A minimal product method and its application to cortical imaging

High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise.

Implementation and evaluation of data analysis strategies for time-resolved optical spectroscopy

Time-resolved optical spectroscopy plays a key role in illuminating the mechanisms of many fundamental processes in physics, chemistry, and biology. However, to extract the essential information from the highly complex time-resolved data, advanced data analysis techniques are required. Here we present the implementation strategies and the evaluation of the familiar global lifetime and target analysis as well as the not so widely adopted lifetime distribution analysis (LDA). Furthermore, we demonstrate the implementation of analysis strategies dealing with a number of artifacts inherently present in data from ultrafast optical experiments. The focus of the work is placed on LDA as it allows invaluable exploration depth of the kinetic information contained in the experimental data. We establish a clear regularization procedure for the use of LDA in ultrafast optical spectroscopy and evaluate the performance of a number of factors that play a role in the reliable reconstruction of lifetime distributions. Our results show that the optimal regularization factor can be determined well with the L-curve and the generalized cross-validation techniques. Moreover, the performance evaluations indicate that the most efficient regularization norm is the identity matrix. The analytical procedures described in this work can be readily implemented and used for the analysis of any time-resolved data.

Photo-physical properties of 2-(1-ethynylpyrene)-adenosine: influence of hydrogen bonding on excited state properties

The photo-physical properties of 2-(1-ethynylpyrene)-adenosine (PyA), a fluorescent probe for RNA dynamics, were examined by solvation studies. The excited-state dynamics display the influence of the vicinity on the spectral features. Combining improved transient absorption and streak camera measurements along with a new analysis method provide a detailed molecular picture of the photophysics. After intramolecular vibrational energy redistribution (IVR), two distinct states are observed. Solvent class (protic/aprotic) and permittivity strongly affect the properties of these states and their population ratio. As a result their emission spectrum is altered, while the fluorescence quantum yield and the overall lifetime remain nearly unchanged. Consequently, the hitherto existing model of the photophysics is herein refined and extended. The findings can serve as basis for improving the information content of measurements with PyA as a label in RNA.

Cortical dipole imaging using truncated total least squares considering transfer matrix error

Cortical dipole imaging has been proposed as a method to visualize electroencephalogram in high spatial resolution. We investigated the inverse technique of cortical dipole imaging using a truncated total least squares (TTLS). The TTLS is a regularization technique to reduce the influence from both the measurement noise and the transfer matrix error caused by the head model distortion. The estimation of the regularization parameter was also investigated based on L-curve. The computer simulation suggested that the estimation accuracy was improved by the TTLS compared with Tikhonov regularization. The proposed method was applied to human experimental data of visual evoked potentials. We confirmed the TTLS provided the high spatial resolution of cortical dipole imaging.

Evaluation of cortical current density imaging methods using intracranial electrocorticograms and functional MRI

OBJECTIVE

EEG source imaging provides important information regarding the underlying neural activity from noninvasive electrophysiological measurements. The aim of the present study was to evaluate source reconstruction techniques by means of the intracranial electrocorticograms (ECoGs) and functional MRI.

METHODS

Five source imaging algorithms, including the minimum norm least square (MNLS), LORETA with L(p)-norm (p equal to 1, 1.5 and 2), sLORETA, the minimum L(p)-norm (p equal to 1 and 1.5; when p=2, the MNLS method is mathematically equivalent to the minimum L(p)-norm) and L(1)-norm (the linear programming) methods, were evaluated in a group of 10 human subjects, in a paradigm with somatosensory stimulation. Cortical current density (CCD) distributions were estimated from the scalp somatosensory evoked potentials (SEPs), at approximately 30 ms following electrical stimulation of median nerve at the wrist. Realistic geometry boundary element head models were constructed from the MRIs of each subject and used in the CCD analysis. Functional MRI results obtained from a motor task and sensory stimulation in all subjects were used to identify the central sulcus, motor and sensory areas. In three patients undergoing neurosurgical evaluation, ECoGs were recorded in response to the somatosensory stimulation, and were used to help determine the central sulcus and the sensory cortex.

RESULTS

The CCD distributions estimated by the L(p)-norm and LORETA-L(p) methods were smoother when the p values were high. The LORETA based on the L(1)-norm performed better than the LORETA-L(2) method for imaging well localized sources such as the P30 component of the SEP. The mean and standard deviation of the distance between the location of maximum CCD value and the central sulcus, estimated by the minimum L(p)-norm (with p equal to 1), L(1)-norm (the Linear programming) and LORETA-L(p) (with p equal to 1) methods, were 4, 7, 7 mm and 3, 4, 2 mm, respectively (after converting into Talairach coordinates). The mean and standard deviation of the aforementioned distance, estimated by the MNLS, LORETA with L(p)-norm (p equal to 1.5 and 2.0), sLORETA and the minimum L(p)-norm (p equal to 1.5) methods, were over 11 mm and 6 mm, respectively.

CONCLUSIONS

The present experimental study suggests that L(1)-norm-based algorithms provide better performance than L(2) and L(1.5)-norm-based algorithms, in the context of CCD imaging of well localized sources induced by somatosensory electrical stimulation of median nerve at the wrist.

