Theory: modeling, localization and imaging

Transcription

1 Electromagnetic Brain Mapping with MEG/EEG Theory: modeling, localization and imaging Sylvain Baillet Imaging Group Cognitive Neuroscience & Brain Imaging Lab. Hôpital de la Salpêtrière CNRS UPR640 - LENA MEG Center University Pierre & Marie CURIE Paris, France MEG/EEG Brain Mapping Course, HBM2006, June 11 Sylvain.Baillet@chups.jussieu.fr Sylvain Baillet HBM06-1/33

2 Course Objectives Provide elements to answer the following questions: Understand the basics of forward & inverse problems Review main methodological principles Discuss the spatial resolution of MEG/EEG source imaging Suggest approaches to the evaluation of performances Sylvain Baillet HBM06-2/33

3 From empirical localization Sylvain Baillet HBM06-3/33

4 to Dynamic Brain Mapping Sylvain Baillet HBM06-4/33

5 Key-concept # 1 : Image Reconstruction Sylvain Baillet HBM06-5/33

6 Image Reconstruction: example Radioastronomy: interferometry VLA (27) 27 units, 25 m diameter = resolution of a 130Km diameter telescope Sylvain Baillet HBM06-6/33

7 Principles of Image Reconstruction (1): Image result from some data processing (2): Multiple sensors are super-additive : multiple measures help enhance image quality Sylvain Baillet HBM06-7/33

8 Key-concepts # 2 Modeling biophysics of measurements From the origins of the signals to sensors Solution to the Forward Problem Adapted from Lauri Parkkonen Sylvain Baillet HBM06-8/33

9 Key-concepts # 3 Estimation Adjust the free parameters of the forward model to match the data and possibly some additional expectations Solution to the Inverse Problem Sylvain Baillet HBM06-9/33

10 Modeling phase Solving the MEG/EEG forward problem Sylvain Baillet HBM06-10/33

11 Modeling neural generators Key-concept # 4 Current dipole Building block for the modeling of coherent activity of cortical pyramidal cell assemblies Sylvain Baillet HBM06-11/33

12 Modeling : Electromagnetic Fields of Neural Activity Distance to sensor (d) A Sensor (measure) Neglect propagation if : Wavelength λ λ >>d Propagation of electromagnetic fields in tissues Sylvain Baillet HBM06-12/33

13 Modeling : Electromagnetic Fields of Neural Activity Hamalainen et al., Rev Mod. Phys., 1993 Sylvain Baillet HBM06-13/33

14 Modeling : Electromagnetic Fields of Neural Activity λ=65m at f = 100Hz in head tissues Sensors: average distance to neural generators = 0.15m Quasistatic assumption : Neglect propagation of EM waves Sylvain Baillet HBM06-14/33

15 Modeling : Fields and potentials produced by a current dipole MEG EEG Differences of scalp electric potentials p ( V ) = J σ Ohm s law Magnetic induction 0 J( r') R B( r) = µ dv' 3 4Π R Biot & Savart p J( r) = J ( r) σ Coupling ( r) V ( r) Physics show MEG & EEG are complementary and can be combined Sylvain Baillet HBM06-15/33

16 Geometric modeling of head tissues Spherical geometry Center of the sphere Sylvain Baillet HBM06-16/33

17 The current dipole in a spherical head Fields and potentials can be analytically derived Fast and exact computation Key-concept # 5 A radial current dipole produces no magnetic field outside a closed spherical volume conductor Silent source configurations also exist for EEG Forward model tells us there will not be a unique solution to the inverse problem: Sources can be recovered up to some silent source configuration Sylvain Baillet HBM06-17/33

18 Realistic modeling of head tissues Processing of individual MRI Anatomical MRI Tissue segmentation Define homogeneous compartments Free software solutions: freesurfer, (BEM, FEM) Realistic modeling Tessellations BEM - FEM Sylvain Baillet HBM06-18/33

19 Estimation phase Solving the MEG/EEG inverse problem Sylvain Baillet HBM06-19/33

20 From forward to inverse: fitting the data? data model residuals - = Adjust model parameters Minimize residuals between source model and data E.g. in the least-squares sense Sylvain Baillet HBM06-20/33

21 There is no unique solution to the identification of the MEG and EEG generators But! Key-concept # 6 One single MEG/EEG dataset can originate from an infinite number of current distributions Ill-posed inverse problem Few solutions are compatible with constraints from : Electrophysiology and cortical anatomy Cross-condition and cross-subjects inferences Multimodal investigations (MEG+EEG+fMRI+ ) Sylvain Baillet HBM06-21/33

22 Inverse modeling: two main approaches Localization approach Imaging approach Point-like, equivalent current dipole models Spatial filters (DICS, SAM, beamformers) Signal classification (MUSIC et al.) How many dipoles? Spatial extension of neural activation? Distributed source models Minimum-norm, LORETA, MNE Under-determined (200 data samples, unknowns) Sylvain Baillet HBM06-22/33

23 Localization & spatial-resolution: phantom study Leahy et al., Clin. Neurophys Sylvain Baillet HBM06-23/33

24 Localization & spatial-resolution: phantom study Dipole localization errors 65 electrodes (equivalent to approx. 128 whole-sclap coverage) 122 MEG channels Localization using R-MUSIC true fitted Leahy et al., Clin. Neurophys Sylvain Baillet HBM06-24/33

25 Dipole fitting illustrated 50% noise RMS Sylvain Baillet HBM06-25/33

26 Dipole fitting illustrated Is it reproductible? 50% noise RMS Sensitive to initialization Sylvain Baillet HBM06-26/33

27 Localization in real life Adjust dipole parameters at a selected signal latency Somatosensory primary finger response t=[20,40] ms Meunier et al., Ann. Neurol., 2001 Sylvain Baillet HBM06-27/33

28 Localization and beyond Meunier et al., Ann. Neurol., 2001 Darvas et al., NeuroImage., 2004 Sylvain Baillet HBM06-28/33

29 Localization and beyond Darvas et al., NeuroImage., 2004 Bias and standard errors can be estimated from data Sylvain Baillet HBM06-29/33

30 Imaging & spatial-resolution: phantom study returns 61 electrodes Conductivity profile Fit a virtual cortical surface to evaluate imaging approaches Baillet et al., Phys. Med. Biol Sylvain Baillet HBM06-30/33

31 Imaging & spatial-resolution: phantom study returns Source magnitudes (arbitrary units) Max True Source Label Original Source Linear estimator (MNE) Wang et al,, 1991 Non-linear estimator (ST-MAP) Baillet et al Baillet et al., Phys. Med. Biol Sylvain Baillet HBM06-31/33

32 Imaging illustrated: tennis-ball interception ms P. Senot et al., submitted release catch Sylvain Baillet HBM06-32/33

33 Review MEG-EEG: yet another application of imaae reconstruction Definitions of forward & inverse problem Basic properties of MEG-EEG inverse problem Non uniqueness if no constaints added Resulting image is dependent on source model and estimation approach Localization and imaging approaches Spatial resolution Absolute spatial resolution is fair (1 cm); Relative spatial resolution is very good MEG > EEG Use statistical inference (coming next in the course) to further refine spatial selectivity Sylvain Baillet HBM06-33/33