Biomag2002

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Biomag2002
Fast anisotropic high resolution finite element
head modeling in EEG/MEG-source localization
C. H.Wolters12, M. Kuhn34, A. Anwander2 and S.
Reitzinger4
1) MPI for Mathematics in the Sciences 3)
Bruker Saxonia Analytik, Leipzig 2) MPI of
Cognitive Neuroscience 4) Inst. for
Comp.Math., J.Kepler Univ., Leipzig,
Germany Linz,
Austria
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

3
Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

4
Biomag2002
Hackbusch, W., Iterative solution of large
linear systems of equations, Springer, New York,
1994
FE equation system and PCG solver
FE discretization, meshsize
Quasistatic approach of Maxwells equations of
electrodynamicsPlonsey and Heppner,Bull.
Math.Biophys., 29,1967
Condition of head geometry matrix
with
Convergence of PCG solver
Problem Bad FE-solver convergence rates for high
resolution modeling
Solution Multigrid-Preconditioning!
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Biomag2002
Hackbusch, W., Iterative solution of large
linear systems of equations, Springer, New York,
1994
Multigrid-Preconditioner for PCG method
Multigrid preconditioner
has the following properties
Condition for preconditioned system

is independent of conductivity parameter jumps
Arithmetic costs of applying
in PCG method is about the
same as applying
Memory requirement is about the same as for
The application of
can well be parallelized
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Biomag2002
Haase, Kuhn Reitzinger, SIAM J.Sci.Comp., in
press, 2002
Algebraic multigrid
Coarse grids are constructed algebraically
Diagonal entries in
, and off diagonal entries to edges
are related to grid points,
Coarsening process
Ruge Stüben, Frontiers in Applied Math. 5,
SIAM, 1986

• (Almost) no direct connection between any two
  coarse grid nodes

• Resulting number of coarse grid nodes as large as
  possible

• Conductivity anisotropy is taken into account

Prolongation and Restriction
Kickinger, Springer Lecture Notes in Comp.Sci.
Eng. 3, 1998
set of coarse neighbors j with a strong
connection to i
Galerkin for coarse grid matrix
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Burkhardt, Wolters Saupe, paper in
preparation, 2002
Biomag2002
5 tissue head modeling using T1- and PD-MRI
T1-MRI
PD-MRI
T1-weighted MRI Appropriate for the
segmentation of ventricle, white matter, cortex,
outer skull surface and scalp.
Proton-Density-weighted MRI Auxiliary modality
for the segmentation of the inner skull surface.
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Burkhardt, Wolters Saupe, paper in
preparation, 2002
Biomag2002
5 tissue head modeling using T1- and PD-MRI

• Voxel similarity based registration using mutual
  information Maes et al.,IEEE Trans.Med.Imag.,
  16(2),1997

• Extraction of MR intensity inhomogeneities during
  segmentation using an adaptive fuzzy C means
  algorithm Pham
  and Prince,Pat.Rec.Let., 20, 1999

5 tissue head model, accurately delineating the
inner skull surface

• Improvement of initial seg. by means of a
  deformable model Kruggel and von Cramon, IEEE
  workshop contribution, Los Alamitos, 2000

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Biomag2002
Wolters, Anwander, Koch, Reitzinger, Kuhn
Svensén, http//www.mpg.de/billing/, 2002
Modeling skull and WM anisotropy
WM tensor eigenvectors
Radial skull tensor eigenvectors Deformable
model
2D projection of WM tensor ellipsoids
Smooth surface spongiosa model

• 8 DTI sessions, each with 4 slices, in-plane
  resolution 2x2mm, 5mm slice thickness

• strongly smoothed and shrunken from outer skull-
  onto outer spongiosa surface

• registration and resampling to 1mm3 by means of
  co-reg. T1-MRI, followed by a subsequent
  tensor-rotation

