Cathcart
Modeling of Biological and Physiological Systems Using a
Block Diagram Programming Language

Tom Cathcart
Agricultural & Biological Engineering
Mississippi State University

Introduction  Michael Person has asked me to review the presentation posted at http://abe.msstate.edu/classes/abe4323/2002/erc/intro_phys_mod_02.html. I posted this presentation to the “Meeting the Challenges” discussion board mainly to emphasize that block diagram modeling packages make modeling accessible to anyone having a fairly basic understanding of algebra and elementary calculus. This group certainly includes, or should include, most biology undergraduates.

The Utility of Mathematical Modeling  Modeling is a useful educational tool for undergraduates. It serves multiple purposes. First, it helps to illustrate that real world systems, even complex real world systems, can be described using mathematics. Second, a mechanistic mathematical model helps the student to understand how a system works. A model is composed of individual equations that demonstrate the relationship of independent to dependent variables. Decomposing a system into its component mathematical relationships serves much the same purpose as dissecting a biological specimen. In both cases, much can be learned about the “whole” by looking at its “parts.” Third, a mathematical model emphasizes the importance of correctly connecting the equations together. In addition to understanding individual equations that make up a model, it is also important to understand that the equations must be assembled logically (i.e., “posed”) before the model can be used to simulate a system. Finally, a good mathematical model is like a good physical model. It can be manipulated and examined to help the student develop a mature understanding of how the system behaves.

Accessibility of Mathematical Modeling  Most mathematical models are implemented using computers. In the past, creating models and simulating systems required proficiency in a high level programming language. The introductory modeling course taught in the past to our engineering students resembled an elementary programming course more than a modeling course. Even students who understood the math often had difficulty with the programming. This situation is now greatly altered. A variety of mathematical modeling packages have, in the last decade or so, emerged to simplify the process of creating models and simulating systems. This list includes VisSim, Stella, and many other packages. At their best, these packages have shallow learning curves and intuitive graphical interfaces. The package that I use in my modeling class (VisSim) uses graphical block diagrams that represent mathematical operations. By wiring the operations together, the students write the governing equations of the model onto the graphical interface. A completed model looks exactly like what it is: an assemblage of mathematical equations. Issues such as time (or space) step and model duration are handled in simple pull down menus. Using this sort of package, an undergraduate with a reasonable understanding of algebra and a cursory understanding of calculus can begin to implement simple models in one to two hours.

Applications in the Biological Sciences  As can be seen in the posted presentation, there are many examples of biological and physiological systems that are amenable to modeling. Some of the examples given in the presentation may be beyond the scope of some undergraduates, but there are many other interesting examples (not shown in the presentation) that are well within the abilities of most undergrads. These examples include simple ordinary differential equations (used for population growth, disease transmission, biochemical processes, etc.) as well as a large number of mainly algebraic models that adequately describe many other processes.

Conclusion  The purpose of “Meeting the Challenges” was to find ways to enhance the mathematical proficiency of biology students. One way to do this is to help biology students master the “applied mathematics” appropriate to their discipline. Having come from a biological sciences background myself, I know that many biology students think of math as an incomprehensible “black box.” A good applied math course can help students overcome the limitations of such a view. In my opinion, the current crop of modeling software packages makes an introductory mathematical modeling course the best sort of applied math course that can be offered.