ELECTROPHYSIOLOGICAL NEUROIMAGING: SOLVING THE INVERSE PROBLEM OF ELECTROENCEPHALOGRAPHY AND BEYOND

B. He, J. Lian
Department of Bioengineering, University of Illinois at Chicago, USA

Abstract: We review the recent development in electrophysiological neuroimaging, which we refer to the approach of quantitatively estimating and localizing the intracranial neural sources corresponding to scalp electroencephalographic recordings. The past decade has shown extraordinary progress in our ability to image brain electrical activity from the scalp EEG. Of particular interest is the recent trend in integrating information from electrophysiological and magnetic resonance imaging, which leads to substantially improved spatial resolution of localizing or estimating brain electrical sources. Examples on electrophysiological neuroimaging will also be provided.

INTRODUCTION

Brain electric activity is spatially distributed over three-dimension (3D) of the brain and evolves with time. Therefore, the ultimate goal of the inverse electroencephalography (EEG) is to non-invasively reconstruct the spatio-temporal distribution of brain electrical activity from scalp EEG measurements.

Pioneered by German scientist Berger in the 1920s, the EEG and associated measurements (such as evoked potentials (EPs) and event-related potenrials (ERPs)) have enjoyed wide clinical acceptance in detecting and characterizing neurological and cognitive processes. The major merit of EEG modality is its unsurpassed millisecond-scale temporal resolution, which is desirable to resolving rapid change in brain processes associated with sensory, motor, and cognitive processes. However, the application of conventional EEG has been hindered due to its limited spatial resolution mainly casued by the head volume conduction effect and limited spatial sampling [1].

A remarkable development in the past decade is that high-resolution EEG systems with 64 to 256 electrodes have been commercially available. This technical advancement has played an important role in the advancement of electrophysiological neuroimaging, providing a necessary condition to reconstruct quantitatively brain electrical activity from the scalp EEG. Despite of the technical advancement in hardware of high resolution EEG systems and dense-array sensors, a great challenge still exits due to the fundamental physical process of volume conduction which generates distortions and smearing of recordable EEG compared with its intracranial neural generators.

A number of efforts have been made in an attempt to compensate the volume conduction distortion and improve the spatial resolution of EEG. One popular approach has been the dipole source localization, in which neural sources are modeled as one or a few current dipoles, and mathematical procedures are employed in order to estimate these equivalent dipoles from the scalp EEG recordings. In the past decade, several new approaches have been aggresively developed in an attempt to estimate not only localized but also distributed neural sources. These include the scalp Laplacian (a spatial enhancement approach), the cortical imaging (a 2D distributed inverse solution), and 3D source imaging appraoches. Of particular interest is the integration of these source imaging approaches with the realistic anatomical information regarding individuals’ brain and head, obtained from individuals’ magnetic resonance images (MRIs).

Below, we review the recent development of these quantitative approaches of reconstructing brain electrical sources from scalp EEG. We will also present examples of electrophysiologucal neuroimaging.

DIPOLE SOURCE LOCALIZATION

Assuming the scalp EEG is generated by one or a few focal sources [2-9], the dipole source localization (DSL) solves the EEG inverse problem by using a nonlinear multidimensional minimization procedure, to estimate the dipole parameters that can best explain the observed scalp potentials in a least-square sense. The dipole source model can be further classified as moving dipoles, fixed dipoles, or rotating dipoles, depending on the degree of freedom of the dipole parameters.

Realistic geometry (RG) head model constructed from MRIs have been widely used in DSL, based on the fact that the inverse solution of DSL is more accurate when using RG head model than the spherical head model [5]. By registration with the MRIs, the 3D coordinates of the estimated dipole sources can be visualized relative to the brain anatomy. Therefore, it has great potential to reveal the electrophysiologically active neural substrate underlying the scalp EEG measurements, facilitate comparison with other functional imaging modalities, and has clinical significance in detecting the epileptic foci [7], presurgical localization of sensorimotor cortex [8], and some other applications.

While the DSL has been demonstrated to be useful in locating a spatially restricted brain electric event, it remains to be demonstrated that how distributed sources can be estimated from simplified source models such as dipoles [9]. To further develop our ability to image distributed brain sources, methods that can treat distributed sources have been aggresively developed in the past decade.

SCALP LAPLACIAN

As one of the distributed source imaging techniques, the surface Laplacian (SL) has been shown to be able to enhance the high-spatial frequency components of cortical electrical activity. The SL has been considered an estimate of the local current density flowing perpendicular to the skull into the scalp, thus it has also been termed as current source density or scalp current density [10,11]. The SL has also been considered as an equivalent surface charge density corresponding to the surface potential [12]. In addition, the relationship between the SL and the cortical potentials has also been explored [10]. Compared to the EEG inverse approaches, the SL approach does not require exact knowledge about the conductivity distribution inside the head and has unique advantage of reference-independence.

