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Petar Petrov MSc thesis defense
- 1. Towards predicting the effects of TMS electro-magnetic stimulation on the human brain Petar Petrov www.ppetrov.net ID#3196607
- 4. Methods
- 5. Results
- 6. Conclusions
- 11. Psychiatry
- 13. Single pulse
- 14. 8-shaped coil
- 15. LOW! Risk
- 18. Diffusion imaging DTI PHILIPS Achieva 3T
- 19. Introduction :: Human Brain
- 20. Introduction :: Human Brain
- 22. Create anatomically correct computer model of a brain, incorporating the four most essential tissue types using MRI
- 30. Require linear solver for Kx=F FEM tets mesh tet = tetrahedral
- 34. Basis functions
- 35. FEM Computation
- 37. Sparseness : many zero entries ( basis functions dependant)
- 38. Symmetry : as result of the weak statement of our problem
- 41. Blue: scalar/vector/tensor data fields
- 45. Emits partial results every given steps to enable interactive use
- 46. Visual convergence as confirmation with manual
- 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
- 58. Case 2 : Isotropic cond.
- 61. Measure 162 electr. pos
- 63. Position @ origin (0,0,0)
- 66. 40mm : 1.67 S/m2
- 67. 34mm : 0,02 S/m2
- 68. 30mm : 0.33 S/m2
- 70. Position @ 25mm offset Z (0,0,25)
- 73. 40mm : 1.67 S/m2
- 80. LEFT (Axial) CENTER (Coronal) RIGHT (Sagittal)
- 85. Smoothing during meshing improves accuracy
- 87. Regular FEM meshes like L# good for Isotropic media
- 93. Yellow : WM
- 94. Violet : GM
- 97. Violet : GM surface rendering
- 98. Results :: Brain
- 103. Higher resolution near the current source
- 104. MRI 3T (Tesla) gives sufficient resolution
- 109. Do we need WM in our model!
- 110. We need to integrate realistic 8-shaped coil current injection (RHS) in SCIRun FEM
- 112. Implement BioMesh3D inside SCIRun
- 113. Include anatomically correct Skull tissue (x-rays)
- 115. OpenCL (general computation on video hardware GPU)
- 116. 4xCORE Intel ~70 GFLOPs
- 117. Ati/Nvidia video cards 600$ ~600 GFLOPs (doubles!!!)
- 118. ??? QUESTIONS ???
- 120. (a.k.a cognitive computing, cognitive architecture)
- 122. IBM cat brain project
- 124. 1971 Leon Chua âMemristorâthe missing circuit element.â
- 125. 2008 HP Labs R. Stanley Williams TiO2 memristor
- 126. ??? MORE QUESTION ???
- 127. !!! THANK YOU !!! For more : www.ppetrov.net
Hinweis der Redaktion
- The general theory of solutions to Laplace'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 Î , the Laplace operator. The Laplace's and Poisson'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