Engineering, 2013, 5, 99-102
http://dx.doi.org/10.4236/eng.2013.510B020 Published Online October 2013 (http://www.scirp.org/journal/eng)
Using Variations of Somatosensory Evoked Potentials to
Quantify Spinal Cord Injury Level
Hasan Mir1, Hasan Al-Nashash1, Douglas Kerr2, Angelo All2, Nitish Thakor2
1Department of E lectrical Engineering, American University of Sharjah, Sharjah, UAE
2Department of Neurology, Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, USA
Received December 2012
ABSTRACT
Existing work indicates that the degree of variation of somatosensory evoked potential (SEP) signals between a healthy
spinal pathway and spinal pathway affected by spinal cord injury (SCI) can be used to evaluate the integrity of the spin-
al pathway. This paper develops a metric that exploits the time-do main features of SEP signals (relative amplitude, time
scaling, and time duration) in order to quantify the level of SCI. The proposed method is tested on actual SEP signals
collected from rodents afflicted with focal demyelination SCI. Results indicate that the proposed method provides a
robust assessment of the different degrees of demyelination in the spinal cord.
Keywords: Somatosensory Evoked Potential (SEP); Spinal Cord Injury (SC I); Signal Morphology
1. Introduction
The spinal cord provides a transmission pathway for
motor and sensory signals between the central and peri-
pheral nervous systems [1]. Thus, any spinal cord injury
(SCI) impairs signal transmission, resulting in sensory
and/or motor function loss. Many patients around the
world suffer from SCI. In the United States alone, it is
estimated that there are more than 250,000 SCI patients
[2]. Given the large number of SCI patients worldwide,
there is a clear need to develop methods for evaluating
the level of SCI. Such methods are important not only for
evaluating the effectiveness of therapeutic mechanisms,
but also in providing timely surg ica l in tervention. Indeed,
immediate treatment of even a small number of spared
fibers after incomplete SCI can greatly improve the pa-
tient’s quality of life.
SCI detection is commonly performed using electro-
physiological [3,4] and imaging [5,6] techniques. Imag-
ing based approaches such as MRI only reveal informa-
tion concerning the injury location and the anatomical
damage, but do not provide information about the func-
tional integrity of the spinal cord. Amongst electrophysi-
ological techniques used in SCI studies, the evoked po-
tential provides an assessment of the electrophysiological
response of the neural system to an external stimulus. In
particular, somatosensory evoked potentials (SEP),
which are cortical signals recorded in response to sensory
stimulation, are obtained by electrical stimulation of the
median nerve at the wrist or the posterior tibial nerve at
the ankle [7]. This technique can be used to monitor the
ongoing neurophysiological changes during the recovery
period after SCI. In [8], it was shown that the similarity
between a reference SEP signal taken from a healthy
spinal pathway and an SEP signal from an injured trans-
mission pathway is a strong indicator of the level of in-
jury. Thus, it provides a complement to qualitative, be-
haviorial based assessments such as the Basso, Beattie,
and Bresnahan (BBB) test [9].
Previous work [10-12] has been done to develop me-
trics for quantifying the level of SCI by comparing the
variation between SEP signals. While such methods
show promise, they do not explicitly account for the
temporal relationships that exist between the SEP signals
under comparison. In this paper, parameters relating the
time -domain variation between SEP signals collected on
rodents are used to evaluate the level of SCI. These pa-
rameters reflect differences in amplitude, duration, and
delay between the SEP signals, and can combined into a
single index to quantify the level of SCI.
The rest of this paper is organized as follows: Section
2 describes the protocol for collecting the SEP signals
from rodents. Section 3 describes metrics for quantifying
the level of SCI. Section 4 presents the results of apply-
ing the methods in Section 3 to the data descr ib ed in S ec-
tion 2.
2. Protocol and Data Collection
In accordance with the Rodent Survival Surgery Manual,
and with approval from the Institutional Animal Care and

