Control signals generated through
Blind Signal Separation of neural recordings
W. Tesfayesus, D.M. Durand
Department of
Biomedical Engineering,
wondimeneh.tesfayesus@case.edu
Abstract
Functional electrical stimulation can be used to
partially restore lost motor activities in neurologically impaired patients.
The control signals for these neural prostheses can be generated from selective
recordings of neural signals through nerve cuff electrodes.
However, selective recordings are still a weighted
aggregate of the electrical activity of the fascicles within the nerve. The
actual fascicular signals remain unknown. We propose to test, through a
simulation study, the hypothesis of using blind source separation (BSS) of
neural recordings made using the FINE to recover independent fascicular signals
which will be used to generate the control signals. In BSS, original source
signals are recovered from a recording of their linear mixtures. We introduce
here a post-BSS processing method that will deterministically relate a
separated fascicular signal to a contact point virtually locating a fascicle
within a nerve.
1. INTRODUCTION
Loss of lower body
function is generally caused by a proximal lesion or interruption of the nerve
connected to the affected peripheral muscles leading to paralysis. One of the
most prevalent methods of restoring lost peripheral function is through
functional electrical stimulation (
2. METHODS
II.1-Simulation of Fasciular
Signals and neural recordings
A fascicular signal is simulated from
superposition of a randomly delayed compound action potential AP(t). AP(t), generated
in Neuron [7], is a triphasic compound action potential with a duration of 1 ms
and represents the signal from a small subpopulation of fibers as voltage with
respect to time. Signal s, which is
the fascicular signal, is generated from N AP(t) signals, according to the
equation shown below, which is given in [13] and shown sufficient to simulate
fascicular electrical activity. In this study N = 61,790.
Background noise invariably present in
neural recordings is simulated by a linear addition of a uniformly distributed
random signal to s. The SNR of the
fascicular signal in this study was approximately 20 dB.
The potential distribution at the surface
of the nerve which comprises electrically active fascicles is simulated through
a finite element software package (ANSOFT). In AUTOCAD, the Flat Interface
Nerve Electrode (FINE) was added to the model as a silicone cover over an area
of the nerve. The conductivities were 0.0826 S/m radial and .5714 S/m
longitudinal for endoneurium, 0.0826 S/m for epineurium, 0.0021 S/m for
perineurium, 2 S/m for saline, and 10-7 S/m for silicone (used to
make the cuff electrodes). The nodes of Ranvier were introduced in the
fascicles as equidistant small cylinders of 6 μm diameter and 4 μm
length. The instantaneous potential distribution all over the cuff electrode
could be obtained whenever electrical activity, signal s(t), travelled through a fibber in one of the fascicles.
Fig 1. (a)
Simulated fascicular signal. The region during which the fascicle is active has
Gaussian distribution. (b) Experimental recorded nerve signal
Fig. 2. Geometry of simulated nerve submerged in
saline. (a) The nerve comprised of four fascicles with the FINE electrode
wrapped around it. (b) The nerve submerged in Saline bath (D = 6mm and L =
60mm).
It should be noted here that the signal in
the fascicles is a traveling signal and the potential distribution generated at
the electrode surface is accordingly time dependent. The potential distribution
at the electrode was also calculated in cases where several fascicles were
simultaneously active.
II.2-
Blind Source Separation and post-BSS processing
M channel recordings of P linearly mixed independent signal sources can be separated to
recover the original P signal sources
as long as M ≥ P.
In our case, the array of recorded signals x(t),
obtained from neural recordings made using the FINE, can be written in terms of
the original source signals s(t), the
mixing matrix A, and recorded noise n(t) as
x(t)
= As(t) + n(t)
The approximated independent sources a(t) would then be
a(t)
= Wx(t)
where W
is a demixing matrix,
W = A-1
W is obtained by minimizing an objective
function which measures the degree of independence between the elements of a obtained using W. Objective functions are real-valued functions of the
distribution of x(t). They should be
at a minimum once the original source signals have been recovered.
The objective
function used here is of the information theoretic class and consists of an approximation
to negentropy, its maxima are at the zero crossing of a known equation. The
solutions to the zeros crossing are estimated using
Post
BSS processing; matching a contact point to a fascicle
Inherently, BSS methods have a permutation
ambiguity. The separated fascicular signals cannot be consistently matched to a
fascicl
3. RESULTS
The simulated
fascicular signals are shown in fig 3.A. The recorded signals at the contact
points are shown in figure 3.B.
The simulated signals
were then separated using FastICA and are shown in figure 3.C. The vector a(t) of separated signals comprises the
estimation of the original fascicular signals which can be recognized by
comparing waveforms of the original and separated signals. In fifty trials the
mean values and the standard deviations of the correlation coefficients between
the original signals and their estimates were 0.86 and 0.15 respectively.
However, the relationship between the reconstructed signals and the fascicles
from which they originate is ambiguous.
Figure 4 is a
colour coded plot of the normalized columns of the estimated mixing matrices.
In figure 5, the original source signals and the estimated source signals after
post-BSS processing are shown.
4.
DISCUSSION AND CONCLUSIONS
We have showed in
this study that fascicular signals can be deterministically estimated from
peripheral nerve recordings using the FINE.
Fig 3. fascicular (A), recordings (B), and separated signals (C). The active regions of the fascicles can clearly be seen in the fascicular and separated signals.
Fig 4 Color coded plot of the columns of the estimated mixing matrix.
While following the arrows, we go from a first estimate of the mixing matrix to
a second estimat
Fig 5. Original
fascicular signals (left figure) and estimated fascicular signals after
post-BSS processing to fix BSS’ inherent permutation ambiguity
The fascicular signals were separated by Independent
Component Analysis, implemented by the FastICA algorithm of Hyvarinen. The
permutation ambiguity of BSS was solved by using a first estimate of the mixing
matrix as a template to rearrange the columns of all subsequent
estimations.
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Acknowledgements
Financial support was provided by NIH grant NS 32855 and the Department of Education GAANN fellowship program.