Hemodynamic Models: Investigation and Application to Analysis in Brain Imaging

1
Hemodynamic Models Investigation andApplication
to Analysis in Brain Imaging

• Thomas Deneux
• PhD advisor Olivier Faugeras

Jury Line Garnero John E. Mayhew Habib
Benali Nikos Paragios Jean-Baptiste Poline
Gilles Dowek Olivier Faugeras
2
Thesis history
EEG-fMRI fusion ?
Hemodynamic Models
EEG-fMRI fusion algorithm
Model identificationin fMRI
Investigation inOptical Imaging
Hypothesis testingand model selection
New blood flow estimation technique
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Outline

• INTRODUCTION AND PROBLEMATIC
• EEG-fMRI fusion ?
• The hemodynamic response ? dynamical systems
• Questions
• APPLICATION TO ANALYSIS
• Reminder on GLM methods
• Adaptation to nonlinear models and results
• Estimation of the neural activity and application
  to EEG-fMRI fusion
• Conclusion
• INVESTIGATION
• Investigation in Optical Imaging nonlinearities
  and delays
• A new technique for the estimation of blood flow
• Conclusion

4
Outline

• INTRODUCTION AND PROBLEMATIC
• EEG-fMRI fusion ?
• The hemodynamic response ? dynamical systems
• Questions
• APPLICATION TO ANALYSIS
• Reminder on GLM methods
• Adaptation to nonlinear models and results
• Estimation of the neural activity and application
  to EEG-fMRI fusion
• Conclusion
• INVESTIGATION
• Investigation in Optical Imaging nonlinearities
  and delays
• A new technique for the estimation of blood flow
• Conclusion

5
EEG-fMRI fusion ?
EEG
Maxwell equations
(LENA laboratory, Paris)
neural activity
?
fMRI
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The hemodynamic response
Blood flow regulation
CASE WESTERN RESERVE UNIVERSITY
Blood volume and oxygenation dynamics
Blood flow
Paramagnetic effect
O2 consumption
signal BOLD
Neural activity
energy consumption
deoxy-hemoglobin
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The Balloon Model (1/2)(Buxton et al., 1998,
Friston et al., 2000)
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The Balloon Model (2/2)
blood inflow
a. u.
time (s)
time (s)
blood volume
deoxyhemoglobin
BOLD signal (at 1.5 T)
time (s)
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Formalization dynamical system(SDE stochastic
differential equations)
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Example outputs
a. u.
change
change
change
time (s)
time (s)
time (s)
time (s)
change
change
change
change
time (s)
time (s)
time (s)
time (s)
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Outline

• INTRODUCTION AND PROBLEMATIC
• EEG-fMRI fusion ?
• The hemodynamic response ? dynamical systems
• Questions
• APPLICATION TO ANALYSIS
• Reminder on GLM methods
• Adaptation to nonlinear models and results
• Estimation of the neural activity and application
  to EEG-fMRI fusion
• Conclusion
• INVESTIGATION
• Investigation in Optical Imaging nonlinearities
  and delays
• A new technique for the estimation of blood flow
• Conclusion

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Analysis of fMRI data
1
0.8
0.6
arb. units
Stimulation
0.4
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time (s)
Neural responseHemodynamic reponsefMRI measure
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Measured BOLD
signal value
270
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Cognitive questionse.g. activated voxel ?
250
0
20
40
60
80
100
120
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160
180
200
time (s)
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General Linear Model methods (1/3)the linear
assumption
HRF
Neural activity
Empirical hemodynamic response function (HRF)

time (s)
time (s)

BOLD (fMRI) response
time (s)
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General Linear Model methods (2/3)the linear
regression

• Model
• Least square estimator

drifts noise
c
b
a
norm. change
1.06
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0.97
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0.96
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General Linear Model methods (3/3)hypothesis
testing (Fisher test)

• 2 models
• Building a statistic
• Which follows a Fisher law under the first model
  hypothesis
• The p-value of indicates whether the first
  model is acceptable.

