Abstract.
The process of extracellular recording from animals cortex is rarely
automated. Moreover, such a procedure requires a constant human supervision
and could be very time consuming. Here we propose a new algorithm that
automatically controls the position of a recording electrode, while
maintaining a certain level of signal quality.
Introduction. Recording the electrical activity from a single
neuron or a group of neurons is a core activity in visual neuroscience.
To investigate increasingly complex issues, multi-electrode recordings
are becoming a preferred experimental method (see e.g. [1-2]). Extra-cellular
signals obtained from chronically implanted electrode arrays are also
a key component of emerging neural prosthetic systems [3-4]. Motivated
by some of the limitations in current multi-electrode technologies and
practice, our program will develop a new class of intelligent computer
controlled multi-electrode systems that can continually and autonomously
adjust their position so as to optimize and maintain the quality of
the recorded signal. For acute multi-electrode experiments, our control
algorithms will simplify the process of managing large electrode arrays
by automating the procedure of positioning and adjusting electrodes
to obtain high signal quality. In this way, our work should improve
the productivity of neuroscientists who use multi-electrode recordings
for their research. The success of this project would eventually lead
to micro-machined (MEMS) implantable movable probe devices. For chronic
experiments or neuro-prosthetic applications, the MEMS versions of our
movable probes will increase the longevity and quality of recording.
They will also allow the isolation of specific populations of neurons
which can, for instance, improve the decoding of information for prosthetics
applications.
Summary. Because of the complexity of experimental set-up, it
is necessary to develop appropriate algorithms and validate concepts
in a simulated environment. We use a previously published model of a
pyramidal cortical cell [5]. The model is stimulated by synaptic inputs
that are uniformly distributed through the dendrites. The potential
around the cell is usually modeled by Laplace equation with appropriate
boundary conditions. Solving the Laplace equation on a complex topology
such is that of a single cell is nearly impossible, therefore we need
to resort to approximating solutions. We use so-called line source approximation
[6], where each compartment is treated as a line segment, and the potential
at an arbitrary point in the space can be simply calculated by summing
the contributions of individual segments. This can be done for an arbitrary
set of points surrounding the neuron, and a typical look of such a field
is shown in Fig. 1. Note how the magnitude of the signal increases as
one gets closer to the cell body, as indicated by different scales.
To make the simulation more realistic we can corrupt the signals by
adding a noise with certain statistical properties. Using only first
order information such as the peak-to-peak amplitude (PTPA) of extracellular
spikes, it is conceivable that one should be able to guide the electrode
to a point close to the cell body. Indeed, moving a probe along a certain
direction and measuring the PTPA of the signal gives rise to an isolation
curve. The optimal position of the electrode is the one for which the
isolation curve is maximized. Since we are dealing with random signals,
the maximization of the isolation curve has to be cast in the framework
of stochastic optimization.
Unconstrained stochastic optimization of a scalar random function is
relatively well understood problem [7]. It is based on stochastic gradient
search method and is similar in nature to the standard optimization,
except that one needs to be more careful regarding the choice of the
step size of iteration. In particular, one has to choose the parameters
that will guarantee the convergence (in probability) of the recursion
to the actual solution. The method itself is based on calculating so-called
stochastic gradient. While provably convergent, this method can result
in continual dithering of the electrode near the isolation curve peak
due to noise influences. These oscillations may cause inflammation or
tissue damage. The electrode’s operation can be smoothed, while
still retaining the desirable properties of convergence to the peak,
by the following modifications that retain the same recursive movement
structure. The isolation curve is assumed to be a weighted sum of smooth
basis functions (we use Gaussian basis functions in the results given
below, but many choices will work). The coefficients in the sum are
determined from sample observations (using a least squares procedure),
and the number of basis functions are chosen using Bayesian probability
theory to prevent data overfitting. The gradient and Hessian are then
estimated from the smooth estimate of the isolation curve, and used
as needed. Moreover, this approach allows for the use of Newton’s
method with better convergence properties than those of the gradient
search method. Together, these improvements ensure convergence of the
algorithm while eliminating unwanted dithering.
The overall algorithm progresses in two stages. In the first exploratory
stage, the electrode moves from its initial placement with fixed step
sizes in order to find initial parameters of the cell isolation curve.
The second optimization stage starts when enough data is collected so
that a model can be fitted through the observations. Thereafter, electrode
movement is based on the evolving isolation curve. Since the moving
electrode can pick up signals from multiple neurons, the recorded spikes
are classified, and the signal source (neuron) that provides the largest
signal PTPA is tracked.
We must stress that in order to estimate the cell isolation curve on-line,
spikes must be detected, aligned, classified etc. in an unsupervised
and real-time fashion. Our algorithm uses a modular structure to implement
these spike processing functions. This modularity allows for easy substitution
of the basic signal processing techniques by improved ones. We have
already implemented some custom spike processing algorithms that are
better suited to the unsupervised needs of movable electrode control.
For example, spike detection is usually an off-line analysis that requires
supervised setting of thresholds or the construction of templates [8-9].
Note that the biphasic spike form can change in shape and amplitude
with electrode movement, making supervised threshold and template techniques
unsuitable. Consequently, we created a new real-time spike detection
method that is based on a wavelet decomposition of the spike train coupled
with a hypothesis testing procedure from signal detection theory. We
have shown using simulations based on real data that the technique outperforms
all other detection methods. To enable consistent tracking of the best
single cell in a multi-cell environment, the detected spikes must then
be properly clustered and identified. While statistically well founded,
many spike classification methods [8,10,11] require large volumes of
data, and are not applicable to our problem where only a few samples
are available. We currently use a classification scheme based on principal
components, although some emerging clustering techniques (e.g. super-paramagnetic
clustering) seem to offer better results.
A picture summarizing the algorithm based on the Gaussian basis function
method is shown in Fig. 2, even though the method based on polynomial
basis functions seems more promising. The algorithm was tested in the
presence of multiple (two) neurons, where the tissue movement due to
electrode penetration was modeled as a simple rigid motion of the two
neurons.
Conclusions. We conclude by summarizing the accomplishments so
far.
We developed a computational environment for modeling extracellular
field potential. By using first order information only, we can guide
the electrode toward the point that provides better quality signals
and SNR. We checked the convergence of the algorithm and the consistency
of the solution by searching along many different directions. Next steps
should include:
Using more sophisticated response characterization (shape, frequency,
phase)
Modeling the load effect of the electrode
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Figure 1. Spatio-temporal variations of the extracellular potential
