Clinical Neurophysiology 116 (2005) 456–465 www.elsevier.com/locate/clinph
Estimation of in vivo human brain-to-skull conductivity ratio from simultaneous extra- and intra-cranial electrical potential recordings Y. Laia,b, W. van Drongelenc, L. Dinga, K.E. Hecoxc, V.L. Towlec, D.M. Frimc, B. Hea,* a
Department of Biomedical Engineering, University of Minnesota, 7-105 BSBE, 312 Church Street, Minneapolis, MN 55455, USA b University of Illinois at Chicago, Chicago, IL, USA c University of Chicago, Chicago, IL, USA Accepted 24 August 2004
Abstract Objective: The present study aims to accurately estimate the in vivo brain-to-skull conductivity ratio by means of cortical imaging technique. Simultaneous extra- and intra-cranial potential recordings induced by subdural current stimulation were analyzed to get the estimation. Methods: The effective brain-to-skull conductivity ratio was estimated in vivo for 5 epilepsy patients. The estimation was performed using multi-channel simultaneously recorded scalp and cortical electrical potentials during subdural electrical stimulation. The cortical imaging technique was used to compute the inverse cortical potential distribution from the scalp recorded potentials using a 3-shell head volume conductor model. The brain-to-skull conductivity ratio, which leads to the most consistent cortical potential estimates with respect to the direct intra-cranial measurements, is considered to be the effective brain-to-skull conductivity ratio. Results: The present estimation provided consistent results in 5 human subjects studied. The in vivo effective brain-to-skull conductivity ratio ranged from 18 to 34 in the 5 epilepsy patients. Conclusions: The effective brain-to-skull conductivity ratio can be estimated from simultaneous intra- and extra-cranial potential recordings and the averaged value/standard deviation is 25G7. Significance: The present results provide important experimental data on the brain-to-skull conductivity ratio, which is of significance for accurate brain source localization using piece-wise homogeneous head models. q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. Keywords: Brain-to-skull conductivity ratio; Skull conductivity; Cortical imaging; Inverse problem; Brain mapping; High-resolution EEG
1. Introduction The electroencephalogram (EEG) is a widely used technique for monitoring brain electrical activity based on the scalp-recorded electrical potentials. The EEG inverse problem is to estimate the neuronal source distributions within the brain that generate the scalp electrical potential measurements (Babiloni et al., 1997, 2001; Cuffin, 1995; Dale and Sereno, 1993; Gevins et al., 1994; Hamalainen and Ilmoniemi, 1984; He, 1999; He et al., 2002; Kearfott et al., 1991; Mosher et al., 1992; Nunez et al.,
* Corresponding author. Tel.: C1 612 626 1115; fax: C1 612 626 6583. E-mail address:
[email protected] (B. He).
1994; Pascual-Marqui et al., 1994; Scherg and von Cramon, 1985; Sekihara and Scholz, 1995). To solve this problem, it is necessary to construct a volume conductor model to describe the electrical properties of the head. The piece-wise homogenous head models, which compose 3 or 4 homogeneous compartments with different conductivity representing the different tissues, are widely adopted. Using such a model, the scalp potentials generated by a current source with a known strength at a known position can be calculated with the parameters of the electrical conductivities of the compartments (Hamalainen and Sarvas, 1989; Mosher et al., 1999; Perrin et al., 1987). For the often used 3-layer concentric spherical head model (Rush and Driscoll, 1968), in which the scalp, skull and brain are modeled as concentric spheres, an analytical
1388-2457/$30.00 q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2004.08.017
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expression for the relation between source parameters and the scalp potential can be obtained. In the boundary element realistic geometric head models, 3 piece-wise homogeneous compartments representing the scalp, the skull and the brain are widely used (Babiloni et al., 1997, 2001; Cuffin, 1995; Hamalainen and Sarvas, 1989; He et al., 1999, 2002; Mosher et al., 1999). Sometimes more than 3 compartments are also used to represent more human tissues such as cerebrospinal fluid (CSF) (de Munck, 1988; Scherg, 1992; Zhou and van Oosterom, 1992). However, the 3 compartments (the scalp, skull and brain) head model has enjoyed wide acceptance by a number of investigators in solving the EEG