- Email: [email protected]
Experimental tests of EEG source localization accuracy in realistically shaped head models
Clinical Neurophysiology 112 (2001) 2288–2292 www.elsevier.com/locate/clinph
Experimental tests of EEG source localization accuracy in realistically shaped head models B. Neil Cuffin*, Donald L. Schomer, John R. Ives, Howard Blume Beth Israel Deaconess Medical Center and Harvard Medical School, 330 Brookline Avenue GZ-522, Boston, MA 00215, USA Accepted 9 August 2001
Abstract Objectives: To determine the accuracy with which electrical sources in the human brain can be located using realistically shaped boundary element models of the head and to compare this accuracy with that using spherical head models. Methods: In a previous study, electroencephalographs (EEGs) produced by sources at known locations in the brains of human subjects were recorded. The sources were created by injecting current into implanted depth electrodes. The locations of the implanted depth and scalp EEG electrodes and head shape were determined from computerized tomography images. The EEGs were used to calculate source locations in spherical head models and localization accuracy was determined by comparing the calculated and actual locations. In this study, these same EEGs are used to determine localization accuracy in realistically shaped head models. Results: An average localization error of 10.5 ðSD ¼ 5:4Þ mm was obtained in the realistically shaped models for all 176 sources in 13 subjects. This compares with 10.6 (5.5) mm in the spherical models. The average localization error for 105 sources at superior locations in the brain is 9.1 (4.2) mm. The average error for 71 inferior location sources is 12.4 (6.4) mm. The corresponding values for the spherical models are 9.2 (4.4) and 12.8 (6.2) mm. Conclusions: The realistically shaped head boundary element models used in this study produced very nearly the same localization accuracy as spherical models. q 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Electroencephalography; Source localization; Depth electrodes; Inverse solutions; Realistic head models; Boundary element models; Dipoles
1. Introduction While scalp-recorded electroencephalographic (EEG) signals are often used to calculate the locations of electrical sources in the human brain, the accuracy of the calculated locations is not well known. This is because accurate comparisons of calculated source locations and actual source locations can generally not be made since the exact location of most intrinsic sources in the human brain is not known. One way to determine localization accuracy is to create sources at known locations in the brain and compare the calculated locations of these sources with their actual locations. In a recent study (Cuffin et al., 2001), sources at known locations were created by injecting current into electrodes which had been implanted in the brains of human subjects for diagnostic purposes. The scalp EEGs produced by these sources were used to calculate the locations of the sources in spherical models of the head. An average localization error
of 10.6 ðSD ¼ 5:5Þ mm was obtained for 177 sources in 13 subjects. The average localization error of sources at superior locations in the brain was 9.2 (4.4) mm and the average error for inferior location sources was 12.8 (6.2) mm. It was concluded that the use of more realistic head models would be required to obtain greater localization accuracy, particularly for sources at inferior locations in the brain where actual head geometry is very non-spherical. In addition, a previous similar study (Cuffin, 1996) has suggested that realistically shaped head models can give greater localization accuracy than spherical models when used with EEGs with good (.60) signal-to-noise ratios (SNR). Various computer modeling studies, e.g. Silva et al., 1999, have indicated that source localization is more accurate with realistically shaped models than spherical models. This is a report of the localization accuracy obtained for the sources of Cuffin et al. (2001) using realistically shaped boundary element models of the head. A comparison with the accuracy using the spherical models is also made.
