Introduction Exploring the Brain’s Activity: a signal and image modeling challenge Maureen Clerc Inria EUSIPCO, Nice, September 2015 Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 1 / 45
Introduction Introduction Functional areas of the brain schematic organization variability of cortical foldings subject-dependent localization through exploration How to localize brain activity: invasively: brain stimulation non-invasively: functional brain imaging Example: presurgical evaluation of epilepsy Epileptogenic regions Eloquent functional regions Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 1 / 45
Introduction Introduction 1924: Hans Berger measures electrical potential variations on the scalp. birth of Electro-Encephalography (EEG) several types of oscillations detected (alpha 10 Hz, beta 15 Hz) origin of the signal unclear at the time scalp topographies ressemble dipolar field patterns dipolar topographies modern on a sphere EEG Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 2 / 45
Introduction From electric to magnetic fields A dipole generates electric + magnetic fields 1963: MCG Magnetocardiography, 1972: MEG Magneto-Encephalography , D. Cohen, MIT. But: very weak signal, only measured in shielded environment Relies on Superconductive QUantum Interference Device. 10 − 9 car at 50m lung particles 10 − 10 screwdriver at 5m human heart 10 − 11 skeletal muscles, fetal heart 10 − 12 transistor at 2m human eye, human brain (alpha) 10 − 13 human brain (evoked response) 10 − 14 (order of magnitude, SQUID system noise level 10 − 15 in Tesla) Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 3 / 45
Introduction MEG instrumentation MEG center, Piti´ e-Salpˆ etri` ere hospital, Paris Advantage of MEG over EEG: spatially more focal Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 4 / 45
Introduction Example: functional imaging within the visual cortex Primary visual cortex = V1 (Brodmann area 17) Receptive field = the visual field neurons respond to Adjacent neurons have overlapping receptive fields. Retinotopy = map between V1 and visual field. Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 5 / 45
Introduction Functional brain imaging: functional MRI fMRI mesures metabolism (local O 2 consumption) Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 6 / 45
Introduction Functional brain imaging: Magneto-Encephalography Sensor measurements Flickering stimulus at 7.5 Hz Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 7 / 45
Introduction Functional brain imaging: Magneto-Encephalography Sensor measurements Flickering stimulus at 7.5 Hz At 15 Hz on MEG sensors, retinotopic organization: topography depends on stimulus position Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 7 / 45
Introduction Functional brain imaging: Magneto-Encephalography stimulus positions Source activity reconstruction [Cottereau, Gramfort et al, HBM 2008] MEG and EEG naturally provide information about timing of brain activity. Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 8 / 45
Introduction Origin of brain activity measured in EEG and MEG [Baillet et al., IEEE Signal Processing Mag, 2001] Pyramidal neurons Current perpendicular Neurons in a post-synaptic currents to cortical surface macrocolumn co-activate Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 9 / 45
Introduction Source models: distributed or isolated Distributed current source defined on a surface S with current density q ( r ): J p ( r ) = q ( r ) n δ S (orthogonal to S ) Isolated current dipole defined at a position p with current (moment) q : J p = q δ p Also linear combinations n J p = � q i δ p i i =1 Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 10 / 45
Inverse source reconstruction Outline Introduction 1 Inverse Source Reconstruction 2 Forward Problem Inverse Problem Anatomically Constrained Regularization Neuroelectrical signal analysis 3 Current challenges 4 Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 11 / 45
Inverse source reconstruction Specificities of MEG and EEG origin of activity: depolarization / repolarization of neural membranes postsynaptic potentials represented by dipoles in grey matter dipole orientation perpendicular to cortex Low freq ( < 1000 Hz): quasistatic approx to Maxwell’s eqs: Electric and magnetic fields become decoupled. Electrostatic equation: Biot-Savart equation: = µ 0 ( J p ( r ′ ) − σ ∇ V ( r ′ )) × � r − r ′ � 3 d r ′ r − r ′ � B ( r ) 4 π ∇ · ( σ ∇ V ) = ∇ · J p r − r ′ = B 0 ( r ) − µ 0 σ ∇ V ( r ′ ) × � r − r ′ � 3 d r ′ � 4 π B 0 ( r ): “primary magnetic field” coming from the sources Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 12 / 45
Inverse source reconstruction Influence of orientation (spherical geometry) [courtesy of S.Baillet] Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 13 / 45
Inverse source reconstruction Influence of depth (realistic geometry) [courtesy of S.Baillet] Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 14 / 45
Inverse source reconstruction Modeling the conductivity σ within the head simplest model: overlapping spheres � no meshing required � analytical methods × crude approximation of head conduction, especially for EEG Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 15 / 45
Inverse source reconstruction Modeling the conductivity σ within the head simplest model: overlapping spheres � no meshing required � analytical methods × crude approximation of head conduction, especially for EEG surface-based-model: piecewise constant conductivity � only surfaces need to be meshed � Boundary Element Method (BEM) × only isotropic conductivities Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 15 / 45
Inverse source reconstruction Modeling the conductivity σ within the head simplest model: overlapping spheres � no meshing required � analytical methods × crude approximation of head conduction, especially for EEG surface-based-model: piecewise constant conductivity � only surfaces need to be meshed � Boundary Element Method (BEM) × only isotropic conductivities most sophisticated model: volume-based conductivity � detailed conductivity model, (anisotropic: tensor at each voxel) � Finite Element Method (FEM), × huge meshes, difficult to handle Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 15 / 45
Inverse source reconstruction Head Geometrical Modeling from T1/T2 MRIs Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 16 / 45
Inverse source reconstruction Forward problem: computing the gain matrix J p sum of n isolated dipoles with fixed position and time-varying moment q i ( t ) = s i ( t ) n i ( n unitary) G 1 ( p 1 , n 1 ) G 1 ( p n , n n ) . . . . M ( t ) = × s 1 ( t ) + · · · + × s n ( t ) . . G m ( p 1 , n 1 ) G m ( p n , n n ) s 1 ( t ) . . = G . s n ( t ) In gain matrix G : columns = sources / lines = sensors. G 1 ( p 1 , n 1 ) . . . G 1 ( p n , n n ) . . ... . . G = . . G m ( p 1 , n 1 ) . . . G m ( p n , n n ) [Kybic et al 2005, Gramfort et al 2010, OpenMEEG software] Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 17 / 45
Inverse source reconstruction Source reconstruction Two types of source models considered: isolated distributed unknowns ≪ measurements unknowns ≫ measurements sensitivity to model order indeterminacy regularization necessary Uniqueness of reconstruction: proven for each model. Ill-posedness, due to instability. Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 18 / 45
Inverse source reconstruction Distributed sources: minimum norm estimators Measurements on m EEG / MEG sensors. Linear relationship between sources and sensor data: M 1 ( t ) G 1 ( p 1 , n 1 ) G 1 ( p n , n n ) s 1 ( t ) . . . . . . . ... . . . . = + N . . . . M m ( t ) G m ( p 1 , n 1 ) . . . G m ( p n , n n ) s n ( t ) m × n m × n n × n M G gain matrix S M = G S + N n ≫ m → regularization necessary Find sources S minimizing E ( S ) + λ R ( S ) where E ( S ) = ( M − G S ) T Σ − 1 ( M − G S ) and R ( S ) source regularization term. [Adde Clerc Keriven 2005] Maureen Clerc (Inria) Exploring the Brain’s Activity EUSIPCO, Nice, September 2015 19 / 45
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