Integration of EEG/MEG with MRI and fMRI

EEG and MEG are important functional neuroimaging modalities for studying the temporal dynamics of neural activities and interactions, but the accurate localization of neural activities still remains a challenging problem. Combining EEG/MEG with MRI or/and functional MRI (fMRI) holds promise to significantly increase the spatial resolution of electromagnetic source imaging, and at the same time, allows tracing the rapid neural processes and information pathways within the brain, which cannot be achieved using these modalities in isolation. In this paper, we review some recent progresses in multimodal neuroimaging, with special emphasis on the integration of EEG, MEG with MRI and fMRI. Some examples are shown to illustrate the importance of the combined source analysis in clinical and experimental studies.

Spatio-temporal cortical source imaging of brain electrical activity by means of time-varying parametric projection filter

In the present study, we explore suitable spatio-temporal filters for inverse estimation of an equivalent dipole-layer distribution from the scalp electroencephalogram (EEG) for imaging of brain electric sources. We propose a time-varying parametric projection filter (tPPF) for the spatio-temporal EEG analysis. The performance of this tPPF algorithm was evaluated by computer simulation studies. An inhomogeneous three-concentric-spheres model was used in the present simulation study to represent the head volume conductor. An equivalent dipole layer was used to represent equivalently brain electric sources and estimated from the scalp potentials. The tPPF filter was tested to remove time-varying noise such as instantaneous artifacts caused by eyes-blink. The present simulation results indicate that the proposed time-variant tPPF method provides enhanced performance in rejecting time-varying noise, as compared with the time-invariant parametric projection filter.

Estimation of Active Cortical Current Source Regions Using a Vector Representation Scanning Approach

The objective of this article is to present a framework for cortical current source reconstruction that extracts a center and magnitude of electrical brain activity from EEG signals. High-resolution EEG recordings, a subject-specific MRI-based electromagnetic boundary element method (BEM) model, and a channel reduction technique are used. This new geometric measure combines the magnitude and spatial location of electrical brain activity of each of the identified subsets of channels into a three-dimensional resultant vector. The combination of the two approaches constitutes a source reconstruction scanning technique that provides a real-time estimation of cortical centers that can be tracked over time. Simulations demonstrate that the ability of this method to find the best-fit cortical location is more robust both in terms of accuracy and precision than traditional approaches for single-source conditions. Experimental validation demonstrates its ability to localize and separate cortical activity in plausible sites for two different motor tasks. Finally, this method provides a statistical measure to compare electrical brain activity associated with different motor tasks.

Boundary element method-based cortical potential imaging of somatosensory evoked potentials using subjects' magnetic resonance images

A boundary element method-based cortical potential imaging technique has been developed to directly link the scalp potentials with the cortical potentials with the aid of magnetic resonance images of the subjects. First, computer simulations were conducted to evaluate the new approach in a concentric three-sphere inhomogeneous head model. Second, the corresponding cortical potentials were estimated from the patients' preoperative scalp somatosensory evoked potentials (SEPs) based on the boundary element models constructed from subjects' magnetic resonance images and compared to the postoperative direct cortical potential recordings in the same patients. Simulation results demonstrated that the cortical potentials can be estimated from the scalp potentials using different scalp electrode configurations and are robust against measurement noise. The cortical imaging analysis of the preoperative scalp SEPs recorded from patients using the present approach showed high consistency in spatial pattern with the postoperative direct cortical potential recordings. Quantitative comparison between the estimated and the directly recorded subdural grid potentials resulted in reasonably high correlation coefficients in cases studied. Amplitude difference between the estimated and the recorded potentials was also observed as indexed by the relative error, and the possible underlying reasons are discussed. The present numerical and experimental results validate the boundary element method-based cortical potential imaging approach and demonstrate the feasibility of the new approach in noninvasive high-resolution imaging of brain electric activities from scalp potential measurement and magnetic resonance images.

High-resolution EEG: on the cortical equivalent dipole layer imaging

BACKGROUND

Brain electrical activity is a spatio-temporally distributed process. Cortical imaging techniques have been developed to reconstruct cortical activity from the scalp electroencephalographic or magnetoencephalographic measurements. Several cortical imaging approaches, such as the epicortical potentials and a dipole layer accounting for the cortical activity, have been used to represent brain electrical activity.

METHODS

A closed cortical dipole layer source model is used to equivalently represent brain electrical activity. The relationship between the primary brain electrical sources and the cortical equivalent dipole layer is derived from the theory of electromagnetics. Computer simulation studies were conducted using a 3-concentric-sphere head model to validate the proposed theory. The cortical equivalent dipole layer imaging approach was tested in both computer simulation and human visual evoked potential (VEP) experiments.

RESULTS

The strength of the cortical equivalent dipole layer is shown to be proportional to the electrical potential over the same surface generated by primary electrical sources, had the outer medium been replaced by air. The proposed theory was validated by computer simulation in a discrete system. Simulation and VEP experimental studies suggest the feasibility of applying the cortical equivalent dipole layer imaging approach for brain imaging.

CONCLUSIONS

The cortical equivalent dipole layer model can equivalently represent the primary brain electrical sources throughout the entire brain surrounded by the dipole layer. The strength of the cortical equivalent dipole layer due to primary sources can be directly calculated according to the theory developed in the present study.