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MEG/EEG beamformer source imaging is a promising approach which can easily address spatiotemporal multi-dipole problems without a priori information on the number of sources and is robust to noise. Despite such promise, beamformer generally has weakness which is degrading localization performance for correlated sources and is requiring of dense scanning for covering all possible interesting (entire) source areas. Wide source space scanning yields all interesting area images, and it results in lengthy computation time. Therefore, an efficient source space scanning strategy would be beneficial in achieving accelerated beamformer source imaging. We propose a new strategy in computing beamformer to reduce scanning points and still maintain effective accuracy (good spatial resolution). This new strategy uses the distribution of correlation values between measurements and lead-field vectors. Scanning source points are chosen yielding higher RMS correlations than the predetermined correlation thresholds. We discuss how correlation thresholds depend on SNR and verify the feasibility and efficacy of our proposed strategy to improve the beamformer through numerical and empirical experiments. Our proposed strategy could in time accelerate the conventional beamformer up to over 40% without sacrificing spatial accuracy.

Magnetoencephalography (MEG) and electroencephalography (EEG) are noninvasive imaging technologies which provide functional information about human brain dynamics by providing millisecond temporal images over the entire brain. These technologies have been widely used to diagnose epilepsy and forward neuroscience research. Particularly, MEG/EEG source localization estimates current sources from measured spatiotemporal data. Inherently, MEG/EEG source localization is mathematically ill-posed; that is, it has no unique solution and is very sensitive to noise. For a couple of decades, many researchers have tried to develop methods to deal with these difficulties in calculation, resulting in extensive research and commercialization of MEG/EEG source localization methods (see [

In the early 1990s, beamformer techniques originated in the field of antenna signal processing [

Recently, source imaging has been gaining more attention on continuous MEG/EEG (unaveraged) and single-trial MEG/EEG data in understanding rapidly changing brain dynamics [

This paper is an extended version of a short conference paper presented in BIOMAG 2010 [

Beamformer techniques are categorized into two classes: one is adaptive and the other is nonadaptive. A nonadaptive spatial filter is independent of the measurement, but an adaptive spatial filter depends on the measurement. Among beamformers, the minimum-variance (MV) beamformer is superior in accuracy to others [

A vector type beamformer enables to estimate simultaneously source orientation and magnitude. A vector type spatial filter consists of a set of three weight vectors,

In this section, a new strategy of reducing scanning points, thereby accelerating beamformer source imaging, is proposed without sacrificing accuracy. In beamformer source imaging, full source space scanning is necessary; sources are located on the brain’s cortical area and thus all scanning of the brain may be time intensive but achieves whole brain images. On the other hand, partial scanning accelerates beamformer source imaging. Evidently, reducing the number of scanning source points while keeping scanning resolution can accelerate the source imaging process without losing spatial resolution significantly. Our proposed idea is reducing the scanning region (eventually reduce the number of scanning points) by using the correlation between measurement and lead-field vectors, defined as

Independence from noise on a signal yields that the 2nd term on the right side of (

Correlation values

RMS correlation values

Scanning regions are reduced by selecting source points with higher RMS correlation values than given correlation thresholds. Correlation thresholds are estimated empirically for various SNRs via the Monte Carlo simulation, while corresponding criteria are formulated in a least square sense (optimization) at a later time.

Beamformer is performed at such reduced source region.

To reduce scanning points, RMS correlation should be computed at every point within the source space. Computing RMS correlations across the entire source space, including a plenty of corresponding time points, may be time intensive. For example, about 500 time samples (2 second-long duration for a 250 Hz acquisition system) are naturally needed to update brain dynamics or decode user intention in existing BCI systems. As shown in (

By projecting a measurement matrix onto eigen-temporal space while ignoring negligibly small eigenvalues and corresponding eigenvectors, the number of time points is dramatically reduced, thereby reducing correlation computation time. Such a procedure is formulated as follows.

Spatiotemporal measurement matrix

Projection matrix

Projected measurement matrix

Reduction of the time dimensionality of the measurement matrix is thus ensured, thereby significantly reducing correlation computation time. Computing time of about 3 seconds is reduced to 0.7 seconds, which will be discussed later in this paper. The effectiveness of this strategy is demonstrated in the following section.

