Mathematical Biology: An Exciting Field of Science

A disturbing statement I often hear some adults say to children about mathematics is, "I never use mathematics in my job." And wishing to express empathy with a child, who is struggling with mathematical abstractions, they say, "I had problems with math also." But the utterance that makes me shutter is, "What can you do with mathematics? Teach?"

My hope with this post is to educate the older ones about the collaboration between mathematics and biology.

Further, I hope to energize adults to encourage the struggling children to master the mathematics placed before them, if only, by informing them about the role mathematics played in some research from the Ohio State University Mathematical Biology Institute.

So what is a Mathematical Biology Institute?

A mathematical biology institutes is a collaboration between practitioners of the mathematical and biological sciences. They are formed to satisfy the need and urgency for additional research at the boundary between the mathematical sciences and the life sciences.

Work in mathematical biology is collaboration between a mathematician and a biologist. The biologist poses a biological question or describes a set of experiments.

The mathematician produces mathematical relationships in order to explain or to predict known outcomes.

The mathematical relationships are usually differential equations. They tie together a small number of relevant biological variables and appropriate rate parameters in order to describe how fast or how slow a biological phenomenon takes place. (A group of mathematical relationships that are used to describe or predict an outcome of a phenomenon is called a model.)

From 2002 to 2008, Distinguished University Professor Dr. Avner Freidman was director of the Ohio State University Mathematical Biology Institute (OSUMBI). Upon leaving the position, he reported on some collaborative efforts at OSUMBI.

The title of his report is What is Mathematical Biology and How Useful is it?. It appears in the Notices of the American Mathematical Society, August 2010.

Here are some models from that report.

Lung Infection with Mycobacterium Tuberculosis (Mtb): In the earlier stage of lung infection with Mtb, cells from the lung's immune system attempt to eradicate the Mtb infection. When unable to do so, the overpowered immune cells communicate to the immune system to dispatch a more aggressive colony of white blood cell to the lungs to eradicate the Mtb cells.

When the "savior" cells become the dominant cell population in the lung they successfully eliminate the Mtb cells. That takes approximately two months. Mathematical biologists seek models that suggest a shortening of the deployment time for these "savior" cells.

Ischemic Wounds: A wound that has a poor blood supply is slow to heal. Such wounds are called ischematic wounds.

A model has been found that shows very good agreement of healing time using data from ischematic and nonischematic wounds. Its results are in agreement with selected experimental results. The model is now slated for testing that can predict improved healing time.

Models of Reconstructive surgery: Reconstructive surgery transfers patient's tissue from one location to another. The surgery is successful when the transferred tissue survives in the new location.

This happens when blood flow in the transferred tissue delivers the adequate oxygen and blood levels.

Without adequate oxygen and blood flow to all parts of the transferred tissue (ischemia), parts or all of the tissue will die.

A mathematical model has been developed to determine the transport of oxygen in a rectangular flap having only one perforated vessel.

The model highlights the size of a perforated vessel that ensures that the transfer will survive after four hours.

Tumor Models: For each level of the food supply to a tumor, a new tumor model points to the tumor behaving like a radially symmetric tumor whose size changes with a changing food supply.

Adjusting this model to simulate a spherical tumor in a fluid-like tissue - as found in a mammary gland or in the brain - admits the possibility that the tumor boundary will grow finger-like appendages. When this happens, the fingers have a high risk of metastasis.

These models project in full view the microscopic world - driven by many variables - onto the human mind screen. They:

a) Highlight the effects of the selected variables on on the biological process,

b) Clarify our understanding of life processes,

c) Direct us to new topics to research,

d) Illuminate ideas for new and better treatments and finally,

e) Benefit us, the public as the beneficiaries of their successes.

To sustain the growth of a promising future for mathematical biology, actions is needed from everyone.

1. From academe: to prepare new workers to continue the work.

2. From government: to perpetuate its funding and excite new collaborations and, of course,

3. From us, the public: to inform and encourage the young who possess talent to continue the work of this field.

In closing, I give my response to each of the three disturbing statements adults say to children.

"I never use mathematics in my job." I agree! It is not likely that jobs of most workers will not require the use of mathematics. But it is likely that jobs of most workers require some reasoning from time to time.

High school mathematics (algebra, geometry, etc.) develops a student's reasoning skills. Yes, other subjects develop reasoning skills, but only mathematics will yield the same answer to all who correctly applied it thereby, making it the only objective teaching method to develop reasoning skills.

"I had problems with math also." Now to the struggling student, I too will empathize. But I would add , "Mathematics is the only way we have to teach reasoning skills, that offers to all competent graders of your analysis the same assessment - correct or incorrect. It is to your advantage to spend as much time as possible to learn this valuable life skill."

"What can you do with mathematics? Teach?"

Teachers of mathematics make a noble contribution to society. They give the society concepts, strategies and models in order to understand and control the world we inhabit.