Sheet Flow Design in the Vasculature of Gas Exchangers

Abstract

The geometric arrangement and organization of the blood capillary systems of the gas exchangers is remarkably different from those that appertain to the systemic circulation. Whereas, for example, the blood capillaries in the muscle tissue occur as long, loosely connected structures (e.g. Mathieu-Costello et al. 1992), the pulmonary blood capillaries form an extremely dense network. Rather than passing through a system of long tubes, the pattern of flow of blood in a classic capillary system, in the gas exchangers, the blood forms an expansive film, a ‘sheet’. Various investigators have analysed and mathematically modelled the size, shape and geometry of the blood capillaries of various gas exchangers to gain an insight into the blood flow dynamics and the rate of gas transfer at the water/air-blood (tissue) interface. The observations and inferences that have been made conflict even on certain fundamental aspects. For example, Guntheroth et al. (1982) regarded the mammalian pulmonary blood capillaries as ‘intersecting tubules’, whereas Weibel (1963) and Weibel and Gomez (1962) considered them to be ‘intersecting, short, circular, cylindrical tubules arranged predominantly in hexagonal arrays’. Hijiya and Okada (1978) suggested that the arrangement of the alveolar blood capillaries is ‘more frequently pentagonal in shape’. Schraufnagel et al. (1986) considered the shape of the alveolar blood capillaries to change from ‘ring’ to ‘square’ configurations between the inspiratory and expiratory phases. On the basis of what they considered to be ‘short and closely knit blood capillaries where the capillary segments were wider than they were long’ and the haemodynamic properties where the vascular compliance was such that ‘only sheet thickness increased when intravascular pressure was raised’, Fung and Sobin (1972) and Sobin et al. (1979) formulated what they named a ‘sheet-flow model’ to analyse the alveolar blood volume and transit time. They considered the pulmonary capillary system to comprise of a construction made up of cellular/tissue ‘posts’ that traversed a vascular space.

One can visualise the production of the final integrated morphological structure as a complicated developmental choreography in which the ontogenies of the separate morphogenetic components are spatially and tempor ally co-ordinated. Atchley and Hall (1991)