Human Brain Cortical Electric Current Source Localization from the Surface Laplacian of a Visual and Motor Event Related Potential

Bae, Byung-Hoon

The surface Laplacian of the human-brain event-related potential were applied to an experiment designed to compare the known cognitive sites for mental tasks with the peak positions of the surface Laplacians of the subject¡¯s cortical electric potentials at each instant during a task. The computer was programmed to present randomly a letter ¡®L¡¯ or ¡®R¡¯ on a computer screen. When the monitor commands the subject to press the keyboard with subject¡¯s left(right) index finger depending on ¡®L¡¯ (¡®R¡¯), the subject presses the left (right) shift-key on the keyboard. Multichannel event-related potentials were used to estimate the distributions of the surface Laplacians of cortically generated electric potentials on the scalp. The locus of the surface Laplacian peak corresponds to the sites and the stages of cortical source localization of the neural activity in both the visual and the motor area. The locus of the surface Laplacian peak seems to track the sequence of known cortical localization of cognitive process.

Accurate localization of electrical sources in the brain is one of the most important questions in EEG (electroencephalography), especially in the analysis of evoked responses and of epileptiform spike activity. Localization of an electric-current dipole in the human brain has had a relatively long history since Brazier[1] first suggested a relation between scalp potential distributions and current sources in the human brain. Most mathematical models for the determination of the location of electrical brain activity from potential recordings at the scalp use the assumption that the number of equivalent dipoles is only one or two[2-4]. However, unfortunately, we can not get any information a priori on how many equivalent dipoles are created in the human brain. This assumption has been a severe limitation of the typical source localization method.

Recently, a new scheme involving the surface Laplacian of the scalp potential has been reported[5-6]. The activity generated by a neuronal source close to the scalp is more easily separated in the distribution of the surface Laplacian than that of the potential. A number of simulations involved with both isolated and distributed sources suggest that the surface Laplacian provides somewhat more accurate estimates of the cortical potential distribution than the scalp potential itself does[7]. The resulting Laplacian EEG maps are substantially sharper than the original EEG potential maps, so that they reveal the pattern where volume current emerges from the cortex and passes through the skull into the scalp and where it returns to the interior. This method is appropriate for locating superficial cortical sources, but not deep sources.

However, considerably less work has been done on the experimental verifications of the surface Laplacian method. This paper presents new experimental evidence on the surface Laplacian. In this paper, the surface Laplacian of a human brain event-related potential was applied to an experiment designed to compare the known cognitive sites for mental tasks with the peak positions of surface Laplacian of the subject¡¯s cortical electric potentials at each instant during the task.

In this experiment, a computerized electroencephalograph was used to measure the event-related potential (ERP). The instrument consisted of an EEG-amplifier, an analog to digital converter and an EEG-computer interface, which sampled the voltages at 21 electrodes at a rate of 1 kHz. The recording impedance was kept below 2 k? . The electronic filter settings were a low-frequency cut-off of 1 Hz and a high-frequency cut-off of 30 Hz. A 60 Hz notch filter was employed. Silver-chloride cup electrodes were applied, using a conductive paste, according to the international 10-20 convention with C_Z as a reference. Figure 1 (a) shows how the experiment was being done. Figure 1 (b) shows the names and placements of the recording electrodes in the international 10-20 system.

(a) (b)

Fig.1

The subject was taught about the experimental protocol and seated comfortably in front of a computer screen at a distance of 1 m from it. The computer was programmed to present randomly a letter ¡®L¡¯ or ¡®R¡¯ on the computer screen. When the monitor commands a subject to press the keyboard with the subject¡¯s left (right) index finger depending on whether ¡®L¡¯ (¡®R¡¯) is displayed, then the subject presses the left (right) shift-key on the keyboard. This procedure is called VCCM (visual command caused movement). The procedure to measure the brain potential in conjunction with VCCM is as follows:

- procedure 1. Computer monitor shows the letter 'L' or 'R' randomly.

- procedure 2. If the subject sees the letter 'L' or 'R' on the monitor, the subject presses the left or the right shift-key using left or the right index finger.

- procedure 3. Computer receives the subject¡¯s brain potentials between

procedure 1 and procedure 2. Then, they are automatically saved to a hard disk.

These procedures were repeated 700 times at each letter, and then the conventional average method[2] was applied to detect the event-related potential. Figure 2 shows some examples of detected event-related potentials at electrode Pz.

