Dynamic Modeling of Spinal Electromyography sEMG during Various Conditions

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Dynamic Modeling of Spinal Electromyography
(sEMG) during Various Conditions

• P. Lohsoonthorn and E. A. Jonckheere
• Dept. of Electrical EngineeringSystems
• University of Southern California
• Los Angeles, CA 90089-2563
• R. Boone
• PRP Enterprises
• Auckland, New Zealand

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This research,which involves human subjects,was
approved by the Institutional Review Board
(IRB)of the University of Southern California
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Alf BreigsAdverse Mechanical Tension in the
Central Nervous System

• The dura mater of the spinal cord is mechanically
  attached to the bony structures at vertebra C2-C3
  (Gray Anatomy).
• The dentate ligament connects the pia mater to
  the dura.
• At the sacral level, the pia matter ends caudally
  in the filum terminale which is attached to the
  periosteum of the coccyx.
• With these mechanical attachments of the spinal
  cord to the vertebra, vertebral misalignment, or
  postural problems, can create pathological
  tensions in the cord, impairing nerve activity.

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The dentate ligament is an extension of the pia
mater that attaches to the dura mater
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The spinal cord hangs on the dentate ligament,
itself attached to the dura mater, so as to avoid
excessive load on the brain stem and the pons
Pia mater
Dentate ligament
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Spinal Cord and Nearby Bony Structures
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The meninges attachments create excitatory
feedback that can make the motor reflex loop
unstable
Lamina IX ?,? motor neurons Facilitation/inhibitio
n
Motor fibers
Anterior or ventral
White mater
Gray mater
Inter neuron
Proprioceptive fibers
Sensory neurons
Posterior or dorsal
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The meninges attachments create excitatory
feedback that can make the motor reflex loop
unstable
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Typical sEMG signal y(k) recorded during this
event shows transitioning between burst and
quiet, background signal
4,000 points/sec sampling rate
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Simple excitatory (E) and inhibitory (I) neurons
models can reproduce transition between rhythms,
(e.g., ?-?, spindling-delta)
The thalamus is also known to sustain bursty,
spiky behavior
N. Kopell, We got rhythms Dynamical Systems of
the Nervous System, Notices of the American
Mathematical Society, Volume 47, Number 1,
January 2000.
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The Three Qualitative Levels to be Confirmed by
sEMG Analysis

• Level 1 early onset of motion, restricted to
  minimal oscillation localized around cervical
  dural attachment area (segmental, monosynaptic?)
• Level 2 motion becomes more refined and involves
  both the occiput-cervical and sacral-coccyx
  vertebral dural regions, resulting in a
  spatio-temporal phenomenon (intersegmental).
• Level 3 a third oscillatorthe chest-thoracic
  oscillatorbecomes entrained (supraspinal).

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General Signal Characteristics

• The overall signal is non-stationary, as
  manifested by autocorrelation and partial
  correlation functions decaying too slowly.
• Surprisingly, the burst part appears more
  stationary than the background part.
• The Dickey-Fuller unit root test reveals that a
  one-fold incrementation is enough to make the
  signal stationary.
• The overall signal seems to be switching among
  several ARIMA models
• One burst model and one background model
• Here, we switch among 12 ARIMA models, most of
  them being bursty.

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ARIMA(p,d,q) Modeling
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Derivation of 12 Baseline ARIMA Models
12 segments of 16 sec. each
Each segment is divided into 13 subsegments of
1.5 sec. each
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Each subsegment is subdivided into 10 intervals.
In each interval, the correlation ak and partial
correlation bk functions are computed.Each
interval defines a pointThen the
subsegment the most representative of the segment
is picked by clustering analysis.
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Clustering of Third Segment
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Once the correct subsegment is identified

• The autocorrelation and partial correlation of
  the subsegment is computed.
• The Smallest CANonical (SCAN) correlation and
  Extended Sample AutoCorrelation Function (ESACF)
  methods indicate that
• The Dickey-Fuller test indicates presence of unit
  root.
• We construct the incremented signal
• The unit root test fails on the incremental
  signal hence
• The chosen subsegment is given a model of the
  form

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Autocorrelation of Model 1
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Autocorrelation of Model 6
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Autocorrelation of Model 12
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Partial Correlation of Model 1
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Partial Correlation of Model 6
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Partial Correlation of Model 12
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Autocorrelation of 3rd Segment
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Partial Correlation of 3rd Segment
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Switching Criterion
To decide which of the 12 models best matches a
set of 25 data point of the experimental sEMG
signal, we use the following criterion
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Specificity of Model Relative to Level (1,2,3)
and Position (prone, supine)
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Transition from Level 2 (Model 3) to Level 3
(Model 4)
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sEMG Signal Variance versus Time
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sEMG Signal Variance versus Level of Care
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Normalized Prediction Error versus Time
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Normalized Prediction Error versus Level of Care
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Conclusions

• The dural attachments create additional paths
  destabilizing the motor reflex loop.
• The resulting rocking motion of the spine,
  passing through Levels 1, 2, 3, has some
  physical therapy benefits.
• The dynamic properties of the sEMG signal
  recorded on the paraspinal muscles provides
  confirmation of the Level at higher level the
  signal is more predictable.
• The real challenges are
• the utilization of the dynamic properties of the
  sEMG signal to map the neural pathways involved
• the understanding the nature of the dural
  attachment feedback.