Correlation distribution between active and inactive points was investigated through numerical experiments in this section. A spherical homogeneous conductor head model with an 8.5 cm radius, centered at origin, was used for forward computing [

Two source locations and head geometry description (a), time courses of dipole sources, first with a solid and second with a dashed line (b), and over-plotted synthetic MEG measurement data (SNR of 1) for 160 sensors (c).

Correlation of full-source space with 10,000 scanning points was computed to illustrate the distribution using (

Correlation distribution for two dipole source problems on the entire source region of the brain. Darker color represents a higher correlation value.

In the previous section, correlation distribution was found to play a key role in getting a priori information on source locations. Intuitively, use of such correlation distribution can accelerate beamformer source imaging when beamformer scanning is confined to regions with relatively high correlation values. To apply such a concept, proper correlation thresholds should be predetermined in a reasonable way. In general, correlation distribution may influence various factors such as source locations, source magnitudes, SNR, and sensor geometry. For simplicity, correlation threshold criterion is assumed to depend only on SNR; estimation is thus possible with information easily obtainable or observable. Under such consideration, the following formulation on correlation threshold corr_{thresh}(SNR) is proposed:

Here

Correlation threshold criterion corr_{thresh}(SNR) was estimated through the Monte Carlo simulation study. The Monte Carlo simulation was conducted with 200 randomly distributed dipole sources at random orientations across the entire brain. For each dipole (fully correlated source between lead-field vector

Empirical MEG noise used in the Monte Carlo simulation study was acquired under the following experimental paradigm.

Empirical MEG data was collected from a healthy male volunteer (24-year-old) who participated after appropriate informed consent was acquired. During spontaneous activity with eyes closed in a magnetically shielded room, an acquisition period of 120 seconds was launched. Data was digitized at 2 kHz with the online lowpass filter set at 500 Hz, postprocessing digital filter applied from 1 to 100 Hz, excluding 50 Hz due to electrical power conditions. Data was collected from a whole-head gradiometer system with 160 channels (MEGVISON Yokogawa system).

Our proposed threshold criterion was generated from a single dipole simulation study; thus other possible source configurations are not sure to be perfectly accounted for. Nevertheless, it was found that our proposal proved quite effective throughout the work.

In this section, investigation into the degree of acceleration and reduction of scanning points resulting from our proposed ETWB strategy was studied. For this purpose, beamformer and proposed scanning reduction strategy was integrated to apply to a simulated two dipole problem, which was generated in Section

SNR = 1: beamformer source reconstruction results using the ETWB strategy. (a) Reduced scanning region (darker shaded region) with a higher correlation value than the predetermined threshold value in (

Figure

Conventional full-scan beamformer was compared with reduced scanning beamformer using the proposed strategy to determine how much scanning reduction was attained over different SNRs (0.1 or 4). The reduced scanning regions by ETWB strategy are illustrated in Figure

With regards to high SNR 4, the same experiment was conducted. Figure

Reduced scanning regions (left) by our proposed beamformer and reconstructed images (right) over simulated data with different SNRs. (a) SNR: 0.1. (b) SNR: 4.

In this section, the performance of our proposed beamformer was investigated over different source correlations between two dipole sources. It is known that beamformer performance degrades for heavily correlated sources. To investigate how much our proposed method relatively effects source correlation, simulated data was generated under the same configurations as in Section

Reduced scanning regions (left) by our proposed strategy and reconstructed images (right). All other configurations (source locations, time courses, and SNR (=1)) are the same as in Figure

In general, as brain sources are activated far away from the sensor surface of the MEG/EEG system, it is dramatically less sensitive to those sources and localization accuracy gets worse. In this section, the performance of beamformer using our proposed strategy is investigated as sources gradually move away from the sensor surface. For this investigation, the same source configuration as in Figure

Further, the performance of our proposed beamformer was tested on extended source models. Extended sources were generated for three different source span diameters: 0, 2.0, and 5.0 cm. Here the source with a 0 cm span diameter means a dipole source. Extended sources were generated on the plane (

Reduced scanning regions by our proposed beamformer over varying source depths. Source configuration is the same as in Figure