* Corresponding author. Tel.: 11-617-667-0242; fax: 11-617-667-7023. E-mail address: [email protected] (B.N. Cuffin). 1388-2457/01/$ - see front matter q 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S13 88- 2457(01)0066 9-1
CLINPH 2001109
B.N. Cuffin et al. / Clinical Neurophysiology 112 (2001) 2288–2292
2. Methods The subjects in this study were medically refractory epilepsy patients undergoing monitoring with implanted depth electrodes prior to surgery. Informed consent was obtained from the subjects. The implanted electrodes used were platinum/iridium rings mounted on hollow plastic catheters containing wires connecting to each ring. The rings are 1 mm in diameter and 2 mm in length and are spaced 5 mm apart along the catheters. The catheters passed through the skull through electrically non-conducting plastic plugs which completely filled the 3 mm diameter holes used to insert the catheters into the brain. The catheters were implanted into the temporal and frontal lobes. Each catheter had 7 or 8 rings and each subject had 4 or 5 catheters on each side of the head. Dipolar sources were created by injecting current pulses through various pairs of implanted depth electrodes. The EEG signals produced by the current pulses were recorded using a modified international 10–20 system grid. Electrode locations were shifted, where necessary, to avoid the surgical wounds in the scalp, for the catheters and additional electrodes were placed where possible. The number of electrodes varied from 21–32. An average SNR value for an EEG recording is defined as the average across all channels of the signal value for a channel divided by the root mean square (RMS) value of an interval preceding the pulse. The 3-dimensional locations of the implanted depth and scalp EEG electrodes were obtained from computerized tomography (CTs) images recorded while both the scalp and depth electrodes were in place. The CTs also provided 3-dimensional data for the geometry of the scalp surface. The CTs were recorded using a GE Medical Systems HiSpeed CT at 140 kV. The resolution of the CTs is 512 £ 512 pixels and the slice thickness is 3 mm. A realistically shaped boundary element model was generated for each subject. The models contain 3 surfaces which define 3 regions representing the scalp, skull, and brain. Each surface contains 1536 triangular element for a total of 4608 elements in each model. The 3-dimensional scalp geometry data from the CTs was used with a harmonic expansion technique (Cuffin, 1996) to generate the shape of the scalp surface. Some triangular elements on the scalp surface were then shifted so that their centroids were at the locations of the actual scalp EEG electrodes. The potentials on these elements were used in the inverse solution calculation method described below. The scalp layer in all models is 5 mm thick and the skull layer 6 mm thick on the superior portion of the models. These are the same layer thicknesses used in the spherical models. The inferior portion of the brain/skull surface was adjusted for each subject to approximately represent the geometry of the actual head in that region. An example of a model is given in Fig. 1. The electrical conductivities of the scalp and brain regions are equal while the skull layer conductivity is 1/40 (0.025) of the scalp and brain regions. This ratio
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of skull to scalp and brain conductivity was found to produce the best localization accuracy, on average, for the 13 subjects using spherical models. The inverse solutions are calculated using a Simplex search method (Press et al., 1989) to find the location, orientation, and amplitude of a dipole in the realistically shaped model which produces the best fit between the potentials on the model and the measured potentials (EEGs). This search method requires repeated calculation of the potentials produced by dipoles at various locations and orientations. These repeated calculations were rapidly performed using a previously developed method (Cuffin, 1995). The modeling and calculation methods were extensively checked by comparisons of the boundary element model results, when in a spherical shape, with analytical results for a sphere. The maximum localization error produced by the boundary element model was found to be approximately 2 mm.
3. Results Table 1 presents average localization errors versus mini-
Fig. 1. Right side views of the scalp surface (top) and brain/skull surface (bottom) of a realistically shaped model. The skull/scalp surface is not shown, but is similar to the scalp surface. The 1X direction is perpendicular to the page to the subject’s right side.
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Table 1 Average localization errors (D) and standard deviations (s) in millimeters versus minimum SNR a SNR .
LOC
#
D
s
0 0 0
A S I
176 105 71
10.5 9.1 12.4
(5.4) (4.2) (6.4)
5 5 5
A S I
167 99 68
10.3 8.9 12.4
(5.3) (3.8) (6.3)
10 10 10
A S I
133 82 51
10.4 8.6 13.3
(5.4) (3.9) (6.3)
15 15 15
A S I
92 56 36
10.3 8.8 12.5
(4.6) (3.8) (5.0)
20 20 20
A S I
55 32 23
10.6 9.0 12.9
(4.1) (3.4) (4.1)
25 25 25
A S I
31 19 12
10.2 9.6 11.1
(3.6) (3.4) (3.7)
30 30 30
A S I
16 10 6
9.8 8.8 11.5
(3.7) (2.0) (5.3)
a Source locations (LOC) are all (A) locations, superior (S) locations, and inferior (I) locations. The number (#) of sources in the averages is also indicated.
