Diffusion bioassays are being extensively used for determining the antibiotic potency of drugs and for predicting genotoxicity and carcinogenicity of chemicals. The drug is placed at the center of a petri dish containing a bacterial lawn in an agar gel, and after a certain incubation period, one observes a concentric ring around the center, marking the toxic area. We propose to develop a mathematical model that will enable us to obtain an equation relating the minimal inhibitory concentration c(tox) to the radius of the toxic zone r(tox), so that by performing diffusion experiments (which are fast, efficient and inexpensive) and measuring the size of r(tox), it will be possible to calculate c(tox). This quantity is very important in evaluating the sensitivity of microorganisms to antibiotics and in determining their therapeutic doses. In the case of DNA damaging agents, we would like to use c(tox) as a criterion for their damaging potency. The mathematical model of the assay is given by a two-dimensional diffusion equation describing the changes in drug concentration due to diffusion, decay of the chemical and consumption by bacteria. The equation will be solved numerically with the aid of the computer, and a program will be specifically designed for this purpose. A vast amount of experimental data is already available and will be analyzed through this model.
| Awerbuch, T E; Ryder, E F; Faraggi, D (1987) A program which determines mutagenic concentrations of chemical carcinogens via a diffusion bioassay. Comput Methods Programs Biomed 25:31-8 |
| Awerbuch, T E; Lustman, L (1987) A mathematical model for determining minimal inhibitory concentrations (MICs) via diffusion assays. J Theor Biol 129:219-30 |
