Oxygen exchange between multiple capillaries and living tissues: An homogenisation study

Andro Mikelić; Mario Primicerio

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 2, page 149-164
  • ISSN: 1120-6330

Abstract

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A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.

How to cite

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Mikelić, Andro, and Primicerio, Mario. "Oxygen exchange between multiple capillaries and living tissues: An homogenisation study." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.2 (2002): 149-164. <http://eudml.org/doc/252407>.

@article{Mikelić2002,
abstract = {A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.},
author = {Mikelić, Andro, Primicerio, Mario},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Oxygen diffusion; Hemodynamics; Homogenisation; oxygen diffusion; hemodynamics; homogenisation},
language = {eng},
month = {6},
number = {2},
pages = {149-164},
publisher = {Accademia Nazionale dei Lincei},
title = {Oxygen exchange between multiple capillaries and living tissues: An homogenisation study},
url = {http://eudml.org/doc/252407},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Mikelić, Andro
AU - Primicerio, Mario
TI - Oxygen exchange between multiple capillaries and living tissues: An homogenisation study
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/6//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 2
SP - 149
EP - 164
AB - A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.
LA - eng
KW - Oxygen diffusion; Hemodynamics; Homogenisation; oxygen diffusion; hemodynamics; homogenisation
UR - http://eudml.org/doc/252407
ER -

References

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  2. Bos, C. - Hoof, L. - Oostendorp, T., Mathematical model of erytrocytes as point-likeT sources. Math. Biosci., 125, 1995, 165-189. Zbl0819.92006
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  8. Krogh, A., The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J. Physiol. (London), 52, 1919, 409-415. 
  9. Keener, J. - Sneyd, J., Mathematical Physiology. Interdisciplinar Appl. Math., 8, Springer-Verlag, 1998. Zblpre05242554MR1673204
  10. Ladyzenskaja, O.A. - Solonnikov, V.A. - Ural'ceva, N.N., Linear and Quasilinear Equations of Parabolic Type. Transl. Am. Math. Soc., 23, 1968. Zbl0174.15403MR241822
  11. Mikelić, A. - Primicerio, M., Homogenization of Heat Equation for Domain with a Network of Pipes with a Well-Mixed Fluid. Ann. Mat. Pura Appl., (IV), vol. CLXVI, 1994, 227-251. Zbl0814.35007
  12. Pao, C.V., Stability analysis of a coupled diffusion-transport system for oxygen transport in blood and tissue. Nonl. Anal. Th. Met. App., 9, 1985, 1037-1059. Zbl0588.35017MR806908DOI10.1016/0362-546X(85)90084-7
  13. Popel, A.S., Theory of oxygen transport to tissue. Crit. Riv. Biomed. Engrs., 17, 1989, 257-321. 
  14. Popel, A.S., Mathematical modelling of oxygen transport near a tissue surface: effect of the surface P O 2 . Math. Biosci., 55, 1981, 231-246. Zbl0457.92009
  15. Popel, A.S., Analysis of capillary-tissue diffusion multicapillary system. Math. Biosci., 35, 1978, 187-211. Zbl0402.92011
  16. Titcombe, M.S. - Ward, M.J., An asymptotic study of oxygen transport from multiple capillaries to skeletral muscle tissue. SIAM J. Appl. Math., 60, 2000, 1767-1788. Zbl0990.92009MR1761770DOI10.1137/S0036139998343356

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