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Received for review J u n e 21, 1989 Revised manuscript received February 22, 1990 Accepted April 25, 1990
COMMUNICATIONS Theoretical Equations for Agar-Diffusion Bioassay On the basis of two-dimensional diffusion, theoretical equations for cup-plate and paper-disk methods of bioassay have been established. With cycloheximide as the test substance, samples were taken at various times and radial distances and the theoretical equations have been verified. Integrating with the concepts of critical concentration and critical time, the possibility of their application for practical uses has been tested, and the results were found to be in conformity with that of the Cooper equation. The method of agar-diffusion bioassay has long been used for estimating the potency of antibiotics, yet its theory has not been sufficiently developed. The most popular theory is that of Cooper and Woodman (1946), starting from linear diffusion. Later, Mitchison and Spicer (19491, Vesterdal(1947), and Humphrey and Lightbrown (1952) put forth similar equations. All of them share the disadvantages that they are based on the diffusion of antibiotics through the homogeneous agar medium, without taking into consideration their partition between the solution and agar phases. We have developed the mathematical models of cupplate and paper-disk methods of bioassay. The latter may also be used for the cylinder-plate method with similar assumptions. Their brief derivations are shown below.
Mathematical Models 1. Cup-Plate Method. Suppose a petri dish of radius b is filled with agar medium and a well of radius a is punched out at the center. An antibiotic solution of known concentration is put into the well. As the antibiotic diffuses through the inoculated medium, the inhibition zone is formed. The depth of the agar medium is rather small compared with the diameter of the petri dish, and the diffusion could be regarded as two dimensional: %I($+;$) at (a