inverse problems. In such a model, effective equivalent conductivity of different value is assigned to each compartment, such as the brain, the skull, and the scalp (Fig. 1). In the piece-wise homogeneous head volume conductor models (spherical or realistic geometric head model), the effective conductivities of the scalp, the skull and the brain need to be determined. In most investigations, the scalp is assumed to have the same conductivity as that of the brain while the skull has much lower conductivity than that of the scalp and the brain (Geddes and Baker, 1967; Gonc¸alves et al., 2003a; Gonc¸alves et al., 2003b; Kosterich et al., 1983; Nicholson, 1965; Oostendorp et al., 2000). EEG source localization is the major interest of solving the EEG inverse problem. It is often sufficient to specify the conductivity ratios of the brain, the scalp and the skull, if one is concerned in localizing the neural sources, or solving other inverse problems when the absolute strength of the sources is not an issue. From the literature, the brain conductivity ranges from 0.12 to 0.48/ U m (Gonc¸alves et al., 2003a,b; Nicholson, 1965), and the human skull from 0.006 to 0.015/U m (Geddes and Baker, 1967; Gonc¸alves et al., 2003a,b; Kosterich et al., 1983;
Fig. 1. The source and volume conductor models used in the present study. The scalp, skull and cortex are modeled by 3 concentric spheres, where the skull is represented by the dark ring. The innermost sphere is a hypothetical dipole layer, on which the dipoles are constructed to generate the recorded scalp potentials as accurately as possible. Scalp electrodes and subdural electrodes are also illustrated by dark dots.
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Oostendorp et al., 2000) or even higher as 0.032–0.080/ U m (Hoekema et al., 2003). It is hard to specify the brain-to-skull conductivity ratio from these values with such large variations. Rush and Driscoll (1968) used the electrolytic tank to measure the impedance of the human skull. The human half-skull was suspended in a head-shaped receptacle in which a layer of fluid was left outside the skull to model the skin and scalp muscles. The resistivity of the fluid permeated skull is assumed to be proportional to that of the permeating fluid. Their study showed an optimal effective resistivity ratio of 80 between the human skull and the permeating fluid. Cohen and Cuffin (1983) used the combined analysis of the electroencephalogram (EEG) and the magnetoencephalogram (MEG) recordings evoked by the same stimulus to do the estimation and the same value of 80 was suggested in their work. In the past decades, the brain-to-skull conductivity ratio of 80 has been widely accepted and used in the EEG inverse and forward problems. Recently, Oostendorp et al. (2000) suggested a different brain-to-skull conductivity ratio from their in vitro and in vivo experiments. They measured the impedance of a piece of skull from a fresh corpse within a saline environment. By taking account of the skull thickness and transect area, they calculated the skull conductivity as 0.015G0.003/U m. For the in vivo measurement, currents were passed through the head by means of two scalp electrodes and the resultant scalp potential distribution was measured in two subjects with two different locations of electrodes for current injecting. Then the skull conductivity was estimated from the scalp potential measurements using a boundary element head model. Both methods revealed a brain-to-skull conductivity ratio as 15. Gonc¸alves et al. (2003a,b) used impedance imaging based methods to estimate the skull conductivity. When a spherical model was used, their results showed a wide variation of the brain-to-skull conductivity ratio sbr/ssk among the 6 subjects (average 72; SD 48%). But when the realistic geometry head model was used, the brain-toskull conductivity ratio approached to 20–50 rather than the commonly accepted value of 80, and the variation in sbr and ssk is decreased by half compared with the results using the spherical model. However, a factor of 2.4 still existed in sbr/ssk among different subjects being studied. In the present study, we estimate the effective brain-toskull conductivity ratio using simultaneous intra-cranial and extra-cranial electrical recordings during subdural stimulations. The effective brain-to-skull conductivity ratio was estimated by minimizing the difference between the recorded cortical potentials and computed cortical potentials. The experiments were conducted in 5 pediatric epilepsy patients.
