Measurement of the Conductivity of Skull, Temporarily Removed During Epilepsy Surgery

Transcription

1 Brain Topography, Volume 16, Number 1, Fall 2003 ( 2003) 29 Measurement of the Conductivity of Skull, Temporarily Removed During Epilepsy Surgery R. Hoekema*, G.H. Wieneke*, F.S.S. Leijten*, C.W.M. van Veelen +, P.C. van Rijen +, G.J.M. Huiskamp*, J. Ansems^, and A.C. van Huffelen* Summary: The conductivity of the human skull plays an important role in source localization of brain activity, because it is low as compared to other tissues in the head. The value usually taken for the conductivity of skull is questionable. In a carefully chosen procedure, in which sterility, a stable temperature, and relative humidity were guaranteed, we measured the (lumped, homogeneous) conductivity of the skull in five patients undergoing epilepsy surgery, using an extended four-point method. Twenty-eight current configurations were used, in each of which the potential due to an applied current was measured. A finite difference model, incorporating the geometry of the skull and the electrode locations, derived from CT data, was used to mimic the measurements. The conductivity values found were ranging from 32 ms/m to 80 ms/m, which is much higher than the values reported in other studies. Causes for these higher conductivity values are discussed. Key words: Skull conductivity; In vivo measurement; Finite difference method; Source localisation. Introduction In equivalent source localization of electrical brain activity, the location and strength of an electric source that generates electrical or magnetic activity on or near the surface of the head are determined. For correct localization, as well as for other approaches to the inverse problem of electroencephalography, such as epicortical potential imaging, a proper volume conductor model and an appropriate model of the source are required. The volume conductor model is based on the geometry of the head and of its conductivity. Geometrical data can be derived from magnetic resonance images or from a simple geometrical model, such as a spherical model, of the head. Finally, the conductivity has to be known. * Dept. of Clinical Neurophysiology, University Medical Center Utrecht, The Netherlands. + Dept. of Neurosurgery, University Medical Center Utrecht, The Netherlands. ^ Instrumental service, University Medical Center Utrecht, The Netherlands. Accepted for publication: June 27, This research was supported by grant # of the Netherlands Organization for Scientific Research NWO. The work done by the Instrumental Service of the University Medical Center Utrecht to develop the measurement set-up and of Dr. J.E.C. Sykes for proofreading the manuscript is gratefully acknowledged. Correspondence and reprint requests should be addressed to Dr. R. Hoekema, Dept. Clinical Neurophysiology, University Medical Center Utrecht, PO box 85500, 3508 GA Utrecht, The Netherlands. r.hoekema@cardio.umcn.nl Copyright 2003 Human Sciences Press, Inc. Because the conductivity of the skull is low compared to that of other tissues, only a fraction of the electric activity of the brain passes through the skull and appears distributed over the head surface as the EEG. Thus, EEG is greatly affected by the conductivity of the skull and, conversely, source localization is highly dependent on the assumed value of this conductivity. Simulation studies have shown that the depth of a source determined while assuming an incorrect skull conductivity may differ from its actual position by up to two centimeters (Huiskamp et al. 1999). Currently available data on bone conductivity are mostly derived from animal material or from post-mortem human material. For example, studies of the rat femoral bone (Kosterich et al. 1984) show that the conductivity of bone is largely dependent on the conductivity of the fluid content of bone. The conductivity of the human skull has been measured using post-mortem skulls (Saha and Williams 1992; Oostendorp 2000) that had been allowed to dry (Saha and Williams 1992) or had been kept in a freezer (Oostendorp 2000). However, the validity of these measurements may be questioned because exposure to air, even for a few minutes, may cause drying out and hence decrease the conductivity of bone (Saha et al. 1984) Skull conductivity has been measured indirectly by using electrical impedance tomography (EIT) techniques (Oostendorp 2000), where a current was applied to the intact head of a living person and the resulting potentials were measured at 32 positions on the head. Skull conduc-