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Nonlinear Model methods (1/2)Model identification

• Deterministic approximation
• Parameter estimation needs the computation of
  the gradient

0.06
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Nonlinear Model methods (2/2)Model comparison

• 2 models
• Building a statistic
• Which follows a Fisher law under the first model
  hypothesis and linear approximations
• The p-value of indicates whether the first
  model is acceptable.

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Experimental results (1/3)Activation detection
on raw signals
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Experimental results (2/3)Average responses
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Experimental results (3/3)Identification and
comparison on average signals
Linear model
M
First model family
Second model family
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Neural activity estimation (1/2)Kalman filter
and smoother

• New dynamical system where the neural activity
  belongs to the hidden-states
• The Extended Kalman Filter (EKF) and Smoother
  (EKS) compute iteratively the distribution of the
  hidden-states (mean variance)

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Neural activity estimation (2/2)Result on the
fMRI experiment
fMRI signal
0.06
0.05
fract. change
0.04
0.03
0.02
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0
-0.01
-0.02
-0.03
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time (s)
Estimated neural activity
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arb. units
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time (s)
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EEG-fMRI fusion (1/2)formalization

• Consider all voxels together and include an EEG
  measure

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EEG-fMRI fusion (2/2)results on synthetic data
activity estimated using fMRI only
neural activity ground truth
a. u.
a. u.
time (s)
activity estimated using EEG only
time (s)
a. u.
fMRI simulation
EEG simulation
time (s)
activity estimated using EEG fMRI
fract. change
a. u.
a. u.
time (s)
time (s)
time (s)
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Conclusion why use biologically plausible models
?

• Not necessary for simple cognitive questions
  (e.g. activation detection)
• Highly necessary for specific questions on
  amplitudes and time courses (e.g. presence of
  neural habituation)
• A convenient framework for neural time course
  estimation, using fMRI alone or in combination
  with another modality (e.g. EEG)

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Outline

• INTRODUCTION AND PROBLEMATIC
• EEG-fMRI fusion ?
• The hemodynamic response ? dynamical systems
• Questions
• APPLICATION TO ANALYSIS
• Reminder on GLM methods
• Adaptation to nonlinear models and results
• Estimation of the neural activity and application
  to EEG-fMRI fusion
• Conclusion
• INVESTIGATION
• Investigation in Optical Imaging nonlinearities
  and delays
• A new technique for the estimation of blood flow
• Conclusion

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Nonlinearities ?

• Nonlinearities in the short time range were
  attributed to neural habituation
• Could they be due to a nonlinear relationship
  between neural activity and the flow response
  instead ?

200ms
1s
21s
41s
81s
5200s
21s (5s ISI)
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Investigation in Optical Imaging (1/3)experiment
presentation
fract. changes
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Investigation in Optical Imaging
(2/3)nonlinearities

• The neural activity is linear with respect to
  the stimulation length
• The blood flow response is nonlinear with respect
  to electrical activity
• A simple flow habituation model can predict part
  of these nonlinearities

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Investigation in Optical Imaging (3/3)delays

• The flow response is delayed compared to the
  volume response
• The elucidation of these delays requires to
  consider each vascular compartment separately

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Blood flow estimation (1/2)
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Blood flow estimation (2/2)

• Estimation of hemoglobin motion requires
• Frame coregistrations
• Vessel direction detection
• Spatial and temporal filterings
• Detection of directions in (1Dtime) images with
  the structure tensor
• Heart pulsation could be detected
• Different compartments showed different responses
  to the visual stimulation

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Conclusion which additional modeling are
required ?

• Blood dynamic dynamics in the artery /
  capillary / vein compartments and possible
  nonlinearities
• Relation between electrical activity and
  hemodynamic Which part of the electrical
  activity (intra-cellular potential, spikes)
  ?Which dependancy on amplitudes, frequencies ?

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Conclusion future works ?

• ANALYSIS
• Apply EEG-fMRI to real data epilepsy, visual
  experiments
• For that purpose, improve the link between
  electrical and metabolic activities
• Also, other techniques than Kalman filter could
  handle more nonlinearities
• INVESTIGATION
• Work on new models of the hemodynamic processes
  (Zheng et al., 2005)
• For that purpose, improve and use the new flow
  estimation technique