mum SNR for 176 dipoles in the 13 subjects. (One dipole has been omitted from the full set of 177 because it is only a few millimeters from the surface of the brain and boundary element models have large errors for such small spacing.) Values are presented for 3 groupings of the sources, i.e. all sources, superior location sources, and inferior location sources. Superior locations are defined as those above a plane through the approximate center of the brain region in the models and inferior locations as below the plane. This plane is approximately at the level of the nasion and inion and the T3 and T4 electrode locations of the international 10–20 system. The average (standard deviation) error for all 176 sources is 10.5 (5.4) mm which is only very slightly smaller than the 10.6 (5.5) mm error obtained using spherical head models. The average localization error for 105 sources at superior locations in the brain is 9.1 (4.2) mm. The average error for 71 inferior location sources is 12.4 (6.4) mm. The corresponding values for the spherical models are 9.2 (4.4) and 12.8 (6.2) mm. For all SNR ranges, the average superior source errors are smaller than the average inferior source errors. The 3.3 mm smaller average error for the 105 superior location sources versus the 71 inferior location sources is statistically significant ðP , 0:0001Þ. This is very nearly equal to the 3.6 mm smaller errors for the superior sources versus the inferior sources in the spherical models which is
Fig. 2. Realistically shaped (RL) minus spherical (SP) model localization errors versus SNR for all 13 subjects. The differences in the errors versus SNR are presented for the all (A), superior (S), and inferior (I) source location groups.
also statistically significant. As for the spherical model solutions, the average errors for all 3 source groups tend to decrease with increasing SNR but the decrease is less than 1 mm from minimum SNR . 0 to .30. Fig. 2 shows the differences in the realistically shaped model and spherical model localization errors versus SNR for the 3 source groups. A negative value indicates that the realistically shaped model solution is more accurate than the corresponding spherical model solution. As indicated by the nearly equal average errors for the realistically shaped and Table 2 Average coordinate axes direction shifts in the realistically shaped models LOC A S I
#
D
s
X
s
Y
s
Z
s
176 105 71
10.5 9.1 12.4
(5.4) (4.2) (6.4)
2 2.6 2 1.5 2 4.3
(5.3) (5.0) (5.3)
2 0.9 2 0.7 2 1.2
(5.2) (5.6) (4.5)
2 2.2 1.2 2 7.2
(8.3) (6.3) (8.5)
B.N. Cuffin et al. / Clinical Neurophysiology 112 (2001) 2288–2292
spherical models, there is no clear decrease in the error for the realistically shaped models for any of the source groups. Table 2 presents the average directions of the errors in the coordinate axes directions shown in Fig. 1. A positive value indicates that the error is outward from the center of the model. The differences in the average X and Z direction shifts between the superior location sources and the inferior location sources are statistically significant ðP , 0:0001Þ. As with the spherical model solutions, the inferior location solutions are shifted upward (2Z direction) toward the center of the model. This average shift is 2.1 mm smaller than in the spherical models but this is not statistically significant. There is a statistically significant ðP , 0:005Þ 2.8 mm larger average 2X shift of the inferior location sources in the realistically shaped models as compared to the spherical models. All other differences in shifts between the realistically shaped and spherical models are not statistically significant.
4. Discussion The very small improvement in average localization accuracy for realistically shaped models (10.5 mm) as compared to spherical models (10.6 mm) is quite an unexpected result. The lack of improvement for the inferior location sources in the realistically shaped models is even more unexpected since these models have the inferior brain/skull surface modified to approximately represent the non-spherical geometry of the head in that region. The average inferior location source solutions in the realistically shaped models are shifted upward away from the brain/skull surface by only a few millimeters less than in the spherical models. The reasons for a lack of improvement in localization accuracy for the realistically shaped models are not clear. However, a comparison (Liu et al., unpublished data) of the potentials produced on the realistically shaped and spherical models with the actual measured potentials (EEGs) for one subject showed that the average RMS error between the realistically shaped model and actual potentials for inferior location sources was 8.5 versus 11.9% for the spherical model. The potentials on the models were calculated for the sources at their actual locations as determined from the CTs. For superior location sources, the average RMS errors were nearly equal for the two models, 6.85 and 6.92%, respectively. The small differences in the realistically shaped and spherical model potentials may be the reason for the small difference in the solutions. A previous study (Yvert et al., 1997) indicates that increasing the number of EEG electrodes beyond the 21–32 used here will not improve localization accuracy by more than a millimeter or two. In a previous study (Cuffin, 1996), there is a suggestion that realistically shaped models can produce greater localization accuracy than spherical models for EEGs with very high SNRs (.60). However, none of the EEGs recorded in
2291
