# MATHEMATICS OF DIFFUSION ASSAYS

> **NIH NIH R01** · HARVARD MEDICAL SCHOOL · 1988 · $60,463

## Abstract

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 petri dish containing a
bacterial lawn in an agar gel, and after a certain incubation
period, one observes concentric rings around the center, marking
the toxic and mutagenic zones.  A mathematical model that
enables to obtain an equation relating the minimal inhibitory
concentration c/tox to the radius of toxic zone rtox was
developed: so that by performing diffusion experiments (which are
fast, efficient and inexpensive) and measuring the size of r/tox, it
is possible to calculate c/tox.  Similarly a relationship was
obtained between the minimal mutagenic concentration c/mut and
the size of the mutagenic zone r/mut.  c/tox is very important in
evaluating the sensitivity of microorganisms to antibiotics and in
determining their therapeutic doses.  In the case of DNA-
damaging agents, c/tox could be used as a criterion for their
damaging potency.

The sensitivity of the models to the various parameters included
in the equations will be investigated.  This will be done via an
appropriate program that computes c/mut and a simulation
program that determines c/tox.  For the purpose of verifying the
model the vast amount of experimental data that is already
available will be compiled and used to calculate c/tox.

The procedure for determining c/tox will be developed into a
"userfriendly" interactive program, thus making it available for
routine use in clinical settings and in laboratories engaged in
screening for potential carcinogens.

## Key facts

- **NIH application ID:** 3175671
- **Project number:** 5R01CA037820-05
- **Recipient organization:** HARVARD MEDICAL SCHOOL
- **SAM.gov UEI:** JDLVAVGYJQ21
- **Principal Investigator:** TAMARA Eugenia AWERBUCH
- **Activity code:** R01 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 1988
- **Award amount:** $60,463
- **Award type:** 5
- **Project period:** 1987-07-15 → 1990-06-30

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/3175671

## Citation

> US National Institutes of Health, RePORTER application 3175671, MATHEMATICS OF DIFFUSION ASSAYS (5R01CA037820-05). Retrieved via MORVS 2026-10-25 from https://api.morvs.ai/grant/nih/3175671. Licensed CC0.

---

*[NIH grants dataset](/datasets/nih-grants) · CC0 1.0*