Page 52 - Biosystems Engineering

CHAPTER 2

Biosystems Analysis

and Optimization

Wouter Saeys and Herman Ramon
Department of Biosystems
Katholieke Universiteit Leuven, Heverlee, Belgium

Tom Coen
INDUCT bvba, Zemst, Belgium

2.1 Introduction
Mathematical description of the dynamic behavior of technical sys-
tems has a long tradition, which first reached a climax in 1687 when
Isaac Newton introduced his three fundamental laws to describe the
motion of a point mass. Nevertheless, it was not until the nineteenth
century before mathematical models were slowly introduced to
describe biological systems (e.g., population growth model intro-
duced by Pierre Verhulst in 1837), and it was only in the twentieth
century that this discipline fully developed. It is expected that the
twenty-first century will be the age of mathematical biology aiming
at an accurate mathematical description of the most important bio-
logical processes (e.g., photosynthesis, respiration, metabolic path-
ways, tissue generation).

2.1.1 Definitions

• Systems analysis or systems theory—quantitative (mathematical)
analysis of dynamic systems.
• Dynamic system—entity that can be isolated from its environ-
ment by a physical or conceptual border and whose state
changes over time. Traditional examples of such dynamic sys-
tems are machinery (car, train, airplane, etc.), electronic circuits,
and chemical processes (reactions, pathways, etc.). However,
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