this study had such high SNRs, so no confirmation of that suggestion can be made from the results of this study. However, it should be noted that EEGs with such high SNRs are difficult to obtain in actual clinical or even research situations so it is unlikely that any improvement in localization accuracy can be obtained under most situations using realistically shaped models and very high SNR EEGs. In the previous study, localization accuracy for realistically shaped models is not clearly better for EEGs with SNRs ,60. Although the reasons for the lack of improvement in localization accuracy for the realistically shaped models are not clear, some reasons can be considered. The expected improvement for the realistically shaped models over the spherical models because of the reduction in the displacement errors of the electrode locations caused by the projection of the actual EEG electrode locations onto surface of the spherical models may not occur because the displacement errors average out for the spherical models. The lack of improvement for the realistically shaped models indicates that there are more significant modeling errors than those caused by non-spherical head shape. Such modeling errors may include inaccurate tissue conductivity values, variations in tissue thickness and/or conductivity with location around the head, tissue anisotropy, etc. A computer modeling study (Ollikainen et al., 1999) has indicated that local skull inhomogeneities can produce localization errors as large as 10 mm. The lack of improvement of the realistically shaped models for inferior location sources even though the inferior brain/skull surface is adjusted to approximately represent that surface may be because this approximate representation is not accurate enough. Accurate representation of this very irregular surface with boundary element models is very difficult and it may be necessary to use finite element models to adequately represent it. In summary, these results indicate that realistically shaped boundary element head models with uniform scalp and skull layer thickness and conductivity do not produce significantly more accurate EEG source localization than spherical models. The reasons for this lack of improvement are not clear and will require additional research to determine.
Acknowledgements Support for this research was provided by N.I.H. grant R01 NS31358.
References Cuffin BN. A method for localizing EEG sources in realistic head models. IEEE Trans Biomed Eng 1995;42:68–71. Cuffin BN. EEG localization accuracy improvements using realistically shaped head models. IEEE Trans Biomed Eng 1996;43:299–303. Cuffin BN, Schomer DL, Ives JR, Blume H. Experimental tests of EEG
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source localization accuracy in spherical head models. Clin Neurophysiol 2001;112:46–51. Ollikainen JO, Vauhkonen M, Karjalainen PA, Kaipio JP. Effects of local skull inhomogeneities on EEG source estimation. Med Eng Phys 1999;21:143–154. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes, New York, NY: Cambridge University Press, 1989 (p. 289–293).
Silva C, Almeida R, Oostendorp T, Ducla-Soares E, Foreid JP, Pimentel T. Interictal spike localization using a standard realistic head model: simulations and analysis of clinical data. Clin Neurophysiol 1999;110:846– 855. Yvert B, Bertrand O, Thevenet M, Echallier JF, Pernier J. A systematic evaluation of the spherical model accuracy in EEG dipole localization. Electroenceph clin Neurophysiol 1997;102:452–459.
Experimental tests of EEG source localization accuracy in realistically shaped head models B. Neil Cuffin*, Donald L. Schomer, John R. Ives, Howard Blume Beth Israel Deaconess Medical Center and Harvard Medical School, 330 Brookline Avenue GZ-522, Boston, MA 00215, USA Accepted 9 August 2001
Abstract Objectives: To determine the accuracy with which electrical sources in the human brain can be located using realistically shaped boundary element models of the head and to compare this accuracy with that using spherical head models. Methods: In a previous study, electroencephalographs (EEGs) produced by sources at known locations in the brains of human subjects were recorded. The sources were created by injecting current into implanted depth electrodes. The locations of the implanted depth and scalp EEG electrodes and head shape were determined from computerized tomography images. The EEGs were used to calculate source locations in spherical head models and localization accuracy was determined by comparing the calculated and actual locations. In this study, these same EEGs are used to determine localization accuracy in realistically shaped head models. Results: An average localization error of 10.5 ðSD ¼ 5:4Þ mm was obtained in the realistically shaped models for all 176 sources in 13 subjects. This compares with 10.6 (5.5) mm in the spherical models. The average localization error for 105 sources at superior locations in the brain is 9.1 (4.2) mm. The average error for 71 inferior location sources is 12.4 (6.4) mm. The corresponding values for the spherical models are 9.2 (4.4) and 12.8 (6.2) mm. Conclusions: The realistically shaped head boundary element models used in this study produced very nearly the same localization accuracy as spherical models. q 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Electroencephalography; Source localization; Depth electrodes; Inverse solutions; Realistic head models; Boundary element models; Dipoles
1. Introduction While scalp-recorded electroencephalographic (EEG) signals are often used to calculate the locations of electrical sources in the human brain, the accuracy of the calculated locations is not well known. This is because accurate comparisons of calculated source locations and actual source locations can generally not be made since the exact location of most intrinsic sources in the human brain is not known. One way to determine localization accuracy is to create sources at known locations in the brain and compare the calculated locations of these sources with their actual locations. In a recent study (Cuffin et al., 2001), sources at known locations were created by injecting current into electrodes which had been implanted in the brains of human subjects for diagnostic purposes. The scalp EEGs produced by these sources were used to calculate the locations of the sources in spherical models of the head. An average localization error
