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Electro- or magnetoencephalography (EEG/MEG) are of the utmost advantage in studying transient neuronal activity and its timing with respect to behavior in the working human brain. Direct localization of the neural substrates underlying EEG/MEG is commonly achieved by modeling neuronal activity as dipoles. However, the success of neural source localization with the dipole model has only been demonstrated in relatively simple localization tasks owing to the simplified model and its insufficiency in differentiating cortical sources with different extents. It would be of great interest to image complex neural activation with multiple sources of different cortical extensions directly from EEG/MEG. We have investigated this crucial issue by adding additional parameters to the dipole model, leading to the multipole model to better represent the extended sources confined to the convoluted cortical surface. The localization of multiple cortical sources is achieved by the use of the subspace source localization method with the multipole model. Its performance is evaluated with simulated data as compared with the dipole model, and further illustrated with the real data obtained during visual stimulations in human subjects. The interpretation of the localization results is fully supported by our knowledge about their anatomic locations and functional magnetic resonance imaging (fMRI) data in the same experimental setting. Methods for estimating multiple neuronal sources at cortical areas will facilitate our ability to characterize the cortical electrical activity from simple early sensory components to more complex networks, such as in visual, motor and cognitive tasks.
In the context of noninvasive localization of neuronal activity, functional MRI (fMRI) based on detectable hemodynamic changes is a well established modality for mapping brain activity with millimeter spatial resolution . However, fMRI lacks the temporal resolution required to observe transient neuronal events due to the slow hemodynamic response (in the order of second) . On the other hand, EEG and MEG directly detect neuronal electrical changes with millisecond temporal resolution, providing valuable information on the timing of neuronal events [2, 3]. Direct localization and imaging of neuronal activity using EEG/MEG thus becomes attractive [4–13]. Such a task requires modeling neuronal activity due to the limited penetration of measurements, and the performance of imaging methods, which estimate values of parameters defined in a neural source model, is essentially dependent on the complexity of localization tasks.
Historically, EEG/MEG measurements have been modeled with the use of equivalent dipoles with parameters for location and moment [4, 5]. This model has been successfully used to study the brain activity related to somatosensory  and auditory tasks , and has also been demonstrated clinically valuable in assisting diagnosis and presurgical evaluation of partial epilepsy patients . Neural events associated with early sensory responses or partial epilepsy are usually of low complexity and can be accurately modeled by a small number of dipoles (typically 1 or 2), which ensures success in the above applications. However, the difficulty faced by the dipole model in localizing complex neural activation is not only due to imaging methods, but also from source models. Mathematically, it is difficult for the imaging methods to find the globally optimal model parameters for multiple sources since the complexity of problems increases exponentially with the complexity of source models, i.e. the number of dipoles. Physiologically, it is believed that EEG/MEG predominantly detects synchronized intracellular current flows in the cortical pyramidal neurons, perpendicularly to the convoluted cortical sheet of grey matter [2, 8]. The extents of such current flows have been estimated to be at least 40 mm2 or possibly even much larger . The dipole model lacks parameters to define this extent information. Current density source models [7–13], with each small element represented by a dipole, have been developed to reconstruct extended sources on presumed source spaces. Compared with the dipole model, current density source models have significantly larger parameter spaces and their resulting mathematical problems are usually linear, but highly underdetermined. The regularization techniques used to tackle this underdetermined problem by minimizing the Euclidean norm (L2-norm) of solutions , or its variants [9–13] usually produce low resolution solutions. In an attempt to produce more focused cortical source distributions, the L1-norm, rather than the L2-norm, of solutions have been explored [12, 13] and resulted optimization problems are solved by nonlinear methods .
In the present study, we investigated the multipole model to account for non-negligible spatial extent with a set of higher-order moment parameters additional to those for the dipole, i.e. location and moment. The multipole expansions have been used to solve MEG inverse problems [18–20]. However, to our knowledge, there is no report with regard to the systematic investigation of the multipole model-based subspace source localization in EEG using a realistic geometry head model. We defined the truncated multipole expansion of EEG potential fields to construct the multipole model in the presence of realistic geometry head model. Since the set of higher-order moments can account for the spatial extent of cortical sources, we intended to investigate their application in imaging the complex neural activation of multiple sources with various extents. We implemented a subspace source localization method with the use of the multipole model and compared its performance with that of the dipole model. We conducted simulation studies to access the performance of the proposed approach, and then demonstrated its capability with the experimental data of visual evoked potentials (VEPs) from six human subjects in comparison with independent fMRI measurements.
