Last update:
May 1, 1998

maw banner

The Mathematics of Morphometrics

Center for Toxicology

Environmental health scientists at The University of Arizona study the effects of chemicals on human health using mathematics and digital images. Data from one such experiment is used in the Environmental Tobacco Smoke Activity of the Chemicals & Human Health section of The Biology Project.

In the Environmental Tobacco Smoke Activity, student use morphometry to study the effects cigaretteof environmental tobacco smoke (second-hand smoke) on lung development. Morphometry is a mathematical data analysis technique. Morphometry allows scientists to use a number of samples from different experimental groups to study the two- and three-dimensional structures present in the samples.

The morphometric mathematical data analysis technique was originally developed by geologists who needed a method for measuring the volume of minerals in rocks. Morphometry was later adapted by a Swiss scientist, Dr. Ewald Weibel, and applied to microscopic images of body tissues and/or cells.

In the Environmental Tobacco Smoke (ETS) activity, lung tissue is prepared for viewing under a microscope.

slice preparation

Next, the image is electronically captured using a digital camera. The image can be analyzed using image-processing software or by hand, lung section using a morphometric technique called "point counting."In the ETS activity, pointing counting allows scientists/students to look at samples of lung tissues on microscope slides and estimate three-dimensional data (such as lung air space volume or alveolar volume) by counting the two-dimensional data on the tissue slides. The three-dimensional data is then used to infer affects of ETS on gas exchange in the lungs.

Mathematics play an extremely important role in toxicological studies such as this one because sophisticated mathematics, including theorems from statistical geometry, are used to prove that using sampling of a limited number of animals can still allow scientists to get good,valid data.

For further information on morphometric analysis of ETS effects on developing lung tissue, follow this link to the Biology Project activity, "Environmental Tobacco Smoke and Lung Development."

online resources