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2. Methods In the present study, the cortical potentials and the scalp potentials were measured at multiple sites simultaneously with the electrical current injected and extracted through two subdural electrodes in pediatric patients undergoing neurosurgical evaluation. These recordings provided an efficient way to perform the in vivo effective conductivity estimation for the multi-shell head model with both extraand intra-cranial recordings. By solving the inverse problem using cortical imaging technique (He, 1998, 1999; He et al., 1996, 1999, 2001; Wang and He, 1998), the cortical potential distribution could be estimated from the scalp potential recordings with different assumed brain-to-skull conductivity ratios. Such estimated cortical potentials were then compared with the cortical potential recordings measured in the same subjects. The conductivity ratio which gave the most consistent cortical potential estimation (minimizing the difference between the measured and estimated cortical potentials) is then considered as the equivalent brain-to-skull conductivity ratio for the head volume conductor model being used. To evaluate the experimental design and test the accuracy of the procedures, computer simulations using the same experimental electrode configurations were performed. 2.1. Simulation methods and protocols In the present study, a 3-layer concentric spherical head model (Rush and Driscoll, 1968) was used to approximately represent the head volume conductor. The cortical imaging technique (CIT) procedure (He, 1998; He et al., 2001; Wang and He, 1998) was used to perform the inverse cortical potential estimation from the scalp potential recordings. In all simulations, the conductivities of the brain and the scalp were set to be equal to unity, so the following estimation of the skull conductivity should be considered as the effective brain-to-skull conductivity ratio. Fig. 1 illustrates the source-conductor model used in the present study. 1. For given initial skull conductivity SSK, the scalp potential (SP) and cortical potential (CP) measurements were simulated by forward calculation from a current dipole inside the brain with known position and moment (Perrin et al., 1987). Then Gaussian white noise (GWN) was added to simulate the noise-contaminated measurements in the human experimentation. The electrode position uncertainties were also simulated by adding GWN on the scalp and cortical electrode positions. 2. A dipole layer was assumed inside the brain to equivalently represent brain electrical sources (Kearfott et al., 1991; Wang and He, 1998) as assumed in step 1, and the lead fields Lscalp and Lcortex connecting the dipole parameters on the dipole layer to the scalp and cortical potentials were calculated, respectively, with assumed skull conductivity ssk;
3. The moment distribution of the dipole layer Pdl was computed by solving the inverse problem using Lscalp obtained in step 2 (Wang and He, 1998). Truncated SVD (TSVD) was used to suppress the noise effect. The noise ratio ranged from 0.05 to 0.2 depending on different noise levels and source configurations. Then the cortical potential estimation CPest was computed by the relationship CPestZLcortex$Pdl. Note that CPest is a nonlinear function of ssk. The optimized value of ssk which can give the most consistent CP estimation was automatically searched by maximizing the correlation coefficient (CC) between CPest and CP, where CC is defined as following CP K CP $ CPest K CPest (1) CC ¼ jjCP K CPjj$jjCPest K CPest jj where CP and CPest indicate the average of the recorded and estimated cortical potentials over electrodes. Then the similarity between the searched optimized values ssk and the initial value SSK generating SP and CP in step 1 was evaluated. In the simulation studies, the current dipole was located at the middle point between the two intra-cranial electrodes used for current injection and extraction. The dipoles were oriented tangentially to the sphere with varying eccentricity. The noise level was defined as the ratio between the standard deviation of GWN and the root mean square (RMS) of the scalp and cortical potential distribution. The placement of the surface electrodes was similar to the experimental settings. That is, 32 scalp electrodes were uniformly distributed on the upper hemisphere of the head, and a 6! 8 subdural electrode array was placed in rectangular array on the cortical surface with the same size and inter-electrode distance as those in the experiment study. To address the effects of the electrode position uncertainty on the performance of the present conductivity estimation, GWN of standard deviation of up to 1 cm in scalp electrode positions and up to 7.5 mm in cortical electrode positions were used in the simulation study. The inter-electrode distances between cortical electrodes were kept unchanged to simulate the actual subdural electrode array, so that there was only shifting of the subdural electrode pads in the simulation. At first, the scalp potential and cortical potential at the given electrodes were calculated using the analytic solution of the spherical model, then the potentials at the electrodes with GWN-contaminated positions were obtained by spline interpolation. Using these potentials as the simulated measurements we have evaluated the consistency of the result of the CP estimation and CP measurement so that the brain-to-skull conductivity ratio estimation can be obtained by minimizing the cost function. Another simulation was designed to address the effect of the skull thickness to the conductivity estimation. At first the scalp potential was calculated using the standard head model with the radii of 1, 0.92 and 0.87 (skull thickness
