Page 26 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

CHAPTER 1

MODELING OF BIOMEDICAL

SYSTEMS

Narender P. Reddy
University of Akron, Akron, Ohio

1.1 COMPARTMENTAL MODELS 4 1.5 ARTIFICIAL NEURAL NETWORK
1.2 ELECTRICAL ANALOG MODELS MODELS 17
OF CIRCULATION 7 1.6 FUZZY LOGIC 22
1.3 MECHANICAL MODELS 11 1.7 MODEL VALIDATION 27
1.4 MODELS WITH MEMORY AND REFERENCES 28
MODELS WITH TIME DELAY 13

Models are conceptual constructions which allow formulation and testing of hypotheses. A mathe-
matical model attempts to duplicate the quantitative behavior of the system. Mathematical models
are used in today’s scientific and technological world due to the ease with which they can be used to
analyze real systems. The most prominent value of a model is its ability to predict as yet unknown
properties of the system. The major advantage of a mathematical or computer model is that the
model parameters can be easily altered and the system performance can be simulated. Mathematical
models allow the study of subsystems in isolation from the parent system. Model studies are often
inexpensive and less time consuming than corresponding experimental studies. A model can also be
used as a powerful educational tool since it permits idealization of processes. Models of physiologi-
cal systems often aid in the specification of design criteria for the design of procedures aimed at alle-
viating pathological conditions. Mathematical models are useful in the design of medical devices.
Mathematical model simulations are first conducted in the evaluation of the medical devices before
conducting expensive animal testing and clinical trials. Models are often useful in the prescription
of patient protocols for the use of medical devices. Pharmacokinetic models have been extensively
used in the design of drugs and drug therapies.
There are two types of modeling approaches: the black box approach and the building block
approach. In the black box approach, a mathematical model is formulated based on the input-output
characteristic of the system without consideration of the internal functioning of the system. Neural
network models and autoregressive models are some examples of the black box approach. In the
building block approach, models are derived by applying the fundamental laws (governing physical
laws) and constitutive relations to the subsystems. These laws together with physical constraints
are used to integrate the models of subsystems into an overall mathematical model of the system.
The building block approach is used when the processes of the system are understood. However,
if the system processes are unknown or too complex, then the black box approach is used. With the
building block approach, models can be derived at the microscopic or at the macroscopic levels.
Microscopic models are spatially distributed and macroscopic models are spatially lumped and are rather

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