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# Petar Petrov MSc thesis defense

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Towards predicting the effects of TMS
electro-magnetic stimulation on the
human brain

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• The general theory of solutions to Laplace&apos;s equation is known as potential theory. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In three dimensions, the problem is to find twice-differentiable real-valued functions , of real variables x, y, and z in 3D such as eq I.1.This is often written as eq. I.2 or eq. I.3. Where eq. I.3 is divergence of the function and eq. I.4 is known as its gradient. Also commonly depicted as Δ , the Laplace operator. The Laplace&apos;s and Poisson&apos;s equations are the simplest examples of elliptic partial differential equations. The partial differential operator, or (which may be defined in any number of dimensions), is called the Laplace operator or just the Laplacian. ---------------------------===================---------------------------------- Also known as the essential boundary condition. The Dirichlet boundary condition given for a an ordinary differential equation: where alpha and beta are given, always constants, and the function is defined in the [0,1] domain. ---------------------------===================---------------------------------- Also known as the natural boundary condition. The Neumann boundary condition is defined below:
• Sparsness : However, examining ill. B.2, reveals that the products and nonzero only where the supports of for basic functions and , e.g. nonzero only on element 2, wheres zero everywhere. Hence, the integrals ,nonzero but . Then, it follows that if two nodes i and j not belong to the same element , then K[ij] =0. Symmetry of K : This property is easy to defend as we can see that interchanging the I and j integral expression for K[ij] not change the value calculated Yet in most physical problems based on conservation laws this symmetry will arise often naturally in the weak formulation. In contrast to the sparseness of K, the symmetry is independent of our choice of basis functions and it is entirely dependent on the type of variational problem we are trying to solve.
• A memristor is a passive two-terminal electronic component for which the resistance (dV/dI) depends in some way on the amount of charge that has flowed through the circuit. When current flows in one direction through the device, the resistance increases; and when current flows in the opposite direction, the resistance decreases, although it must remain positive. When the current is stopped, the component retains the last resistance that it had, and when the flow of charge starts again, the resistance of the circuit will be what it was when it was last active
• ### Petar Petrov MSc thesis defense

1. 1. Towards predicting the effects of TMS electro-magnetic stimulation on the human brain Petar Petrov www.ppetrov.net ID#3196607
2. 2. Outline <ul><li>Introduction
3. 3. Research Goals
4. 4. Methods
5. 5. Results
6. 6. Conclusions
7. 7. Future Improvements
8. 8. Final Frontier </li></ul>
9. 9. Introduction :: TMS <ul><li>What is TMS ? Acronym: Transcranial Magnetic Stimulation </li></ul>
10. 10. Introduction :: TMS <ul><li>History </li><ul><li>Circa 1985 </li></ul><li>Applications </li><ul><li>Behavior science
11. 11. Psychiatry
12. 12. Causes neuron activation </li></ul><li>Brief Description </li><ul><li>Non-invasive
13. 13. Single pulse
14. 14. 8-shaped coil
15. 15. LOW! Risk </li></ul></ul>
16. 16. Introduction :: MRI <ul><li>Modern medical imaging techniques based on Magnetic Resonance Imaging </li></ul><ul><li>Anatomical scan MRI
17. 17. Functional scan fMRI
18. 18. Diffusion imaging DTI </li></ul>PHILIPS Achieva 3T
19. 19. Introduction :: Human Brain
20. 20. Introduction :: Human Brain
21. 21. Research Goals <ul><li>Study the effects of TMS on the human brain using computer model and virtual simulation </li><ul><li>Choose a numerical solution suited for the physics of anisotropic ! electro-conductivity
22. 22. Create anatomically correct computer model of a brain, incorporating the four most essential tissue types using MRI
23. 23. Create, test and validate a working FEM solution </li></ul><li>Clinical motivation </li><ul><li>Improve future TMS lab session (aided neuronavigation) </li></ul></ul>
24. 24. Theoretical Background <ul><li>Generalization of the Ohm's law for volume conductors
25. 25. Quasi-static limit </li><ul><li>Assume no wave-like effects </li></ul><li>Boundary Conditions </li><ul><li>Dirichlet's boundary condition
26. 26. Neumann's boundary condition </li></ul></ul>
27. 27. Methods :: Numerical Solution <ul><li>BEM : Boundary Element / Volume Method </li><ul><li>Boundary conditions on surfaces only
28. 28. Not suited for high anisotropy materials </li></ul><li>FDM : Finite Difference Method </li><ul><li>Derivative approx. of a function as difference quotient (Tylor's polyon.)