2 30 Hoekema et al. Table I. Specific conductivity of bone reported in the literature. All conductivities/resistivities are converted to (ms/m). Substance Conductivity (ms/m) Freq. (Hz) Temp. Ref. Human skull (soaked in saline) n.a. Akhtari et al. (2000) Human skull (compact) (soaked) n.a. Law (1993) Human skull (live) n.a. Akhtari et al. (2000) Human skull (in vivo) Oostendorp et al. (2000) Human skull (in vitro) e5 37 Oostendorp et al. (2000) Human skull (dry, then soaked) n.a. Law (1993) tivity was then calculated from volume conduction computations, where the ratio between the conductivity of the skull and the conductivity of the rest of the head was estimated. For these computations, assumptions about the geometry of the head must be made, which decrease the accuracy of the computed skull conductivity. Recently, new information on the conductivity of the skull has been published, where the conductivity of each of the three layers of the skull was determined separately (Akhtari et al. 2000, 2002) on post-mortem material as well as on small pieces of freshly obtained material from the operation theater. The reported values of the specific conductivity of skull are summarized in table I. The frequency dependence was reported to be minimal in the Hz range. During epilepsy surgery, part of the skull is removed and laid aside for a number of hours. At the end of the operation, this skull piece is put back. This piece of skull can be used to measure the skull conductivity of individual patients, avoiding all the drawbacks of measurements described in the literature. The skull piece is fresh and thus still filled with its natural content and is at body temperature. The (anisotropic) conductivity of the skull piece can be measured without needing to take the conductivity of surrounding tissues into account, as is the case in the electrical impedance tomography (EIT)-based methods. We measured the conductivity of such skull specimens under strictly sterile conditions with 32 electrodes, applied to both surfaces of the skull piece. A pair of electrodes served as a current source and the other electrodes were used to measure the potential. Measurements were done in an infant incubator, at 37 C and under a high relative humidity. Methods Material Measurements were performed on an agar-agar phantom, a post-mortem skull piece (female, age 68), and the temporal part of the skull of five epilepsy patients operated on for mesiotemporal lobe epilepsy. All patients gave their informed consent. The study was approved by the Medical Ethics Committee of the University of Utrecht. Care was taken not to delay the operation. Measurement Set-up The measurement set-up consisted of two electrode holders with 16 electrodes each. Each electrode consisted of a stainless steel bar 10 cm long and 0.4 cm in diameter, with a spherical tip on one side and an electrical connector on the other side. The electrode was surrounded by a Teflon layer for insulation. The electrodes were placed vertically in the holders, in a 4 4 array with an inter electrode distance of 1 cm. The position of these electrodes was fixed horizontally, but the electrodes could be moved vertically. A spring was attached to each electrode, forcing it to move in the direction of the electrode tip. It was possible to fix the electrodes in vertical direction as well. One electrode holder was placed in the set-up with the electrode tips facing upward, the other with the tips facing downward. The latter holder could be moved as a whole in a vertical direction, to let the electrodes make contact with the sample (see figure 1). Before measurements, the set-up was steam sterilized. Measurement Measurements using patient material took place during epilepsy surgery of five patients suffering from temporal lobe epilepsy. The apparatus was placed in an infant incubator, set at 37 C and a relative humidity of 95% at least one hour before measurements were taken. The infant incubator was used to prevent the skull piece from cooling and drying. It was placed in the operating theater. Immediately after removal of the skull piece, it was placed in the incubator. The skull piece was placed on the bottom holder with the electrodes facing upward. The upper holder was lowered until all electrodes made firm contact with the sample and was then fixed.

