Mathematical modelling of spatial resolution and the neural correlations of consciousness
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《中华医药杂志》英文版
【Abstract】 Objective We use a combination of mathematical modelling and experimental records of the potentials generated by known electric dipoles to answer if the sorts of patterns recorded in Freemans rabbits did exist in humans, would it be possible to resolve them from scalp recordings, or would dural or sub-dural records be necessary.Methods Construction of a mathematical model of the electric potentials. Use validation of the mathematical model and interrogation of the validated model to determine what sort of dipole separation would produce patterns. Interrogation of the model to determine how far above dipole pairs with this separation. Results Our model shows that even with spatial filtering, the electrode array can not be more than 4.5mm above the surface of the cortex for the sorts of patterns we are looking for to be resolved.Conclusion It is highly unlikely that two cortical dipoles spaced 3mm apart could ever be resolved in scalp recordings, whatever deblurring methods were used. The conclusion seems inevitable that if patterns like those recorded by Freeman and Baird (1987) do occur in humans, dural or sub-dural recording will be necessary to detect them.
【Key words】 neural correlates of consciousness; Spatial Resolution; mathematical model
INTRODUCTION
Nearly twenty years ago, Walter Freeman and colleagues published a series of seminal papers showing that it is possible to distinguish whether or not a rabbit is experiencing a particular olfactory, auditory or visual sensation by examining the spatial pattern of voltage recorded at an array of electrodes on the surface of the rabbits brain[1-4]. To use a phrase that became current only after these papers appeared, the spatial electromagnetic patterns reported there would appear to qualify admirably as neural (or at least neurally generated) correlates of consciousness (NCCs).
In view of the explosion of interest over the last decade in finding NCCs, it is perhaps remarkable that Freemans findings have never been extended to human subjects. Why not? The most obvious potential problem is that the original rabbit recordings were taken from the surface of the brain, while the relative ease of recording human EEG from the scalp means that the sorts of dural or sub-dural recordings necessary have simply not been done in human subjects. But is this a reasonable answer? If the sorts of patterns recorded in Freemans rabbits did exist in humans, would it be possible to resolve them from scalp recordings, or would dural or sub-dural records be necessary? We use a combination of mathematical modelling and experimental records of the potentials generated by known electric dipoles to answer this question.
METHODS
The general approach was to proceed in 3 stages:
(1) Construction of a mathematical model of the electric potentials that would be produced by dipoles of appropriate size and orientation to represent pyramidal cells in the cerebral cortex (Kandel et al 1997), as recorded by a linear electrode array on the surface of the brain.
(2) Validation of the mathematical model using actual recordings of potentials generated by known dipoles in a homogeneous medium with conductivity similar to that of brain.
(3) Interrogation of the validated model to determine what sort of dipole separation would produce patterns with the spatial frequency recorded by Freeman and colleagues (i.e. approximately 0.2 cycles/mm)
(4) Interrogation of the model to determine how far above dipole pairs with this separation one could record and still resolve the spatial pattern seen immediately above the dipoles.
Mathematical modelling
The brain was treated as a homogeneous medium with a conductivity of 0.33s/m (Geddes and Baker 1967), open to the air at its upper surface. Neural activity was simulated by introducing either radial dipoles, which were orientated orthogonally to the surface of the medium to simulate activity in gyri, or tangential dipoles, which were oriented parallel to the surface of the medium to simulate activity in sulci. All dipoles had an inter-pole distance of 2mm, which is about the width of the cerebral cortex.
Because there was a free surface at the upper boundary, the medium could not be treated as infinite. Thus the method of images was used to generate the dipole fields: i.e. a mirror image dipole was simulated above the free surface, and its field was added to that of the actual dipole below the surface of the medium.
For one radial dipole, the general mathematical model was derived as:
and for one tangential dipole, the model was:
where I is the injection current of the dipoled is the distance between the two poles of the dipoles is the conductivity of the medium
H is the distance from the dipole to the free surfaceh is the distance from the electrode array to the free surfaces is the horizontal distance from dipole to arrayx is the distance of each electrode along the array.
For three adjacent radial dipoles, the model was:
and m is the distance between dipoles.
The models were implemented in Matlab and the results displayed as plots of the voltage seen at each electrode in a linear array along the x axis. In some cases, a Laplacian filter (implemented by subtracting from the voltage at each electrode the average of the voltages at the two adjacent electrodes) was used to filter out low spatial frequencies and sharpen the image.
