14th Annual Dynamical Neuroscience Satellite Symposium

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14th Annual Dynamical Neuroscience Satellite
Symposium Frontiers in Neural Signal
Processing INTRODUCTION TO THE ANALYSIS OF
NEURAL SPIKING DATA Uri Eden Department of
Mathematics and Statistics Boston
University http//neurostat.mgh.harvard.edu/Prepr
ints.htm October 12, 2006
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Outline

• Motivating Problem Parkinsons disease and
  aberrant firing in the subthalamic nucleus (STN)
• Neural encoding using point process spiking
  models and GLM
• Encoding analysis of STN using GLM
• Tutorial Modeling spiking data with GLM

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Parkinsons Disease

• A chronic, progressive disorder of the central
  nervous system
• Caused by degeneration of dopaminergic neurons in
  the substantia nigra pars compacta (SNc)
• Hallmark Clinical Triad Rigidity, Tremor,
  Akinesia
• Associated with aberrant firing patterns
  throughout the basal ganglia

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The Basal Ganglia Network
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The Basal Ganglia Network
Lang, AE Lozano AM (1998) NEJM 3391130-1143
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The Basal Ganglia Network
Lang, AE Lozano AM (1998) NEJM 3391130-1143
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Deep Brain Stimulation
Lang, AE Lozano AM (1998) NEJM 3391130-1143
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Deep Brain Stimulation

• Localization of stimulating electrode guide in
  STN by
• 1) MRI/CT based stereotactic guidance
• 2) Characteristic spiking properties of neural
  recordings obtained during placement

Lang, AE Lozano AM (1998) NEJM 3391130-1143
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Spiking Activity in STN
Data acknowledgements Dr. Ramin Amirnovin, Dr.
Emad Eskandar,
Dept. of Neurosurgery, MGH
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Directed Hand Movement Task

• Characterize short and long term history effects
• Compare activity between different directions
• Compare activity prior to target presentation and
  during movement

Amirnovin et al., 2004, J. Neurosci.
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Short and Long-Term History Effects
Autocorrelation Function
Interspike Interval Histogram
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Direction Selectivity
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Effects of Movement
Rest
Movement
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Modeling Objectives

• Construct a single model capturing these effects
• Estimate model parameters and determine
  uncertainty of estimates
• Measure goodness-of-fit between model and
  observed data
• Determine relative effects of different model
  components

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Stochastic Neural Modeling
Input
Output
X
N
Point Process System Model
Eden, UT, Frank, LM, Solo, V, Barbieri, R
Brown, EN (2004) Neural Comp. 16971-998
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Point Process Likelihood
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Stochastic Neural Modeling
Input
Output
X
N
Point Process System Model
Eden, UT, Frank, LM, Solo, V, Barbieri, R
Brown, EN (2004) Neural Comp. 16971-998
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The Conditional Intensity Function

• Unified mathematical construct to model any
  neural spiking process
• Generalizes Poisson rate function
• Defines
• Provides building blocks for data likelihood and
  posterior distributions

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Conditional Intensity Models
A conditional intensity model is a function
In discrete time
Intensity Model Observed Spike Data Data
Likelihood
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The Generalized Linear Model
The Exponential Family of Distributions
To establish a Generalized Linear Model set the
natural parameter to be a linear
function of the covariates In this case
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Stochastic Models
Neural Spiking Models
Generalized Linear Models (GLM)
Linear Regression

• Properties of GLM
• Convex likelihood surface
• Estimators asymptotically have minimum MSE

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GLM Neural Models

• By selecting an appropriate set of basis
  functions we can capture any complex relation.
• Analysis of relative contributions of components
  to spiking

Truccolo W, Eden UT, Fellows MR, Donoghue JP,
Brown EN. (2004) J. Neurophys 931074-1089
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Neural Intensity Model for STN
Period-specific (stimulus) effect
Effect of spiking history
Conditional firing intensity function
long term Network dynamics
short term Intrinsic dynamics
Compute maximum likelihood estimates for
parameters using GLM
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Model Parameter Estimates
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Goodness-of-fit
Problem
Distribution of arbitrary statistics of spike
times, , are difficult to compute.
Solution
Time-rescaling theorem If we make the change of
variables, and the intensity model is correct,
then the will be i.i.d. exponential
random variables.
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Time Rescaling
Intensity (Hz)
z3
Rescaled Time
z2
z1
t3
t1
t2
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KS Plots
Graphical measure of goodness-of-fit, based on
time rescaling, comparing an empirical and model
cumulative distribution function. If the model
is correct, then the rescaled ISIs are
independent, identically distributed random
variables whose KS plot should produce a 45 line
Ogata, 1988.
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Component Model Fits
Short-term History Component
Stimulus Component
Long-term History Component
Full Model
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Component Model Fits
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Population Results

• Of the 24 oscillatory neurons analyzed
• All showed refractoriness
• 23 showed bursting
• 14 increased in intensity with movement
• 11 were directionally selective
• 21 had a period of relative inhibition at 20-30
  ms followed by increased firing probability at
  50-90 ms
• In all 21, this effect was attenuated by movement

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Summary

• Using a single GLM intensity model we captured
• Previously observed phenomena
• Refractoriness, bursting, movement related
  increase in intensity, directional selectivity,
  increased spiking probability at ISIs of 50-90
  ms, attenuation of oscillations with movement
• A previously undescribed phenomenon
• Decreased probability of firing at ISIs of 20-40
  ms
• Relative contributions of model components
• Short term intrinsic history is most predictive
  of spikes, yet most analyses ignore this
  component

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Summary

• The likelihood function for any point process can
  be expressed in a characteristic form, as a
  function of the conditional intensity.
• Generalized linear models extend linear
  regression methods making them appropriate to
  capture the statistical properties of spike train
  time series.
• Time rescaling provides goodness-of-fit measures
  for point process data.
• GLM analysis of STN suggests that movement
  pathologies are related to dysregulated network
  dynamics and that intrinsic properties are vital
  in describing spiking structure.

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To Be Continued