood perfusion, Int. J. Eng. Sci., 34, 1019-1031, 1996.
73. Vankan, W. I., Huyghe, J. M., Janssen, T J. D., Huson, A., Hacking, W. J. G., and Schreiner, W., Finite element analysis of blood flow through biological tissue, Int. J. Eng. Sci., 35, 375-385, 1997.
74. Huyghe, J. M., Oomens, C. W., van Campen, D. H., and Heethaar, R. M., Low Reynolds number steady state flow through a branching network of rigid vessels, Biorheology, 26, 55-71, 1989.
75. Huyghe, J. M. and van Campen, D. H., Finite deformation theory of hierarchically arranged porous solids: I. Balance of mass and momentum, Int. J. Eng. Sci., 33, 1861-1871, 1995.
76. Huyghe, J. M. and van Campen, D. H., Finite deformation theory of hierarchically arranged porous solids: II. Constitutive behavior, Int. J. Eng. Sci., 33, 1873-1886, 1995.
77. Huyghe, J. M. and Janssen, J. D., Quadriphasic mechanics of swelling incompressible porous media, Int. J. Eng. Sci., 34, 793-802, 1997.
78. Mow, V. C., Kuei, S. C., Lai, W. L., and Armstrong, C., Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments, J. Biomech. Eng., 102, 73-84, 1980.
79. Mow, V. C. and Lai, W. L., Recent developments in synovial joint mechanics, SIAM Rev., 22, 275-317, 1980.
80. Coleman, B. D. and Noll, W., The thermodynamics of elastic materials with heat conduction, Arch. Ration. Mech. Anal., 13, 167-178, 1963.
81. Goodman, M. A. and Cowin, S. C., A continuum theory for granular materials, Arch. Ration. Mech. Anal., 44, 249-266, 1972.
82. Cowin, S. C. and Hegedus, D.M., Bone remodeling. I: A theory of adaptive elasticity, J. Elasticity, 6, 313-325, 1976.
83. Rivlin, R. S., Comments on some recent researches in thermodynamics, Recent Adv. Eng. Sci., 8, I-23, 1973.
84. Rivlin, R. S., The thermodynamics of materials with fading memory, in Theoretical Rheology, Hotton. J. F., Pearson, J. R. A., and K. Walters, Eds., Academic Science Publishers, New York, 1975, 83-103.
85. Lavenda, B. H., Thermodynamics of Irreversible Processes, Constable, London, 1978; reprinted Dover, New York, 1993.
86. Woods, L. C., Beware of axiomatics in applied mathematics, Bull. Inst. Math. Appl., 9, 40-44, 1973.
87. Woods, L. C., The bogus axioms of continuum mechanics, Bull. Inst. Math. Appl., 17, 98-102, 1981.
88. Biot, M. A., Generalized Lagrangian equations of non-linear reaction-diffusion, Chem. Phys., 66, II-26, 1982.
89. Casey, J., On elastic-thermo-plastic materials at finite deformations, Int. J. Plasticity, 14, 173-191, 1998.
90. Krishnaswamy, S. and Batra, R. C., A thermomechanical theory of solid-fluid mixtures, Math. Mech. Solids, 2, 143-151, 1997.
91. Huyghe, J. M., Private communication, 1998.
92. Slattery, J. C., Flow of viscoelastic fluids through porous media, A. I. Ch. E. J., 13, 1066-1071, 1967.
93. Whitaker, S., Diffusion and dispersion in porous media, A. I. Ch. E. J., 13, 420-427, 1967.
94. Burridge, R. and Keller, J. B., Poroelasticity equations derived from microstructure, J. Acoust. Soc. Am., 70, 1140-1146, 1981.
95. Cowin, S. C., Summary of discussions on fluid infiltrated geomaterials, in Mechanics of Geomaterials, Z. P Bazant, Ed., Wiley, New York, 1985, 581-582.
96. Piekarski, K. and Munro, M., Transport mechanism operating between blood supply and osteocytes in long bones, Nature, 269(5623), 80-82, 1977.
97. Munro, M. and Piekarski, K., Stress induced radial pressure gradients in liquid-filled multiple concentric cylinders, J. Appl. Mech., 99, 218-221, 1977.