The exact EEG field in the infinite homogeneous medium of conductivity σ due to a cortical source with arbitrary extent can be expressed in an infinite Taylor series expansion .
where E∞(r) is the EEG field, measured at location r, and J(r′)is the current density distribution within area Ω around the expansion point l (Fig. 1 (a)). If the sizes of current sources are very small compared to their distances to electrodes, they can be approximated by the zeroth-order term, a dipole ∫Ω J(r′)d3r′. The convoluted and extended cortical sources (Fig. 1) are considered violations of the above assumption. In the present study, we model such sources with the multipole model by considering the contribution from, besides a dipole, the first-order term in Eq. (1), a quadrupole ∫Ω J(r′)(r′−l)d3r′. The term is the vector lead field for a dipole and the term is the tensor lead field for a quadrupole (see Fig. 2 (a)). Until now, we have only considered the field of the multipole model (dipole + quadrupole) in an infinite homogeneous volume conductor, which is, however, unrealistic for EEG inverse problems. A reasonable approximation for the electrical conductivity profile of the human head is the three-compartment (i.e. the scalp, skull, and brain) piecewise-homogeneous (their conductivity values are 0.33/Ω.m, 0.0165/Ω.m, and 0.33/Ω.m, respectively ) volume conductor. Theoretically, it has been proven that the lead field related to the higher-order moments in multipole expansions can be derived by successive differentiation of the lead field related to the dipole moments [23, 24], which is independent of the choice of volume conductor models. However, practically, the successive differentiation method might not be possible without the knowledge of explicit mathematical functions for spatially continuous lead fields caused by dipoles. In the present study, we take advantage of the merit of the boundary element method (BEM) to avoid the computation of successive differentiation of dipole lead fields. According to the BEM theory [25, 26], the EEG field due to the primary current source in a piecewise-homogeneous volume conductor model can be connected to the EEG field caused by the same primary current source in the infinite homogeneous media using the following relationship:
where D is the diagonal matrix containing constant coefficients and B is the function of the geometry and conductivity profiles of the human head, independent of source distributions. Once the volume conductor model is determined, the potentials V in the realistic head model can be derived from the potentials V∞ in the infinite homogeneous medium. Note V∞ from either a dipole or quadrapole can be calculated by Eq. (1). In , Hämäläinen and Sarvas introduced a more accurate method, i.e. the isolated skull approach (ISA), to calculate V with a special treatment for the low-conductivity skull. Although the ISA method complicates the simple relationship between V∞ and V in Eq. (2), it remains unchanged that EEG fields under the realistic head model can be obtained directly from EEG fields under the infinite homogeneous medium (if it is known) without the need to consider how primary current sources are modeled. Fig. 2 (b) and (c) illustrate the independent EEG field patterns on the electrode space by both dipoles and quadrapoles under the realistic head model. While Fig. 2 (b) only considers the realistic layout of EEG electrodes, Fig. 2 (c) further incorporates realistic head conductivity profiles using BEM.
The MUSIC algorithm  scans the entire possible source space and calculates the projection of gain vectors at each scanned point onto the so-called noise-only subspace. Let A(r, q) be the gain vector for the dipole at location r with dipolar moment q. The noise-only subspace can be estimated from the EEG correlation matrix, RE = ARSAT + RN, where RS and RN are the source signal and noise correlation matrices, respectively. Here, A is the gain matrix consisting of concatenated gain vectors from all signal sources. The signal subspace are spanned by those p eigenvectors, obtained from the eigen-decomposition of RE, with corresponding eigenvalues higher than the noise level in RN. The remaining eigenvectors span the noise-only subspace , where M is the number of electrodes. The projection of A(r, q) onto the noise-only subspace is defined by PnA(r,q), where . The MUSIC estimator normalizes the projection against the Frobenius norm of the gain vector, and finally has the expression as (see  for details). Its square root is known as the subspace correlation (SC) between these subspaces. In the present study, JMUSIC(r,q) is extended to include the quadrupolar moment, denoted as m, from a quadrupole. The MUSIC estimator thus becomes .