Experimental validation of the model
The mathematical model was validated using real dipoles immersed in a saline solution. Dipoles were constructed from pairs of 1mm diameter copper or stainless steel rods, with short lengths of 1mm diameter silver wires soldered to the tip of each rod to minimize polarization. Each rod was insulated from its partner and both members of the pair were insulated from the medium using heat shrink, leaving only a 2mm length of the silver tips exposed. The distance between tips in a pair was 2mm. For tangential dipoles, the exposed tips were side by side. For radial dipoles, one of the silver tips was bent in a partial S shape so that its exposed portion was directly below the tip of the other rod. The saline bath was filled with 0.15% NaCl, which had a measured conductivity of 0.32s/m at 40Hz. Sinusoidal signals of either 30 or 40Hz were produced by a Wavetek 191 signal generator and connected to the dipoles via an isolating transformer, so that the bath was floating with respect to ground. Current delivered to each dipole was monitored and adjusted to (usually) 5.7 μV. Electrode arrays with various interelectrode distances were constructed either from sintered Ag/AgCl pellets or electrolytically chlorided Ag wires. Voltages were recorded between each electrode and a distance reference electrode, using battery powered amplifiers that incorporated neither high nor low pass filters because the 24 bit ADCs sampled at 312kHz (Bold, Diprose and Pockett, submitted). Mains pickup was eliminated by recording in a Faraday cage. Electrodes distant from the dipole sometimes recorded sine waves with peak to peak voltages <20 μV and, because no averaging was used, signal measurements in these cases were somewhat affected by instrumentatal noise. Signal amplitude was therefore estimated using a Matlab routine that fitted a sinusoid to the data in each channel. When measuring the effects of tangential dipoles, signal polarity was taken into account by measuring the amplitude of the sinusoid at a fixed time after the start of data acquisition.
RESULTS AND CONCLUSION
In our mathematical model, brain activity is represented as a series of spatially independent but synchronously active cortical dipoles, similar to those depicted by Kandel et al (1991). The first problem was to determine whether the model accurately predicts the electric field patterns generated by such dipoles, as recorded between electrodes at the surface of the medium in which the dipoles are positioned and a distant reference electrode. Figure 1 shows a comparison between patterns predicted by the mathematical model and patterns measured experimentally, firstly for radial dipoles (representing activity in gyri) and secondly for tangential dipoles (representing sulcal activity), with the tangential dipoles positioned either parallel to or orthogonal to the recording array. Good agreement is seen between the output of the model and the experimental measurements. This validates the mathematical model as producing an adequate simulation of the fields
Dotted lines are experimental data, solid lines are mathematical predictions. For experimental data, electrodes are spaced 2.5mm apart and electrode arrays are approximately 5mm away horizontally from the near edge of the dipoles
Top left Two radial dipoles 2mm apart.Top right Two radial dipoles 10mm apart.Bottom left One tangential dipole parallel to electrode array. Bottom right One tangential dipole orthogonal to electrode array, positive pole closer to array
Figure 1 Comparison of experimental data with predictions of model
Electrodes in these simulations are spaced 0.5mm apart
Top panel Electrodes 0.5mm above dipoles.Middle panel Electrodes 2mm, 2.25mm and 2.5mm above dipoles. Bottom panel Electrodes 3.5mm and 4mm above dipoles, Laplacian filter employed
Figure 2 Predicted measurements at different distances from three radial dipoles separated by 3mmgenerated by dipoles like those widely accepted as occurring in the neocortex (Kandel et al 1991 pp 783-4), when those dipoles are situated just below the free surface of a conductive medium that might reasonably be taken as simulating a segment of brain from which the overlying skull has been removed.
Thus validated, the model is used to produce an electromagnetic pattern having roughly the same spatial frequency as the patterns measured at the surface of rabbit brains by Freeman and colleagues. Following the methods of Freeman and Baird[2], the electrodes in this simulation were spaced 0.57mm apart and the electrode array was positioned at the surface of the medium, 0.5mm above the dipoles. The top panel in Figure 2 shows that in this simulation, a spatial pattern with a frequency of approximately 1 cycle/5mm (0.2 cycles/mm), which is in the middle of the range of spatial frequencies that characterized the patterns found by Freeman and colleagues, was produced by three radial dipoles spaced 3mm apart.
