Biomedical Engineering Reference
In-Depth Information
collected using existing bioinstrumentation, biosensors, and biosignal processing, as dis-
cussed in Chapters 8-10. Typically, the recorded data are transformed from measurement
data into estimates of the variables used in the model. Collecting appropriate data is usually
the most difficult aspect of the discovery process.
Model building typically involves estimating the parameters of the model that optimize,
in a mean square error sense, the output of the model or model prediction,
x
i
, and the
data,
, is given by
minimizing the sum of squared errors between the model prediction and the data
x
i
. For example, one metric for estimating the parameters of a model,
S
X
n
X
n
2
e
2
S
¼
i
¼
1
x
i
x
i
ð
Þ
i
¼
1
i
¼
x
i
:
where e
i
This technique
provides an unbiased estimate with close correspondence between the model prediction
and the data.
In order to provide a feeling for the modeling process described in Figure 13.1, this
chapter focuses on one particular system—the fast eye movement system—the modeling
of which began with early muscle modeling experiences in the 1920s and continues today
with neural network models for the control of the fast eye movement system. This physio-
logical system is probably the best understood of all systems in the body. Some of the
reasons for this success are the relative ease in obtaining data, the simplicity of the system
in relation to others, and the lack of feedback during dynamic changes in the system. In this
chapter, a qualitative description of the fast eye movement system is presented, followed by
the first model of the system by Westheimer, who used a second-order model published
in 1954. The 1964 model of the system by Robinson is next presented because of its funda-
mental advances in describing the input to the system. With the physical understanding of
the system in place, a detailed presentation of muscle models is given with the early work
of Levin and Wyman in 1927, and Fenn and Marsh in 1935. These muscle models are impor-
tant in developing a realistic model that accurately depicts the system. Using the more accu-
rate muscle models, the fast eye movement model is revisited by examining the model
presented by Bahill and coworkers and then several models by Enderle and coworkers.
Next, the control mechanism for this system is described from the basis of physiology,
systems control theory, and neural networks based on anatomical pathways. Finally, the
topic of system identification or parameter estimation closes the chapter. The literature on
the fast eye movement system is vast, and the material covered in this chapter is not
exhaustive but rather a representative sample from the field. Not covered in this chapter
at all is how visual information is collected and processed by the body and how the body
reacts to the information.
is the error between the data
x
i
and the model prediction
13.2 A
N OVERVIEW OF THE FAST EYE MOVEMENT S
YSTEM
The visual system is our most important sensory system. It provides a view of the world
around us captured with receptors in the eyeball that is transmitted to the central nervous
system (CNS). The eye movement or oculomotor system is responsible for movement of the
