Biomedical Engineering Reference
In-Depth Information
The first modeling approach, the “white box,” would require the highest level of physiological
detail. Starting with behavior and tracing back, the system comprises muscles, peripheral nerves, the
spinal cord, and ultimately the brain. This would be a prohibitively difficult task with the present
level of knowledge because of the complexity, interconnectivity, and dimensionality of the involved
neural structures. Model implementation would require the parameterization of a complete motor
system [
4
] that includes the cortex, cerebellum, basal ganglia, thalamus, corticospinal tracts, and
motor units. Because all of the details of each component/subcomponent of the described motor
system remain largely unknown and are the subject of study by many neurophysiological research
groups around the world, it is not presently feasible to implement white-box modeling for BMIs.
Even if it was possible to parameterize the system to some high level of detail, the task of imple-
menting the system in our state-of-the-art computers and DSPs would be an extremely demanding
task. The appeal of this approach when feasible is that a physical model of the overall system could
be built, and many physiological questions could be formulated and answered.
The “gray box” model requires a reduced level of physical insight. In the “gray box” approach,
one could take a particularly important feature of the motor nervous system or of one of its com-
ponents, incorporate this knowledge into the model, and then use data to determine the rest of the
unknown parameters. One of the most common examples in the motor BMI literature is Geor-
gopoulos' population vector algorithm (PVA) [
5
]. Using observations that cortical neuronal firing
rates were dependent on the direction of arm movement, a model was formulated to incorporate the
weighted sum of the neuronal firing rates. The weights of the model are then determined from the
neural and behavioral recordings.
The last model under consideration is the “black box.” In this case, it is assumed that no
physical insight is available to accomplish the modeling task. This is perhaps the oldest type of
modeling where only assumptions about the data are made, and the questions to be answered are
limited to external performance (i.e., how well the system is able to predict future samples, etc.).
Foundations of this type of time series modeling were laid by Wiener for applications in antiaircraft
gun control during World War II [
22
]. Although military gun control applications may not seem
to have a natural connection to BMIs, Wiener and many other researchers provided the tools for
building models that correlate unspecified time series inputs (in our case, neuronal firing rates) and
desired targets (hand/arm movements). We will treat black box modeling in this chapter.
The three input-output modeling abstractions have gained a large support from the scientific
community and are also a well-established methodology in control theory for system identification
and time series analysis [
2
]. Here, we will concentrate on the last two types that have been applied
by engineers for many years to a wide variety of applications and have proven that the methods pro-
duce viable phenomenological descriptions when properly applied [
23
,
24
]. One of the advantages
of the techniques is that they quickly find, with relatively simple algorithms, optimal mappings (in