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0.05), respectively. Then both the CIT-estimated and analytical CPs were calculated based on a reduced-skullthickness head model. The brain-to-skull conductivity ratio sbr/ssk which gave the most consistent CP estimation was considered as the final estimation. This simulation is used to evaluate the results for the pediatric patients who may be noted for their thinner skull thickness. 2.2. Human experiment and data analysis Data was collected according to a protocol, approved by the Institutional Review Boards (IRBs) of the University of Minnesota and the University of Chicago, in the context of presurgical evaluation of pediatric patients with intractable epilepsy in the Pediatric Epilepsy Center at the University of Chicago Children’s Hospital. At first, the preoperative LTM (long term monitoring) EEG data was recorded to evaluate interictal spikes and seizure activity. In a subsequent session, electrodes were implanted subdurally for detailed monitoring of cortical activity. Subdural electrode arrays (sizes 1!8, 2!8, 6!8, or 8!8, Radionics, Randolph, MA, USA) were implanted by standard craniotomy over the cerebral convexities (frontal, parietal, occipital) or in the anterior- or subtemporal regions. Monitoring wires were tunneled subcutaneously in a radial fashion around the skin incision. At time of removal, electrodes were generally well seated against the brain with minimal, if any, subdural blood clot between electrodes and brain surface. Pathological examination of monitored tissue revealed some focal inflammation in the brain covered by the electrode arrays, but no significant alteration of the cortical architecture was observed. During 2 s epochs, sinusoidal electrical current provided by an electrically isolated biphasic stimulator (Grass S12, Astro-Med, Inc., West Warwick, RI) at a frequency of 50 Hz and amplitudes between 1 and 10 mA was delivered via a pair of intra-cranial electrodes. Both extra- and intra-cranial
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electrical potential signals were recorded simultaneously during cortical current stimulation using BMSI6000 (Nicolet Biomedical, Madison, WI). The data were measured at a bandwidth of 1–100 Hz and sampled at a rate of 400 Hz. The scalp electrode positions were measured with a 3D digitizer (Polhemus, Colchester, VT). Intra-cranial electrode positions were determined by co-registering the postoperative X-ray image (Fig. 2(a), with implanted subdural electrodes) with the preoperative anatomical MRI, which had been done using Curry software (Neuroscan Labs, TX). The experimental scalp and cortical potential recordings were then analyzed to perform the brain-to-skull conductivity ratio estimation for each subject. As described above, the measurements were responses for the subdural sinusoidal current stimulations. To suppress noise, the signals were filtered with cut-off frequencies of 10 and 70 Hz. For the cases studied, the frequency of the injecting current was 50 Hz and the EEG sampling rate was 400 Hz, so there would be 8 measurements in one cycle during stimulation (0.02 s). The total duration of the stimulation was 2 s, so there would be 800 potential measurements for each stimulation at every single scalp and cortical electrode, and these measurements are in 100 cycles. To further improve the signal to noise ratio (SNR), the responses were averaged over the 100 cycles so finally we had 8 averaged SP and CP recordings in one cycle, which were used to perform the CP estimation and comparison using the CIT algorithm. For each of the 8 averaged simultaneous SP and CP measurements, the CP was estimated from the SP, and the optimized value which gave the most consistent estimation with the recorded CP distribution was considered as the effective brain-to-skull conductivity ratio. The similar estimation was performed for each of the 8 measurements per cycle. The average of these 8 estimates and the estimates at the highest SNR were assessed for the brain-to-skull conductivity ratio estimation.
Fig. 2. Left: postoperative patient’s X-ray image with intra-cranial electrodes indicated by light gray dots on the cortical surface. Right: resection picture showing the subdural electrodes implanted through craniotomy.