of 10.6 ðSD ¼ 5:5Þ mm was obtained for 177 sources in 13 subjects. The average localization error of sources at superior locations in the brain was 9.2 (4.4) mm and the average error for inferior location sources was 12.8 (6.2) mm. It was concluded that the use of more realistic head models would be required to obtain greater localization accuracy, particularly for sources at inferior locations in the brain where actual head geometry is very non-spherical. In addition, a previous similar study (Cuffin, 1996) has suggested that realistically shaped head models can give greater localization accuracy than spherical models when used with EEGs with good (.60) signal-to-noise ratios (SNR). Various computer modeling studies, e.g. Silva et al., 1999, have indicated that source localization is more accurate with realistically shaped models than spherical models. This is a report of the localization accuracy obtained for the sources of Cuffin et al. (2001) using realistically shaped boundary element models of the head. A comparison with the accuracy using the spherical models is also made.
* Corresponding author. Tel.: 11-617-667-0242; fax: 11-617-667-7023. E-mail address: [email protected] (B.N. Cuffin). 1388-2457/01/$ - see front matter q 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S13 88- 2457(01)0066 9-1
CLINPH 2001109
B.N. Cuffin et al. / Clinical Neurophysiology 112 (2001) 2288–2292
2. Methods The subjects in this study were medically refractory epilepsy patients undergoing monitoring with implanted depth electrodes prior to surgery. Informed consent was obtained from the subjects. The implanted electrodes used were platinum/iridium rings mounted on hollow plastic catheters containing wires connecting to each ring. The rings are 1 mm in diameter and 2 mm in length and are spaced 5 mm apart along the catheters. The catheters passed through the skull through electrically non-conducting plastic plugs which completely filled the 3 mm diameter holes used to insert the catheters into the brain. The catheters were implanted into the temporal and frontal lobes. Each catheter had 7 or 8 rings and each subject had 4 or 5 catheters on each side of the head. Dipolar sources were created by injecting current pulses through various pairs of implanted depth electrodes. The EEG signals produced by the current pulses were recorded using a modified international 10–20 system grid. Electrode locations were shifted, where necessary, to avoid the surgical wounds in the scalp, for the catheters and additional electrodes were placed where possible. The number of electrodes varied from 21–32. An average SNR value for an EEG recording is defined as the average across all channels of the signal value for a channel divided by the root mean square (RMS) value of an interval preceding the pulse. The 3-dimensional locations of the implanted depth and scalp EEG electrodes were obtained from computerized tomography (CTs) images recorded while both the scalp and depth electrodes were in place. The CTs also provided 3-dimensional data for the geometry of the scalp surface. The CTs were recorded using a GE Medical Systems HiSpeed CT at 140 kV. The resolution of the CTs is 512 £ 512 pixels and the slice thickness is 3 mm. A realistically shaped boundary element model was generated for each subject. The models contain 3 surfaces which define 3 regions representing the scalp, skull, and brain. Each surface contains 1536 triangular element for a total of 4608 elements in each model. The 3-dimensional scalp geometry data from the CTs was used with a harmonic expansion technique (Cuffin, 1996) to generate the shape of the scalp surface. Some triangular elements on the scalp surface were then shifted so that their centroids were at the locations of the actual scalp EEG electrodes. The potentials on these elements were used in the inverse solution calculation method described below. The scalp layer in all models is 5 mm thick and the skull layer 6 mm thick on the superior portion of the models. These are the same layer thicknesses used in the spherical models. The inferior portion of the brain/skull surface was adjusted for each subject to approximately represent the geometry of the actual head in that region. An example of a model is given in Fig. 1. The electrical conductivities of the scalp and brain regions are equal while the skull layer conductivity is 1/40 (0.025) of the scalp and brain regions. This ratio
2289
of skull to scalp and brain conductivity was found to produce the best localization accuracy, on average, for the 13 subjects using spherical models. The inverse solutions are calculated using a Simplex search method (Press et al., 1989) to find the location, orientation, and amplitude of a dipole in the realistically shaped model which produces the best fit between the potentials on the model and the measured potentials (EEGs). This search method requires repeated calculation of the potentials produced by dipoles at various locations and orientations. These repeated calculations were rapidly performed using a previously developed method (Cuffin, 1995). The modeling and calculation methods were extensively checked by comparisons of the boundary element model results, when in a spherical shape, with analytical results for a sphere. The maximum localization error produced by the boundary element model was found to be approximately 2 mm.