So far, many kinds of simulated data over different SNRs, different source depths, different source correlations as well as different extended source spans have been tested to compare reduced scanning beamformer using our proposed strategy to conventional full-scan beamformer. Overall, our proposed beamformer shows its relative acceleration in time and yields comparable in accuracy to the conventional beamformer. Figure

For single dipole problem, 1,000 dipoles were randomly distributed within the spherical head model. For each dipole, 7 single dipole problems with different SNRs (between 0.01 and 8) were generated by adding white Gaussian noise, thus yielding 7,000 single dipole problems. Particularly, for different diameter of source simulation, 6 different diameters of source (between 0 and 50 mm) at each source were considered. Thus 6,000 single source problems were generated with keeping SNR of 1 in this case.

For two-dipole problem, 1,000 pairs of two dipoles were randomly chosen among 1000 dipoles generated in single dipole problems. For each pair, two-dipole problems were generated with 7 different SNRs (between 0.01 and 8), 7 different source correlation coefficients (between 0 and 1), and 6 different interdistance between two sources (between 0 and 100 mm). Hence, total 294,000 two-dipole problems were generated to test.

For each problem, the number of scanning point and computational time were estimated. Evidently, computational time is linearly proportional to the reduced scanning points. In our proposed strategy, we found that averaged correlation computing time including SVD computation was about 0.15 seconds, which was added to computational time. The averaged computational time of the conventional beamformer was about 1.035 seconds. Each point in Figure

Figure

It is remarkable that correlation computation time did not change with respect to SNRs; however, we found that computation time of SVD varied slightly over SNRs. We guess that such small variation of SVD computing time may stem from different matrix characteristics. Total original scanning points amounted to 10,000 and the temporal size of the measurement matrix was 500. Figure

Comparative computational time of our proposed strategy and conventional beamformer over different problems varying SNR, source correlation, diameter of source, and distance between two sources. Each problem requires a total of 10,000 scanning points and has temporal window of 500 time samples. Each point is the averaged computational time with standard deviation.

In the present section, reduced scanning beamformer with our proposed strategy was applied to empirical MEG data. Four kinds of empirical MEG datasets were acquired on a whole-head gradiometer MEGVISION Yokogawa system with 160 channels—median nerve stimulations (right hand/left hand) and auditory stimulations (left ear/right ear). Experimental paradigm is detailed as follows.

A healthy male volunteer (24-year-old) participated in the MEG measurement after appropriate informed consent. First, the somatosensory electrostimulation median nerve of his right/left hand was stimulated and all measurements were done in a magnetically shielded room. During measurement, the subject was instructed to keep his eyes closed. A 2.9 (right)/3.5 (left) mA current and a 2 Hz sampling were applied with 0.3-millisecond current pulses. Interstimulus-interval (ISI) was randomized with 0.5 s duration. Second, the auditory stimulation of his right/left ear was stimulated with eyes closed. A 80 dB sound pressure and a 2 Hz sampling were applied with 40 ms plateau with 10 ms rise and falls. Also, ISI was randomized with a 2 s duration (random 50%, 1–3 s). Data were digitized at 2 kHz, lowpass filtered at 500 Hz as well as postprocessed via a digital filter at 1–100 Hz (median nerve stimulation)/1–50 Hz (auditory stimulation), excluding 50 Hz due to electrical power conditions. In the case of median nerve stimulation, a total 399 (right-hand)/418 (left-hand) single trials were acquired. Total 73 (right-ear)/70 (left-ear) single trials were obtained in the case of auditory simulations.

Each collected single trial data (unaveraged) with 0–250 millisecond (time-locked, 500 time samples) time window after stimulation onset were analyzed. Such analysis can better facilitate real-time brain activity monitoring for neurofeedback and brain computer interface (BCI) [

Averaged-over-trial-reconstructed source power maps of both conventional beamformer (left) and reduced scanning beamformer with our proposed strategy (right) for empirical median nerve stimulation data. (a) Right-hand movement. (b) Left-hand movement.

Beamformer source imaging for averaged median nerve stimulation data yielded focused source activity in the upper contralateral posterior central sulcus (not shown here), which is relevant to existing literature (see [

Comparative total computing time (in seconds) of single trial analysis for different empirical data between conventional full-scan beamformer and reduced scanning beamformer with our proposed strategy. Source region with a total of 8,640 scanning points and a temporal window of 500 time samples were used. Experiments were conducted on a PC (Intel Core 2 Duo CPU 2.4 GHz, 32 bit OS, and 4 GB RAM).