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3. Results 3.1. Computer simulation Several parameters play important roles in the inverse cortical potential estimation and conductivity estimation. These parameters include the configuration of scalp and cortical electrodes, the eccentricity of the dipole layer and the eccentricity of dipole (Wang and He, 1998). The placement of the electrodes used in the simulation study was similar to that used in the human experiments. Before the conductivity ratio estimation, the eccentricity of the dipole layer was determined to obtain optimal CC between the CP measurement and estimation (Wang and He, 1998). In all simulations, the radii of the brain, the skull and the scalp were set to 0.87, 0.92 and 1.00, respectively. The Simplex algorithm (He et al., 1987; Lagarias et al., 1998; Nelder and Mead, 1965) was used to search for the optimal brain-to-skull conductivity ratio that provided the most consistent CP estimation from the scalp potential distribution, with different initial brain-to-skull conductivity ratios. Three initial brain-to-skull conductivity ratios SBR/ SSK (15,40,80) were selected to test if the procedure is independent of the initial values. Fig. 3 indicates that all extrema were obtained at the values close to the initial
brain-to-skull conductivity ratio SBR/SSK. Fig. 3 also suggests that high spatial sampling of the scalp EEG gives better performance and the procedure can accurately retrieve the brain-to-skull conductivity ratio when 128 electrodes were used (upper panels). When fewer electrodes, such as 32 electrodes in a clinical setting, were used, the brain-to-skull conductivity ratio was also retrieved but slightly shifted from the actual conductivity values being used in the simulation (Fig. 3; lower panels). Note that such shift was observed always in one direction—that is, the estimated brain-to-skull conductivity ratios were slightly higher than the initially set conductivity values. The sbr/ssk estimates were 18 for initial value 15, 44 for 40 and 87 for 80. Other initial values were also tested and similar results obtained. These simulation results suggest that the present conductivity estimation procedure is independent of the initial value of the skull conductivity SSK. Table 1 shows the estimates for 6 different initial SSK with 20% GWN being added to the SP (32 electrodes) and 10% GWN to the CP (6!8 electrodes). The truncated SVD algorithm was used in the regularization procedure to suppress the noise effect. The averaged estimation error for the brain-to-skull conductivity ratio is less than 10%, suggesting the robustness of the estimation procedure regardless of the initial values of conductivity ratio used
Fig. 3. Object function RE (relative error) and CC (correlation coefficient) obtained in the computer simulation. Upper left: RE for the cortical potential (CP) measurement and estimation using 128 scalp electrodes. Upper right: CC for the CP measurement and estimation using 128 scalp electrodes. Lower left: RE for the CP measurement and estimation using 32 scalp electrodes. Lower right: CC for the CP measurement and estimation using 32 scalp electrodes. Dotted, initial value SBR/SSK 15; dashed, initial value SBR/SSK 40; solid, initial value SBR/SSK 80.
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Table 1 sbr/ssk estimation for different initial values SBR/SSK with occurrence of potential noise (PN) and electrode-position noise (EN) Initial brain-to-skull conductivity ratio SBR/SSK sbr/ssk (PN) %ERR (PN) sbr/ssk (EN) %ERR (EN)
10
20
40
60
80
100
11.15 11.50 10.86 8.60
22.08 10.40 21.23 6.15
43.86 9.65 43.82 9.55
65.36 8.93 65.11 8.52
87.72 9.65 86.49 8.11
107.53 7.53 107.43 7.43
%ERR refers to the relative error between sbr/ssk and SBR/SSK. 20% SP and 10% CP white Gaussian noise (WGN), 7.5 mm scalp and 5 mm cortical electrode position noise were used in this simulation. 32 scalp electrodes were uniformly distributed over the upper hemisphere of the head model. The cortical electrodes were in 6!8 rectangular arrays with 5 mm inter-distance.
