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.
@article{RLIN_2002_9_13_2_149_0,
author = {Andro Mikeli\'c and Mario Primicerio},
title = {Oxygen exchange between multiple capillaries and living tissues: An homogenisation study},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {13},
year = {2002},
pages = {149-164},
zbl = {1180.92020},
mrnumber = {1949488},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_2_149_0}
}
Mikelić, Andro; 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, Tome 13 (2002) pp. 149-164. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_2_149_0/
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