Experiment (No. of trials) | Elapsed time of beamformer imaging (sec) | Improvement (%) | |

Full-scan | Reduced scanning | ||

Median-right (399) | 723.3 | 418.8 | 42.1 |

Median-left (418) | 760.6 | 430.2 | 43.4 |

Auditory-right (73) | 132.1 | 74.7 | 43.5 |

Auditory-left (70) | 126.9 | 72.1 | 43.2 |

These results tell that overall improvement in computing time of reduced scanning beamformer with our proposed strategy is over 40%. In conclusion, our proposed reduced scanning beamformer is feasible and very applicable in accelerating the conventional beamformer.

In this work, one beamformer using ETWB strategy was proposed to reduce the beamformer scanning regions by computing correlation distribution, thereby accelerating beamformer. Similar to the ETWB strategy, another strategy is possibly proposed by doing eigen-temporal projection and in addition doing eigen-spatial projection. We call this strategy eigen-spatiotemporal window-based method (we call it ESTWB). The discarding of relatively insignificant sensor information via the ESTWB strategy seems more efficient in relation to computation time while the ETWB strategy will inherently provide a more accurate correlation distribution as well as yielding more reliable beamformer source imaging. In addition to ETWB and ESTWB strategies, temporal downsampling is another idea; however, it possibly loses useful information.

Computing correlation in (

Furthermore, there exist other strategies to speed up scanning methods. One can consider downsampling in spatial scanning to reduce computation effort. It is commonly applicable in scanning methods like beamformer. When our strategy would be applied together, scanning methods should be boosted easily. Another easy strategy is to increase computational resources such as parallel computing to use many personal computers at the same time. This provides powerful computing ability; thus tens to hundreds of times improvement would be possible. Certainly, such a strategy demands a relatively high cost; thus, it may be not easily affordable to most investigators. It is noted that our proposed strategy of simple consideration of correlation distribution can be achieved on a single personal computer.

As discussed in Section

In real-time monitoring or BCI systems, seamless monitoring or control decision is of great importance. In reality, most systems have some delay coming from computation implicitly required to do any defined action; however, such delay is reasonably small or one may design the system to have delay constant or within an affordable bound; thus it looks real-time system to user. Particularly, source imaging analysis introduced in these systems may not avoid significant delay incurring from intense computation. However, well-desiged system to hide such significant delay may be possible. For example, assuming that every 1-second-long window data is collected to analyze and source imaging requires 1 second, such system may be designed that data is analyzed to give final result to the system during system being collected next 1 second-long data; then system continues to do the same procedure. This system can achieve seamless procedure (it looks real-time system from user) with constant delay of 1 second. From this perspective on real-time monitoring or BCI systems, the faster source imaging can achieve the higher monitoring scan or decision rate. Therefore, our proposed strategy yielding about 40% speed-up of source imaging is well applicable in this reasoning.

On the other hand, in BCI systems, one could define a region-of-interest (ROI) manually [

Through the Monte Carlo simulation, our correlation threshold criterion, depending on SNR, was formulated in a least square sense. This criterion was dependent on sensor configuration (geometry); so it should be reestimated under other sensor configurations. Factors other than SNR may have some effects on correlation thresholds. Accordingly, more thorough research is currently under investigation.

Even though the conventional vector-type MV-beamformer among the beamformer variants was adopted in this work, scalar-type or other nonadaptive beamformers are similarly applicable. Furthermore, this strategy is very straightforward for EEG or simultaneous MEG/EEG data application, and subsequent work on simultaneous MEG/EEG beamformers [

This work was supported by a KRF grant (KRF-331-2008-1-D00768), NRF grant (NRF-2010-32A-B00283), the PLSI supercomputing resources of KISTI, the BioImaging Research Center at GIST, and the National IT Industry Promotion Agency (NIPA-2011-C1090-1131-0006). The authors appreciate Dr. Haruta at Yokogawa Electric Corp for his assistance with MEG data acquisition.