Since Hjorth’s early exploration on scalp Laplacian EEG [13], a number of attempts have been made to develop reliable and easy-to-use SL techniques. Of noteworthy is the development of spherical spline SL [11], ellipsoidal spline SL [14], and the RG spline SL [15,16]. We have recently developed a new RG spline SL algorithm, which not only takes into consideration of the RG of the scalp surface, but also simplifies the regularization procedure by reformulating the SL operator [16]. Simulation studies have demonstrated that the new spline SL algorithm is robust against measurement noise and has consistent performance for different number of recording electrodes. Figure 1 shows an example on surface Laplacian imaging of two localized brain electric sources in a RG head model. One simulated dipole source is located in right medial temporal lobe with orientation tangential to the cortical surface, and another simulated dipole is located in right inferior frontal lobe with radial orientation. The generated scalp potentials are contaminated with 5% Gaussion white noise, and show a blurred dipole pattern of distribution with frontal positivity and posterior negativity. The surface Laplacian map, however, effectively reduces the blurring effect caused by the head volume conductor, and clearly reveals two localized activities corresponding to the underlying dipole sources.

(a) (b) (c)

Figure 1. Surface Laplacian imaging of simulated dipole sources. (a) Illustration of two simulated dipoles. (b) Noise-contaminated scalp potential map. (c) Surface Laplacian map.

CORTICAL IMAGING TECHNIQUES

The recent development of cortical imaging technique, which attempts to deconvolve the spatial smoothing effect of the head volume conduction, thus achieving high resolution imaging over the surface of the brain, has shown great promise in achieving the goal of brain electric source imaging. One approach is the cortical current imaging, in which an equivalent cortical current dipole distribution is directly estimated from the scalp potentials [17-19, 49]. It has been demonstrated that the strength of the equivalent current dipole layer is proportional to the electric potential over the same surface generated by primary electric sources, had the outer media been replaced by air [19]. Another approach is the cortical potential imaging, which estimates the epicortical potentials from the scalp EEG [20-28]. Because the cortical potential distribution can be experimentally measured [22, 29,30] and compared to the inverse imaging results, the cortical potential imaging approach is of clinical importance.

Recently we have developed a new cortical potential imaging algorithm [23], in which both the RG and the head inhomogeneity can be taken into consideration using the boundary element method (BEM). This BEM-based algorithm offers unique features of connecting directly the cortical potentials to the scalp potentials via a transfer matrix with inclusion of the low-conductivity skull layer. The BEM-based cortical potential imaging approach has been systematically evaluated in computer simulations and validated in somatosensory evoked potential (SEP) experiments in three patients by quantitative comparison of the estimated cortical potentials with the direct potential recordings from a subdural grid over the somatosensory cortex [30]. A representative example is shown in Figure 2. Figure 2a shows the recorded pre-operative scalp potential map at 30 ms after the onset of right median nerve stimuli in one subject, which shows blurred dipolar pattern of parietal positivity/frontal negativity over the left scalp. By solving the inverse problem, the corresponding cortical potentials at the 32 subdural grid electrodes were estimated (Fig. 2b), and compared with the post-operative subdural grid recordings (Fig. 2c). Both the estimated and directly recorded grid potentials show localized positive/negative peaks in the posterior edge of the electrode array, and reveal similar dipolar grid potential pattern. Note that polarity inversion was clearly demarcated in both the estimated and recorded grid potential maps. The correlation coefficient between the estimated and recorded grid potentials is as high as 0.84, which explains the similarities in spatial pattern between the estimated and measured grid potential maps.

(a) (b) (c)

Figure 2. Cortical potential imaging of N30/P30 component of SEP in one patient (from [30] with permission). (a) Scalp potential map. (b) Recorded grid potential map. (c) Estimated grid potential map.

3D BRAIN ELECTRIC SOURCE IMAGING

Tremendous effort has been made during the past several years for the 3D neuroimaging, in which the brain electric sources are distributed in 3D brain volume. The most popular linear inverse solution is the minimum norm (MN) solution [31], which estimates the 3D brain source distribution with the smallest L2-norm solution vector that would match the measured data. To compensate for the undesired depth dependency of the original MN solution, which favors superficial sources, different weighting methods were introduced. The representative approaches include the diagonal matrix weighted minimum norm (WMN) solution [32,33], and the Laplacian weighted minimum norm (LWMN) solution [34]. The WMN compensates for the lower gains of deeper sources by lead field normalization, while the LWMN combines the lead field normalization with the spatial Laplacian operator, thus gives the depth-compensated inverse solution under the constraint of smoothly distributed sources.

