Seizure prediction by non-linear time series analysis of brain electrical activity

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Seizure prediction by non-linear time series
analysis of brain electrical activity
Ilana Podlipsky
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Epilepsy

• Epilepsy
• Synchronous firing of neurons which create high
  amplitude electrical discharges this storm
  inhibits other neural signals from getting
  through and disables function areas of the brain
• Statistics
• Everyone's brain has the ability to produce a
  seizure under the right conditions
• 1 in 20 will have an epileptic seizure at some
  time in their life
• Treatment
• Once diagnosed with epilepsy, people are
  generally given anti-epileptic medication. With
  the appropriate treatment, up to 70 of people
  could be seizure free.
• Characteristics / symptoms
• Seizures (40 different types)
• Aura, a sensory hallucination, often precludes
  a seizure
• EEG
• Recording of neural activity of targeted neurons
  / neural regions in brain
• Outputs brainwaves with associated rhythms and
  frequencies

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Examples of Seizure Morphologies
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The problem

• 30 of epileptics left untreated and victim of
• violent seizures
• Injuries resulting from epilepsy is most often
• caused by convulsive seizures
• If a lead-time could be provided by a seizure
• detection system, physical injury would be
  greatly reduced and quality of life increased

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Distinctive Features of Epilepsy

• The epileptogenic process is characterized by
  abnormal synchronous burst discharges in neuronal
  cell assemblies recordable during and in between
  seizures (Matsumoto Ajmone-Marsan 1964a,
  Matsumoto Ajmone Marsan 1964b Babb et al.
  1987).
• The transition to a seizure is caused by an
  increasing spatial and temporal non-linear
  summation of the activity of discharging neurons
  (Calvin 1971 Calvin et al. 1973).
• Due to the typically unpredictable occurrence of
  seizures it remains difficult to investigate the
  rules governing the initiation of seizure
  activity in humans.

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Brain as a Dynamic System

• A dynamical system consists of
• State
• Dynamics
• State the information necessary at any time
  instant to describe the future evolution of a
  system
• Dynamics defines how the state evolves over
  time

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Attractors and Dimensions

• Attractor
• Set of states towards which the system evolves
  Characterizes the long term behavior of the
  system
• Dimension of a system
• Describes the amount of information required to
  specify a point on the attractor - the long term
  behavior of a system
• More complex behavior more information is
  required to describe this behavior higher
  dimension of the system

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Brain as a Dynamic System

• The application of the theory of non-linear
  dynamics offers information about the dynamics of
  the neuronal networks.
• Several authors have shown that EEG/ECoG signals
  exhibit chaotic behavior (Basar,1990 Frank et
  al,1990 Pijn et al,1991).
• The correlation dimension D2 (Grassberger and
  Procaccia1983), provides good information about
  EEG complexity and chaotic behavior. (Mayer-Kress
  and Layne (1987) )

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Dynamics of Epileptic EEG

• The spatio-temporal dynamics of the epileptogenic
  focus is characterized by temporary transitions
  from high-to low-dimensional system states
  (dimension reductions) (Lehnertz Elger
  1995,1997).
• These dimension reductions allow the
  lateralization and possibly localization of the
  epileptogenic focus
• (Lehnertz Elger 1995,1997).

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Seizure prediction by non-linear time series
analysis of brain electrical activityChristian
E. Elger, Klaus Lehnertz (1998)

• Do prolonged and pronounced transitions from high
  - to low - dimensional system states characterize
  a pre-seizure phase?
• The identification of this phase would enable new
  diagnostic and therapeutic possibilities in the
  field of epileptology.

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Methods

• Electrocorticograms (ECoG) and stereoelectroenceph
  alograms (SEEG) of 16 patients
• 68 EEG epochs were analyzed.
• Fifty-two data sets of state 1 mean duration
  19.5 6.9 min range 640 min minimum distance
  to any seizure 24 h.
• 16 data sets of state 2 mean duration before the
  electrographic seizure onset 15.1 5.8 min
  range 1030 min seizure onset was defined as
  earliest signs of ictal ECoG/SEEG patterns).

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
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Methods

• A moving window dimension analysis was applied
• Data sets were segmented into half-overlapping
  digitally low-pass filtered consecutive epochs of
  30 s duration.
• Calculation of the modified correlation integral
  - the mean probability that the states at two
  different times are close.
• Estimate of the correlation dimension D2 for each
  epoch.

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
13
Calculation of correlation dimension

• Digital low-pass filtering (cut-off frequency 40
  Hz)
• Construction of m-dimensional vectors Xm(i) (i
  1, N m 1,. . . , 30) from the initial ECoG
  samples v(i) (i 1, N) of a given electrode
  using the method of delays (Takens, 1981)

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
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Correlation Integral

• For a stepwise decreasing radius r of a
  hypersphere centered at each vector Xm(i) for
  increasing m the correlation integral Cm(r) was
  calculated as (Grassberger and Procaccia, 1983)
• Counts the number of pairs of points with
  distance less then r.
• For small r Cm(r) rD2
• D2 slope of (in a linear region)

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Calculation of Correlation Dimension

• The correlation dimension D2 is obtained by
• D2slope of
• for decreasing r in a linear region
• Alternatively
• If no linear region
• is found D2 10

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Results

• For each selected electrode of the ECoG sets, a
  time profile of the estimated D2, values was
  constructed.
• The seizure (S) exhibits lowest dimension values.

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
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Results

• For both states maximum dimension reductions were
  always found inside the epileptogenic focus
  regardless of spike activity.
• During state 2, maximum dimension reductions were
  always observed in time windows immediately
  preceding seizures.
• In state 1
• Dimension reductions with a mean of 1.0 range
  0.5-2.5.
• Mean duration of 5.25min range 1.0010.75 min.
• In state 2
• Dimension reduction mean 2.0 range 1.03.5.
• Mean duration 11.50 min range 4.2525.00 min.
• Highly significant differences between maximum
  state 1 and pre-seizure state dimension
  reductions (Dr Z 3.41, P 0.0006Tr Z
  3.52, P 0.0004).

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
18
Discussion

• A reduced dimensionality of brain activity, as
  soon as it is of sufficient size and duration,
  precisely defines states which proceed to a
  seizure.
• I was demonstrated that the features of the
  pre-seizure state differ clearly from the one
  found during seizure.
• Pronounced dimension reductions of pre-seizure
  electrical brain activity are restricted to the
  area of the epileptogenic focus, they can reflect
  increasing degree of synchronicity of
  pathologically discharging neurons.

Seizure prediction by non-linear time series
analysis of brain electrical activity Christian
E. Elger, Klaus Lehnertz (1998)
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Discussion

• Correlation Dimension measure as presented here
  is subjective.
• Highly sensitive to noise.
• Subject specific.