Accurate Pediatric Head Models for EEG Source Localization Jasmine Song, Sergei Turovets, Pavel Govyadinov, Kyle Morgan, Colin Davey, Phan Luu, Don M. Tucker, Fred Prior and Linda Larson-Prior Electrical Geodesics, Inc., 1600 Millrace Dr. Suite 200 Eugene, OR, USA Introduction Accurate source localization with dense array electroencephalography (dEEG) requires an accurate lead field matrix (LFM), specifying the “forward” lead fields, from each cortical source to each head surface electrode. Children differ from adults in source geometry, skull thickness, and tissue conductivity. We conducted a simulation to examine the error of source localization when an adult skull conductivity model is used for a child’s dEEG source localization. Dynamic Brain Activity ◮ Cortex brain activity generates scalp EEG. ◮ Dynamic brain activity requires high temporal and spatial resolutions. ⊲ EEG: high temporal(∼1 millisecond) but poor spatial(2D) resolution. ⊲ fMRI: good spatial(3D) but poor temporal(∼1 second) resolution. ◮ Dynamic brain activity needs to solve EEG Source Localization(ESL). ESL for Pediatric Head Model ◮ While MRI and CT for adult head models are routinely available, they are NOT available for pediatric head models for EEG, MEG, NIRS or EIT. ◮ Forward problem consists of calculating the electric potentials on the scalp, given the source distribution within the brain and a head model. ⊲ Structural images (MRI, CT, GPS) ⇒ Segmentation and Registration ⇒ Head Geometry ⊲ Conductivity estimation ◮ Inverse problem consists of finding the magnitude and orientation of the source distribution, given the electric potentials on the head’s surface and a head model. ⊲ Highly Underdetermined: Distributed source localization (regularization) or Equivalent current dipole Segmentation, Registration and Dipoles Sensors on pediatric head were registered by geodesic photogrammetry (GPS) [3]. A relative thresholding method segmented scalp, skull, csf, gray and white matter. The cortical surface was extracted and a dipole was put in each cortical patch by our in-house software BrainK [2]. (a) Segmentation (b) Sensors on Scalp (c) Cortical surface (d) Dipoles Forward Problem ◮ Poisson’s Equation for potential: ▽· (σ ▽ φ)= −I δ (r − r + )+ I δ (r − r − ) ◮ Boundary condition: σ (▽φ) · n =0 ◮ Methods for the forward problem: BEM, FEM & FDM ⇒ ⇒ ◮ Inverse Conductivity Estimation: min σ  1 N N  i =1 (φ p i − V i ) 2  1/2 , where φ p = F (σ (r )) ◮ FDM Multi-Component ADI Algorithm [4] ⊲ Unconditionally stable in 3D ⊲ Accuracy ∼ O (τ +Δx 2 +Δy 2 +Δz 2 ) φ n+1 i − φ n τ + δ x φ n+1 i + δ y φ n j + δ z φ n k = S φ n+1 j − φ n τ + δ x φ n+1 i + δ y φ n+1 j + δ z φ n k = S φ n+1 k − φ n τ + δ x φ n+1 i + δ y φ n+1 j + δ z φ n+1 k = S where φ n =(φ n i + φ n j + φ n k )/3 and δ x ,y ,z is an 1-D second order spatial difference operator. Inverse Problem ◮ Mathematical Linear Model is Φ= KJ + E , ⊲ Φ ∈ R N e ×N t : a scalp potential; J ∈ R N j ×N t :a source distribution; K ∈ R N e ×N j : a lead field matrix; E∈ R N e ×N t : a measurement error. ⊲ N e : the number of sensors, N v : the number of source locations, N j : the number of dipoles, N t : the number of time points. ⊲ If the orientations of dipoles are known, N j = N v , otherwise N j =3N v . ⊲ The inverse problem is ill-posed. (N e ≪ N j ). ◮ The regularized solution for Inverse Problem is ˆ J = arg min J {‖Φ − KJ ‖ 2 + α‖J ‖ 2 }, where α ≥ 0 and ‖·‖ 2 is the square of the l 2 -norm. ⊲ Minimum Norm (MN): ˆ J = K T [KK T + αI N e ] −1 Φ. ⊲ sLORETA [1]: ˆ J ∗ l =[C ˆ J ] −1/2 ll ˆ J l , where C ˆ J = K T [KK T + αI N e ] −1 K for l =1,..., N v . Skulls of Infant Head models (a) Skull from original CT of 6 m.o. baby (b) Adult skull warped to the baby brain (c) Scaled adult head to the baby head size (a) True (b) Warped (c) Adult True model contains frontal and occipital fontanelles. Both warped and adult head models don’t have fontanelles. Conductivity Values in Literatures (S/m) Conductivity values of the absolute and relative conductivity of the compartments reported in the (adult) human head. Compartment Geddes & Baker Oostendorp Goncalves Guttierrez Lai (1967) (2000) (2003) (2004) (2005) scalp 0.43 0.22 0.33 0.749 0.33 skull 0.006-0.015 0.015 0.0082 0.012 0.0132 csf - - - 1.79 - brain 0.12-0.48 0.22 0.33 0.313 0.33 σ scalp /σ skull 80 15 23-49 26 25 Conductivity and Geometry Effects on ESL ◮ LED: Euclidean distance (mm) between the locations of true dipole and the dipole with maximum intensity in the source distribution. ◮ Assume that true skull conductivity is 0.1. ◮ LFMs with 0.1 obtain the minimum LED in three geometries by MN and sLORETA. Method Head Geometry Skull Conductivity (S/m) 0.004 0.018 0.1 ∗ 0.2 0.35 0.44 MN True 17.3 15.5 15.1 15.1 15.2 15.2 Warped 18.4 16.2 15.2 15.3 15.4 15.5 Adult 19.8 18.3 13.9 14.9 16.3 16.6 sLORETA True 3.7 0.3 0 0 0 0.0 Warped 7.6 1.1 0 0 0.0 0.1 Adult 10.6 4.6 0 0.1 0.5 1.0 Geometry and Conductivity Effects on ESL True Dipole (0.1) MN sLORETA True (0.1) 18 0 Warped (0.004) 23 11 Adult (0.004) 23 16 A dipole in the true model and scalp potential of the forward projections of the dipole; ESL by MN and sLORETA. LED= 0 ∼ 23 mm. Conclusion ◮ Electromagnetic image analysis and ESL are powerful tools in neuroscience. ◮ Anatomically accurate infant head model is the important key factor for ESL. ◮ Multiple medical applications such as presurgical planning in epilepsy, neuro-rehabilitation for stroke, traumatic brain injury and autism. References [1] Pascual-Marqui R D 2002 Methods and Findings in Experimental and Clinical Pharmacology 24 5-12 [2] Li K, Malony A and Tucker D M 2006 First International Conference on Computer Vision Theory and Applications (VISAPP), Portugal, February pp 354-364 [3] Russell G S, Eriksen K J, Poolman P, Luu P and Tucker D M 2005 Clinical Neurophysiology 116 1130-40 [4] Salman A, Turovets S, Malony A and Volkov V 2008 International Workshop on OpenMP (IWOMP 2005/2006) LNCS 4315 pp 119-130 http://www.egi.com jsong@egi.com