in the simulation study. Also note that the estimates of the brain-to-skull conductivity ratios sbr/ssk were always slightly higher than the initial values SBR/SSK, which may be caused by the insufficient spatial sampling of the SP. The effect of the electrode position noise to the conductivity estimation is also shown in Table 1. In this table, GWN of SD of 7.5 mm was added to scalp electrode positions and GWN of SD of 5 mm was added to cortical electrode positions. In all simulations with different initial brain-to-skull conductivity ratios, the CP estimation showed high consistency with the simulated CP measurements with all CC being greater than 98%. The conductivity estimation showed less than 10% error for various conductivity ratios with electrode position noise added to the scalp and cortical electrodes. Other noise levels (up to 1 cm scalp electrode position noise and up to 7.5 mm cortical electrode position noise) were also tested and similar results obtained, which suggests that the present conductivity estimation approach is robust to the electrode position noise. The effect of the skull thickness on the conductivity estimation is shown in Table 2. Two initial brain-to-skull conductivity ratios SBR/SSK 25 and 80 were selected. The reduced skull thickness was 0.045, 0.04, 0.035 and 0.03, respectively, which are corresponding to 10–40% decrease to the original value of 0.05 used to obtain the scalp potential. It is clearly shown that the decrease in the skull thickness causes decrease in the estimated skull conductivity. 3.2. Human experiments As described in the Section 2, during each stimulation, 8 averaged signals were used to get 8 conductivity estimates. The average of these 8 estimates is considered to represent the effective brain-to-skull conductivity ratio. Results for subject #1 are listed in Table 3 with stimulations at 4 different locations (frontal and parietal lobes). For each of these locations, there are 3–4 different current intensities (6–9 mA). The averaged sbr/ssk for subject #1 is 23. Assuming the noise is additive, the 8 averaged signals are supposed to have different signal-to-noise ratio (SNR). The signals with the largest amplitude are supposed to have the largest SNR. In Table 4, the results obtained from the signals with the largest SNR are listed. It can be clearly
seen that the averages for current intensity (23.21 for 6 mA, 22.94 for 7 mA, 22.89 for 8 mA and 22.78 for 9 mA) are quite close, but the averages for current location (22.99 for FG25–26, 24.04 for FG15–16, 23.59 for FG19–20, 21.51 for PG 47–48) have relatively larger variations. This suggests that the effective brain-to-skull conductivity ratio is more sensitive to the current location than the current intensity. The similar processing was performed to the other 4 subjects’ experimental data and the results are summarized in Table 5. All 5 subjects were pediatric epilepsy patients aging from 8 to 12. It can be observed from this table that when more scalp electrodes were used in the experiment, normally the variation (evaluated by STD) of the estimations decreased. This in another way explains that the higher spatial sampling rate gives better performance by the present method. The estimates from the signals with the largest SNR are close to the overall averaged values in most subjects, which are more trustworthy when large difference exists between them. Table 2 sbr/ssk estimation using different skull thickness SBR/SSK
Skull thickness 0.045
0.04
0.035
0.03
25 80
25.91 83.87
27.30 86.41
29.79 91.51
31.46 97.96
Two different initial values SBR/SSK 25 and 80 were used. The scalp potentials were simulated using the head model with skull thickness 0.05. Table 3 sbr/ssk estimation with mean value and standard deviation from the averaged scalp and cortical potential recordings for patient #1 (12 years old, male) Current intensity (mA) 6 7 8 9
Current location
FG25–26
FG15–16
FG19–20
PG47–48
23.01G1.24 22.38G1.41 22.17G0.94 23.59G1.32
22.05G1.35 24.25G1.69 22.16G1.93 N/A
23.18G1.53 22.75G2.33 22.61G1.60 24.12G1.35
22.83G1.81 22.68G1.90 23.21G2.26 21.89G1.50
Currents were injected and extracted through 4 pairs of subdural electrodes with different current intensity. N/A means not available, FG frontal grid, PG parietal grid. Thirty-two scalp electrodes were used to record the scalp EEG.
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Table 4 sbr/ssk estimation using the averaged scalp and cortical potential recordings with the largest SNR for patient #1 Current intensity (mA) 6 7 8 9 Average
Current location
Average
FG25–26
FG15–16
FG19–20
PG47–48
22.88 23.47 22.17 23.46 22.99
23.99 24.14 23.98 N/A 24.04
24.21 23.51 22.63 24.02 23.59
21.75 20.64 22.78 20.85 21.51
23.21 22.94 22.89 22.78
Fig. 4. Summary of sbr/ssk estimations obtained from experimental data analysis for all 5 patients. The 3 bars from left to right represent results from EEGs with the largest SNR, the mean values and standard deviations, respectively. The inter-subject mean value of sbr/ssk is 24.8, with standard deviation of 6.6.
Averages were taken on both current location and current intensity.
The 3 bars in each group in Fig. 4 refer to the estimates from signals with the largest SNR, averaged estimates and standard deviations of the estimates among various current intensities and locations in each subject. For each subject, consistent results within a reasonable range were obtained for different current injecting/extracting locations, for different current intensities at the same locations, and for potential measurements at different time point from the same current configurations. The averaged sbr/ssk were 23, 29, 34, 20, 18 for the 5 patients, respectively. The intersubject average and standard deviation are 24.8 and 6.6, respectively.
