Vision Science Program UC Berkeley

A Robust Method for Localizing the Sources of the Visual Evoked Potential

Note: This is a transcription of a poster originally presented by the following:

Yibin Tian1 Shahram Dastmalchi1 Stanley Klein1 Thom Carney2

1Vision Science group, School of Optometry, University of California at Berkeley, Berkeley, CA 94720

2Neurometrics Institute, Berkeley CA

Contents

  1. Introduction
  2. Experimental Methods
  3. Data and Results
  4. Dipole Localizing Process
  5. Conclusion and Discussion
  6. References

Introduction

The visual evoked potential (VEP) can be used to localize active neural regions responding to visual stimuli. The goal of our project is to develop an effective dipole source localization (DSL) algorithm when multiple sources are present. There are at least two problems with past DSL efforts: 1) when the dipoles are close in space (as in V1 and V2) the local minimum ambiguity makes it impossible to identify the individual sources; 2) the anisotropic brain conductivity distorts the voltage distribution on the scalp and hence the dipole locations.

Experimental Methods

Our approach to deal with the first problem (local minima) is not only to use a dense array of electrodes (nelec=48, see Fig1) but also to use a dartboard m-sequence array of stimuli (nstim = 60, see Fig2). Using such stimuli enables us to make assumptions about the retinotopic layout of the neural sources in V1 and V2, therefore disambiguate the sources[1]. Our approach to cope with the second problem (distortion) is to focus on the relative shifts in dipole locations and magnitudes rather than the absolute dipole parameters. The multi-stimulus and multi-electrode techniques also improve the signal to noise ratio.

Fig 1

A diagram of the placement of 48 electrodes on the subject's head.

Multi-electrode array(48 electrodes). Electrodes are almost equidistant; the head curvature makes those at the periphery look closer.

Fig 2

A representation of the stimulus used. A dartboard-type stimulus divided into 60 patches.

Multi-stimulus array(60 patches).Each patch is used to activate a small area in the brain, which is modeled as a current dipole (similar to a tiny battery).Each patch is modulated independently with a checkerboard as is shown at the upper right corner.

Data and Results

Fig 3

Red through green to blue. Red represents high voltages, blue represents low voltages, green represents 0 voltage. High Voltage
0
Low Voltage

Raw Data

A 44 by 6 array of small color maps indicating voltages.

Two-dipole fitting results

A 44 by 6 array of small color maps indicating voltages.

Dipole 1 fitting results

A 44 by 6 array of small color maps indicating voltages.

Dipole 2 fitting results

A 44 by 6 array of small color maps indicating voltages.

Voltage distribution on the scalp viewed from the back of the head(each little patch represents a head). Different colors in the figures represent different voltage values as indicated by the color bar at the right.The data and results shown only correspond to half-annulus(6 out of 60 patches, numbered from 37 to 42 in the lower visual field, see Fig2) in the time period from 38ms to 181ms. Dipoles activated by these patches have a common time function, which is shown by the simultaneous changes of the voltage values cross time in dipole 1 and dipole 2.

Fig 4

A plot of Z in mm vs Y (relative offset). There are four plots with 3d rendered cones representing the dipoles.

Dipoles localized in the right hemisphere of subject HB activated by half-annulus patches (viewed from the right of the head). The cones are dipoles, the colors of which indicate their magnitudes. The dipoles related to each half-annulus are connected in a line, and shifted horizontally for better view.The numbers beside the dipoles correspond to those patches in Fig2.

Dipole localizing Process

Fig 5

Step 1: Get real voltage. Step 2:Guess dipole location, and calculate corresponding voltage on the scalp. Step 3: Calculate the squared error (SSE) between the real voltage and scalp voltage. Step 4: If SSE is not less than a given value, go back to Step 2, otherwise, accept the guess.

The dipole localizing process is shown in Fig5, which utilizes the least square minimization method. The most important technique in this search process is to use temporal constraint, which is one common time function for all the dipoles activated by the patches in the same annulus, as shown among patches in Fig3 (Dipole 1 fitting results) & (Dipole 2 fitting results). This makes the dipole localization much more accurate.

Another crucial consideration in the search process is the head model used. Currently we make use of the Berg 3-shell spherical head model[2].

Conclusion and Discussion

The most detailed spatial and temporal retinotopic map in visual cortex(V1) from VEP has been obtained with the aforementioned techniques, and is mostly consistent with the classical V1 organization coming from other approaches.

The central problem in multi-dipole DSL is the cross-contamination that results from the spatial closeness of dipoles. Our solution to this problem is to assume the continuity of the time functions and dipole magnitudes across patches.

Another problem in DSL is that the anisotropic brain conductivity warps the dipole locations. More realistic head models would help mitigate both the warping and the cross-contamination problems.

Besides, the poor electrode coverage may lead to a sampling problem that electrodes miss the voltage peak as shown in Fig6. Our simulations show that when the displacement of the electrodes increases, the standard errors of the dipole localizations become bigger and bigger(see Fig7).

Fig 6

Sampling problem with displaced electrodes

A graphic representing the problem when the direction of the dipole points to a non-sampled region. The peak of the resultant voltage is not measured, but the weaker voltages in the periphery of the resultant electric field are measured and can be difficult to interpret.

Fig 7

A plot of angle of rotation vs standard error. As the angle increases or decreases from zero, the error increases.

Simulations of the effect of poor electrode coverage. For dipoles at five locations with the same magnitude, electrodes are rotated from –900 to +900 to simulate the displacement level. The standard errors(SE) in DSL are plotted with different colors for different dipoles.

References

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