Brain (Tech) NCRR Overview Magnetic Leadfields and Superquadric Glyphs

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 [Plonsey and Heppner, 1969] Maxwell equations Maxwell equations of electrodynamics MEG [Nolting, 1992]

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 MEG node-oriented lead field

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 MEG node-oriented lead field

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 MEG node-oriented lead field

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 MEG node-oriented lead field

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Efficient and memory-economical setup

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 with condition number Convergence of the CG solver: FE discretization, meshsize: Strategy: MultiGrid (MG)-Preconditioning! Example: Efficient and memory-economical setup

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Principle of the AMG: Smoother is given (Gauss-Seidel) Algebraic Multigrid Coarse grids and interpolation matrices are constructed from the entries of K –Diagonal entries nodes –Nondiagonal entries edges Coarse grids and interpolation matrices are constructed from the entries of K –Diagonal entries nodes –Nondiagonal entries edges Only one high resolution FE mesh! AMG-interpolation non-optimal: –Some few error components are not well reduced, i.e., some few eigenvalues of the AMG iteration matrix are close to 1 AMG-interpolation non-optimal: –Some few error components are not well reduced, i.e., some few eigenvalues of the AMG iteration matrix are close to 1 Problems: Strategy: AMG-CG!

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 SGI Origin2000, 195MHz, MIPS Single processor: Solver comparison

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Multiple right-hand sides (RHS) saved as block-vector  memory access to matrix in matrix-vector op. once per block  Improved cache hit rate Multiple right-hand sides (RHS) saved as block-vector  memory access to matrix in matrix-vector op. once per block  Improved cache hit rate Treatment of multiple right-hand sides All matrix-vector operations in AMG-CG adapted to blockvectors: CG: Matrix-blockvector, block scalar products AMG: block smoother, block defect, block restriction/prolongation

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Unknowns:147,287 MEG-channels: 147 3RHS-AMG-CG symIC(0)-CG Factor: 9 Mac G4, 3RHS- AMG-CG: 14min FE iterative solver approach for the lead field bases setup Aniso./Inhom. does not change performance

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Efficiency of the lead field bases approach Head model: Tetrahedral FE, 147,287 nodes, 892,119 elements

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Efficiency of the lead field bases approach Head model: Tetrahedral FE, 147,287 nodes, 892,119 elements Influence space: brain surface mesh, 2mm resolution, 9555 nodes

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Efficiency of the lead field bases approach Head model: Tetrahedral FE, 147,287 nodes, 892,119 elements Influence space: brain surface mesh, 2mm resolution, 9555 nodes Number of FE forward solutions: EEG, 71 electrodes: 9555 * 3 = MEG, 147 channels: 9555 * 2 = (tangential constraint) Number of FE forward solutions: EEG, 71 electrodes: 9555 * 3 = MEG, 147 channels: 9555 * 2 = (tangential constraint) Dipole model: Blurred dipole [Buchner et al., 1997]

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Distributing the memory for 1mm FE- modeling

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 ``Element-wise’’ partitioning into subdomains Parallel MultiRHS-AMG-CG: Communication is only necessary for: Smoother (  -Jacobi within interface nodes, Gauss-Seidel between blocks and for inner nodes) distribution of coarse grid solution inner products within PCG method Towards 1mm FE resolutions: Parallel AMG- CG on distributed memory computers

C.H.Wolters et al., talk at BWH in Boston, August 6, 2004 Solver time comparison: Unknowns: PC cluster, each processor 1.7GHz, 256KB cache Performance of parallel MultiRHS-AMG-CG

Brain (Tech) NCRR Superquadric Tensor Glyphs Ellipsoidal Glyphs No shape difference Visual ambiguity Barr ‘81

Brain (Tech) NCRR Superquadric Tensor Glyphs Eigenvalue differences imply assymetry Better visualization: Anisotropy Skewness