title: A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.
abstract: The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.
authors: Electrical Geodesics, Inc., Eugene, OR 97403, USA ; Department of Computer and Information Science, 1202 University of Oregon, Eugene, OR 97403, USA.
authors: Sergei
authors: 0000-0001-6956-0389
authors: S
authors: Turovets
authors: Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk, Belarus.
authors: Vasily
authors: 0000-0003-0350-4186
authors: V
authors: Volkov
authors: Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk, Belarus.
authors: Aleksej
authors: A
authors: Zherdetsky
authors: Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk, Belarus.
authors: Alena
authors: A
authors: Prakonina
authors: Department of Computer and Information Science, 1202 University of Oregon, Eugene, OR 97403, USA.
authors: Allen D
authors: AD
authors: Malony
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D001921:Brain / Q000473:pathology; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D020342:Finite Element Analysis; D005583:Fourier Analysis; D006257:Head / Q000502:physiology; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008962:Models, Theoretical; D016012:Poisson Distribution; D012984:Software; D013525:Surgical Instruments; D014025:Titanium / Q000737:chemistry; D066127:White Matter / Q000473:pathology
chemical_list: D014025:Titanium