The next question is whether or not it would be possible to detect patterns like this when recording not from the surface of the brain but from the scalp. Far from being 0.5mm above the cortex, the surface of the human scalp is an average of 15 or 16mm above the cortex, depending on the brain area over which measurements are taken[5]. Can the spatial electromagnetic pattern produced by dipoles 3mm apart still be detected if the recording array is positioned 15mm above the dipoles? The middle and bottom panels of Figure 2 show that it can not. With unfiltered simulated data, the recording array has to be less than 2.5mm above the dipoles for the pattern diagnostic of dipoles spaced 3mm apart to be detected (middle panel). Even using a spatial filter to reduce the blurring effects of volume conduction, the recording array has to be less than 4.5mm above a triplet of dipoles separated by 3mm before it can be resolved that there are three dipoles, not one (bottom panel of Figure 2).
What does this mean in anatomical terms? According to our measurements (see Figure 3), the average thickness of the human skull is 4.1±0.6mm over the temporal cortex, 6.3±0.9mm over the motor cortex, 5.9±0.9mm over the prefrontal cortex and as much as 9.1±1.5mm in the ridge of thick bone called the frontal crest, which marks the fusion of the frontal suture over the prefrontal cortex (all measurements given as mean±SD, n=11) Subtacting these measurements from the 15~16mm cortex-scalp distance reported by McConnell et al (2001), it can be calculated that the distance from the surface of the cortex to the skull varies from approximately 6mm to 12mm, depending on location. Since our model shows that even with spatial filtering, the electrode array can not be more than 4.5mm above the surface of the cortex for the sorts of patterns we are looking for to be resolved, this means that in most regions, the sub-dural and sub-arachnoid spaces would have to collapse to a considerable extent when the skull was opened in order for these patterns to be detected even from the surface of the dura.
Figure 3 Skull thickness in different regions
This scatter plot displays the relationship between thickness measured in the prefrontal crest and other prefrontal regions, and over the motor and temporal cortices, for each of 11 different skulls. Each symbol indicates the mean of three measurements in the relevant area of one skull.Note that although there is a tendency for thickness over the motor cortex to be greater than over either temporal or prefrontal cortex, this relationship is not universal for all subjects.
Figure 4 shows that even if one only uses the model described here, which ignores the extra blurring effect of the low conductivity of the skull, two radial dipoles in the cortex would have to be at least 18mm apart before they could be resolved in records taken from the scalp, where this is 15mm above the dipoles. Considering the fact that the simulations conducted here essentially represent a best-case scenario, and that the skull (which has a conductivity of around 1/80 that of brain) would almost certainly make the situation in scalp recordings considerably worse than the model predicts, it is highly unlikely that two cortical dipoles spaced 3mm apart could ever be resolved in scalp recordings, whatever deblurring methods were used. The conclusion seems inevitable that if patterns like those recorded by Freeman and Baird (1987) do occur in humans, dural or sub-dural recording will be necessary to detect them.
Simulated electrodes are 1mm apart. Distances between dipoles shown on figureFigure 4 Simulations of measurements taken 15mm above a pair of dipoles separated by various distances
The final question we address concerns the maximum electrode spacing that would be sufficient to detect such patterns even in dural or sub-dural recordings.
Menon[5] concluded that if patterns covaring with perceptual categorization do occur in humans, detection of them in ECoG recordings would require electrode spacings under 5mm. The simulations depicted in Figure 5 reduce this figure to 1.5mm.
Figure 5 Maximum interelectrode spacing necessary to resolve two dipoles 3mm apart, recording array 0.5mm above dipoles
This simulation shows that even with a recording array positioned as close as 0.5mm above the dipoles, the electrodes have to be spaced 1.5mm or less apart in order to resolve two dipoles 3mm apart.
REFERENCES
1. Freeman WJ, Viana di,Prisco G. Relation of olfactory EEG to behavior: time series analysis. Behavioral Neuroscience,1986,100:753-763.
2. Freeman WJ, Baird B. Relation of olfactory EEG to behavior: spatial analysis. Behavioral Neuroscience,1987,101:393-408.
3. Freeman WJ, Grajski KA. Relation of olfactory EEG to behavior: factor analysis. Behavioral Neuroscience,1987,101:766-777.
4. Freeman WJ, van Dijk BW.Spatial patterns of visual cortical fast EEG during condition reflex in a rhesus monkey. Brain Research,1987,422:267-276.
5. McConnell KA, Nahas Z, Shastri A,et al.The transcranial magnetic stimulation motor threshold depends on the distance from coil to underlying cortex: a replication in healthy adults comparing two methods of assessing the distance to cortex. Biological Psychiatry,2001,49:454-459.