Assume the signal subspace Es can be partitioned into two orthogonal subsets, , and that Es equals their direct sum, i.e. . The corresponding projection matrices are . The projection onto the noise-only subspace can then be formulated into another expression , . From now on, (r,q,m) will be omitted to simplify the notation unless it is necessary to distinguish from (r,q). When (r,q,m) are at their true values, is close to zero, which makes approximately equal to . To design an estimator to make the difference between these two projections larger when (r,q,m) are near the true values (to be distinguished from true sources), the square of the Frobenius norm is replaced with the power r , (where D means distance and M means MUSIC). It is known that r < 2 generates much higher spatial resolvability than r = 2 (i.e. MUSIC) [29, 30]. In this study, we use r = 1 and select and . The estimator JD1−M can be easily formed and related to JMUSIC by . Since is approximately equal to , the two terms in the denominator are very close, and it could be approximately calculated by 
The performance of the new estimator has been well demonstrated in terms of the spatial resolvability of sources in one-dimensional radar sensor array problems [29, 30] and we adopt it in our three-dimensional (3D) EEG sensor array problem. The scanning procedure is performed in two steps. In the first step, the MUSIC scan is performed to determine the JMUSIC(r) value for each scanned location. Note that the metric JMUSIC(r) is a vector since the dipole has three independent moments and the quadrapole has five independent moments, which forms the multipole model of eight independent moments. Then, the preferred moments are estimated as the singular vectors associated with the smallest singular values by the singular value decomposition (SVD) analysis . In the second step, the metric JMUSIC(r) is normalized by the projection defined in the denominator of Eq. (3) with the known dipolar and quadrupolar moments obtained in the first step in order to obtain JD1−M(r). The SC here is defined as the square root of JD1−M(r) similarly as for MUSIC.
Six subjects (2 females and 4 males) participating in the visual evoked experiments gave their written informed consent in accordance with a protocol approved by the Institutional Review Board of the University of Minnesota. The stimuli were generated with STIM2 software (Compumedics Neuroscan, Charlotte, NC). Subjects were trained to focus on the central fixation point (‘X’ marker) with circular checkerboards presented in both left and right lower visual field (Fig. 4 (a)) every 500 ms with a 50-ms duration. Two subjects performed additional experiments in which the position of the circle in the right lower quadrant was adjusted, and the left one remained unchanged. The evoked potentials were continuously recorded by a 122-channel SynAmp system (Compumedics Neuroscan, Charlotte, NC), low-pass filtered at 30 Hz, and sampled at 1000 Hz. After segmentation into single sweep epochs of 50 ms before and 300 ms after the stimulus onset, a baseline correction was performed for each segment. Bad channels in which the signal included unexpected fluctuations were rejected manually. The evoked potentials were then obtained by averaging the corrected segments. The structure MRI (T1-weighted, Turboflash sequence, TR/TE=20 ms/5 ms, matrix size: 256 × 256, FOV: 256 × 256mm2, slice number: 256, slice thickness: 1 mm) and fMRI (T2*-weighted, EPI sequence, TR/TE=1000 ms/35 ms, matrix size: 64 × 64, voxel size: 4 × 4 mm2, slice number: 10 covering the visual cortex, slice thickness: 3 mm) data were collected using a 3T MRI system (Siemens Trio, Siemens, Erlangen, Germany). The fMRI experiment was conducted in a block design manner. Task periods (20 s each block) were interleaved with control periods (40 s each block). The data analysis was performed using the software package STIMULATE . The fMRI images were analyzed using the period cross-correlation method, in which the cross-correlation coefficient (CC) between the blood-oxygen-level dependent (BOLD) fMRI signal time course and a reference function was calculated for each voxel, and those voxels with CC > 0.5 were considered to be activated.
