The diffusion of oxygen and lactic acid through tissues

Abstract The diffusion of dissolved substances through cells and tissues is a determining factor in many vital processes. The slowness of diffusion on the scale of ordinary sensible objects gives to the unaided imagination an imperfect realisation of its speed and importance in systems of the dimensions of the living cell. The diffusion constant k is expressed in terms of the number of unit quantities of substance which diffuse per minute across an area of 1 sq. cm. in a gradient of concentration per cm. of 1 unit quantity per c. c. For aqueous solutions of ordinary substances k is usually of the order of 2 to 10 times 10-4. The diffusion constant is of the dimensions L2T-1, 2 in length, -1 in time. Expressing it in units of 1μ (0·0001 cm.) instead of 1 cm., and of 1σ (0·001 sec.) instead of minutes, k is of the order of unity, instead of multiple of 10-4. Thus the diffusion constant is a fairly large quantity for systems involving distances of the order of 1μ and times of the order of 1σ. A cylinder 1 cm. in diameter composed of material similar to frog's nerve, if suddenly placed in oxygen, would take 185 minutes to attain 90 per cent. of is full saturation with that gas. An actual nerve 0·7 mm. thick would take 54 seconds for the same stage of saturation to be reached. A single nerve fiber 7μ thick would take only 5·4 σ. Again, the rapidity of diffusion attainable in systems of small dimensions is the basis of the capillary circulation, and therewith of the whole design of the larger animals; and the rate at which diffusion an supply oxygen to a fatigued muscle for the removal of lactic acid is an important factor in determining the speed at which recovery can occur.