6. Menon V, Freeman WJ, Cutillo BA, et al. Spatio-temporal correlations in human gamma band electrocorticograms. Electroencephalography and clinical Neurophysiology,1996,98:89-102.
This paper was supported by Heilongjiang provincial government education department foundation of overseas scholar, No.1 151H
1.Department of Imaging, Mudanjiang Medical College,Mudanjiang,Heilongjiang Province 157022,China
2.Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
(Editor Guo Hui-ling)ARTICLES(ZHOU Zhi-Zun, S.Pockett, )
【Key words】 neural correlates of consciousness; Spatial Resolution; mathematical model
INTRODUCTION
Nearly twenty years ago, Walter Freeman and colleagues published a series of seminal papers showing that it is possible to distinguish whether or not a rabbit is experiencing a particular olfactory, auditory or visual sensation by examining the spatial pattern of voltage recorded at an array of electrodes on the surface of the rabbits brain[1-4]. To use a phrase that became current only after these papers appeared, the spatial electromagnetic patterns reported there would appear to qualify admirably as neural (or at least neurally generated) correlates of consciousness (NCCs).
In view of the explosion of interest over the last decade in finding NCCs, it is perhaps remarkable that Freemans findings have never been extended to human subjects. Why not? The most obvious potential problem is that the original rabbit recordings were taken from the surface of the brain, while the relative ease of recording human EEG from the scalp means that the sorts of dural or sub-dural recordings necessary have simply not been done in human subjects. But is this a reasonable answer? If the sorts of patterns recorded in Freemans rabbits did exist in humans, would it be possible to resolve them from scalp recordings, or would dural or sub-dural records be necessary? We use a combination of mathematical modelling and experimental records of the potentials generated by known electric dipoles to answer this question.
METHODS
The general approach was to proceed in 3 stages:
(1) Construction of a mathematical model of the electric potentials that would be produced by dipoles of appropriate size and orientation to represent pyramidal cells in the cerebral cortex (Kandel et al 1997), as recorded by a linear electrode array on the surface of the brain.
(2) Validation of the mathematical model using actual recordings of potentials generated by known dipoles in a homogeneous medium with conductivity similar to that of brain.
(3) Interrogation of the validated model to determine what sort of dipole separation would produce patterns with the spatial frequency recorded by Freeman and colleagues (i.e. approximately 0.2 cycles/mm)
(4) Interrogation of the model to determine how far above dipole pairs with this separation one could record and still resolve the spatial pattern seen immediately above the dipoles.
Mathematical modelling
The brain was treated as a homogeneous medium with a conductivity of 0.33s/m (Geddes and Baker 1967), open to the air at its upper surface. Neural activity was simulated by introducing either radial dipoles, which were orientated orthogonally to the surface of the medium to simulate activity in gyri, or tangential dipoles, which were oriented parallel to the surface of the medium to simulate activity in sulci. All dipoles had an inter-pole distance of 2mm, which is about the width of the cerebral cortex.
Because there was a free surface at the upper boundary, the medium could not be treated as infinite. Thus the method of images was used to generate the dipole fields: i.e. a mirror image dipole was simulated above the free surface, and its field was added to that of the actual dipole below the surface of the medium.
For one radial dipole, the general mathematical model was derived as:
and for one tangential dipole, the model was:
where I is the injection current of the dipoled is the distance between the two poles of the dipoles is the conductivity of the medium
H is the distance from the dipole to the free surfaceh is the distance from the electrode array to the free surfaces is the horizontal distance from dipole to arrayx is the distance of each electrode along the array.
For three adjacent radial dipoles, the model was:
and m is the distance between dipoles.
The models were implemented in Matlab and the results displayed as plots of the voltage seen at each electrode in a linear array along the x axis. In some cases, a Laplacian filter (implemented by subtracting from the voltage at each electrode the average of the voltages at the two adjacent electrodes) was used to filter out low spatial frequencies and sharpen the image.
