Biomedical Engineering Reference
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the ongoing neurophysiological changes throughout the recovery period after SCI.
Previous studies using SEP data for SCI detection have used changes in latency and
peak amplitude of SEP signals. The inherent disadvantage of time analysis is that
spectral changes cannot be detected. Moreover, some SEP signals, as we will demon-
strate later in this chapter, do not have a detectable latency or peak amplitude
following severe SCI.
A spectral coherence measure method based on SEP signals was successfully
used to provide a quantitative measure of SCI [42, 43]. Spectral coherence is the nor-
malized cross-power spectrum computed between two signals. The coherence func-
tion
gives
a
measure
of
similarity
between
signals
and
is
related
to
the
cross-correlation function. The magnitude-squared spectral coherence
) func-
tion of two signals
x
and
y
is a normalized version of the cross PSD between
x
and
y
and is defined as [39, 40]:
γ
xy
²(
ω
2
()
() ()
S
ω
ωω
()
xy
2
(3.15)
γω
=
xy
S
S
xx
yy
where
S
xy
(
ω
) is the cross-power spectrum between the
x
and
y
signals,
S
xx
(
ω
) is the
power spectrum of the
x
signal, and
S
yy
(
) is the power spectrum of the
y
signal.
Spectral coherence was used to study the SEP signals from 15 female adult
Fischer rodents before and after SCI [44]. Injury was induced by dropping a 10.0-g
rod with a flat circular impact surface onto the exposed spine from heights of 6.25,
12.5, 25, or 50 mm for mild, moderate, severe, and very severe injury. To generate
stimulation for SEP, subcutaneous needle electrodes were used for left and right
median and tibial nerves (1-Hz frequency, 3.5-mA amplitude, 200-
ω
s duration, and
50% duty cycle) without direct contact with the nerve bundle. Contralateral SEP
recordings were used for the left and right forelimbs, as well as the hind limbs. The
recorded SEP signal was then sampled at 5 kHz.
As expected, high coherence was observed to occur at low frequencies. Closer
observation of the average of the spectral coherence for the right hind limb baseline
with the right forelimb baseline for all rats (Figure 3.4) helped us choose a band of
125 to 175 Hz.
The spectral coherence variations over time before and after injury helped iden-
tify the effects of injury on limbs. Because the injury affected primarily the hind
limbs, the coherence associated with the forelimbs was relatively high (
μ
0.7)
throughout the period of observation. In practice, SEP information is not available
before injury. Hence, forelimb signals were used as control signals.
Figure 3.5 shows the spectral coherence (SC) for rats that were subjected to a
medium SCI level. It is interesting to note that Rat 10's right hind limb seems to have
recovered with an SC reading of 0.4 on day 4 after injury to an SC of 0.82 on day 82.
Rats 11 and 13 do not show good right hind limb recovery.
Spectral coherence reveals information specific to each rat that is missing in con-
ventional methods of assessing spinal cord injury. The results for improvement in
global spectral coherence over the recovery period may differ among the rats from
the same injury group. This could be due to several reasons such as the differences in
every individual's recovery or the exact location of injury.
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