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M/EEG forward problem & solutions

M/EEG forward problem & solutions. Brussels 2011 SPM-M/EEG course January 2011. C. Phillips, Cyclotron Research Centre, ULg, Belgium. Forward Problem. Inverse Problem. Source localisation in M/EEG. Head anatomy. Forward problem. Head model : conductivity layout

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M/EEG forward problem & solutions

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  1. M/EEG forward problem& solutions Brussels 2011 SPM-M/EEG course January 2011 C. Phillips, Cyclotron Research Centre, ULg, Belgium

  2. Forward Problem Inverse Problem Source localisation in M/EEG

  3. Head anatomy Forward problem Head model : conductivity layout Source model : current dipole Solution by Maxwell’s equations

  4. Maxwell’s equations (1873) Ohm’s law : Continuityequation :

  5. Solving the forward problem • From Maxwell’s equations find: • where M are the measurements and f(.) depends on: • signal recorded, EEG or MEG • head model, i.e. conductivity layout adopted • source location • source orientation & • amplitude

  6. Solving the forward problem • From Maxwell’s equations find: • with f(.) as • an analytical solution • highly symmetrical geometry, e.g. spheres, concentric spheres, etc. • homogeneous isotropic conductivity • a numerical solution • more general (but still limited!) head model

  7. Analytical solution Example: 3 concentric spheres • Pro’s: • Simple model • Exact mathematical solution • Fast calculation • Con’s: • Human head is not spherical • Conductivity is not homogeneous and isotropic.

  8. Overlapping spheres in MEG Better but…

  9. Numerical solution • Usually “Boundary Element Method” (BEM) : • Concentric sub-volumes of homogeneous and isotropic conductivity, • Estimate values on the interfaces. • Pro’s: • More exact head shape • modelling • Con’s: • Mathematical approximations of solution •  numerical errors • Slow and intensive calculation

  10. Features of forward solution • Find forward solution (any): • with f(.) • linear in • non-linear in • If source location is fixed, then

  11. SPM solutions Source space & head model • Template Cortical Surface (TCS), in MNI space. • Canonical Cortical Surface (CCS) = TCS warped to subject’s anatomy • Subject’s Cortical Surface (SCS) = extracted from subject’s own structural image (BrainVisa/FreeSurfer)

  12. SPM solutions Jérémie Mattout, Richard N. Henson, and Karl J. Friston, 2007, Canonical Source Reconstruction for MEG

  13. SPM solutions Source space & head model • Template Cortical Surface (TCS), in MNI space. • Canonical Cortical Surface (CCS) = TCS warped to subject’s anatomy • Subject’s Cortical Surface (SCS) = extracted from subject’s own structural image (BrainVisa/FreeSurfer) Forward solutions: • Single sphere • Overlapping spheres • Concentric spheres • BEM • … (new things get added to SPM & FieldTrip)

  14. Conclusions • Solving the Forward Problem is not exciting but necessary… • Solution depends on data at hand: • MEG vs. EEG: • single sphere or overlapping spheres vs. 3 concentric spheres or BEM • Structural image available? • CCS (good enough) or SCS (tedious work) vs. TCS (best proxy) • Sensor location/head position available?

  15. Thank you for your attention

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