Oxygen Transport Across Space-Filling Biological Membranes
Abstract
Space-filling fractal surfaces play a fundamental role in how organisms function and how structure determines function at various levels. We performed analytic computations of the oxygen flux across the space-filling system of alveolar membranes in the lung, as a function of diffusion coefficient and membrane permeability, using the rope-walk algorithm. Structural variables include the fractal dimension of the surface, alveolar diameter, and diameter of the gas-exchange unit. The system exhibits transitions between the regimes of complete/partial/no screening. For the human lung we find agreement between the computed and experimental flux, that the lung operates near the transition from partial to no screening, and that the gas exchange satisfies four criteria of optimal design: maximum flux, minimum waste of surface area, minimum permeability, and maximum fault tolerance. This extraordinary, multiply optimized performance is a direct consequence of the space-filling membrane architecture. The fractal lung model, applied to other species, predicts that the oxygen consumption rate scales with body mass as in Kleiber's law.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MAR.P9009H