Optimum capillary number for oxygen delivery to tissue in man

Akira Kamiya, Shinya Takeda, Masahiro Shibata

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12 Citations (Scopus)


The optimum number of total capillaries in the whole human body was estimated from the analysis of the efficiency for oxygen (O2) transport in the vascular-tissue system. We used a tissue model composed of uniform spheres in which O2 diffuses from the capillary located at the centre of each sphere towards the surrounding tissue consuming O2 at a constant rate. The tissue mass supplied by a single capillary was estimated as the area of positive O2 concentration under a given condition of capillary flow and O2 consumption rate. Total tissue mass was determined as the function of the capillary number n and the total blood flow. On the other hand, the energy cost required to maintain the vascular system with n terminals was assessed by using the minimum volume model (Kamiya and Togawa, Bull. math. Biophys. 34, 431-438, 1972). The efficiency of the entire vascular-tissue system was evaluated by calculating the ratio of total tissue mass/cost function. The result of the calculation using physiological data of cardiac output and O2 consumption for an average human adult during a heavy exercise revealed the maximum efficiency occurring at the capillary number 3.7×1010 which coincided well with its normal range of physiological estimates (3.2×1010-4.2×1010). We concluded that the entire vascular-tissue system is constructed so as to attain the highest efficiency in O2 transport at its maximum activity.

Original languageEnglish
Pages (from-to)351-361
Number of pages11
JournalBulletin of Mathematical Biology
Issue number3
Publication statusPublished - 1987 May
Externally publishedYes

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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