Introduction: Many simple organisms do not have specialized respiratory structures and instead obtain oxygen by diffusion through their body surfaces.

Importance: We can use a simple equation to assess properties of an organism that can survive by diffusion alone.

Question: How is the oxygen need of an organism related to its metabolism and size?



concentration of O2 required at surface of organism for survival (atm)


rate of oxygen consumption ((cm3 O2/cm3 tissue)/min)


radius of spherical organism (cm)


diffusion constant ((cm2/atm)/min)


Methods: E. Newton Harvey (1928) developed the following equation to describe the concentration of oxygen required to supply a spherical organism with oxygen by diffusion:

where S is the required concentration of oxygen at the surface of an organism, C is the rate of oxygen consumption (cm^3 of oxygen/cm^3 tissue/min), r is the radius of the organism (cm), and K is the diffusion constant (cm^2/atm/min).

We can plot S as a linear function of C and as a parabolic function of r. A diffusion constant of 11x10^-6 cm^2/atm/min is typical for many animal tissues

Interpretation: We can see that as organism metabolism (oxygen consumption) or organism size increases, a greater amount of oxygen is needed at the surface of the organism for survival. Well areated water typically contains 0.21 atm oxygen. We can compare the intercept S = 0.21 with the graphs of C and r. Even well-aerated water is well below the required oxygen level for organisms of large size or high metabolism.

Conclusions: By trying hypothetical organisms in the equation, one sees that for an organism to survive by diffusion alone, it must either be very small or have a very low metabolic rate. Larger organisms or those with high metabolic rates must develop respiratory structures in order to meet their oxygen needs.

Additional Question:

1. How does the slope of S as a linear function of C change with increasing radius? What does this imply about an organism?

Source: Schmidt-Nielsen, K. 1990. Animal Physiology: Adaptation and environment, Cambridge University Press, Cambridge

Harvey, E. N. 1928. The oxygen consumption of luminous bacteria. J. Gen. Physiol. 11:469-475.

Copyright 1999 M. Beals, L. Gross, S. Harrell