EEGMEG source reconstruction

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EEG/MEGsource reconstruction
Jean Daunizeau Vladimir Litvak Wellcome Trust
Centre for Neuroimaging 9 / 05 / 2008
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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Introduction EEG/MEG and neuroimaging
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Introduction forward/inverse problems
definitions
? Forward problem modelling

• Inverse problem estimation of the model
  parameters

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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Forward problem physical model of bioelectrical
activity
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Forward problem the general linear model
Y KJ E1
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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Inverse problem an ill-posed problem

• Jacques Hadamard (1865-1963)
• Existence
• Unicity
• Stability

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Inverse problem an ill-posed problem

• Jacques Hadamard (1865-1963)
• Existence
• Unicity
• Stability

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Inverse problem cortically distributed current
dipoles
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Inverse problem regularization
data fit
constraint (regularization term)
W I minimum norm method
W ? LORETA (maximum smoothness)
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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Bayesian inference principle
likelihood
prior pdf
model evidence
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Bayesian inference hierarchical generative model
Q (known) variance components
(?,µ) (unknown) hyperparameters
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Bayesian inference hierarchical generative model
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Bayesian inference SPM implementations
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Outline

• Introduction
• Forward problem
• Inverse problem
• Bayesian inference applied to the EEG/MEG inverse
  problem
• Conclusion

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Conclusion at the end of the day
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Conclusion summary
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Many thanks to Karl Friston, Stephan Kiebel,
Jeremie Mattout
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Bayesian inference expectation-maximization (EM)
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Bayesian inference expectation-maximization (EM)