H. MIR ET AL.
100
Use Committee at the Johns Hopk ins Un iversity, the SE P
data used in this paper was obtained by inducing focal
demyelination lesion in dorsal pathways of rodents’s
spinal cord. Recombinant myelin oligodendrocyte glyco-
protein (MOG) corresponding to the N-terminal se-
quence of rodent MOG amino acids 1 to 125 (MOG1-
125) was emulsified in incomplete Freund’s adjuvant
(S igma-Aldrich) as 1:1 mixture (Imject IFA; Pierce). 100
μl = 50 μg of this emulsified MOG1-125 (co urtesy o f Dr.
Sha Mi, Biogen-Idec, Cambridge, MA) was injected sub-
cutaneously near the base of the tail of each rodent at 2
contralateral sites (50 μl per area to minimize irritation to
the skin). The rodents were subjected to T9 laminectomy
and either (2 × 2 μl) cytokines (250 ng of TNF-α, 150U
of INF-γ and 40 ng of IL-6) or (1 µg) ethidium bromide
or a combination of the two was injected into dorsal
white matter using Hamilton needle (31 G). This causes
inflammatory demyelinating lesions, similar to the active
demyelinating plaques that characterize multiple sclero-
sis (MS). Every seven days thereafter, SEP recordings
were performed. The signal-to-noise ratio of the SEP
signals was improved via averaging.
3. Quantification Metrics
Consider two signals: a reference signal
)(
1
ts
and a test
signal
)(
2
ts
, both defined over some time interval
21
ttt ≤≤
, as shown in F igure 1. It may be observed that
compared to the reference signal
)(
1
ts
, the test signal
)(
2ts
exhibits the following characteristics:
1) The amplitude scale has changed;
2) The time scale has changed;
3) The relative time positions have shifted.
Various methods have been proposed in the literature
to quantify the variation between two signals. Amongst
the simplest methods, the Euclidean (
2
l
) distance pro-
vides a simple measure of signal v ariation. However, it is
not appropriate for cases when the two signals are not
temporally aligned, as in Figure 1. A more sophisticated
measure is provided by the Pearson correlation coeffi-
cient (PCC), defined as:
( )( ) ( )
( )( )
( )( )
212
1
12 22
22
12
11
d
,= dd
t
t
tt
tt
s tstt
stst sttstt ρ
∫
∫∫
(1)
The PCC is a measure of linear dependence, and is
commonly used as a metric to quantify the similarity
between two signals. A key weakness of the PCC, how-
ever, is its insensitivity to amplitud e differences.
In this paper, a more robust means to characterize the
variation between two signals is proposed. Towards this
end, consider again the effects shown in Figure 1. Let
the transformation parameters
),,( τβα
denote the
change in the amplitude scale, time scale, and relative
Figure 1. An illustration of signal variations between a re-
ference and test signal.
time position, respectively. As such, an approximation
)(
ˆ
1
ts
of the reference signal
)(
1
ts
may be generated by
transforming the test signal
)(
2
ts
in the following
manner:
( )







−
β
τ
α
t
sts 21 =
ˆ
(2)
In order to determine the degree to which trans-
formation parameters approximate the reference signal
)(
1
ts
, define the error signal
( )( )
tstste
11
ˆ
=)( −
(3)
The energy of the error signal will be used to define
the cost function
22
1
=( )d
t
t
J ett
∫
(4)
A suitable solution for the value of the transformation
parameters
),,( τβα
as such may be found through
solving the optimization pr oblem
( ) dt
t
stsJ
t
t
2
21
2
1 ,,,,
argmin
=
argmin 






−
−
∫
β
τ
α
τβατβα
(5)
The solution to (5) can be found using standard
optimization algorithms such as the Nelder-Mead method
[13].
To quantify the degree of SCI, a measure is proposed
that combines the deviation of the transformation para-
meters from their ideal values. In the ideal case of no
signal warping, the amplitude and time scale parameters
α
and
β
have a value of one, while the time shift
parameter τ has a value of zero. As such, a suitable
metric to quantify the overall degree of signal variation
(and hence the level of SCI) is:
( )( )() τβαλ +−+− 11=,
21
tsts
(6)