3 Skull Conductivity Measurements 31 Figure 1. Measurement set-up. A series of measurements was taken, in each of which two electrodes served as current electrodes, two electrodes were used as reference and ground electrodes respectively, and all other electrodes were used to measure the potential distribution over the sample. Thus, an extended four-point measurement was made. A 10-Hz current was used, generated by a battery-powered function generator. The amplitude of the current was determined from the potential drop over a 1kΩ series resistance in the current loop. Twenty-eight symmetrical current electrode pairs, with an inter-electrode distance of 3 cm or more, were used sequentially. After the measurement, the electrodes were fixed in their vertical position, thus preserving the skull profile. With a skin marker, the locations where five of the sixteen top electrodes touched the sample were marked. The top holder was lifted and the skull piece was removed from the measurement set-up. At the position of the marks, the neurosurgeon made shallow burr holes (diameter 4 mm, depth 2 mm) to allow identification of the measurement sites using post-operative CT imaging. The skull piece was then placed in a bath containing saline and antibiotics and subsequently replaced in the patient at the end of surgery, as usual. Geometrical Data A low-dose CT scan of the patient s head was made a few days after surgery. The protocol used was a 3/3/1 spiral CT (slice thickness 3 mm, skew 3 mm, reconstruction pixel size 1 mm). A gantry tilt of about 11 was used in order to prevent the eye lenses from being imaged. The mas value was 25 (25 ma, 1 sec rotation). From this CT, the geometry of the skull piece was reconstructed, using the Curry software package (version 3.0, Neuroscan) and dedicated 3-D visualization software (Viergever et al. 2001). The burr holes were identified by inspection of the volume renderings obtained with these software packages. The same procedure was followed for the post-mortem skull piece.

4 32 Hoekema et al. Data Post Processing For each current electrode pair, a 10-second measurement epoch was selected in which the amount of noise and artifacts was minimal. The amplitude of the recorded potentials in the 9-11 Hz frequency band was determined using a Fast Fourier Transform and the phase of each signal (0 or 180 ) was determined by visual inspection. If the signal from a certain electrode was very noisy or if the signal was clipped by the amplifier, this signal was omitted in the subsequent analysis. The current, ground, and reference electrodes were also omitted in the subsequent analysis. Model The next step in determining the conductivity of the skull piece was to build a volume conductor model of the skull piece and attached electrodes. Using the model and a given set of conductivity values, the potential distribution due to the applied current could be calculated for the entire skull piece, thus mimicking the electrical measurement. A finite difference approach was chosen, which allows construction of the model directly from the CT data. A multigrid solver was used to efficiently solve the potential distribution due to the applied current (Hoekema et al. (1998), Brandt (1984), Alcouffe et al. (1981)). Finite Difference Model Finite difference models were constructed, containing typically rectangular cells. A skull piece was modeled by assigning a conductivity to groups of cells. The cells surrounding the skull piece had a conductivity which was 10 5 times lower than that of the skull piece, in order to prevent any current from leaking out of the skull piece. The border of the model was set at 0V (Dirichlet boundary condition) and the electrodes were modeled as point electrodes bordering a group of eight cells. The potential distribution in this model, due to an applied current through two of the electrodes, was computed by solving Poisson s equation: σ u=f,withδu=0 where u represents the potential distribution, f is the source term, and σ represents the conductivity value. δu represents the boundary value of u, which is 0V. This equation can be discretized using Taylor series expansion and is set up for each vertex of the finite difference model. The result is an equation for each vertex, containing the potential on that vertex, the potential on the neighboring vertices, the conductivity value in each orthogonal direction, the cell size, and the source term for that vertex (non-zero only at the current electrode vertices). Thus a set of many equations is made with as many unknowns. In the case at hand, there were cells, which equals to equations and unknowns. Because of its size, this set of equations cannot be solved analytically, and therefore, an iterative procedure was used, in this case Gauss Seidel line relaxation in combination with a multigrid method. In this multigrid method, several discretizations of the volume conductor are used. Conductivity Value The potential distribution in the finite difference model, caused by the current injected in the skull piece, was computed for each current electrode pair and for a certain value of the conductivity of the skull piece. Thus, the complete measurement was mimicked for that conductivity value. By tuning the conductivity values in the model in such a way that the computed potential distribution matched the measured potentials, the conductivity of the skull sample was estimated. In case of a homogeneous skull piece, the potential is linearly dependent on the conductivity value, so tuning is just a matter of scaling. A two-step approach was followed: first, the conductivity was tuned such that the computed and measured potentials were of the same order of magnitude. Second, a scatter plot was made between the computed and measured potentials. The slope of a first order trend line through all data points was used to fine-tune the conductivity value. The match was performed for all 28 current combinations and the mean conductivity and its standard deviation were determined for each subject. Results The first phantom, a disk shaped agar agar jelly, was measured by using the described set up and by using a straightforward four point method where four stainless steel rods were inserted at 8 mm intervals in the agar-agar jelly. Both methods yielded almost the same conductivity, 40 ms/m and 44 ms/m. Figure 2 shows, for one pair of current injecting electrodes, the measured and computed potential distribution in the top and bottom set of 16 electrodes. The measured and the simulated amplitudes for a conductivity of 40 ms/m are shown. The geometrical model used in the simulations was derived from a simple measurement of the thickness, diameter, and electrode locations on the agar-agar jelly. Figure 3 shows a volume rendering of the CT data of one of the five patients. The skull piece used in the measurements is clearly visible, as well as the shallow burr holes that were made to indicate the location of five of the electrodes. In figure 4 the volume conductor as deter-