Different variants of the MN solution were also proposed, by incorporating a priori information as constraint in a Bayesian formulation [35], or by estimating the source-current covariance matrix from the measured data in a Wiener formulation [36]. In addition, a “weighted resolution optimization” method has been proposed [37] in an effort to optimize the resolution matrix. Recently, alternative approaches have been developed to solve the 3D inverse problem by changing the commonly used equivalent dipole source model (EDS). One of the approaches, termed ELECTRA [38], reformulated the inverse problem to solve the 3D electric potential distribution over the brain volume. Another approach developed by He and colleagues [39] employed an equivalent current source model (ECS), based on the observation that the equivalent volume current source (monopole) can be used to equivalently represent the bioelectric sources originating from neuronal membrane excitation. The major advantage of these approaches is that the number of unknowns in the new source models is reduced to one third of that in the conventional equivalent dipole source model (each dipole has three directional components). The reduction in the dimension of the solution space not only can improve the computational efficiency, but also can reduce the underdetermination of the inverse problem.

As an example, Figure 3 shows the results of 3D source imaging of P100 activity in pattern reversal visual evoked potential (VEP) experiment based on ECS models [39]. The LWMN approach was used to solve the linear inverse problem. Two subjects were respectively given left and right visual field stimuli, with expectation of visual cortex activation on the contralateral hemisphere of the brain. But paradoxically, the half visual field stimuli elicited stronger positive potential distribution over the midline or ipsilateral side of the scalp. Nonetheless, the ECS estimate clearly indicate that the contralateral visual cortex was activated, thus effectively eliminated the misleading far field observed in the scalp potential. In addition, the source/sink distribution estimated by the ECS approach suggests a current flow pathway consistent with the EDS imaging results (not shown).

(a) (b)

Figure 3. 3D source imaging of P100 activity of VEP (from [39] with permission). (a) Scalp potential map of subject A elicted by left visual field stimuli. (b) Scalp potential map of subject B elicited by right visual field stimuli. (c) ECS estimate corresponding to scalp potential map shown in (a). (d) ECS estimate corresponding to scalp potential map shown in (b).

SPATIAL FILTER APPROACH

Beam-forming techniques and variants have also been used for brain electric source localization. The feasibility of MEG/EEG source localization has been demonstrated by means of the statistical MUSIC method [40]. In this approach, the multiple dipole locations are found by scanning potential locations using a simple one dipole model. To localize distributed brain electrical sources, A linearly constrained minimum variance filtering approach has been developed for EEG source localization, by designing a bank of narrowband spatial filters where each filter passes signals originating from a specified location within the brain while attenuating signals from other locations [41]. An adaptive spatial filter has recently been developed for solving the MEG inverse problem [42].

MULTIMODAL NEUROIMAGING

Great progress has been made in the past several years for multi-model integration of EEG and functional MRI (fMRI), with the aim to achieve higher spatio-temporal resolution than either method alone. Growing body of evidence suggest that there is close spatial coupling between elecrophysiologic signals and hemodynamic response [43,44].

Early investigations on multi-model integration used the activation foci derived from positron emission tomography (PET) or fMRI to seed the iterative optimization procedure of the DSL, in order to provide an objective initial guess of the dipole-source locations [45,46]. Higher-order integration has also been explored by solving the distributed EEG inverse problem using fMRI information as constraint. Based on the Wiener linear inverse filter, Dale and Sereno proposed a framework to integrate EEG, MEG, and MRI (structural MRI and fMRI) to improve the performance of the cortical current imaging [17]. In a simulation study, Liu et al. demonstrated that a 90% fMRI weighting has best performance in separation of activity between fMRI correctly localized sources and minimization of errors caused by fMRI missing sources [47]. The combination of brain inverse problem with fMRI has also been successfully explored in experimental settings, such as the movement-related potentials [18] and VEP [48].

SUMMARY

Tremendous progress has been made in the past decades for noninvasive imaging of brain activity by solving the EEG inverse problem with integration with anatomical information obtained by MRI. The integration of EEG and fMRI has shown great promise in mapping brain activity with high resolution in both space and temporal domains. In spite of the existing challenges, with the integrated effort of algorithm development, experimental exploration, and the availability of more powerful computing and recording resources, it can be foreseen that electrophysiological neuroimaging will have an important impact on the fields of clinical neurosurgery, neural pathophysiology, cognitive neuroscience and neurophysiology.

ACKNOWLEDGEMENT

This work was supported in part by NSF CAREER Award BES-9875344, and a grant from IRIB Program.

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