Gyri-precise head model of transcranial direct current stimulation: Improved spatial focality using a ring electrode versus conventional rectangular pad

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided. This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels and different simulated source depths has shown that for single source localization, regularized sLORETA gives the best solution in terms of both localization error and ghost sources. Furthermore the computationally intensive solution given by SLF was not found to give any additional benefits under such simulated conditions.

/pdf/review-on-solving-the-inverse-problem-in-eeg-source-analysis-2j79a4u8wn.pdf

Review on solving the inverse problem in EEG source analysis

The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.

The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors.

Digital holography is an emerging field of new paradigm in general imaging applications. We present a review of a subset of the research and development activities in digital holography, with emphasis on microscopy techniques and applications. First, the basic results from the general theory of holography, based on the scalar diffraction theory, are summarized, and a general description of the digital holographic microscopy process is given, including quantitative phase microscopy. Several numerical diffraction methods are described and compared, and a number of representative configurations used in digital holography are described, including off-axis Fresnel, Fourier, image plane, in-line, Gabor, and phase-shifting digital holographies. Then we survey numerical techniques that give rise to unique capabilities of digital holography, including suppression of dc and twin image terms, pixel resolution control, optical phase unwrapping, aberration compensation, and others. A survey is also given of representative application areas, including biomedical microscopy, particle field holography, micrometrology, and holographic tomography, as well as some of the special techniques, such as holography of total internal reflection, optical scanning holography, digital interference holography, and heterodyne holography. The review is intended for students and new researchers interested in developing new techniques and exploring new applications of digital holography.

/pdf/principles-and-techniques-of-digital-holographic-microscopy-56tmwltigo.pdf

Principles and techniques of digital holographic microscopy

Electric field and stimulating influence generated by deep brain stimulation of the subthalamic nucleus

Modeling in magnetoencephalography (MEG) and electroencephalography (EEG) requires knowledge of the in vivo tissue resistivities of the head. The aim of this paper is to examine the influence of tissue resistivity changes on the neuromagnetic field and the electric scalp potential. A high-resolution finite element method (FEM) model (452162 elements, 2-mm resolution) of the human head with 13 different tissue types is employed for this purpose. Our main finding was that the magnetic fields are sensitive to changes in the tissue resistivity in the vicinity of the source. In comparison, the electric surface potentials are sensitive to changes in the tissue resistivity in the vicinity of the source and in the vicinity of the position of the electrodes. The magnitude (strength) of magnetic fields and electric surface potentials is strongly influenced by tissue resistivity changes, while the topography is not as strongly influenced. Therefore, an accurate modeling of magnetic field and electric potential strength requires accurate knowledge of tissue resistivities, while for source localization procedures this knowledge might not be a necessity.

Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head

https://stuff.mit.edu/people/ppurdon/multimodal/haueisen2002.pdf

The influence of brain tissue anisotropy on human EEG and MEG.

The structure of the anatomical surfaces, e.g., CSF and gray and white matter, could severely influence the flow of volume currents in a head model. This, in turn, will also influence the scalp potentials and the inverse source localizations. This was examined in detail with four different human head models. Four finite element head models constructed from segmented MR images of an adult male subject were used for this study. These models were: (1) Model 1: full model with eleven tissues that included detailed structure of the scalp, hard and soft skull bone, CSF, gray and white matter and other prominent tissues, (2) the Model 2 was derived from the Model 1 in which the conductivity of gray matter was set equal to the white matter, i.e., a ten tissue-type model, (3) the Model 3 was derived from the Model 1 in which the conductivities of gray matter and CSF were set equal to the white matter, i.e., a nine tissue-type model, (4) the Model 4 consisted of scalp, hard skull bone, CSF, gray and white matter, i.e., a five tissue-type model. How model complexity influences the EEG source localizations was also studied with the above four finite element models of the head. The lead fields and scalp potentials due to dipolar sources in the motor cortex were computed for all four models. The inverse source localizations were performed with an exhaustive search pattern in the motor cortex area. The inverse analysis was performed by adding uncorrelated Gaussian noise to the scalp potentials to achieve a signal to noise ratio (SNR) of -10 to 30 dB. The Model 1 was used as a reference model. The reference model, as expected, performed the best. The Model 3, which did not have the CSF layer, performed the worst. The mean source localization errors (MLEs) of the Model 3 were larger than the Model 1 or 2. The scalp potentials were also most affected by the lack of CSF geometry in the Model 3. The MLEs for the Model 4 were also larger than the Model 1 and 2. The Model 4 and the Model 3 had similar MLEs in the SNR range of -10 dB to 0 dB. However, in the SNR range of 5 dB to 30 dB, the Model 4 has lower MLEs as compared with the Model 3. These results indicate that the complexity of head models strongly influences the scalp potentials and the inverse source localizations. A more complex head model performs better in inverse source localizations as compared to a model with lesser tissue surfaces. The CSF layer plays an important role in modifying the scalp potentials and also influences the inverse source localizations. In summary, for best results one needs to have highly heterogeneous models of the head for accurate simulations of scalp potentials and for inverse source localizations.

/pdf/influence-of-head-models-on-eeg-simulations-and-inverse-5ro9ctnocr.pdf

Influence of head models on EEG simulations and inverse source localizations

The current dipole is a widely used source model in forward and inverse electroencephalography and magnetoencephalography applications. Analytic solutions to the governing field equations have been developed for several approximations of the human head using ideal dipoles as the source model. Numeric approaches such as the finite-element and finite-difference methods have become popular because they allow the use of anatomically realistic head models and the increased computational power that they require has become readily available. Although numeric methods can represent more realistic domains, the sources in such models are an approximation of the ideal dipole. In this paper, we examine several methods for representing dipole sources in finite-element models and compare the resulting surface potentials and external magnetic field with those obtained from analytic solutions using ideal dipoles.

Dipole models for the EEG and MEG

The influence of volume currents on the magnetic field is an important question in magnetoencephalography since the spherical volume conductor is still widely used for source localization. In theory, the magnetic field of a radial dipole in a homogeneous sphere is zero. In realistic models of the head, the field is suppressed when compared with a tangential dipole. To determine the influence of the volume currents, this suppression ratio (magnetic field of the radial dipole divided by the field of the tangential dipole) needs to be quantified. Large-scale finite element method models of the human head and the rabbit head were constructed and the suppression ratio was computed. The computed suppression value of 0.28 in the rabbit head was similar to the previously measured experimental value. In the human head, an average suppression ratio of 0.19±0.07 was found for different regions and depths in the gray matter. It was found that the computed magnetic field of radial sources varied significantly with the conductivities of the surrounding tissues where the dipole was located. We also modeled the magnetic field of an epileptic interictal spike in a finite element model of the rabbit head with a single dipole and with extended sources of varying length (1–8 mm). The extended source models developed were based on invasive measurements of an interictal spike within the rabbit brain. The field patterns of the small (1–2 mm) extended sources were similar to a single dipolar source and begin to deviate significantly from a dipolar field for the larger extended sources (6–8 mm).

Ceon Ramon

Papers

Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head

The influence of brain tissue anisotropy on human EEG and MEG.

Influence of head models on EEG simulations and inverse source localizations

Dipole models for the EEG and MEG

On the influence of volume currents and extended sources on neuromagnetic fields: a simulation study.