4. Discussion The present study represents, to our knowledge, the first effort to estimate the effective in vivo human brain-to-skull conductivity ratio in a 3-shell head volume conductor, by using the multi-channel simultaneous intra- and extracranial electrical potential recordings. This approach offers unique features in estimating the effective brain-to-skull conductivity ratio. First, both the intra-cranial (cortex) and the extra-cranial (scalp) potential fields generated by subdural current stimulation were simultaneously measured. Such simultaneous measurements of electrical potentials over multiple sites within and outside of the skull enable stable estimation of the effective conductivity of the skull layer between the measurement surfaces, with reference to the conductivity of the brain tissue/scalp. Second, the cortical imaging algorithm offers an efficient Table 5 Summary of the 5 patients’ gender and age, number of scalp electrodes, overall averaged sbr/ssk estimations, standard deviations and mean sbr/ssk estimations by the EEGs with the highest SNR Patient
Gender
Age
# Scalp ele
Mean
STD
Mean (SNRmax)
1 2 3 4 5
M M F M M
12 12 8 10 8
32 20 28 36 38
22.9 29.5 34.3 19.6 18.4
1.61 3.43 2.82 2.16 1.93
23.0 27.2 34.7 17.8 18.6
way to do the inverse cortical potential estimation. The present results show the feasibility of applying the CIT algorithm to conductivity estimation. While the size of the patient group is limited, the consistent results obtained from the 5 subjects suggest that the human brain-to-skull conductivity ratio is about 25G7 instead of the widely used value 80 (Cohen and Cuffin, 1983; Rush and Driscoll, 1968) and somehow larger than the value of 15 as reported by Oostendorp et al. (2000). To build the spherical head model, the radii of the multi-spheres must be specified. The scalp electrode positions have been measured with a 3D digitizer (Polhemus, Colchester, VT), which were used to estimate the center and radius of the outermost sphere by a best-fit method. Then these real positions were transformed into the spherical coordinates. The radii of the other two spheres were specified according to a 1:0.92:0.87 scale. This scale may not be accurate for different individuals especially for children who are noted with thinner skull, and it is expected that the over estimation of the skull thickness could be compensated by a higher conductivity estimation. To evaluate the effect of skull thickness on the conductivity estimation, simulation studies have been performed. As noted in Table 2, the 20% decrease in skull thickness causes 5–10% conductivity decrease, while 40% thickness decrease causes 20–25% conductivity decrease. It is worthy of noting that, despite the flat shape of the CC function (Fig. 3), all the estimates obtained from different time point, different current intensities and different stimulation locations are within a reasonable range, suggesting that the results are reliable. To avoid the bias generated by the Simplex algorithm to search the optimum conductivity value, we used instead the function f ðsbr =ssk Þ ^ Z10ð1=ccðs br =ssk ÞÞ in the cases with flat CC to make the shape of the object function sharper. Fig. 3 illustrates that when Relative Error (RE) instead of CC is used, the distribution of the error measure becomes more distinguishable than CC. It would also be interesting to explore that how the conductivity estimation would be changed had the CSF been taken into consideration in the head model. To answer this question, we have implemented a forward
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model based on a 4-layer spherical head model (de Munck, 1988; Zhou and van Oosterom, 1992), from which the analytical solution can be used to obtain the dipoleinduced scalp potential and cortical potential. We have conducted a simulation study to evaluate the effect of the CSF on the skull conductivity estimation, where the scalp potential was generated using the 4-sphere head model (radii 1, 0.92, 0.87, 0.84, conductivities 1, 1/25, 3, 1) including CSF but the conductivity estimation was based on the 3-sphere head model (radii 1, 0.92, 0.87, conductivities 1, 1/X, 1, where X is the brain-to-skull conductivity ratio to be determined) without CSF. A higher conductivity value of 1/22.6 than the initial value of 1/25 was obtained in this case, which is reasonable because the increase in the skull conductivity estimation compensate the missing high-conductivity CSF layer in the 3-sphere model. The similar findings have also been obtained in the experimental data analysis. The estimated conductivities are 1/18.4 and 1/22.9 for two patients using the 3-sphere head model. By taking the CSF into consideration, they become 1/19.8 and 1/25.1, respectively. From the above results, the changes in the conductivity estimation are about 10% in both computer simulation and real data analysis. These initial computer simulation and experimental results do not seem to indicate that the change in the head model (4-sphere instead of 3-sphere) would induce significant change in the skull conductivity estimation. However, further investigation is needed to fully address this issue. The plastic pad on which the subdural grids were placed may have certain effect on the estimation results of the effective brain-to-skull conductivity ratio. Since placement of such plastic subdural electrode pad would make it harder for currents to flow out of the skull, the