scholarly journals High-Resolution EEG Source Localization in Segmentation-Free Head Models Based on Finite-Difference Method and Matching Pursuit Algorithm

2021 ◽  
Vol 15 ◽  
Author(s):  
Takayoshi Moridera ◽  
Essam A. Rashed ◽  
Shogo Mizutani ◽  
Akimasa Hirata
Keyword(s):  
Inverse Problem ◽  
High Resolution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Source Localization ◽  
Difference Method ◽  
Computational Cost ◽  
Head Model ◽  
Eeg Source Localization ◽  
The Brain

Electroencephalogram (EEG) is a method to monitor electrophysiological activity on the scalp, which represents the macroscopic activity of the brain. However, it is challenging to identify EEG source regions inside the brain based on data measured by a scalp-attached network of electrodes. The accuracy of EEG source localization significantly depends on the type of head modeling and inverse problem solver. In this study, we adopted different models with a resolution of 0.5 mm to account for thin tissues/fluids, such as the cerebrospinal fluid (CSF) and dura. In particular, a spatially dependent conductivity (segmentation-free) model created using deep learning was developed and used for more realist representation of electrical conductivity. We then adopted a multi-grid-based finite-difference method (FDM) for forward problem analysis and a sparse-based algorithm to solve the inverse problem. This enabled us to perform efficient source localization using high-resolution model with a reasonable computational cost. Results indicated that the abrupt spatial change in conductivity, inherent in conventional segmentation-based head models, may trigger source localization error accumulation. The accurate modeling of the CSF, whose conductivity is the highest in the head, was an important factor affecting localization accuracy. Moreover, computational experiments with different noise levels and electrode setups demonstrate the robustness of the proposed method with segmentation-free head model.

scholarly journals CMMSE: A technique for generating adapted discretizations to solve partial differential equations with the generalized finite difference method

2021 ◽  
Author(s):  
Augusto César Ferreira ◽  
Miguel Ureña ◽  
HIGINIO RAMOS
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Meshless Method ◽  
Computational Cost ◽  
Partial Differential

The generalized finite difference method is a meshless method for solving partial differential equations that allows arbitrary discretizations of points. Typically, the discretizations have the same density of points in the domain. We propose a technique to get adapted discretizations for the solution of partial differential equations. This strategy allows using a smaller number of points and a lower computational cost to achieve the same accuracy that would be obtained with a regular discretization.

An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

2014 ◽  
Vol 67 (5) ◽  
pp. 825-844 ◽  
Author(s):  
Wei-Kuo Tseng
Keyword(s):  
Inverse Problem ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Computational Cost ◽  
Inverse Solution ◽  
Series Expansions ◽  
Trigonometric Functions ◽  
Innovative Method

An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse problem will be useful for solving problems in navigation as well as geodesy. The algorithm to be described derives from a series expansion that replaces integrals for distance and longitude, while avoiding reliance on trigonometric functions. In addition, these series expansions are economical in terms of computational cost. For end points located at each side of a vertex, certain numerical difficulties arise. A finite difference method together with an innovative method of iteration that approximates Newton's method is presented which overcomes these shortcomings encountered for nearly antipodal regions. The method provided here, which does not involve an auxiliary sphere, was aided by the Computer Algebra System (CAS) that can yield arbitrarily truncated series suitable to the users accuracy objectives and which are limited only by machine precisions.

A finite difference method with reciprocity used to incorporate anisotropy in electroencephalogram dipole source localization

2005 ◽  
Vol 50 (16) ◽  
pp. 3787-3806 ◽  
Author(s):  
Hans Hallez ◽  
Bart Vanrumste ◽  
Peter Van Hese ◽  
Yves D'Asseler ◽  
Ignace Lemahieu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Source Localization ◽  
Difference Method ◽  
Dipole Source ◽  
Dipole Source Localization

scholarly journals A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Taohua Liu ◽  
Muzhou Hou
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Difference Method ◽  
Computational Cost ◽  
First Order ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Implicit Finite Difference

Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K) and computational cost of O(Klog⁡K). Traditionally, the Gaussian elimination method requires storage of O(K2) and computational cost of O(K3). Finally, the accuracy and efficiency of the method are checked with a numerical example.

scholarly journals Solving of Two-Dimensional Unsteady-State Heat-Transfer Inverse Problem Using Finite Difference Method and Model Prediction Control Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Shoubin Wang ◽  
Rui Ni
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Measurement Errors ◽  
Control Method ◽  
Two Dimensional ◽  
Measurement Point ◽  
Prediction Control

The Inverse Heat Conduction Problem (IHCP) refers to the inversion of the internal characteristics or thermal boundary conditions of a heat transfer system by using other known conditions of the system and according to some information that the system can observe. It has been extensively applied in the fields of engineering related to heat-transfer measurement, such as the aerospace, atomic energy technology, mechanical engineering, and metallurgy. The paper adopts Finite Difference Method (FDM) and Model Predictive Control Method (MPCM) to study the inverse problem in the third-type boundary heat-transfer coefficient involved in the two-dimensional unsteady heat conduction system. The residual principle is introduced to estimate the optimized regularization parameter in the model prediction control method, thereby obtaining a more precise inversion result. Finite difference method (FDM) is adopted for direct problem to calculate the temperature value in various time quanta of needed discrete point as well as the temperature field verification by time quantum, while inverse problem discusses the impact of different measurement errors and measurement point positions on the inverse result. As demonstrated by empirical analysis, the proposed method remains highly precise despite the presence of measurement errors or the close distance of measurement point position from the boundary angular point angle.

scholarly journals Efficient finite-difference method for computing sensitivities of biochemical reactions

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180303 ◽  
Author(s):  
Vo Hong Thanh ◽  
Roberto Zunino ◽  
Corrado Priami
Keyword(s):  
Data Structure ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Computational Cost ◽  
Reaction Rates ◽  
Biochemical Reactions ◽  
Simulation Step ◽  
Coupling Strategy ◽  
Single Data

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking stochastic noise into account. This paper proposes a new finite-difference method for efficiently computing sensitivities of biochemical reactions. We employ propensity bounds of reactions to couple the simulation of the nominal and perturbed processes. The exactness of the simulation is preserved by applying the rejection-based mechanism. For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to compute sensitivities of many reaction rates simultaneously. Moreover, the data structure does not require to be updated frequently, hence improving the computational cost. This feature is especially useful when applied to large reaction networks. We benchmark our method on biological reaction models to prove its applicability and efficiency.

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