Experimental validation of the model
The mathematical model was validated using real dipoles immersed in a saline solution. Dipoles were constructed from pairs of 1mm diameter copper or stainless steel rods, with short lengths of 1mm diameter silver wires soldered to the tip of each rod to minimize polarization. Each rod was insulated from its partner and both members of the pair were insulated from the medium using heat shrink, leaving only a 2mm length of the silver tips exposed. The distance between tips in a pair was 2mm. For tangential dipoles, the exposed tips were side by side. For radial dipoles, one of the silver tips was bent in a partial S shape so that its exposed portion was directly below the tip of the other rod. The saline bath was filled with 0.15% NaCl, which had a measured conductivity of 0.32s/m at 40Hz. Sinusoidal signals of either 30 or 40Hz were produced by a Wavetek 191 signal generator and connected to the dipoles via an isolating transformer, so that the bath was floating with respect to ground. Current delivered to each dipole was monitored and adjusted to (usually) 5.7 μV. Electrode arrays with various interelectrode distances were constructed either from sintered Ag/AgCl pellets or electrolytically chlorided Ag wires. Voltages were recorded between each electrode and a distance reference electrode, using battery powered amplifiers that incorporated neither high nor low pass filters because the 24 bit ADCs sampled at 312kHz (Bold, Diprose and Pockett, submitted). Mains pickup was eliminated by recording in a Faraday cage. Electrodes distant from the dipole sometimes recorded sine waves with peak to peak voltages <20 μV and, because no averaging was used, signal measurements in these cases were somewhat affected by instrumentatal noise. Signal amplitude was therefore estimated using a Matlab routine that fitted a sinusoid to the data in each channel. When measuring the effects of tangential dipoles, signal polarity was taken into account by measuring the amplitude of the sinusoid at a fixed time after the start of data acquisition.
RESULTS AND CONCLUSION
In our mathematical model, brain activity is represented as a series of spatially independent but synchronously active cortical dipoles, similar to those depicted by Kandel et al (1991). The first problem was to determine whether the model accurately predicts the electric field patterns generated by such dipoles, as recorded between electrodes at the surface of the medium in which the dipoles are positioned and a distant reference electrode. Figure 1 shows a comparison between patterns predicted by the mathematical model and patterns measured experimentally, firstly for radial dipoles (representing activity in gyri) and secondly for tangential dipoles (representing sulcal activity), with the tangential dipoles positioned either parallel to or orthogonal to the recording array. Good agreement is seen between the output of the model and the experimental measurements. This validates the mathematical model as producing an adequate simulation of the fields
Dotted lines are experimental data, solid lines are mathematical predictions. For experimental data, electrodes are spaced 2.5mm apart and electrode arrays are approximately 5mm away horizontally from the near edge of the dipoles
Top left Two radial dipoles 2mm apart.Top right Two radial dipoles 10mm apart.Bottom left One tangential dipole parallel to electrode array. Bottom right One tangential dipole orthogonal to electrode array, positive pole closer to array
Figure 1 Comparison of experimental data with predictions of model
Electrodes in these simulations are spaced 0.5mm apart
Top panel Electrodes 0.5mm above dipoles.Middle panel Electrodes 2mm, 2.25mm and 2.5mm above dipoles. Bottom panel Electrodes 3.5mm and 4mm above dipoles, Laplacian filter employed
Figure 2 Predicted measurements at different distances from three radial dipoles separated by 3mmgenerated by dipoles like those widely accepted as occurring in the neocortex (Kandel et al 1991 pp 783-4), when those dipoles are situated just below the free surface of a conductive medium that might reasonably be taken as simulating a segment of brain from which the overlying skull has been removed.
Thus validated, the model is used to produce an electromagnetic pattern having roughly the same spatial frequency as the patterns measured at the surface of rabbit brains by Freeman and colleagues. Following the methods of Freeman and Baird[2], the electrodes in this simulation were spaced 0.57mm apart and the electrode array was positioned at the surface of the medium, 0.5mm above the dipoles. The top panel in Figure 2 shows that in this simulation, a spatial pattern with a frequency of approximately 1 cycle/5mm (0.2 cycles/mm), which is in the middle of the range of spatial frequencies that characterized the patterns found by Freeman and colleagues, was produced by three radial dipoles spaced 3mm apart.
The next question is whether or not it would be possible to detect patterns like this when recording not from the surface of the brain but from the scalp. Far from being 0.5mm above the cortex, the surface of the human scalp is an average of 15 or 16mm above the cortex, depending on the brain area over which measurements are taken[5]. Can the spatial electromagnetic pattern produced by dipoles 3mm apart still be detected if the recording array is positioned 15mm above the dipoles? The middle and bottom panels of Figure 2 show that it can not. With unfiltered simulated data, the recording array has to be less than 2.5mm above the dipoles for the pattern diagnostic of dipoles spaced 3mm apart to be detected (middle panel). Even using a spatial filter to reduce the blurring effects of volume conduction, the recording array has to be less than 4.5mm above a triplet of dipoles separated by 3mm before it can be resolved that there are three dipoles, not one (bottom panel of Figure 2).
