抄録
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.
| 本文言語 | English |
|---|---|
| ページ（範囲） | 351-361 |
| ページ数 | 11 |
| ジャーナル | Bulletin of Mathematical Biology |
| 巻 | 49 |
| 号 | 3 |
| DOI | |
| 出版ステータス | Published - 1987 5月 |
| 外部発表 | はい |
ASJC Scopus subject areas
- 神経科学（全般）
- 免疫学
- 数学 (全般)
- 生化学、遺伝学、分子生物学（全般）
- 環境科学（全般）
- 薬理学
- 農業および生物科学（全般）
- 計算理論と計算数学