H. MIR ET AL.
101
4. Experimental Results
Adult female Fischer rodents were injected with rMOG,
after which SEP signals from the forelimb (
)(
1
ts
) and
hindlimb (
)(
2
ts
) were collected at various stages. The
forelimb SEP signal is used to provide a reference
(healthy) signal, since injury is inflicted below the
forelimb and thus does not impair the spinal pathway. In
view of the level of SCI, the injury severity is classified
into three grades which are termed moderate, severe, and
very severe. For the results in this section, the value of
the PCC
( )()()
tsts
21
, ρ
and the proposed quantification
metric
( )()()
tsts
21
, λ
are computed for SEP signals
collected on a representative rodent sample and discussed
below.
Figures 2-4 show SEP signals for various levels of
SCI. In addition to showing the forelimb and hindlimb
SEP signals
)(
1
ts
and
)(
2
ts
, the transformed hindlimb
SEP signal







−
β
τ
α
t
s2
is also shown, where the para-
Figure 2. SEP signals for moderate SCI.
Figure 3. SEP signals for severe SCI.
Figure 4. SEP signals for very severe SCI.
meters
),,( τβα
were computed as the solution to (5)
using the implementation of the Nelder-Mead method
provided by the MATLAB function f minsearch. It can be
seen that the forelimb SEP signal is fairly stable across
all injury levels, lending credence to its use as a reference
SEP signal. Conversely, because SCI is inflicted above
the hindlimb, the corresponding SEP signal exhibits a
large variation across injury levels. These variations can
be exploited to quantify the level of SCI.
It may also be noted in Figures 2-4 that that the
optimization in (5) produces a solution that naturally
matches the position and width the characteristic peak
that is present in all SEP signals. Even though the
amplitude scale parameter α is perhaps the most direct
indicator of injury level, the time scale and time shift
parameters also contribute to quantifying the severity of
SCI. Table 1 provides a comparison of the PCC
( )()()
tsts
21
, ρ
and the proposed quantification metric
( )()()
tsts
21
, λ
for the various level of SCI. It is apparent
that the PCC yields non-monotonic and similar values
across injury levels, r esu lting from the insens itiv ity of the
PCC to amplitude differences. In comparison, the pro-
posed quantification metric yields values that are re-
presentative of the degree of time-domain variation be-
tween the signals. This gives the proposed metric an
advantage in clinical settings, since the values it yields
are directly related to the level of SCI, and the relatively
large spread of values aids in performing a quick and
simple injury assessment.
5. Conclusions
The level of SCI is indicated by the degree of time-
domain variations between the SEP signals from a
healthy spinal pathway and an injured spinal pathway.
Conventional metrics for quantifying the variation be-
tween two signals, such as the PCC, do not account for
important signal characteristics and can yield erroneous
results. The quantification method developed in this
paper uses the differences in amplitude, duration, and
delay between SEP signals, to quantify the level of SCI.
Results for SEP signals collected on rodents show that
the proposed quantification metric yields values that
reflect the degree of variation between forelimb and
hindlimb signals, and can thus provide a robust eva-
luation of the level of SCI.
Table 1. Comparison of SCI Levels and metric.
Metric Moderate Severe Very Severe
( )( )() tsts 21 , ρ
0.62 0.77 0.69
( )( )() tsts 21 , λ
0.64 1.80 6.88
46810 12 14
-50
0
50
100
150
200
Time (ms)
Amplitude (
µ
V)
Forelimb SEP
Hindlimb SEP
Transformed Hindli m b SEP
468 10 12 14
-50
0
50
100
150
200
Time (ms)
Amplitude (
µ
V)
Forelimb SEP
Hindlimb SEP
Transformed Hindlim b SEP
468 10 12 14
-50
0
50
100
150
200
Time (ms)
Amplitude (
µ V)
Forelimb SEP
Hindlimb SEP
Transformed Hindlim b SEP

H. MIR ET AL.
102
6. Acknowledgements
This work was supported b y the Maryland Ste m Cell Re-
search Fund 2007-MSCRFII-0159-00 .
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