estimated effective brain-to-skull conductivity ratio maybe higher than the actual value. It is noteworthy that the currents injected and extracted through two adjacent subdural electrodes were in principle tangential to the sphere, it is anticipated that a significant portion of the currents may be able to bypass the plastic pad, thus having less effect on the conductivity estimation as compared with radial current dipoles. From Fig. 4, inter-subject variations in estimated brainto-skull conductivity ratios can be obviously observed, as suggested by other studies (Gonc¸alves et al., 2003a,b). In addition, for each subject, we can also observe that there are also intra-subject variations from different experimental settings (injecting/extracting location and current intensity). These variations may be explained as follows. First, the anisotropic properties of the human skull (the tangential and radial skull conductivity may differ with each other by a factor of 10, Marin et al., 1998) may contribute to the variation in conductivity estimation (van den Broek et al., 1998). When the current is injected and extracted at different locations, it may cause different impedance distribution inside the skull so that the estimation for the effective brain-to-skull conductivity ratio may be different
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when being estimated using an isotropic skull model. Second, the skull inhomogeneities (Ollikainen et al., 1999) may also introduce variations in the conductivity estimation when the piecewise homogeneous head model is used in the present study. For inhomogeneous models, different ways (Gencer and Acar, 2004; Nunez, 1987) were suggested to estimate the local conductivities and to image the conductivity distribution. Third, we have limited scalp spatial sampling (less than 40 channels). This may impair the accuracy of the inverse cortical potential estimation and so the shape of the object function (CC between the measurement and estimation) could be changed. Finally, the spherical head model would lead to the loss of some geometry details of the volume conductor (Menninghaus et al., 1994). This may also introduce deviation of the lead fields corresponding to different stimulation sites, so the change in object function for conductivity estimation. In the study by Gonc¸alves et al. (2003a,b), the conductivity estimation variations were reduced by half when a realistic geometric head model was employed. However, Table 3 suggests that such variation is not substantial in the present study, as compared with inter-subject variation and the variation from other values reported in the literature (Oostendorp et al., 2000; Rush and Driscoll, 1968). Note that the aim of the present study is to investigate the conductivity values of the head volume conductor from invasive measurements. The present results are thus aimed at providing a reference for the reasonable brain-to-skull conductivity ratio for accurate brain source localization using piece-wise homogeneous head models. It is not intended to suggest that invasive recordings are needed for brain source localization. Also note that the present results on the estimation of brain-to-skull-conductivity ratio should only be used for the 3-shell head models. As the piecewise homogeneous head models are limited in providing approximation to the head volume conductor, the estimation of the brain-to-skull-conductivity ratio is also limited that it can be used when such models are valid for the problem of interest. Because of the limited size of the surveyed subjects, it is hard to make a strong generalization from the results currently available. Nonetheless, the clear trend as observed from all 5 subjects studied suggests that the effective brain-to-skull conductivity ratio is higher than the classic value of 80, rather being closer, although slightly higher, than that reported by Oostendorp et al. (2000). Note that all subjects studied in the present study are pediatric epilepsy patients aging from 8 to 12. Their skull tissue normally contains a larger amount of ions and water and so may have a higher conductivity than the adults’ calcified cranial bones (Peyman et al., 2001; Scho¨nborn et al., 1998). For adult subjects, the brain-to-skull conductivity ratio maybe higher than 25 as obtained in the pediatric patients. While it remains an open question to determine the effective brain-to-skull conductivity ratio in adult population, the present study provides, for the first time,
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estimation of the in vivo effective brain-to-skull conductivity ratio in human subjects from simultaneous intra- and extra-cranial electrical potential recordings. The present results support the previous findings that a lower value of the effective brain-to-skull conductivity ratio should be used as compared with the classic value of 80. Future investigations should address a wider spectrum of subject age in a larger subject population, and use of realistic geometry head conductor models.
Acknowledgements The authors wish to thank Xin Zhang for useful discussions, Ying Ni for assistance in data preparation, and Yingchun Zhang for assistance in the implementation of computer codes for the 4-spheres model. This work was supported in part by NIH R01EB00178, NSF BES-0218736, NSF BES-0411898, and NSF CAREER Award BES9875344.
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