John S. George

Neuromagnetic source imaging with FOCUSS: a recursive weighted minimum norm algorithm

The paper describes a new algorithm for tomographic source reconstruction in neural electromagnetic inverse problems. Termed FOCUSS (FOCal Underdetermined System Solution), this algorithm combines the desired features of the two major approaches to electromagnetic inverse procedures. Like multiple current dipole modeling methods, FOCUSS produces high resolution solutions appropriate for the highly localized sources often encountered in electromagnetic imaging. Like linear estimation methods, FOCUSS allows current sources to assume arbitrary shapes and it preserves the generality and ease of application characteristic of this group of methods. It stands apart from standard signal processing techniques because, as an initialization-dependent algorithm, it accommodates the non-unique set of feasible solutions that arise from the neuroelectric source constraints. FOCUSS is based on recursive, weighted norm minimization. The consequence of the repeated weighting procedure is, in effect, to concentrate the solution in the minimal active regions that are essential for accurately reproducing the measurements. The FOCUSS algorithm is introduced and its properties are illustrated in the context of a number of simulations, first using exact measurements in 2- and 3-D problems, and then in the presence of noise and modeling errors. The results suggest that FOCUSS is a powerful algorithm with considerable utility for tomographic current estimation.

Conductivity tensor mapping of the human brain using diffusion tensor MRI

Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, σ and d) in agreement with theoretical bounds and experimental measurements presented here (σ/d ≈ 0.844 ± 0.0545 S⋅s/mm3, r2 = 0.945). The extension to other biological transport phenomena is also discussed.

The Influence of Brain Tissue Anisotropy on Human EEG and MEG

The influence of gray and white matter tissue anisotropy on the human electroencephalogram (EEG) and magnetoencephalogram (MEG) was examined with a high resolution finite element model of the head of an adult male subject. The conductivity tensor data for gray and white matter were estimated from magnetic resonance diffusion tensor imaging. Simulations were carried out with single dipoles or small extended sources in the cortical gray matter. The inclusion of anisotropic volume conduction in the brain was found to have a minor influence on the topology of EEG and MEG (and hence source localization). We found a major influence on the amplitude of EEG and MEG (and hence source strength estimation) due to the change in conductivity and the inclusion of anisotropy. We expect that inclusion of tissue anisotropy information will improve source estimation procedures.

Bayesian inference applied to the electromagnetic inverse problem.

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill‐posed character. Rather than calculating a single “best” solution according to some criterion, our approach produces a large number of likely solutions that both fit the data and any prior information that is used. Whereas the range of the different likely results is representative of the ambiguity in the inverse problem even with prior information present, features that are common across a large number of the different solutions can be identified and are associated with a high degree of probability. This approach is implemented and quantified within the formalism of Bayesian inference, which combines prior information with that of measurement in a common framework using a single measure. To demonstrate this approach, a general neural activation model is constructed that includes a variable number of extended regions of activation and can incorporate a great deal of prior information on neural current such as information on location, orientation, strength, and spatial smoothness. Taken together, this activation model and the Bayesian inferential approach yield estimates of the probability distributions for the number, location, and extent of active regions. Both simulated MEG data and data from a visual evoked response experiment are used to demonstrate the capabilities of this approach. Hum. Brain Mapping 7:195–212, 1999 Published 1999 Wiley‐Liss, Inc. This article is a US government work and, as such, is in the public domain in the United States of America.

