- 1. Towards predicting the effects of TMSelectro-magnetic
stimulation on the human brain Petar Petrov www.ppetrov.net
ID#3196607
2. Outline
- Introduction 3. Research Goals 4. Methods 5. Results 6.
Conclusions 7. Future Improvements 8. Final Frontier
9. Introduction :: TMS
- What is TMS ?Acronym: Transcranial Magnetic Stimulation
10. Introduction :: TMS
- History
- Applications
- Behavior science 11. Psychiatry 12. Causes neuron
activation
- Brief Description
- Non-invasive 13. Single pulse 14. 8-shaped coil 15. LOW!
Risk
16. Introduction :: MRI
- Modern medical imaging techniques based on Magnetic Resonance
Imaging
- Anatomical scan MRI 17. Functional scan fMRI 18. Diffusion
imaging DTI
PHILIPSAchieva 3T 19. Introduction :: Human Brain 20.
Introduction :: Human Brain 21. Research Goals
- Study the effects of TMS on the human brain using computer
model and virtual simulation
- Choose a numerical solution suited for the physics
ofanisotropic ! electro-conductivity 22. Create anatomically
correct computer model of a brain, incorporating the four most
essential tissue types using MRI 23. Create, test and validate a
working FEM solution
- Clinical motivation
- Improve future TMS lab session (aided neuronavigation)
24. Theoretical Background
- Generalization of the Ohm's law for volume conductors 25.
Quasi-static limit
- Assume no wave-like effects
- Boundary Conditions
- Dirichlet's boundary condition 26. Neumann's boundary
condition
27. Methods :: Numerical Solution
- BEM : Boundary Element / Volume Method
- Boundary conditions on surfaces only 28. Not suited for high
anisotropy materials
- FDM : Finite Difference Method
- Derivative approx. of a function as difference quotient
(Tylor's polyon.) 29. Elements can overlap
- FEM : Finite Element Method
- Approximate PDEs as Ordinary 30. Require linear solver
forKx=F
FEM tets mesh tet = tetrahedral 31. Methods :: FEM
- Constructing FEM solution
- Variational statement of the problem(a.k.a. weak formulation)
32. Symmetric variational problem 33. Galerkin's approximation 34.
Basis functions 35. FEM Computation
36. Methods :: FEM
- Stiffness MatrixKprops.
- Summability: integrals can summed over the whole domain 37.
Sparseness: many zero entries ( basis functions dependant) 38.
Symmetry: as result of the weak statement of our problem
39. Methods :: SCIRun
- Example SCIRun FEM simulation solution network
- Grey boxes : modules 40. Colored lines :
- Yellow: mesh field 41. Blue: scalar/vector/tensor data fields
42. Purple: colormap (grad) 43. Pink: graphic primitives
44. Methods :: SCIRun
- SolveLinearSystemmodule
- Iterative solver with terminating target error 45. Emits
partial results every given steps to enable interactive use 46.
Visual convergence as confirmation with manual 47. Gives the
approximate result to :
- System of linear eq. Ax=B with N nodes mesh
A[NxN]x[Nx1]=B[1xN]
48. Methods :: SCIRun BioMesh3D
- FEM meshconstructionGenerate tetrahedral elements
- Stage 1: extract volume segmentations form input voxel(nrrd
file) 49. Stage 2: extract material surfaces for each type 50.
Stage 3: calculate medial-axis for each surface 51. Stage 4:
compute sizing-field (local feature size) 52. Stage 5: generate
initial sampling of material interfaces 53. Stage 6: from the seeds
generate particle (Energy) optimization 54. Stage 7: generate
surface mesh 55. Stage 8:fill the mesh and generate tetrahedral FEM
mesh
56. Methods :: Model Validation
- 4-shells spherical model 57. 3 test cases
- Case 1 : Isotropic cond. 58. Case 2 : Isotropic cond. 59. Case
3 : Anisotropic cond.
- 2 parameters for BioMesh3D
- Pre-smoothing(matt_radii) 60. Nodes
distribution(sizing_field)
- 1 analytical 'golden' solution
- Validate FEM results 61. Measure 162 electr. pos
62. Methods :: Model Validation
- Case 1 config
- 2 x dipoles 63. Position @ origin (0,0,0) 64. Orientation
- Facing up X 65. Facing up Z
- Shells (radii:cond)
- 44mm : 0.33 S/m2 66. 40mm : 1.67 S/m2 67. 34mm : 0,02 S/m2 68.
30mm : 0.33 S/m2
69. Methods :: Model Validation
- Case 3 config
- 2 x dipoles 70. Position @25mm offset Z (0,0,25) 71.
Orientation
- Facing up X 72. Facing up Z
- Shells (radii:cond)
- 44mm : 0.33 S/m2 73. 40mm : 1.67 S/m2 74. 34mm :ANISO !