29. 29. Elements can overlap </li></ul><li>FEM : Finite Element Method </li><ul><li>Approximate PDEs as Ordinary
30. 30. Require linear solver for Kx=F </li></ul></ul>FEM tets mesh tet = tetrahedral
31. 31. Methods :: FEM <ul><li>Constructing FEM solution </li><ul><li>Variational statement of the problem (a.k.a. weak formulation)
32. 32. Symmetric variational problem
33. 33. Galerkin's approximation
34. 34. Basis functions
35. 35. FEM Computation </li></ul></ul>
36. 36. Methods :: FEM <ul><li>Stiffness Matrix K props. </li><ul><li>Summability : integrals can summed over the whole domain
37. 37. Sparseness : many zero entries ( basis functions dependant)
38. 38. Symmetry : as result of the weak statement of our problem </li></ul></ul>
39. 39. Methods :: SCIRun <ul><li>Example SCIRun FEM simulation solution network </li><ul><li>Grey boxes : modules
40. 40. Colored lines : <data type> </li><ul><li>Yellow: mesh field
41. 41. Blue: scalar/vector/tensor data fields
43. 43. Pink: graphic primitives </li></ul></ul></ul>
44. 44. Methods :: SCIRun <ul><li>SolveLinearSystem module </li><ul><li>Iterative solver with terminating target error
45. 45. Emits partial results every given steps to enable interactive use
46. 46. Visual convergence as confirmation with manual
47. 47. Gives the approximate result to : </li><ul><li>System of linear eq. Ax=B with N nodes mesh A[NxN]x[Nx1]=B[1xN] </li></ul></ul></ul>
48. 48. Methods :: SCIRun BioMesh3D <ul><li>FEM mesh construction Generate tetrahedral elements </li><ul><li>Stage 1 : extract volume segmentations form input voxel (nrrd file)
49. 49. Stage 2 : extract material surfaces for each type
50. 50. Stage 3 : calculate medial-axis for each surface
51. 51. Stage 4 : compute sizing-field (local feature size)
52. 52. Stage 5 : generate initial sampling of material interfaces
53. 53. Stage 6 : from the seeds generate particle (Energy) optimization
54. 54. Stage 7 : generate surface mesh
55. 55. Stage 8 :fill the mesh and generate tetrahedral FEM mesh </li></ul></ul>
56. 56. Methods :: Model Validation <ul><li>4-shells spherical model
57. 57. 3 test cases </li><ul><li>Case 1 : Isotropic cond.
58. 58. Case 2 : Isotropic cond.
59. 59. Case 3 : Anisotropic cond. </li></ul><li>2 parameters for BioMesh3D </li><ul><li>Pre-smoothing (matt_radii)
60. 60. Nodes distribution (sizing_field) </li></ul><li>1 analytical 'golden' solution </li><ul><li>Validate FEM results
61. 61. Measure 162 electr. pos </li></ul></ul>
62. 62. Methods :: Model Validation <ul><li>Case 1 config </li><ul><li>2 x dipoles
63. 63. Position @ origin (0,0,0)
64. 64. Orientation </li><ul><li>Facing up X
65. 65. Facing up Z </li></ul></ul><li>Shells (radii:cond) </li><ul><li>44mm : 0.33 S/m2
66. 66. 40mm : 1.67 S/m2
67. 67. 34mm : 0,02 S/m2
68. 68. 30mm : 0.33 S/m2 </li></ul></ul>
69. 69. Methods :: Model Validation <ul><li>Case 3 config </li><ul><li>2 x dipoles
70. 70. Position @ 25mm offset Z (0,0,25)
71. 71. Orientation </li><ul><li>Facing up X
72. 72. Facing up Z </li></ul></ul><li>Shells (radii:cond) </li><ul><li>44mm : 0.33 S/m2
73. 73. 40mm : 1.67 S/m2
74. 74. 34mm : ANISO ! </li><ul><li>Tangent 0.04309
75. 75. Radial 0.004309 </li></ul><li>30mm : 0.33 S/m2 </li></ul></ul>
76. 76. Methods :: Solution Error Metrics <ul><li>Relative Difference
77. 77. Maximum Relative Difference
78. 78. Vector Correlation </li><ul><li>Spatial error </li></ul></ul>
79. 79. Methods :: Tissue Segmentation <ul><li>Using “unified classification method” statistical analysis on voxel space image to determine tissue types
80. 80. LEFT (Axial) CENTER (Coronal) RIGHT (Sagittal) </li></ul>
81. 81. Methods :: Brain Model <ul><li>Brain anisotropic conductivity tensors field ( Coronal view ) </li></ul>
82. 82. Methods :: Brain Model <ul><li>White Matter WM : 1st eigenvector of tensor(prime direction) </li></ul>
83. 83. Methods :: Brain Model <ul><li>WM MRI-DTI scalar encoded tensor field </li></ul>
84. 84. Results :: Model Validation <ul><li>At most 30% difference for the most complicated case3
85. 85. Smoothing during meshing improves accuracy </li></ul>