5 Skull Conductivity Measurements 33 Figure 2. Results for agar-agar phantom. In the top four plots, the measured and simulated amplitudes for each potential electrode are shown, where zero potential is white, positive and negative potentials are darker for larger values. Upper left panel: measured potentials in top electrodes; upper right panel: computed potentials in top electrodes; lower left panel: measured potentials in bottom electrodes; lower right panel: computed potentials in bottom electrodes. Numbers indicate electrode rows and columns (1 cm apart). In the bottom plot, the measured potentials are shown as a function of the computed potentials, as well as a trend line through the data points.

6 34 Hoekema et al. Figure 3. Rendering of CT data of patient #3 showing the left side of the skull. The skull piece used in the conductivity measurements is visible, as well as the shallow holes indicating the location of the electrodes on the skull piece. In the middle of the skull piece, two other holes are visible, that were used to fix the dura on the skull. mined from the CT data is shown in three cross sections. The electrode locations and the isopotential lines, indicating the potential distribution due to the current electrode combination in one of the measurements, are also shown. The difference in the position of the actual electrodes and those used in the finite difference model was on average 0.5 ± 0.5 mm, which is small compared to the inter-electrode distance. Potential measurements and simulations for one pair of current injecting electrodes for the post mortem skull and patient #1 are shown in figures 5 and 6. The conductivity of this skull piece was estimated as 21 ms/m and the conductivity of the skull piece of patient #1 was estimated as 80 ms/m. Note that, although the same current electrode pair was used, the potential distributions for the skull piece and patient #1 are clearly different. The conductivity of each of these skull pieces and the age of the patients is given in table II. Conductivity seemed to be associated with patient age. Discussion In a carefully chosen procedure, in which sterility, a stable temperature, and relative humidity were guaranteed, we measured the (lumped, homogeneous) conductivity of the skull in five patients undergoing epilepsy surgery, using an extended four-point method. Twenty-eight current configurations were used, in each Figure 4. Volume conductor model of skull piece (gray) and electrode locations (black dots). A cross-section in three different directions is shown. The thin lines indicate isopotential lines of the potential distribution computed for one of the current electrode pairs. of which the potential due to an applied current was measured. A finite difference model, incorporating the geometry of the skull and the electrode locations, derived from CT data, was used to mimic the measurements. The results for the agar-agar phantom show that our approach, using a finite difference model with realistic geometry, yields a conductivity identical to the one obtained using the four-point method. Moreover, the potential profile, as simulated in the model, was almost identical to that measured in both the agar-agar phantom and the skull measurements (see figure 2, 5 and 6). This indicates that the physical modeling was accurate, for both simple and complex objects. The conductivity of the post mortem skull piece (21 ms/m) was much higher than that (13 ms/m) reported earlier (Oostendorp 2000). The discrepancy between the two values may be attributed to differences in the immersion fluid. In our experiments the skull was soaked in saline and formalin, whereas in the literature, the sample was soaked in saline only. Indeed, it was the realization that measurement of in vitro post mortem skull will not lead to accurate conductivity measurements, because the skull is not in its natural state, that led us to the semi in vivo approach of measuring on a skull piece temporarily removed during epilepsy surgery.