98. Kufahl, R. H. and Saha, S., A theoretical model for stress-generated fluid flow in the canaliculi-lacunae network in bone tissue, J. Biomech., 23, 171-180, 1990.
99. Detournay, E. and Cheng, H.-D.A., Fundamentals of poroelasticity, in Comprehensive Rock Engineering: Principles, Practice & Projects, Hudson, J. A., Ed., Pergamon, New York, 1993, 113-171.
100. Biot, M. A. and Willis, D. G., The elastic coefficients of the theory of consolidation, J. Appl. Mech., 24, 594-601, 1957.
101. Simon, B. R., Multiphase poroelastic finite element models for soft tissue structures, Appl. Mech. Rev., 45, 191-218, 1992.
102. Coussy, O., Mechanics of Porous Continua, Wiley, New York, 1995.
103. Skempton, A. W., The pore pressure coefficients A and B, Géotechnique, 4, 143-147, 1954.
104. Gurtin, M. E., The linear theory of elasticity, in Handbuch der Physik, S. Flügge, Ed., Springer Verlag, Berlin, 1972, 1-296.
105. Sandhu, R. S. and Wilson, E. L., Finite element analysis of seepage in elastic media, J. Eng. Mech. Div. Am. Soc. Civ. Eng., 95, 641-652, 1969.
106. Ghaboussi, J. and Wilson, E. L., Flow of compressible fluid in porous elastic media, Int. J. Numer. Methods Eng., 5, 419-442, 1973.
107. Spilker, R. L., Suh, J. K., Vermilyea, M. E., and Maxian, T. A., Alternate hybrid, mixed and penalty finite formulations for the biphasic model of soft hydrated tissues, in Biomechanics of Diarthrodial Joints, Vol. 1, Mow, V. C., Ratcliffe, A. and Woo, S. L. Y., Eds., Springer, New York, 1990, 400-435.
108. Hibbitt, D., Karlson B., and Sorensen, P., ABAQUS Theory Manual, Version 5.5, Hibbitt, Karlson & Sorensen, Inc., 1995, pp. 2.7.1-1 to 2.7.5-2.
109. Vankan, W. J., Huyghe, J. M., Drost, M. R., Janssen J. D., and Huson A., A finite element model for hierarchical porous media, Int. J. Numer. Methods Eng., 40, 1019-1031, 1997.
110. Chandrasekharaiah, D. S. and Cowin, S. C., Unified solutions for theories of thermoelasticity and poroelasticity, J. Elasticity, 21, 121-126, 1989.
111. Chandrasekharaiah, D. S. and Cowin, S. C., A complete solution for a unified system of field equations of thermoelasticity and poroelasticity, Acta Mech., 99, 225-233, 1993.
112. Simon, B. R., Zienkiewicz, O. C., and Paul, D. K., An analytical solution for the transient response of saturated porous elastic solids, Int. J. Numer. Anal. Methods Geomech., 8, 391-398, 1984.
113. Zhang, D. and Cowin, S. C., Oscillatory bending of a poroelastic beam, J. Mech. Phys. Solids, 42, 1575-1599, 1994.
114. Zhang, D. and Cowin, S. C., Load carrying capacity of the pore pressure in a poroelastic beam subject to oscillatory excitation, in Mechanics of Poroelastic Media, A. P. S. Selvaduri, Ed., Solid Mechanics and Its Application Series, Vol. 35, Wolters Kluwer Academic Publishers, Dortrecht, 1996, 273-298.
115. Manfredini, P., Cocchetti, G., Maier, G., Redaelli, A., and Montevecchi, F. M., Poroelastic finite element analysis of a bone specimen under cyclic loading, J. Biomech., 32, 135-144, 1999.
116. Anderson, C. B., Mechanics of fluids, in Marks’ Standard Handbook for Mechanical Engineers, Baumeister, T., Ed., McGraw-Hill, New York, 1967, 3.48-3.76.
117. Cowin, S. C. and Sadegh, A. M., Non-interacting modes for stress, strain and energy in hard tissue, J. Biomech., 24, 859-867, 1991.
118. Cowin, S. C., The mechanical properties of cortical bone, in Bone Mechanics, S. C. Cowin, Ed., CRC Press, Boca Raton, FL, 1989, 97-127.