- Tangent 0.04309 75. Radial 0.004309
- 30mm : 0.33 S/m2
76. Methods :: Solution Error Metrics
- Relative Difference 77. Maximum Relative Difference 78. Vector
Correlation
79. Methods :: Tissue Segmentation
- Using unified classification method statistical analysis on
voxel space image to determine tissue types 80. LEFT (Axial)CENTER
(Coronal)RIGHT (Sagittal)
81. Methods :: Brain Model
- Brain anisotropic conductivity tensors field ( Coronal view
)
82. Methods :: Brain Model
- White Matter WM : 1st eigenvector of tensor(prime
direction)
83. Methods :: Brain Model
- WM MRI-DTI scalar encoded tensor field
84. Results :: Model Validation
- At most 30% difference for the most complicated case3 85.
Smoothing during meshing improves accuracy
86. Results :: Model Validation
- Regular FEM mesh (L,L1-lattice) not adequate! For case3 87.
Regular FEM meshes like L# good for Isotropic media
88. Results :: Model Validation
- Comparing surf. potentialscase 3 (left) against case 2
(right)
89. Results :: Model Validation
- Case 2Isotropicwith dipole I-source @ (0,0,25) facing up X
90. Results :: Model Validation
- Case 3Anisotropicwith dipole I-source @ (0,0,25) facing up
X
91. Results :: Model Validation
- Isotropic case 2 E-field spatial distribution patterns
- Anisotropic case3 E-field spatial distribution patterns
92. Results :: BioMesh3D
- Horizontal cross section cut of a 3 tissue tet-mesh 93. Yellow
: WM 94. Violet : GM
95. Results :: BioMesh3D 96. Results :: BioMesh3D
- Yellow : WM surface rendering 97. Violet : GM surface
rendering
98. Results :: Brain 99. Results :: Brain
- Isotropic WM ; E-field is blue arrows and current is
streamlines
REDisWM fibers 100. Results :: Brain
- Anisotropic WM ; E-field is blue arrows and current is
streamlines
REDisWM fibers 101. Results :: Brain
- ISOWM Brain cut near the current source; E-field
- AISOWM Brain cut near the current source; E-field
102. Conclusions
- Geometry does matter!
- Smoothness on the boundary between different regions 103.
Higher resolution near the current source 104. MRI 3T (Tesla) gives
sufficient resolution 105. We might need to take different approach
towards WM, than adaptive meshing
- Anisotropic effects
- Clear difference in patterns distribution
- Low thresholding used however (~5% of MAX E-field)
- Resource bottle-neck (3xAMD64 6GB RAM)
- SCIRun is still interactive ~ 1M tet-elements 106. Meshing via
BioMesh3D for 4tissue Brain ~ 3days!
- The error introduced through interpolation is relatively
low!
107. Future Directions
- Empirical validation of our SCIRun FEM models
- TMS + EEG (low spatial distribution information) 108. TMS +
fMEI (still experimental @ UMC Utrecht)
- Does Anisotropic WM modeling affects TMS clinical lab
application ?
- We have shown a clear difference, but is it relevant? 109. Do
we need WM in our model! 110. We need to integrate realistic
8-shaped coil current injection (RHS) in SCIRun FEM
111. Future Improvements
- Meshing and modeling FEM
- Non-uniform treatment of different tissues (BioMesh3D) 112.
Implement BioMesh3D inside SCIRun 113. Include anatomically correct
Skull tissue (x-rays) 114. Noise in during MRI scan (see GM
segmentation)
- Performance FEM
- Hit real-time performance for ~2.5 Millions Tet-elements 115.
OpenCL (general computation on video hardware GPU) 116. 4xCORE
Intel ~70 GFLOPs 117. Ati/Nvidia video cards 600$ ~600 GFLOPs
(doubles!!!)
118. ??? QUESTIONS ??? 119. The Final Frontier (of
computing)
- Beyond the 3D FEM millions of elements to the biological neuron
nets of 10^15 of elements (neurons+synapses) 120. (a.k.a cognitive
computing, cognitive architecture) 121. THE CONVENTIONAL way
- Using conventional hardware (transistors and4 binary operators
( AND ,OR ,XOR ,NOT ) mimic/model Neuron 122. IBM cat brain project
123. Blue Brain Project (reverse engineer Human Brain)
- THE SCI_FI way ;)
- MEMRISTORs! .... or TERMINATOR101 circa 2014 124. 1971 Leon
Chua Memristorthe missing circuit element. 125. 2008 HP Labs R.
Stanley Williams TiO2 memristor
126. ??? MORE QUESTION ??? 127. !!! THANK YOU !!! For more :
www.ppetrov.net