Electro-magneto-encephalography and fundamental solutions

Dassios, George; Fokas, A. S.

doi:10.1090/s0033-569x-09-01144-7

Cited by 5 publications

(8 citation statements)

References 20 publications

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“…Therefore, it can be considered as the fundamental solution of the MEG problem for the spherical geometry [12]. Consequently, any discrete, or continuous, current distribution can be obtained through summation, or integration, respectively, of the above fundamental solution [13].…”

Section: The Meg Problem For a Single Dipolementioning

confidence: 99%

On the Inverse MEG Problem with a 1-D Current Distribution

Dassios¹,

Satrazemi²

2015

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The inverse problem of magnetoencephalography (MEG) seeks the neuronal current within the conductive brain that generates a measured magnetic flux in the exterior of the brain-head system. This problem does not have a unique solution, and in particular, it is not even possible to identify the support of the current if it extends over a three-dimensional set. However, a localized current supported on a zero-, one-or two-dimensional set can in principle be identified. In the present work, we demonstrate an analytic algorithm that is able to recover a one-dimensional distribution of current from the knowledge of the exterior magnetic flux field. In particular, we consider a neuronal current that is supported on a small line segment of arbitrary location and orientation in space, and we reduce the identification of its characteristics to a nonlinear algebraic system. A series of numerical tests show that this system has a unique real solution. A special case is easily solved via the use of trivial algebraic operations.

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Section: The Meg Problem For a Single Dipolementioning

confidence: 99%

On the Inverse MEG Problem with a 1-D Current Distribution

Dassios¹,

Satrazemi²

2015

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“…Therefore, they can be considered as the corresponding fundamental solutions for these two problems [17]. The relative solutions due to any distribution of current dipoles can be obtained by integrating these fundamental solutions over the source variable r r r 0 [18].…”

Section: The Single Dipole Excitationmentioning

confidence: 99%

Inversion of electroencephalography data for a 2-D current distribution

Dassios

Satrazemi

2014

Math. Meth. Appl. Sci.

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It is known from the fundamental work of Albanese and Monk that, the recovery of the support of a three dimensional current, within a conducting medium, from measurements of the generated exterior electric potential, is not possible. However, it is possible to recover the support of any other current, which is supported on a set of dimension lower than three. Nevertheless, no algorithm for such an inversion is known. Here, we propose such an algorithm for a two dimensional current distribution, and in particular, we apply this algorithm to the inverse problem of electroencephalography in the case where the neuronal current is restricted to a small disk of arbitrary location and orientation within the brain. The solution of this inverse problem is reduced to the solution of a nonlinear algebraic system, and numerical tests show that the there exists a unique real solution to this system.

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“…The solution − (r; r 0 ), given in (8), provides the solution of the interior problem (2), and the solution + (r; r 0 ), given in (11), provides the solution of the exterior problem 3, both for the case of a point excitation at r 0 . Therefore, they can be considered as the corresponding fundamental solutions for these two problems [15]. The relative solutions due to any distribution of current dipoles can be obtained by integrating these fundamental solutions over the source variable r 0 [11].…”

Section: The Eeg Problem and Its Fundamental Solutionmentioning

confidence: 99%

“…3 ) = J (r 0 ) provides an average moment and l = ( 1 , 2 , 3 ) =̂⋅ ∇ ⊗ J (r 0 ) provides an average directional derivative of the current along the direction̂. Next we calculate the total potential which is generated by the approximate current (15). In fact, since our ultimate goal is to invert the EEG data that will give us the quantities Q, r 0 ,…”

Section: The Potential Of a Linearly Distributed Currentmentioning

confidence: 99%

On the Inverse EEG Problem for a 1D Current Distribution

Dassios

Fragoyiannis

Satrazemi

2014

Journal of Applied Mathematics

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Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.

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Electro-magneto-encephalography and fundamental solutions

Cited by 5 publications

References 20 publications

On the Inverse MEG Problem with a 1-D Current Distribution

On the Inverse MEG Problem with a 1-D Current Distribution

Inversion of electroencephalography data for a 2-D current distribution

On the Inverse EEG Problem for a 1D Current Distribution

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