We simulated cortical sources on the realistic cortical surface, segmented from a subject’s MRI data (Fig. 1) using the Curry software (Compumedics Neuroscan, Charlotte, NC). The surface was triangulated with high-density meshes, which made a single triangle small enough (about 2.55 mm2) to be represented by a dipole. A cortical source was reconstructed starting from a seed triangle and then increasing its extent by adding the neighboring triangles iteratively. The dipole moment at each triangle was perpendicular to the cortical surface and calculated as the multiplication of its area with the dipole moment density, assumed to be 100 pAm/mm2 . Cortical sources are randomly generated 1000 times at different locations. To study EEG field patterns generated by such a cortical source, we performed SVD on its lead field matrix (i.e. concatenating gain vectors for dipoles at all triangles within the extension of the cortical source) in order to find the effective dimension of its EEG field. The patterns within this dimension (denoted as the major patterns) will account for 99% of the total variance of its EEG fields according to SVD. We analyzed the major patterns of EEG fields generated by these cortical sources of different extents (eight levels, Fig. 3 (a)). Generally, when the source extent increases, the number of major patterns needed to represent them increases (i.e. the effective dimensions for larger cortical sources peak at the larger values (Fig. 3 (b))). Furthermore, the effective dimensions for sources with the same number of neighborhoods are not fixed at a single value (e.g. the effective dimension for cortical sources with seven neighborhoods ranges between three and seven and peaks at five), due to different source distribution complexities at different cortical positions.
To perform a comparison between the multipole model (or the dipole model) and these cortical sources, we computed SCs between the multipolar lead field (or dipolar lead field) about an expansion point at the centroid of cortical sources and EEG major patterns for the same cortical sources . In order to achieve good representations, it is desirable that these SCs are approximately one. The averaged SC values over 1000 samples for each major pattern are shown in Fig. 3 (c). The multipole model has eight independent patterns which can possibly account for up to eight major patterns (i.e. the maximal effective dimension is eight), while the dipole model has only three independent patterns. The SC values may drop below a certain threshold value (e.g. 0.99) before reaching the maximal dimension, which indicates that some major patterns may not be well accounted for by source models. Our data suggest that most simulated cortical sources have the effective dimension of less than six and their corresponding major patterns can be well represented by the multipole model, as opposed to the dipole model. A quantitative measure, the upper extent limit of cortical sources that a model can stand for, is calculated for each simulated source under the condition that the SC values for all major patterns of the source are higher than 0.99. The upper extent limits using the multipole model (lower quartile, median, upper quartile) are about (1.02, 2.20, 3.55) cm2 and they are only about (0.02, 0.30, 1.95) cm2 for the dipole model (Fig. 3 (d)). The multipole model is thus better in representing EEG fields generated by extended cortical sources. The large variation in the measure appears to be location-dependent (Fig. 3 (e)). The cortical sources of large upper extent limits are mostly located on the smooth surfaces and those of small upper extent limits appear on the curved structures.
To investigate complex neural activations with multiple cortical sources, we simulated three temporally independent sources (with 200 time points) within the visual cortex (Fig. 4 (a)). The extent of the first source was about one fourth to one fifth of the other two (0.39, 1.81, and 2.01 cm2 for three sources) to simulate the relatively larger receptive fields in the associated visual cortex than in the primary visual cortex. The simulated EEG data was contaminated by the real noise recorded from a subject in the resting condition and calibrated to an 8 dB signal-to-noise ratio. The p value was set to three, as we simulated three sources. We scanned the 3D source space (every 3 mm) enclosed by the cortical surface to obtain 3D SC tomographies using both dipole and multipole models. The local minima (i.e. peaks) in the 3D SC tomographies were searched and each local peak was regarded as a source. All local peaks were categorized into the corresponding simulated source which had the closest distance as compared to other simulated sources, and the detection rates were calculated based on the categorization results over 30 repeats. The detection rates with the multipole model for three cortical sources were each 100 percent, and their average localization errors were 2.9, 3.2, and 2.1 mm (Fig. 4 (b)). Their approximately zero SC values (< 0.05) against the noise-only subspace indicate reliable source identification . The dipole model, however, can only detect two sources while overlooking one source. Furthermore, the uncovered source had the large extent while the focal source was always successfully detected.
The VEP time courses between 50 ms and 250 ms (Fig. 5 (b)) from multiple sensors were used to calculate the correlation matrix RE to identify the noise-only subspace. The p largest eigenvalues to determine the span of signal subspaces were chosen at the merging point between two curves for singular values of correlation matrices for pre-stimulus data and post-stimulus data (50 ms – 250 ms) . The p values for all subjects are listed in Table 1. Two sets of 3D SC tomographies (with the 3 mm resolution) were obtained during the subspace scanning using dipole and multipole models. The local SC extrema were searched within the visual and parietal cortices and those extrema with SC < 0.05 were regarded as detected sources.