Conductivity Mapping of Biological Tissue Using Diffusion MRI

The understanding of electrical injury pathophysiology has benefited greatly from models of electrical current propagation in tissue.1 However, the accuracy of such models could potentially be improved by incorporating quantitative values for tissue. While it is not possible with the present technology to measure the conductivity of deep tissue noninvasively, it has recently been proposed that the conductivity tensor can be approximated from the diffusion tensor as measured by diffusion MRI.2–4 Here, we show how the conductivity tensor can be derived from the water diffusion tensor by a differential effective medium approximation.2,3 Electrical conductivity maps of human brain white matter are also presented. The basis for a general relation between conductivity and diffusion in porous media, such as biological tissue, stems from the mutual restriction of both the ionic and water mobility by the geometry of the medium. The effective restricted mobilities can then be related through a parameterization of the geometric boundary conditions. The claim is not, of course, that there is a fundamental relationship between the free mobilities, but rather that the restricted mobilities are related through the geometry. If we assume, in the spirit of the Neumann principle, that the conductivity and water self-diffusion tensors share eigenvectors, then the tensors can be related by a similarity transformation, = R (D)RT, where is the conductivity tensor, R is the column matrix of the water diffusion tensor eigenvectors, and (D) is the diagonalized conductivity tensor as a function of the diagonalized water diffusion tensor D. We can measure the water diffusion tensor with diffusion MRI, and we wish to find the function (D) that relates the conductivity v and diffusion dv eigenvalues. The relationship between the general transport eigenvalues v, representing either v or dv, can be related to the geometry of the medium by the Sen-Scala-Cohen effective medium relation:

Rapid optical coherence tomography and recording functional scattering changes from activated frog retina

Optical coherence tomography (OCT) has important potential advantages for fast functional neuroimaging. However, dynamic neuroimaging poses demanding requirements for fast and stable acquisition of optical scans. Optical phase modulators based on the electro-optic effect allow rapid phase modulation; however, applications to low-coherence tomography are limited by the optical dispersion of a broadband light source by the electro-optic crystal. We show that the optical dispersion can be theoretically estimated and experimentally compensated. With an electro-optic phase modulator-based, no-moving-parts OCT system, near-infrared scattering changes associated with neural activation were recorded from isolated frog retinas activated by visible light.

Temporal dynamics of visual-evoked neuromagnetic sources: Effects of stimulus parameters and selective attention

Results are reviewed from several neuromagnetic studies which characterize the temporal dynamics of neural sources contributing to the visual evoked response and effects of attention on these sources. Different types of pattern-onset stimuli (< or = 2 degrees) were presented sequentially to a number of field locations in the right visual field. Multiple dipole models were applied to a sequence of instantaneous field distributions constructed at 10 ms intervals. Best-fitting source parameters were superimposed on Magnetic Resonance images (MRI) of each subject to identify the anatomical structure(s) giving rise to the surface patterns. At least three sources, presumably corresponding to different visual areas, were routinely identified from 80-150 ms following the onset of visual stimulation. This observation was consistent across subjects and studies. The temporal sequence and strength of activation of these sources, however, were dependent upon the specific stimulus parameters used to evoke the response (e.g., eccentricity) and on the relevance of the stimulus to the subject. In addition, our results provide evidence for the recurrence of activity in striate and extrastriate regions, following the initial cycle of responses.

Towards effective and rewarding data sharing.

Recently issued NIH policy statement and implementation guidelines (National Institutes of Health, 2003) promote the sharing of research data. While urging that “all data should be considered for data sharing” and “data should be made as widely and freely available as possible” the current policy requires only high-direct-cost (>US

Spatio-temporal mapping of rat whisker barrels with fast scattered light signals

500,000/yr) grantees to share research data, starting 1 October 2003. Data sharing is central to science, and we agree that data should be made available.

Scattered-Light Imaging in Vivo Tracks Fast and Slow Processes of Neurophysiological Activation

Optical techniques offer a number of potential advantages for imaging dynamic spatio-temporal patterns of activity in neural tissue. The methods provide the wide field of view required to image population activation across networks, while allowing resolution of the detailed structure of individual cells. Optical probes can provide high temporal resolution without penetrating the tissue surface. However, functional optical imaging has been constrained by the small size of the signals and the sluggish nature of the metabolic and hemodynamic responses that are the basis of most existing methods. Here, we employ both high-speed CCD cameras and high-sensitivity photodiodes to optimize resolution in both space and time, together with dark-field illumination in the near-infrared, to record fast intrinsic scattering signals from rat somatosensory cortex in vivo. Optical responses tracked the physiological activation of cortical columns elicited by single whisker twitches. High-speed imaging produced maps that were initially restricted in space to individual barrels, and then spread over time. Photodiode recordings disclosed 400-600 Hz oscillatory responses, tightly correlated in frequency and phase to those seen in simultaneous electrical recordings. Imaging based on fast intrinsic light scattering signals eventually could provide high resolution dynamic movies of neural networks in action.