0000000000448370

AUTHOR

Michael Mccourt

showing 4 related works from this author

The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG

2015

The estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution pro- cess requires an accurate and fast forward solver. In this paper the method of fundamental solutions is, for the first time, proposed as a meshfree, boundary-type, and easy-to-implement alternative to the boundary element method (BEM) for solving the M/EEG forward problem. The solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three-dimensional Laplace equation. Numerical accuracy, convergence, and computational load are investigated. The proposed met…

Laplace's equationQuantitative Biology::Neurons and Cognitionmedicine.diagnostic_testApplied MathematicsPhysics::Medical PhysicsMathematical analysisMagnetoencephalographyInverse problemElectroencephalographySettore MAT/08 - Analisi NumericaSettore ING-IND/31 - ElettrotecnicaComputational MathematicsConvergence (routing)medicineMethod of fundamental solutionsBoundary value problemkernel-based methods method of fundamental solutions EEG MEGBoundary element methodMathematicsSIAM Journal on Scientific Computing
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A novel numerical meshless approach for electric potential estimation in transcranial stimulation

2015

In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.

Regularized meshless methodMathematical optimizationmethod of fundamental solutionQuantitative Biology::Neurons and CognitionNumerical analysistranscranial electrical stimulationCurrent density distributionGrid basedBoundary valuesPhysics and Astronomy (all)Settore MAT/08 - Analisi NumericaSettore ING-IND/31 - ElettrotecnicaApplied mathematicsMethod of fundamental solutionsMeshfree methodsmeshless methodElectric potentialnumerical approximationMathematics
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A Meshfree Solver for the MEG Forward Problem

2015

Noninvasive estimation of brain activity via magnetoencephalography (MEG) involves an inverse problem whose solution requires an accurate and fast forward solver. To this end, we propose the Method of Fundamental Solutions (MFS) as a meshfree alternative to the Boundary Element Method (BEM). The solution of the MEG forward problem is obtained, via the Method of Particular Solutions (MPS), by numerically solving a boundary value problem for the electric scalar potential, derived from the quasi-stationary approximation of Maxwell’s equations. The magnetic field is then computed by the Biot-Savart law. Numerical experiments have been carried out in a realistic single-shell head geometry. The p…

Computer scienceBiomagnetics magnetoencephalography (MEG) method of fundamental solutions (MFS) meshfree methodsScalar potentialInverse problemSolverBoundary knot methodElectronic Optical and Magnetic MaterialsSettore ING-IND/31 - ElettrotecnicaSettore MAT/08 - Analisi NumericaClassical mechanicsApplied mathematicsMethod of fundamental solutionsBoundary value problemElectrical and Electronic EngineeringBoundary element method
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An augmented MFS approach for brain activity reconstruction

2017

Abstract Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving rise to electric and magnetic fields, which can be modeled by the quasi-stationary approximation of Maxwell’s equations. Electroencephalography (EEG) and magnetoencephalography (MEG) techniques allow for reconstructing the cerebral electrical currents and thus investigating the neuronal activity in the human brain in a non-invasive way. This is a typical electromagnetic inverse problem which can be addressed in two stages. In the first one a physical and geometrical representation of the head is used to find the relation between a given source mo…

Electromagnetic fieldNumerical AnalysisGeneral Computer Sciencemedicine.diagnostic_testApplied MathematicsScalar (physics)010103 numerical & computational mathematicsMagnetoencephalographyInverse problem01 natural sciencesFinite element methodTheoretical Computer Science010101 applied mathematicsSettore MAT/08 - Analisi NumericaSettore ING-IND/31 - ElettrotecnicaMethod of Fundamental Solutions Boundary value problems M/EEG LOOCV algorithmModeling and SimulationmedicineMethod of fundamental solutionsBoundary value problem0101 mathematicsBoundary element methodAlgorithmMathematics
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