Biomedical Engineering Reference
In-Depth Information
13.1 INTRODUCTION
physiological model is a mathematical representation that approximates
the behavior of an actual physiological system.
A
quantitative
physiological models, most often
used by biologists, describe the actual physiological system without the use of mathematics.
Quantitative physiological models, however, are much more useful and are the subject of
this chapter. Physiological systems are almost always dynamic and mathematically charac-
terized with differential equations. The modeling techniques developed in this chapter
are intimately tied to many other interdisciplinary areas, such as physiology, biophysics,
and biochemistry, and involve electrical and mechanical analogs. A model is usually con-
structed using basic and natural laws. This chapter extends this experience by presenting
models that are more complex and involve larger systems.
Creating a model is always accompanied by carrying out an experiment and obtaining
data. The best experiment is one that provides data that are related to variables used in the
model. Consequently, the design and execution of an experiment is one of the most important
and time-consuming tasks in modeling. A model constructed from basic and natural laws
then becomes a tool for explaining the underlying processes that cause the experimental data
and predicting the behavior of the system to other types of stimuli. Models serve as vehicles
for thinking, organizing complex data, and testing hypotheses. Ultimately, modeling's most
important goals are the generation of new knowledge, prediction of observations before they
occur, and assistance in designing new experiments.
Figure 13.1 illustrates the typical steps in developing a model. The first step involves
observations from an experiment or a phenomenon that leads to a conjecture or a verbal
description of the physiological system. An initial hypothesis is formed via a mathematical
model. The strength of the model is tested by obtaining data and testing the model against
the data. If the model performs adequately, the model is satisfactory, and a solution is stated.
If the model does not meet performance specifications, then the model is updated, and addi-
tional experiments are carried out. Usually some of the variables in the model are observable
and some are not. New experiments provide additional data that increase the understanding
of the physiological system by providing information about previously unobservable vari-
ables, which improves the model. The process of testing the model against the data continues
until a satisfactory solution is attained. Usually a statistical test is performed to test the good-
ness of fit between the model and the data. One of the characteristics of a good model is how
well it predicts the future performance of the physiological system.
The introduction of the digital computer, programming languages, and simulation software
has caused a rapid change in the use of physiological models. Before digital computers, math-
ematical models of biomedical systems were either oversimplified or involved a great deal
of hand calculation, as described in the Hodgkin-Huxley investigations published in 1952.
Today, digital computers have becomes so common that the terms
Qualitative
simulation
have almost become synonymous. This has allowed the development of much more realistic
or homeomorphic models that include as much knowledge as possible about the structure
and interrelationships of the physiological system without any overriding concern about the
number of calculations. Models of neuron networks and muscle cross-bridge models involving
thousands of differential equations are becoming quite commonplace.
modeling
and