119. Hill, R., The elastic behavior of a crystalline aggregate, Proc. Phys. Soc. London, A65, 349-354, 1952.
120. Nowinski, J. L. and Davis, C. F., A model of the human skull as a poroelastic spherical shell subjected to a quasistatic load, Math. Biosci., 8, 397-416, 1970.
121. Nowinski, J. L. and Davis, C. F., Propagation of longitudinal waves in circularly cylindrical bone elements, J. Appl. Mech., 39, 578-584, 1971.
122. Nowinski, J. L., Bone articulations as systems of poroelastic bodies in contact; AIAA J., 9, 62-67, 1971.
123. Nowinski, J. L. and Davis, C. F., The flexure and torsion of bones viewed as poroelastic bodies., Int. J. Eng. Sci., 10, 1063-1079, 1972.
124. Nowinski, J. L., Stress concentrations around a cylindrical cavity in a bone treated as a poroelastic body, Acta Mech., 13, 281-292, 1972.
125. Johnson, M. W., Chakkalakal, D. R., Harper, R. A., Katz, J. L., and Rouhana, S. W., Fluid flow in bone in vitro, J. Biomech., 18, 881-885, 1982.
126. Johnson, M. W., Behavior of fluid in stressed bone and cellular stimulation, Calcif. Tissue Int., 36, S72-S764, 1984.
127. Wang, L., Fritton, S., Cowin, S. C., and Weinbaum, S., Fluid pressure relaxation depends upon osteonal microstructure: modeling of an oscillatory bending experiment, J. Biomech., 32, 663-672, 1999.
128. Rubin, C. T., Pratt, G. W., Porter, A. L., Lanyon, L. E., and Poss, R., The use of ultrasound in vivo to determine acute change in the mechanical properties of bone following intense physical activity, J. Biomech., 20, 723-727, 1987.
129. Wyllie, M. R., Gregory, A. R., and Gardner, G. H. F., An experimental investigation of factors affecting elastic wave velocities in porous media, Geophysics, 23, 459-493, 1958.
130. McKelvie, M. L. and Palmer, S. B., The interaction of ultrasound with cancellous bone, Phys. Med. Biol., 36, 1331-1340, 1991.
131. Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range, J. Acoust. Soc. Am., 28, 168-178, 1956.
132. Biot, M. A., Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range, J. Acoust. Soc. Am., 28, 179-191, 1956.
133. Biot, M. A., Generalized theory of acoustic propagation in porous dissipative media, J. Acoust. Soc. Am., 34, 1254-1264, 1962.
134. Plona, T. J., Observation of a second bulk compressive wave in a porous medium at ultrasonic frequencies, Appl. Phys. Lett., 36, 259, 1980.
135. Berryman, J. G., Confirmation of Biot’s theory, Appl. Phys. Lett., 37, 382-384, 1980.
136. Lakes, R. S., Yoon, H. S., and Katz, J. L., Slow compressional wave propagation in wet human cortical bone, Science, 220, 513-515, 1983.
137. Williams, J. L., Ultrasonic wave propagation in cancellous and cortical bone: prediction of some experimental results by Biot’s theory, J. Acoust. Soc. Am., 91, 1106-1112, 1992.
138. Lakes, R. S., Private communication, 1998.
139. Barenblatt, G. I., Zheltov, I. P., and Kockina, I. N., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata), Prikl. Mat. Mekh. (English translation), 24, 1286-1303, 1960.
140. Barenblatt, G. I. and Zheltov, I. P., On the basic equations of seepage of homogeneous liquids in fissured rock, Akad. Nauk SSSR (English translation), 132, 545-548, 1960.
141. Barenblatt, G. I. and Chernyi, G., On moment relations of surfaces of discontinuity in dissipative media, Prikl. Mat. Mekh. (English translation), 27, 1205-1218, 1963.
142. Barenblatt, G. I., On certain boundary value problems for the equations of seepage of liquid in fissured rocks, Prikl. Mat. Mekh. (English translation), 27, 513-518, 1963.
143. Warren, J. E. and Root, P. J., The behavior of naturally fractured reservoirs, Soc. Petrol. Eng. J., 3, 245-255, 1963.
144. Wilson, R. K. and Aifantis, E. C., On the theory of consolidation with double porosity, Int. J. Eng., 20, 1009-1035, 1982.
145. Barenblatt, G. I., Entov, V. M., and Ryzhik, V. M., Theory of Fluid Flows through Natural Rocks, Kluwer, Dordrecht, 1990.
