During my senior year in high school I knew that I like mathematics and biology but I didn't know which I liked better, or into which career path I should go. Being accepted at Rose Poly help me make that decision. After four years at Rose taking both mathematics and many engineering courses I had a BS in mathematics but I also knew that I liked "hands on" and not the theoretical. At that time Dr. Robert Arthur started a graduate Biomedical Engineering program at Rose and there was my answer – mathematics, engineering, and biology too.
After completing my MS degree in bioengineering at Rose I was accepted into a PhD program in Physiology at the Medical College of Wisconsin. Physiology seems a bit of a stretch from mathematics and engineering but it really isn't because physiology is the study of the multiple and very complex control systems within our bodies. Approaching physiology with an engineering control systems approach was very useful. Further, my PhD dissertation included writing a computer program to digitally filter respiration rate data obtained by measuring transthoracic impedance in humans and ponies. So I used mathematics, computer programming, and engineering to solve a problem that a pure biologist couldn't have done.
After graduation, my first job was on the faculty of the University of California in Irvine. They had the contract to operate the toxicology laboratory at Wright–Patterson Air Force base in Dayton, OH. As Director of the Respiratory Toxicology Unit there I had to set up a computerized laboratory to measure respiratory physiology functions in rats and dogs that could be used to evaluate whether compounds being used by the Air Force impaired respiratory functions. Mathematics and engineering were integral in designing, constructing, and operating this laboratory.
After a couple of other stops on the way I am now Director of Toxicology at MPI Research in Mattawan, MI. We are a large international contract laboratory conducting the preclinical studies required by the US FDA and other worldwide regulatory agencies prior to dosing a new drug the first time into humans. This is a pivotal step in drug development as it determines how a drug is toxic and at what dose levels this occurs. I am no longer on the bench but I still use mathematics every day.
(1) The studies we conduct all use statistical analysis as a tool to evaluate whether a change at a higher dose level is statistically significant and therefore probably drug related. Understanding the underlying mathematical assumptions in the various statistical tests available is necessary in selecting the most appropriate test.
(2) Evaluating the drug levels in plasma after dosing is also a key endpoint in these studies. By mathematically analyzing these plasma values over time we can calculate parameters such as clearance half times (the time it takes for the drug to drop to 50% of its original value). We also can integrate the Area Under the Curve (AUC) for these data as a biomarker for the dose that actually got into the animal; not everything gets absorbed. The AUC level that caused toxicity can then be used as a reference level to compare with the AUC data from the first time the drug is given in man to keep the human dose level well below a toxic level.
(3) Another use of mathematics is in developing Physiologically Based Pharmacokinetic (PBPK) models. Instead of just curve fitting equations to the plasma data, we create a model of the body based on blood flows, blood volumes, tissue mass for various organs, and partition coefficients for the drug in various tissues and blood. This mathematical model allows for further evaluation and understanding of the control systems affecting drug level in various organs and over time.
(4) And last, on the chemical side of the industry, once a toxic level or hazard is known, then risk estimation kicks in and reference values for acceptable levels of a particular chemical in the water, air, or food can be calculated and enforceable regulatory standards set.
While I am not really a mathematician, all of these positions have involved mathematics and I have found this to have been a very rewarding career. I do sort of feel like Christopher Columbus however, I started off not knowing where I was going, I wasn't exactly sure where I was once I got here, and I did it all on borrowed money.