3. Results Table 1 presents average localization errors versus mini-
Fig. 1. Right side views of the scalp surface (top) and brain/skull surface (bottom) of a realistically shaped model. The skull/scalp surface is not shown, but is similar to the scalp surface. The 1X direction is perpendicular to the page to the subject’s right side.
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Table 1 Average localization errors (D) and standard deviations (s) in millimeters versus minimum SNR a SNR .
LOC
#
D
s
0 0 0
A S I
176 105 71
10.5 9.1 12.4
(5.4) (4.2) (6.4)
5 5 5
A S I
167 99 68
10.3 8.9 12.4
(5.3) (3.8) (6.3)
10 10 10
A S I
133 82 51
10.4 8.6 13.3
(5.4) (3.9) (6.3)
15 15 15
A S I
92 56 36
10.3 8.8 12.5
(4.6) (3.8) (5.0)
20 20 20
A S I
55 32 23
10.6 9.0 12.9
(4.1) (3.4) (4.1)
25 25 25
A S I
31 19 12
10.2 9.6 11.1
(3.6) (3.4) (3.7)
30 30 30
A S I
16 10 6
9.8 8.8 11.5
(3.7) (2.0) (5.3)
a Source locations (LOC) are all (A) locations, superior (S) locations, and inferior (I) locations. The number (#) of sources in the averages is also indicated.
mum SNR for 176 dipoles in the 13 subjects. (One dipole has been omitted from the full set of 177 because it is only a few millimeters from the surface of the brain and boundary element models have large errors for such small spacing.) Values are presented for 3 groupings of the sources, i.e. all sources, superior location sources, and inferior location sources. Superior locations are defined as those above a plane through the approximate center of the brain region in the models and inferior locations as below the plane. This plane is approximately at the level of the nasion and inion and the T3 and T4 electrode locations of the international 10–20 system. The average (standard deviation) error for all 176 sources is 10.5 (5.4) mm which is only very slightly smaller than the 10.6 (5.5) mm error obtained using spherical head models. The average localization error for 105 sources at superior locations in the brain is 9.1 (4.2) mm. The average error for 71 inferior location sources is 12.4 (6.4) mm. The corresponding values for the spherical models are 9.2 (4.4) and 12.8 (6.2) mm. For all SNR ranges, the average superior source errors are smaller than the average inferior source errors. The 3.3 mm smaller average error for the 105 superior location sources versus the 71 inferior location sources is statistically significant ðP , 0:0001Þ. This is very nearly equal to the 3.6 mm smaller errors for the superior sources versus the inferior sources in the spherical models which is
Fig. 2. Realistically shaped (RL) minus spherical (SP) model localization errors versus SNR for all 13 subjects. The differences in the errors versus SNR are presented for the all (A), superior (S), and inferior (I) source location groups.