• forced to stay inside the skull layer

• gaps filled with isotropic tensors

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a) Hexahedra mesh Smoothing surfaces of cube
meshes by nodeshifting
Software VGRID, http//www.simbio.de, Hartmann
and Kruggel, submitted paper, 2002
Finite element mesh generation
Nodeshift Camacho, Hopper, Lin Meyers,
J.Biomech. 30 (10), 1997
Biomag2002
b) Tetrahedra mesh Surface based Delaunay
triangulation Software CURRY,
http//www.neuro.com/neuroscan/prod05.htm,
Wagner, Ph.D. thesis, 1998
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a) Conductivity tensor ellipsoids of the skull
roof for 15 anisotropy Visualization
module VM, SimBio, M.Svensén, http//www.simbio.de
,
Biomag2002
Wolters, Anwander, Koch, Reitzinger, Kuhn
Svensén, http//www.mpg.de/billing/, 2002
Validation of anisotropic FE volume conductor
b) Conductivity tensor ellipsoids of WM layer
Anwander, Wolters, Dümpelmann, Knösche,
Biomag2002, poster presentation.
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Condition numbers of realistically shaped 5
compartment FE models Courtesy of A.Basermann,
Basermann, Num. Lin. Alg. Appl., 7, 2000
Single processor SGI Origin2000, 195MHz, MIPS
10000 ILDLT-solver from software PILUTS,
A.Basermann, http//www.simbio.de
Biomag2002
Wolters, Ph.D. thesis, 2002
Solver comparison for realistic FE models
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Multilevel k way partitioning scheme for
irregular graphs
Biomag2002
Wolters, Kuhn, Anwander Reitzinger,
Comp.Vis.Sci. 5(3), 2002
Data partitioning
Software METIS, Karypis and Kumar,
Jour.Par.Dist.Comp. 48 (1), 1998
Element-wise partitioning into subdomains
Order index sets for
each unknown by means of
Haase, Kuhn Reitzinger, SIAM J.Sci.Comp., in
press, 2002
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Biomag2002
Haase, Kuhn Reitzinger, SIAM J.Sci.Comp., in
press, 2002
Parallel AMG
Condition for the minimization of communication
amount If then the Multigrid-operations can
be performed without any communication.
Haase, B.G.Teubner, 1999
Parallel coarsening

• Splitting of interface nodes Beginning with the
  ones with largest to the ones with smallest index
  set cardinality

• Coherence of interface node splitting

• Connections between different interfaces are
  ignored.

Parallel prolongation

• No fine interface node is allowed to be
  interpolated from coarse neighboring nodes with
  smaller index set cardinality.

Communication is only necessary for

• MG-smoother (Gauss-Seidel for inner and Jacobi
  for interface nodes)

• distribution of coarse grid solution

• inner products within PCG method

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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Wolters, Kuhn, Anwander Reitzinger,
Comp.Vis.Sci. 53, 2002
Biomag2002
Performance of parallel solver methods
SGI Origin2000, each processor 195MHz, MIPS 10000
Solver time comparison
Speedup results
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Biomag2002
Wolters, Ph.D. thesis, 2002
Influence on forward solution
ELAN source in the left temporal cortex
Left thalamic source
Friederici, Wang, Herrmann, Maess Oertel, Hum.
Brain Map.11, 2000
110 anisotropic WM
isotropic
isotropic
110 anisotropic skull/WM
Isopotential distribution from -0.3 to 0.3
Isopotential distribution from -0.5 to 0.5
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Biomag2002
Wolters, Ph.D. thesis, 2002
Influence on localization of ELAN sources
The 4 ELAN reference dipoles
Friederici, Wang, Herrmann, Maess Oertel, Hum.
Brain Map.11, 2000
Dipole fit using simulated annealing, 8 sources
Current density, L1 norm
Rienaecker, Knoll Buchner, Hans Berger
Conference, Jena, 1996
Wolters, Beckmann, Rienaecker Buchner, Brain
Topography 12 (1), 1999
L1 norm
L1 norm
SA-TSVD
SA-COF
EEG, 110 anisotropic skull and WM
EEG, isotropic
MEG, 110 anisotropic WM
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Biomag2002
Content

• Theory for solving high resolution FE forward
  problems
• Anisotropic volume conductor modeling using
  multimodal MRI
• Performance studies of FE solvers I (single
  processor)
• Parallelization strategies
• Performance studies of FE solvers II (multiple
  processors)
• Influence of tissue anisotropy on EEG/MEG source
  reconstruction
• Conclusions

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Biomag2002
Conclusions

• Parallel AMG-CG Fast and memory economical way
  for solving realistic anisotropic EEG/MEG forward
  problems, thus enabling high resolution FE source
  localization

Skull anisotropy has a non-negligible influence
on EEG simulation
See also Marin, Guerin, Baillet, Garnero
Meunier, Hum. Brain Map .6, 1998
Anwander, Wolters, Dümpelmann, Knösche,
Biomag2002, poster presentation.
Influence of WM anisotropy on both EEG and MEG is
especially dependent on the orientation of the
source with regard to the orientation of the
surrounding tissues.
See also Haueisen, Tuch, Ramon, Schimpf, Wedeen,
George Belliveau, NeuroImage 15, 2002
Anwander, Wolters, Dümpelmann, Knösche,
Biomag2002, poster presentation.
Software NeuroFEM-Pebbles

• Simple Linux PC cluster with 100 MBit Ethernet

• Software available on request