What does this mean in anatomical terms? According to our measurements (see Figure 3), the average thickness of the human skull is 4.1±0.6mm over the temporal cortex, 6.3±0.9mm over the motor cortex, 5.9±0.9mm over the prefrontal cortex and as much as 9.1±1.5mm in the ridge of thick bone called the frontal crest, which marks the fusion of the frontal suture over the prefrontal cortex (all measurements given as mean±SD, n=11) Subtacting these measurements from the 15~16mm cortex-scalp distance reported by McConnell et al (2001), it can be calculated that the distance from the surface of the cortex to the skull varies from approximately 6mm to 12mm, depending on location. Since our model shows that even with spatial filtering, the electrode array can not be more than 4.5mm above the surface of the cortex for the sorts of patterns we are looking for to be resolved, this means that in most regions, the sub-dural and sub-arachnoid spaces would have to collapse to a considerable extent when the skull was opened in order for these patterns to be detected even from the surface of the dura.
Figure 3 Skull thickness in different regions
This scatter plot displays the relationship between thickness measured in the prefrontal crest and other prefrontal regions, and over the motor and temporal cortices, for each of 11 different skulls. Each symbol indicates the mean of three measurements in the relevant area of one skull.Note that although there is a tendency for thickness over the motor cortex to be greater than over either temporal or prefrontal cortex, this relationship is not universal for all subjects.
Figure 4 shows that even if one only uses the model described here, which ignores the extra blurring effect of the low conductivity of the skull, two radial dipoles in the cortex would have to be at least 18mm apart before they could be resolved in records taken from the scalp, where this is 15mm above the dipoles. Considering the fact that the simulations conducted here essentially represent a best-case scenario, and that the skull (which has a conductivity of around 1/80 that of brain) would almost certainly make the situation in scalp recordings considerably worse than the model predicts, it is highly unlikely that two cortical dipoles spaced 3mm apart could ever be resolved in scalp recordings, whatever deblurring methods were used. The conclusion seems inevitable that if patterns like those recorded by Freeman and Baird (1987) do occur in humans, dural or sub-dural recording will be necessary to detect them.
Simulated electrodes are 1mm apart. Distances between dipoles shown on figureFigure 4 Simulations of measurements taken 15mm above a pair of dipoles separated by various distances
The final question we address concerns the maximum electrode spacing that would be sufficient to detect such patterns even in dural or sub-dural recordings.
Menon[5] concluded that if patterns covaring with perceptual categorization do occur in humans, detection of them in ECoG recordings would require electrode spacings under 5mm. The simulations depicted in Figure 5 reduce this figure to 1.5mm.
Figure 5 Maximum interelectrode spacing necessary to resolve two dipoles 3mm apart, recording array 0.5mm above dipoles
This simulation shows that even with a recording array positioned as close as 0.5mm above the dipoles, the electrodes have to be spaced 1.5mm or less apart in order to resolve two dipoles 3mm apart.
REFERENCES
1. Freeman WJ, Viana di,Prisco G. Relation of olfactory EEG to behavior: time series analysis. Behavioral Neuroscience,1986,100:753-763.
2. Freeman WJ, Baird B. Relation of olfactory EEG to behavior: spatial analysis. Behavioral Neuroscience,1987,101:393-408.
3. Freeman WJ, Grajski KA. Relation of olfactory EEG to behavior: factor analysis. Behavioral Neuroscience,1987,101:766-777.
4. Freeman WJ, van Dijk BW.Spatial patterns of visual cortical fast EEG during condition reflex in a rhesus monkey. Brain Research,1987,422:267-276.
5. McConnell KA, Nahas Z, Shastri A,et al.The transcranial magnetic stimulation motor threshold depends on the distance from coil to underlying cortex: a replication in healthy adults comparing two methods of assessing the distance to cortex. Biological Psychiatry,2001,49:454-459.
6. Menon V, Freeman WJ, Cutillo BA, et al. Spatio-temporal correlations in human gamma band electrocorticograms. Electroencephalography and clinical Neurophysiology,1996,98:89-102.
This paper was supported by Heilongjiang provincial government education department foundation of overseas scholar, No.1 151H
1.Department of Imaging, Mudanjiang Medical College,Mudanjiang,Heilongjiang Province 157022,China
2.Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
(Editor Guo Hui-ling)ARTICLES(ZHOU Zhi-Zun, S.Pockett, )