Biomedical Engineering Reference
In-Depth Information
peak-to-peak amplitude on average, and they are biphasic or triphasic in morphology depending
upon the relationship of the electrode with respect to the cell body. Because of the electrophysi-
ological morphology of the action potential (1-msec biphasic wave), the signals contain frequency
in the range of 300 Hz to 7 kHz; therefore, it is common to high-pass filter the signal collected by
the electrode at 300 Hz. The specificity of the spike firing is unparalleled (i.e., one can spike sort
[
64
] the data to attribute it to a specific neuron). SUA can then be modeled as a Poisson-distributed
point process [
65-68
]. The tradeoffs from a signal processing perspective embedded in the LFP and
spike representation should be clear: LFPs loosely measure the electrical field characteristics of a re-
gion of brain tissue and the time varying activity of one or more neural populations; therefore, they
are unspecific about a single neural behavior. On the other hand, the spike trains are very specific
about the excitability of a given neuron, but they coarsely subsample the neural population. Unfor-
tunately, the relationships between spike trains and LFPs are not well understood. It is reasonable
to model LFP, ECoG, and EEG as nonstationary, perhaps nonlinearly generated random processes,
whereas SUAs require a point process modeling.
From this discussion, it should also be apparent that there is insufficient functional knowledge of
neural population dynamics in neuroscience to help guide a principled engineering approach to create
realistic models of brain function or even of neural population dynamics. Therefore, we are left with
the conventional engineering, statistics, and physics tools to quantify physical phenomena. Naturally,
the predominance of linear approaches, Gaussian statistics, can be expected, but they should be taken
with a grain of salt because they have been developed for a set of constraints likely not operational in
brain function. In fact, the golden rule taken from years of working in this area is that justifying with
data the assumptions of the modeling approach is critical for progress. The time dimension is of utmost
importance for the brain because its role is to anticipate what is going to happen in an unpredictable
and complex world. Therefore, assumptions that disregard variability over time (such as the stationarity
assumption in random processes) should be avoided. Unfortunately, the tools of nonlinear dynamics are
not sufficiently developed to help in this process, but we hope that someday they will come to age.
1.5 MoToR BMIS
Because of the breadth of the BMI topic, this topic will be speciically focusing on motor BMIs
and will only describe properties of neurons sampled from the motor system and signal processing
models and algorithms for SUA inputs. The model inputs either use point processes per se or a
time-to-amplitude conversion that is called
counting
in point processes [
67
] or
rate coding
(binning)
in neurosciences [
69
] that allows the use of conventional time series analysis as found in signal pro-
cessing. A brief summary of BMIs for command and control using the EEG will be provided here
and in the appendix for completeness.