Strikingly different results were obtained with the dipole and multipole models (Table 1). The numbers of sources detected by the multipole model range from 4 to 7 in six subjects and only 1 or 2 sources can be identified by the dipole model within the same group of subjects. Since the time window (50–250 ms after stimulus onset) studied covers most early VEP components, i.e. C1, P1, and N1 complex (Fig. 5 (b)), and their anatomic locations have been well studied [31, 33], we correlated the anatomic locations of identified sources by the multipole model to the locations for VEP components (two examples in Fig. 5 (c–d)). The distribution of these sources is quite symmetric between left and right hemispheres due to the presence of simultaneous stimuli in both the left and right visual fields (Fig. 5 (a)). One source (Fig. 5 (i)) located in the middle of the left and right striate cortices is considered the source for C1 [31, 33]. Two sources (Fig. 5 (ii, iii)) located within the left and right dorsal extrastriate cortices are early P1 components . Another two (Fig. 5 (iv, v)) within the left and right ventral extrastriate cortices are late P1 components . The remaining two sources (Fig. 5 (vi, vii)) in the left and right parietal cortices are N155 components . Table 1 shows that the source locations found in all subjects using the multipole model are quite consistent with the early VEP components’ locations while the sources identified by the dipole model are not.
We further directly studied the correlation between the VEP sources and the fMRI activations under the same experimental protocol. Since the fMRI scans only covered the visual cortex, the VEP sources identified within the parietal cortex would not be addressed here. The major fMRI activations (Fig. 6) in the same two subjects were similarly found in the striate, dorsal and ventral extrastriate cortices. Other than these activations, few BOLD responses within the visual cortex were observed for either subject that would, in fact, indicate the consistence, in terms of location, between the localized VEP sources (identified with the multipole model) and the fMRI activations. The major discrepancy between them appears within the striate cortex where the VEP sources are located midway between the fMRI activations, which are well separated in both hemispheres. Another small discrepancy appears in the left dorsal extrastriate cortex, where the fMRI activations seem to have the largest involvement, especially compared with the activations within the striate cortices. For the other four subjects, the fMRI activations were observed in all seven locations discussed above (Table 1), while some are missed as VEP sources.
The VEP sources in striate cortices were recovered in all participating subjects, which may indicate that the neural responses arising from the primary visual cortex are more consistent than those from other cortices. However, these sources cannot resolve the neural responses like fMRI activations in the anatomically separated hemispheres. We studied the SC peak distributions around the identified sources with circular checkerboards posited at different visual angles (left: 2.5°, right: 2.5°; and left: 2.5°, right: 10°). The SC peak under the condition of 2.5° vs. 2.5° was more symmetric than that under the condition with different visual angles (2.5° vs. 10°) (Fig. 7, left). The plots on the MRI slices close to the left and right middle walls (Fig. 7, right) further illustrate that the peaks’ extents on the left wall were deeper than those on the right wall along the calcarine fissure under the 2.5° vs. 10° condition, while there was no obvious difference under the 2.5° vs. 2.5° condition. This observation is consistent with the current physiological understanding of the retinotopic maps in the primary visual cortex. These data suggest that the VEP sources identified in the striate cortex stand for the neural activations in two distinct striate cortices.
We have investigated EEG source localization by integrating the multipole model with the subspace source localization method, in localizing complex neural activations with multiple cortical sources. Cortical sources have non-negligible extents because of two reasons. The first and most important reason is that, even from a conservative estimation, the smallest extent of EEG detectable neuronal activity is as large as about 0.4 cm2 . Our results indicate that the dipole model can only sufficiently explain the potential fields generated by sources with a median extent of about 0.3 cm2, meaning that it is not a satisfactory model for at least half the randomly simulated sources in the present study. However, the multipole model is able to represent most cortical sources with a median extent of about 2.2 cm2. The second reason is due to the complicated cortical structure, which causes the cortical source moments to change rapidly even within small spatial ranges and, as a consequence, significantly biases its potential fields from those modeled by dipoles. Two metrics, i.e. the effective dimension and upper extent limit, thus exhibit certain variations between cortical areas with large curvatures (e.g. ridges of gyri and bottoms of sulci) and those areas with smooth surfaces (e.g. walls on sulcus banks).
