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Statistical Parametric Mapping The Analysis Of Functional Brain Images

Electrodes for high-definition transcutaneous DC stimulation for applications in drug-delivery and electrotherapy, including tDCS

A recently developed formulation of the inverse source problem as a Fredholm integral equation of the first kind provides motivation for the development of analytical characterizations of the nonuniqueness in the inverse source problem. Nonradiating sources, i. e., sources for which the field is identically zero outside a finite region, are introduced. It is then shown that the null space of the Fredholm integral equation is exactly the class of nonradiating sources.

Non-uniqueness in the inverse source problem in acoustics and electromagnetics

On the importance of electrode parameters for shaping electric field patterns generated by tDCS

We investigate the effect of tissue heterogeneity and anisotropy on the electric field and current density distribution induced in the brain during magnetic stimulation. Validation of the finite-element (FE) calculations in a homogeneous isotropic sphere showed that the magnitude of the total electric field can be calculated to within an error of approximately 5% in the region of interest, even in the presence of a significant surface charge contribution. We used a high conductivity inclusion within a sphere of lower conductivity to simulate a lesion due to an infarct. Its effect is to increase the electric field induced in the surrounding low conductivity region. This boost is greatest in the vicinity of interfaces that lie perpendicular to the current flow. For physiological values of the conductivity distribution, it can reach a factor of 1.6 and extend many millimeters from the interface. We also show that anisotropy can significantly alter the electric field and current density distributions. Either heterogeneity or anisotropy can introduce a radial electric field component, not present in a homogeneous isotropic conductor. Heterogeneity and anisotropy are predicted to significantly affect the distribution of the electric field induced in the brain. It is, therefore, expected that anatomically faithful FE models of individual brains which incorporate conductivity tensor data derived from diffusion tensor measurements, will provide a better understanding of the location of possible stimulation sites in the brain.

The Electric Field Induced in the Brain by Magnetic Stimulation : A 3-D Finite-Element Analysis of the Effect of Tissue Heterogeneity and Anisotropy

Electrical impedance tomography (EIT) is a recently developed medical imaging method which has the potential to produce images of fast neuronal depolarization in the brain. Previous modelling suggested that applied current needed to be below 100 Hz but the signal-to-noise ratio (SNR) recorded with scalp electrodes during evoked responses was too low to permit imaging. A novel method in which contemporaneous evoked potentials are subtracted is presented with current applied at 225 Hz to cerebral cortex during evoked activity; although the signal is smaller than at DC by about 10×, the principal noise from the EEG is reduced by about 1000×, resulting in an improved SNR. It was validated with recording of compound action potentials in crab walking leg nerve where peak changes of −0.2% at 125 and 175 Hz tallied with biophysical modelling. In recording from rat cerebral cortex during somatosensory evoked responses, peak impedance decreases of −0.07 ± 0.006% (mean ± SE) with a SNR of >50 could be recorded at 225 Hz. This method provides a reproducible and artefact free means for recording resistance changes during neuronal activity which could form the basis for imaging fast neural activity in the brain.

A novel method for recording neuronal depolarization with recording at 125–825 Hz: implications for imaging fast neural activity in the brain with electrical impedance tomography

For the novel application of recording of resistivity changes related to neuronal depolarization in the brain with electrical impedance tomography, optimal recording is with applied currents below 100 Hz, which might cause neural stimulation of skin or underlying brain. The purpose of this work was to develop a method for application of low frequency currents to the scalp, which delivered the maximum current without significant stimulation of skin or underlying brain. We propose a recessed electrode design which enabled current injection with an acceptable skin sensation to be increased from 100 μA using EEG electrodes, to 1 mA in 16 normal volunteers. The effect of current delivered to the brain was assessed with an anatomically realistic finite element model of the adult head. The modelled peak cerebral current density was 0.3 A/m2, which was 5 to 25-fold less than the threshold for stimulation of the brain estimated from literature review.

http://www.mathcs.emory.edu/~horesh/publications/journal/Gilad%202007%20-%20Design%20of%20electrodes%20and%20current%20limits%20for%20low%20frequency%20electrical%20impedance%20tomography%20of%20the%20brain.pdf

Design of electrodes and current limits for low frequency electrical impedance tomography of the brain

Impedance changes recorded with scalp electrodes during visual evoked responses: implications for Electrical Impedance Tomography of fast neural activity.

A method for recording resistance changes non-invasively during neuronal depolarization with a view to imaging brain activity with electrical impedance tomography

O Gilad

Papers

A novel method for recording neuronal depolarization with recording at 125–825 Hz: implications for imaging fast neural activity in the brain with electrical impedance tomography

Design of electrodes and current limits for low frequency electrical impedance tomography of the brain

Impedance changes recorded with scalp electrodes during visual evoked responses: implications for Electrical Impedance Tomography of fast neural activity.

A method for recording resistance changes non-invasively during neuronal depolarization with a view to imaging brain activity with electrical impedance tomography

Stroke type differentiation by multi-frequency electrical impedance tomography (MFEIT)–a feasibility study