Biological Systems Modeling and Controls

Biological systems modeling has been around for quite a few years. Initially the domain of the mathmatician and the biologist, biological modeling is in a rennasance. This growth is due to a range of factors including easier to use modeling tools, faster computers, and lower costs. In my opinion, though, one of the biggest sources for growth is the expansion in biological, biomedical, and biotechnological engineering. These fields brought together a population of mathematically adept individuals, a need for predictive solutions to design problems, and (to be perfectly honest) money to pay for model development.

The materials that can be found below are the lectures and notes from a class in biological systems modeling taught at Utah State University and at the University of Maryland, College Park. They are the foundation for what I hope will become a text in biological systems modeling and basic controls theory. As such, they are materials in flux. I will be adding new materials and editing existing materials on a reguluar basis. Furthermore, there are some gaps in the materials. Some of these gaps stem from the use of articles and book chapters that I have the students read. Other gaps are topics that I simply haven't gotten around to filling.

The materials are intended for use at the college level for students in their junior or senior year of engineering, since they assume a knowledge of calculus and of differential equations. In addition, a basic understanding of biology is essential.

Modeling as Design

• Modeling As Design (.pdf)
• Processes and Signals (.pdf)

Multiple State Models - Population Dynamics and Models for Disease

Readings

• Population Dynamics I (.pdf)
• Population Dynamics II (.pdf)
• Population Dynamics (.pdf)
• The SIP Model .(pdf)

Example Models

• Model - 2 Species Competition Model Documentation Files (.html)
• Model - SIP Model Documentation Files (.html)

Transfer Functions

• Reading - Transfer Functions I (.pdf)
• Reading - Transfer Functions II (.pdf)
• Handout - Effort and Flow Variables (.pdf)

Block Diagrams and Higher Order Systems

• Reading - Block Diagrams (.pdf)
• Reading - Second Order Systems (.pdf)

Regulation and Control Systems

• Reading - Homeostatic Control (Daisy World) (.pdf)

Example Models

• Model - Daisy World Overview (.pdf)
• Model - Daisy World Documentation Files (.html)

Stability and Root Locus Plots

• Handout - Manual Root Locus Instructions (.pdf)

Appendices and Supporting Materials

MATLAB & Simulink

• Handout - The Simulink Block Sets (.pdf)
• Reading - Processes and Signals (.pdf)

Laplace Transforms and Differential Equations Refresher

• Reading - Laplace Transform Problems (.pdf)
• Handout - Useful Laplace Transforms (.pdf)
• Handout - Solving Laplace Transforms in MATLAB (.pdf)
• Handout - Solving Differential Equations in MATLAB (.pdf)

Some Useful Books and Readings

• Bibliography