also statistically significant. As for the spherical model solutions, the average errors for all 3 source groups tend to decrease with increasing SNR but the decrease is less than 1 mm from minimum SNR . 0 to .30. Fig. 2 shows the differences in the realistically shaped model and spherical model localization errors versus SNR for the 3 source groups. A negative value indicates that the realistically shaped model solution is more accurate than the corresponding spherical model solution. As indicated by the nearly equal average errors for the realistically shaped and Table 2 Average coordinate axes direction shifts in the realistically shaped models LOC A S I
#
D
s
X
s
Y
s
Z
s
176 105 71
10.5 9.1 12.4
(5.4) (4.2) (6.4)
2 2.6 2 1.5 2 4.3
(5.3) (5.0) (5.3)
2 0.9 2 0.7 2 1.2
(5.2) (5.6) (4.5)
2 2.2 1.2 2 7.2
(8.3) (6.3) (8.5)
B.N. Cuffin et al. / Clinical Neurophysiology 112 (2001) 2288–2292
spherical models, there is no clear decrease in the error for the realistically shaped models for any of the source groups. Table 2 presents the average directions of the errors in the coordinate axes directions shown in Fig. 1. A positive value indicates that the error is outward from the center of the model. The differences in the average X and Z direction shifts between the superior location sources and the inferior location sources are statistically significant ðP , 0:0001Þ. As with the spherical model solutions, the inferior location solutions are shifted upward (2Z direction) toward the center of the model. This average shift is 2.1 mm smaller than in the spherical models but this is not statistically significant. There is a statistically significant ðP , 0:005Þ 2.8 mm larger average 2X shift of the inferior location sources in the realistically shaped models as compared to the spherical models. All other differences in shifts between the realistically shaped and spherical models are not statistically significant.
4. Discussion The very small improvement in average localization accuracy for realistically shaped models (10.5 mm) as compared to spherical models (10.6 mm) is quite an unexpected result. The lack of improvement for the inferior location sources in the realistically shaped models is even more unexpected since these models have the inferior brain/skull surface modified to approximately represent the non-spherical geometry of the head in that region. The average inferior location source solutions in the realistically shaped models are shifted upward away from the brain/skull surface by only a few millimeters less than in the spherical models. The reasons for a lack of improvement in localization accuracy for the realistically shaped models are not clear. However, a comparison (Liu et al., unpublished data) of the potentials produced on the realistically shaped and spherical models with the actual measured potentials (EEGs) for one subject showed that the average RMS error between the realistically shaped model and actual potentials for inferior location sources was 8.5 versus 11.9% for the spherical model. The potentials on the models were calculated for the sources at their actual locations as determined from the CTs. For superior location sources, the average RMS errors were nearly equal for the two models, 6.85 and 6.92%, respectively. The small differences in the realistically shaped and spherical model potentials may be the reason for the small difference in the solutions. A previous study (Yvert et al., 1997) indicates that increasing the number of EEG electrodes beyond the 21–32 used here will not improve localization accuracy by more than a millimeter or two. In a previous study (Cuffin, 1996), there is a suggestion that realistically shaped models can produce greater localization accuracy than spherical models for EEGs with very high SNRs (.60). However, none of the EEGs recorded in
2291
this study had such high SNRs, so no confirmation of that suggestion can be made from the results of this study. However, it should be noted that EEGs with such high SNRs are difficult to obtain in actual clinical or even research situations so it is unlikely that any improvement in localization accuracy can be obtained under most situations using realistically shaped models and very high SNR EEGs. In the previous study, localization accuracy for realistically shaped models is not clearly better for EEGs with SNRs ,60. Although the reasons for the lack of improvement in localization accuracy for the realistically shaped models are not clear, some reasons can be considered. The expected improvement for the realistically shaped models over the spherical models because of the reduction in the displacement errors of the electrode locations caused by the projection of the actual EEG electrode locations onto surface of the spherical models may not occur because the displacement errors average out for the spherical models. The lack of improvement for the realistically shaped models indicates that there are more significant modeling errors than those caused by non-spherical head shape. Such modeling errors may include inaccurate tissue conductivity values, variations in tissue thickness and/or conductivity with location around the head, tissue anisotropy, etc. A computer modeling study (Ollikainen et al., 1999) has indicated that local skull inhomogeneities can produce localization errors as large as 10 mm. The lack of improvement of the realistically shaped models for inferior location sources even though the inferior brain/skull surface is adjusted to approximately represent that surface may be because this approximate representation is not accurate enough. Accurate representation of this very irregular surface with boundary element models is very difficult and it may be necessary to use finite element models to adequately represent it. In summary, these results indicate that realistically shaped boundary element head models with uniform scalp and skull layer thickness and conductivity do not produce significantly more accurate EEG source localization than spherical models. The reasons for this lack of improvement are not clear and will require additional research to determine.
Acknowledgements Support for this research was provided by N.I.H. grant R01 NS31358.
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