Geodesic
Oxygen exchange between multiple capillaries and living tissues: An homogenisation study
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 149-164.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
Uno studio di omogeneizzazione. Si studia un modello matematico per un problema di perfusione sanguigna in un tessuto vivente da parte di un sistema di capillari paralleli. Si suppone che l’ossigeno sia trasportato in due forme: libero di diffondere e legato (agli eritrociti nel sangue, alla mioglobina nel tessuto). Si dimostra l’esistenza di una soluzione debole e si utilizza un procedimento di omogeneizzazione per il caso di capillari distribuiti aleatoriamente. 
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     title = {Oxygen exchange between multiple capillaries and living tissues: {An} homogenisation study},
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Mikelić, Andro; Primicerio, Mario. Oxygen exchange between multiple capillaries and living tissues: An homogenisation study. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 149-164. http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a9/

[1] H.W. Alt - S. Luckhaus, Quasilinear elliptic-parabolic equations. Math. Z., 183, 1983, 311-341. | fulltext EuDML | DOI | MR | Zbl

[2] C. Bos - L. Hoof - T. Oostendorp, Mathematical model of erytrocytes as point-likeT sources. Math. Biosci., 125, 1995, 165-189. | Zbl

[3] J. Carrillo, Entropy Solutions for Nonlinear Degenerate Problems. Arch. Rational Mech. Anal., 147, 1999, 263-361. | DOI | MR | Zbl

[4] C.D. Eggleton - A. Vardapalli - T.K. Roy - A.S. Popel, Calculation of intracapillary oxygen tension distribution in muscle. Math. Biosci., 167, 2000, 123-143. | Zbl

[5] J.E. Fletcher, Mathematical modelling of the microcirculation. Math. Biosci., 38, 1978, 155-202. | MR | Zbl

[6] A. Fasano - A. Mikelić, Porous media with partially soluble permeable grains. Nonlinear differ. equ. appl. (NoDEA), 7, 2000, 141-156. | Zbl

[7] V.V. Jikov - S.M. Kozlov - O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin 1994. | DOI | MR | Zbl

[8] A. Krogh, 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] J. Keener - J. Sneyd, Mathematical Physiology. Interdisciplinar Appl. Math., 8, Springer-Verlag, 1998. | MR | Zbl

[10] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type. Transl. Am. Math. Soc., 23, 1968. | MR | Zbl

[11] A. Mikelić - M. Primicerio, 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. | Zbl

[12] C.V. Pao, Stability analysis of a coupled diffusion-transport system for oxygen transport in blood and tissue. Nonl. Anal. Th. Met. App., 9, 1985, 1037-1059. | DOI | MR | Zbl

[13] A.S. Popel, Theory of oxygen transport to tissue. Crit. Riv. Biomed. Engrs., 17, 1989, 257-321.

[14] A.S. Popel, Mathematical modelling of oxygen transport near a tissue surface: effect of the surface $P_{O_{2}}$. Math. Biosci., 55, 1981, 231-246. | Zbl

[15] A.S. Popel, Analysis of capillary-tissue diffusion multicapillary system. Math. Biosci., 35, 1978, 187-211. | Zbl

[16] M.S. Titcombe - M.J. Ward, An asymptotic study of oxygen transport from multiple capillaries to skeletral muscle tissue. SIAM J. Appl. Math., 60, 2000, 1767-1788. | DOI | MR | Zbl