146. Mak, A. F. T., Huang, D. T., Zhang, J. D., and Tong, P. Deformation-induced hierarchical flows and drag forces in bone canaliculi and matrix microporosity, J. Biomech., 30, 11-18, 1997.
147. Jendrucko, R. J., Hyman, W. A., Newell, P. H., and Chakraborty, B. K., Theoretical evidence for the generation of high pressures in bone cells, J. Biomech., 9, 87-91, 1976.
148. Pollack, S. R., Salzstein, R., and Pienkowski, D., The electric double layer in bone and its influence on stress-generated potentials, Calcif. Tissue Int., 36, S77-S81, 1984.
149. Salzstein, R. A., Pollack, S. R., Mak, A. F. T., and Petrov, N., Electromechanical potentials in cortical bone—I. A continuum approach, J. Biomech., 20, 261-270, 1987.
150. Salzstein, R. A. and Pollack, S. R., Electromechanical potentials in cortical bone—II. Experimental analysis, J. Biomech., 20, 271-280, 1987.
151. De Groot, S. R. and Mazur, P., Non-Equilibrium Thermodynamics, North Holland, Amsterdam, 1969.
152. Lee, R. C., Frank, E. H., Grodzinsky, A. J., and Roylance, A. J., Oscillatory compressional behavior of articular cartilage and its associated electrochemical properties, J. Biomech. Eng., 103, 280-292, 1981.
153. Coelho, D., Shapiro, M., Thovert, J. F., and Adler, P. M., Electroosmotic phenomena in porous media, J. Colloid Interface Sci., 181, 169-190, 1996.
154. Zeng, Yu, Cowin, S. C., and Weinbaum, S., A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon, Ann. Biomed. Eng., 22, 280-292, 1994.
155. Zhang, D., Cowin, S.C., and Weinbaum, S., Electrical signal transmission and gap junction regulation in bone cell network: a cable model for an osteon, Ann. Biomed. Eng., 25, 357-374, 1997.
156. Zhang, D., Weinbaum, S., and Cowin, S. C., Electrical signal transmission in a bone cell network: the influence of a discrete gap junction, Ann. Biomed. Eng., 26, 644-659, 1998.
157. Scott, G. C. and Korostoff, E., Oscillatory and step response electromechanical phenomena in human and bovine bone, J. Biomech., 23, 127-143, 1990.
158. Otter, M. W., Palmieri, V. R., Wu, D. D., Seiz, K. G., MacGinitie, L. A., and Cochran, G. V. B., A comparative analysis of streaming potentials in vivo and in vitro, J. Orthop. Res., 10, 710-719, 1992.
159. Starkebaum, W., Pollack, S. R., and Korostoff, E., Microelectrode studies of stress-generated potentials in four-point bending of bone, J. Biomed. Mater. Res., 13, 729-751, 1979.
160. Wang, L., Cowin, S. C., Weinbaum, S., and Fritton, S., Modeling tracer transport in an osteon under cyclic loading, Ann. Biomed. Engr., in press.
161. Frost, H. M., Specific surface and specific volume of normal human lamellar bone, Henry Ford Hosp. Med. Bull., 10, 35-41, 1962.
162. Schaffler, M. B. and Burr, D. B., Stiffness of compact bone: effects of porosity and density, J. Biomech., 21, 13-16, 1988.
163. Starkebaum, W., Pollack, S. R., and Korostoff, E., Microelectrode studies of stress-generated potentials in four-point bending of bone, J. Biomed. Mater. Res., 13, 729-751, 1979.
164. Rouhana, S. W., Johnson, M. W., Chakkalakal, D. R., Harper, R. A., and Katz, J. L., Permeability of compact bone, Joint ASME-ASCE Conf. Biomechanics Symp., AMD 43, 169-172, 1981.
165. Frost, H. M., Measurement of osteocytes per unit volume and volume components of osteocytes and canaliculae [sic] in man, Henry Ford Hosp. Med. Bull., 8, 208-211, 1960.
166. Baylink, D. and Wergedal, J., Bone formation and resorption by osteocytes, in Cellular Mechanisms for Calcium Transfer and Homeostasis, Nichols, G., Jr., Ed., Academic Press, New York, 1971, 257-289.