Transport of nutrients in bones

SIAM Journal on Applied Mathematics

Volumn 65, Issue 6, 2005, Pages 2128-2140

  Goldsztein, Guillermo H ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bones; Effective diffusion; Mathematical modeling; Nutrient transport; Porous media; Solute transport

Indexed keywords

EFFECTIVE DIFFUSION; LACUNAR-CANALICULAR SYSTEMS; NUTRIENT TRANSPORT; SOLUTE TRANSPORT;

BONE; DIFFUSION; FLOW OF FLUIDS; HEALTH CARE; MATHEMATICAL MODELS; POROUS MATERIALS;

ONCOLOGY;

EID: 29144495708     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040616632     Document Type: Conference Paper

References (18)

1. R. ARIS, On the dispersion of solute matter in a fluid flowing through a tube, Proc. Roy. Soc. London A, 235 (1956), pp. 67-77.
2. R. A CHOLE AND S. P. TINLING, Incomplete coverage of mammalian bone cell matrix by lining cells, Ann. Ontology Rhinology and Laryngology, 102 (1993), pp. 543-550.
3. R. R. COOPER, J. W. MILGRAM, AND R. A. ROBINSON, Morphology of the osteon, J. Bone Jt. Surg., 48 (1966), pp. 1239-1271.
4. S. COWIN, Bone poroelasticity, J. Biomech., 32 (1999), pp. 217-238.
5. M. L. KNOTHE TATE, U. KNOTHE, AND P. NIEDERER, Experimental elucidation of mechanical load-induced fluid flow and its potential role in bone metabolism and functional adaptation, Am. J. Med. Sci., 316 (1998), pp. 189-195.
6. M. L. KNOTHE TATE AND U. KNOTHE, An ex vivo model to study the transport processes and fluid flow in loaded bone, J. Biomech., 33 (2000), pp. 247-254.
7. M. L. KNOTHE TATE AND P. NIEDERER, A theoretical FE-based model developed to predict the relative contribution of convective and diffusive mechanisms for the maintenance of local equilibria within cortical bone, in Advances in Heat and Mass Transfer in Biotechnology, S. Clegg, ed., American Society of Mechanical Engineers, New York, 1998, pp. 133-142.
8. M. L. KNOTHE TATE, P. NIEDERER, AND U. KNOTHE, In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading, Bone, 22 (1998), pp. 107-117.
9. M. L. KNOTHE TATE, Mixing mechanisms and net solute transport in bone, Ann. Biomed. Eng., 29 (2001), pp. 810-811.
10. M. L. KNOTHE TATE, Interstitial fluid flow, in Bone Biomechanics Handbook, S.C. Cowin, ed., CRC Press, New York, 2001, Vol. 23, pp. 1-29.
11. R. H. KUFAHL AND S. SAHA, A theoretical model for stress-generated fluid flow in the canaliculilacunae network in bone tissue, J. Biomech., 23 (1990), pp. 171-180.
12. G. LI, J. T. BRONK, K. N. AN, AND P. J. KELLY, Permeability of cortical bone of canine tibiae, Microcirculation Res., 34 (1987), pp. 302-310.
13. S. C. MILLER AND W. S. S. JEE, Bone lining cells, in Bone, Vol. 4: Bone Metabolism and Mineralization, K. V. Hall, ed., CRC Press, Boca Raton, 1992, pp. 1-19.
14. W. F. NEUMAN AND M. W. NEUMAN, The chemical dynamics of bone, University of Chicago Press, Chicago, 1958.
15. K. PIEKARSKI AND M. MUNRO, Transport mechanism operating between blood supply and osteocytes in long bones, Nature, 269 (1977), pp. 80-82.
16. G. I. TAYLOR, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. London A, 223 (1953), pp. 446-468.
17. L. WANG, S. C. COWIN, S. WEINBAUM, AND S. P. FRITTON, Modeling tracer transport in an osteon under cyclic loading, Ann. Biomed. Eng., 28 (2000), pp. 1200-1209.
18. L. WANG, S. C. COWIN, S. WEINBAUM, AND S. P. FRITTON, In response to "Mixing mechanisms and net solute transport in bone" by M.L. Knothe Tate, Ann. Biomed. Eng., 29 (2001), pp. 812-816.