Numerical approximations of the mean absorption cross-section of a variety of randomly oriented microalgal shapes

J Math Biol. 2003 Oct;47(4):325-36. doi: 10.1007/s00285-003-0215-9. Epub 2003 Jun 12.


The size, shape, and absorption coefficient of a microalgal cell determines, to a first order approximation, the rate at which light is absorbed by the cell. The rate of absorption determines the maximum amount of energy available for photosynthesis, and can be used to calculate the attenuation of light through the water column, including the effect of packaging pigments within discrete particles. In this paper, numerical approximations are made of the mean absorption cross-section of randomly oriented cells, aA. The shapes investigated are spheroids, rectangular prisms with a square base, cylinders, cones and double cones with aspect ratios of 0.25, 0.5, 1, 2, and 4. The results of the numerical simulations are fitted to a modified sigmoid curve, and take advantage of three analytical solutions. The results are presented in a non-dimensionalised format and are independent of size. A simple approximation using a rectangular hyperbolic curve is also given, and an approach for obtaining the upper and lower bounds of aA for more complex shapes is outlined.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Absorption
  • Algorithms
  • Eukaryota / chemistry
  • Eukaryota / cytology*
  • Eukaryota / physiology
  • Kinetics
  • Light*
  • Models, Biological*
  • Photosynthesis / physiology
  • Pigments, Biological / chemistry
  • Surface Properties
  • Water / chemistry


  • Pigments, Biological
  • Water