An interpolation procedure is needed to estimate the scalp voltage distribution from the discrete brain potential measurements at the different electrode sites. Many interpolation techniques are available, however, least-square interpolation is useful for this purpose since it provides an estimated equation for the voltage that is differentiable. In this report the least-square interpolation assumes the following model function for the voltage as a function of the electrode grid coordinates x, y:

(3.1)

In order to determine the 16 unknown coefficients ? _i of the linearized reduced-form expression above, the following cost function needs to be minimized:

(3.2)

is the measured surface potential at an electrode i,

is the approximated surface potential at an electrode i, and

is the number of electrodes.

Since the function is inherently linear in the parameters ? _i to be estimated, the 16 parameters are obtained by the minimization conditions , where i=1,2,...,16.

These conditions makes 16 simultaneous equations as follows:

(3.3)

By substituting Eq. (3.1) into Eq. (3.3), it can be written in matrix forms as

. (3.4)

Here,

, , . (3.5)

Figure 3 shows the configuration of voltage interpolation. The smaller square (solid line) zone in Fig. 3 was chosen for the interpolation, because it seems to be a more reliable data region than that of the larger square (dotted line). The small circles show the projected electrode positions. The upper graph shows an example of an interpolated potential distribution obtained by using Eq. (3.1) for which the ? _i¡¯s were found by solving Eq. (3.4) which was solved by the LU(left upper)-decomposition method[12].

Then, the approximated surface Laplacian of the voltage distribution,

, (3.6)

can be directly calculated from Eq. (3.1). Finally, a contour plot of surface Laplacian is superimposed over outline of the head(Figs.4 & 5).

Fig.3

Figure 4 shows the time series of the surface Laplacian map for the Left VCCM-ERP, which means that computer monitor showed the letter 'L', then the subject pressed left shift-key using his left index finger. Figure 5 shows the time series of the surface Laplacian map for the Right VCCM-ERP. The contour plots have been superimposed over a stylized outline of the brain to show the sites of the highest surface Laplacian peaks. The symbol ¡®+¡¯ or ¡®-¡¯ represents the polarity of the surface Laplacian peak.

The locus of the surface Laplacian peak generally tracks the sequence of cortical localization of cognition that has been inferred for visual and motor tasks from physiological studies[13,14]. An early period of high correlation occurs in the occipital and frontal region at t=100 msec. These are prior to the plausible latency of primary visual processing[13]. The peak is moved from the occipital region into the right temporal-parietal region and the peak of the frontal region is remarkably increased at t=100 to 160 msec. These loci may be due to a manifestation of analysis of the letter ¡®L¡¯ or ¡®R¡¯ and decision making. From 100 to 160 msec, the surface Laplacian maps of the Left VCCM-ERP(Fig.4) are nearly identical with those of the Right VCCM-ERP(Fig.5), which means that the early cognitive processes of the Left-VCCM are identical with that of the Right-VCCM. Finally, the locus of high correlation of surface Laplacian with finger movement reaches the motor cortex at 200 to 300 msec. It is important to notice that the position of the peak appears in the left motor cortex when the subject uses his right index finger to press the keyboard. On the contrary, the peak appears in the right motor cortex for the left index finger. The peak position of the surface Laplacian for the motor potential clearly reflected the sharply focused current sources spanning the left or right hand areas of the motor cortex.

100 msec 160 msec

200 msec 250 msec

275 msec 300 msec

¡¡100 msec 160 msec

200 msec 250 msec

275 msec 300 msec

Fig.5

The surface Laplacian was applied to an experiment designed to compare the known cognitive sites for mental tasks with the peak positions of surface Laplacians of a subject¡¯s cortical electric potentials at each instant during the task. The experimental results were very consistent with the known sites and stages of cortical source localization of neuronal activity in the visual and the motor area[13,14].

Although a number of simulations involved with both isolated and distributed sources suggest that the surface Laplacian provides somewhat more accurate estimates of the cortical potential distribution than the scalp potential itself does, considerably less work has been done on the theoretical analysis and interpretation of the surface Laplacian method[6]. It will be necessary to examine the principles of the surface Laplacian rigorously.

In this research, the interpolation scheme for the brain potential is rather simple and crude, and the boundary effect may give a wrong source localization at the boundary. In a forthcoming paper, these problems will be explored and investigated.

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