86. 86. Results :: Model Validation <ul><li>Regular FEM mesh (L,L1-lattice) not adequate! For case3
87. 87. Regular FEM meshes like L# good for Isotropic media </li></ul>
88. 88. Results :: Model Validation <ul><li>Comparing surf. potentials case 3 (left) against case 2 (right) </li></ul>
89. 89. Results :: Model Validation <ul><li>Case 2 Isotropic with dipole I-source @ (0,0,25) facing up X </li></ul>
90. 90. Results :: Model Validation <ul><li>Case 3 Anisotropic with dipole I-source @ (0,0,25) facing up X </li></ul>
91. 91. Results :: Model Validation <ul><li>Isotropic case 2 E-field spatial distribution patterns </li></ul><ul><li>Anisotropic case3 E-field spatial distribution patterns </li></ul>
92. 92. Results :: BioMesh3D <ul><li>Horizontal cross section cut of a 3 tissue tet-mesh
93. 93. Yellow : WM
94. 94. Violet : GM </li></ul>
95. 95. Results :: BioMesh3D
96. 96. Results :: BioMesh3D <ul><li>Yellow : WM surface rendering
97. 97. Violet : GM surface rendering </li></ul>
98. 98. Results :: Brain
99. 99. Results :: Brain <ul><li>Isotropic WM ; E-field is blue arrows and current is streamlines </li></ul>RED is WM fibers
100. 100. Results :: Brain <ul><li>Anisotropic WM ; E-field is blue arrows and current is streamlines </li></ul>RED is WM fibers
101. 101. Results :: Brain <ul><li>ISO WM Brain cut near the current source; E-field </li></ul><ul><li>AISO WM Brain cut near the current source; E-field </li></ul>
102. 102. Conclusions <ul><li>Geometry does matter! </li><ul><li>Smoothness on the boundary between different regions
103. 103. Higher resolution near the current source
104. 104. MRI 3T (Tesla) gives sufficient resolution
105. 105. We might need to take different approach towards WM, than adaptive meshing </li></ul><li>Anisotropic effects </li><ul><li>Clear difference in patterns distribution </li><ul><li>Low thresholding used however (~5% of MAX E-field) </li></ul></ul><li>Resource bottle-neck (3xAMD64 6GB RAM) </li><ul><li>SCIRun is still interactive ~ 1M tet-elements
106. 106. Meshing via BioMesh3D for 4tissue Brain ~ 3days! </li></ul><li>The error introduced through interpolation is relatively low! </li></ul>
107. 107. Future Directions <ul><li>Empirical validation of our SCIRun FEM models </li><ul><li>TMS + EEG (low spatial distribution information)
108. 108. TMS + fMEI (still experimental @ UMC Utrecht) </li></ul><li>Does Anisotropic WM modeling affects TMS clinical lab application ? </li><ul><li>We have shown a clear difference, but is it relevant?
109. 109. Do we need WM in our model!
110. 110. We need to integrate realistic 8-shaped coil current injection (RHS) in SCIRun FEM </li></ul></ul>
111. 111. Future Improvements <ul><li>Meshing and modeling FEM </li><ul><li>Non-uniform treatment of different tissues (BioMesh3D)
112. 112. Implement BioMesh3D inside SCIRun
113. 113. Include anatomically correct Skull tissue (x-rays)
114. 114. Noise in during MRI scan (see GM segmentation) </li></ul><li>Performance FEM </li><ul><li>Hit real-time performance for ~2.5 Millions Tet-elements
115. 115. OpenCL (general computation on video hardware GPU)
116. 116. 4xCORE Intel ~70 GFLOPs
117. 117. Ati/Nvidia video cards 600\$ ~600 GFLOPs (doubles!!!) </li></ul></ul>
118. 118. ??? QUESTIONS ???
119. 119. The Final Frontier (of computing) <ul><li>Beyond the 3D FEM millions of elements to the biological neuron nets of 10^15 of elements (neurons+synapses)
120. 120. (a.k.a cognitive computing, cognitive architecture)
121. 121. THE CONVENTIONAL way </li><ul><li>Using conventional hardware (transistors and 4 binary operators ( AND , OR , XOR , NOT ) mimic/model Neuron
122. 122. IBM cat brain project
123. 123. Blue Brain Project (reverse engineer Human Brain) </li></ul><li>THE SCI_FI way ;) </li><ul><li>MEMRISTORs! .... or TERMINATOR101 circa 2014
124. 124. 1971 Leon Chua “Memristor—the missing circuit element.”
125. 125. 2008 HP Labs R. Stanley Williams TiO2 memristor </li></ul></ul>
126. 126. ??? MORE QUESTION ???
127. 127. !!! THANK YOU !!! For more : www.ppetrov.net