The sufficient explanation of potential fields generated by extended sources means that there is a lower level of modeling error. Such modeling error often leads to ambiguous and erroneous results in imaging methods . This would become a more important issue in dealing with complex neural activation with multiple sources since the extent contrast among sources and, sequentially, their different sensitivities in EEG sensors, would significantly influence the performance of imaging methods. In the subspace source localization method, inaccurate source modeling decreases the source detection sensitivity, which makes real sources much easier to be buried in noise. When coupled with the sensitivity shift caused by the array ambiguity phenomenon, meaning that the linear combination of some true sources produces the same output as a single source at other location, the subspace source localization method will lose the detection of real sources and will pick up false sources. This phenomenon has been seen in the simulations (Fig. 4) and the recovered VEP sources with the dipole model, which are not consistent with our physiological understanding and fMRI data (Table 1). The multipole model provides more accurate modeling for cortical sources, and therefore, provides anatomically interpretable and fMRI-consistent source localization results. A recent study using the multipole model to solve inverse problems  with regularized solutions has been reported. While it was mainly restricted to biomagnetic problems with simple source configurations, i.e. a single source, in the spherical volume conductor model, the present study attempts to localize multiple sources associated with complex neural activations in the realistic geometry human head model. Previous simulation studies  have indicated that the influence from the volume conductor model in localizing spatially extended sources is significant even for MEG data, which is less affected by the low conductivity of the skull.
It is worthy to note that the multipole model represents spatially extended sources through expanding their potential fields instead of directly defining source parameters. In other words, the explicit relation between the higher-order moment parameter (i.e. quadrupolar moments) and the extent of sources is not yet clear. How to interpret estimated quadrupolar moments and correlate them back to source extents needs further investigation. It is also noted that the integration of the multipole model with the subspace source localization method will not be able to overcome the fundamental limitation of the subspace source localization method in recovering highly temporally-correlated sources. The sensitivity decrease and the sensitivity shifts discussed above could also be caused by this reason, which may explain why some VEP sources could not be recovered in some subjects. Furthermore, the multipole model seems more dependent on the accuracy of the chosen dimension of the signal subspace (i.e. the p value) as compared to the classic MUSIC method using the dipole model, where this value is usually overestimated in practice. From our experience, using significantly overestimated p values with the multipole model will generate false sources. More advanced methods  in determining the dimension of the signal subspace might be adopted in future studies.
The multiple sources recovered by the present approach can be reasonably physiologically interpreted as cortical sources of the early VEP components, which is also well supported by the findings in fMRI (Fig. 6). It should be noted that the use of hemodynamic imaging to substantiate the estimated VEP sources is based on the assumption that the hemodynamic response obtained with fMRI is co-localized with the same neural source that gives rise to the VEP. With regard to visual-evoked activity, such co-localization appears to be optimal for the primary visual cortex and is less clear for extrastriate visual cortices . This may, in part, explain the discrepancies between EEG and fMRI in the precise locations of sources in the left dorsal extrastriate cortex (Fig. 6). However, these discrepancies are also possibly caused by the relatively large distribution in neural activity, as indicated by fMRI data, which shifts the best expansion point during the multipole expansion and creates the location discrepancy. The sources in the primary visual cortex appearing midway between the two hemispheres may be due to the same reason.
In conclusion, we have introduced the use of a multipole model in conjunction with the subspace source localization method, a practice that advances the capability of source localization methods based on electromagnetic signals from simple tasks (1 or 2 sources) to complex tasks (up to 7 sources in the present study). We demonstrated its applicability using real data obtained from a visual stimulation. The multipole model differs from the classic dipole model and the current density source model, in that it keeps its parameter space on the order as in the dipole model, and at the same time, stands for the extended cortical sources as in the current density source model. More importantly, it improve the precision of associated imaging methods in localizing multiple sources in the human cortex by avoiding modeling inaccuracy, and more generally, promises to image distributed cortical activations during task performance or rest in physiological, or possibly even pathological, conditions.
The authors would like to thank Arvind Gururajan, Han Yuan, and Varun Garg for technical assistance in VEP experiments. This work was supported in part by NIH RO1EB00178, RO1EB007920, NSF BES-0411898, and a grant from the Institute for Engineering in Medicine of the University of Minnesota. L.D. was supported in part by a Doctoral Dissertation Fellowship from the University of Minnesota. The 3T MRI scanner was partially supported by NIH P41RR008079 and P30NS057091.