Fractal Geometry and Design of Gas Exchangers

Abstract

The airways of the mammalian lung form a complex multigenerational dichotomous branching arrangement (Figs. 138, 141, 142). The trachea corresponds to the stem of a botanical tree and the alveoli, the terminal gas exchange components (Figs. 78, 79, 84, 85), to its leaves. The arterial and venous systems of the pulmonary vascular system generally follow congruent bifurcative patterning (Figs. 139–142). Since tree-like designs are produced by external and internal factors engaging the genotype, they should manifest optimal morphological constructions. On tree-like designs, McMahon and Kronauer (1976) observed that ‘every tree is continually sensing its own overall geometry, altering its proportions in such a way as to keep that geometry stationary during growth’. In the physics of internalized flow, the size, shape and geometry of the confining space regulate the flow of the transmitted fluid. In the gas exchangers, the morphoarchitectonics of the conducting systems should set the flow dynamics of the respiratory fluid media, namely, water, air and blood. It is conceivable that over the evolutionary continuum, the conducting systems have been refined to grant cost-effective transfer and optimal presentation and exposition of the respiratory media (Sect. 12). Regarding aspects such as minimization of resistance, work and power loss, from engineering and mathematical fluid flow analyses, it has indeed been shown that the lung has contracted premium designs. Woldenberg et al. (1970) termed the prevalent states in which the erected designs have conferred efficient flux of air and blood simply ‘law and order’.

Although the materials found in biology are often very different from those used in engineering, the geometrie s of the structures in which mater ials can be employed to carry loads are generally much the same. Nature is frequently more clever than engineers at developing the potential of a given structural concept. Gordon (1988)