7 Skull Conductivity Measurements 35 Figure 5. Results for post mortem skull piece. For legend see figure 2.

8 36 Hoekema et al. Figure 6. Results for patient #1. For legend see figure 2.

9 Skull Conductivity Measurements 37 Table II. Conductivity of the skull pieces and phantoms Measurement Age σ (ms/m) Sd (ms/m) Agar-agar phantom Post mortem skull Patient Patient Patient Patient Patient The conductivity of the ex vivo skull pieces was about 10 times higher than values reported in the literature (table I). In this very small patient group, conductivity was higher in younger patients than in older patients. Like others (Oostendorp 2000; Akhtari et al. 2000; Akhtari et al. 2002), we found a skull conductivity value that was higher than the value commonly used in source localization of brain activity. This result was expected, since the standard value was measured in non-physiological circumstances: Rush and Driscoll (1968, 1969) derived the ratio between scalp, skull, and brain conductivity of 1:1/80:1 using a cadaver half skull, submerged in a conducting fluid of unknown electrical properties. The conductivity value reported by Law (1993) was derived from a dry cadaver skull that was soaked with saline. Although this study is valuable because of its adequate description of the geometry of the skull, the reported conductivity may be different from the conductivity of alive skull. Akhtari et al. (2000) recently determined the conductivity of the three different layers of a human cadaver calvarium and of pieces of skull obtained from patients undergoing epilepsy surgery, as in the present study (Akhtari et al. 2002) The bulk conductivity of the skull samples ex vivo was higher than the standard value used in literature whereas that of the cadaver skull was in the order of the standard value. However, the skull pieces in their study had undergone several manipulations before the measurements were taken. For example, exposure to air may have dramatically changed the conductivity of the bone samples (Saha et al. 1984). Furthermore, Akthari and co-authors did not mention whether they preserved (body) temperature and humidity during the measurements, which we consider a prerequisite for successful measurement of skull conductivity. Given the high conductivity found in this study, one might be tempted to attribute the results to an artifact. One such artifact could be that saline, which is applied during the opening of the skull for cooling purposes, may have left a thin conductive layer on the skull piece. This layer could have provided a shunting effect when the measurements were taken. In the homogeneous geometrically realistic model, however, the measured and simulated potential patterns were similar. This suggests that if this layer existed, it was present all over the piece and with a uniform thickness. This was confirmed by additional measurements on the post-mortem skull piece. The effect of such a layer should be studied under more controlled conditions. In any application of equivalent source localization, the ratios of the tissue conductivities are more important than the single values of the conductivities. From our results, one might be tempted to conclude that the conductivity ratio that Rush and Dricoll derived should be 1:1/8:1 rather that 1:1/80:1. This however doesn t fit with other studies on equivalent source localization (Oostendorp 2000), where a ratio of 1:1/20:1 seems to be the upper limit. Since the value of "average brain conductivity", which involves an average over several disparate, inhomogeneously conducting tissues, is not fully known, it is at present impossible to determine the correct conductivity ratio and hence, one should still be cautious to use a different conductivity ratio. The question remains how a single, standard conductivity value for the skull, whether it is low or high, can be justifiably applied in individual models in order to obtain accurate source localization. It has been shown (Law 1993; Huiskamp et al. 1999) that skull thickness plays a role as well, so at least individual skull geometry has to be derived from either CT or multimodal MR images. Also, the skull is not homogeneous, and this inhomogeneity may be different for different parts of the skull. In the finite difference model we used a different conductivity value can be assigned to dense and trabecular bone and the geometry of each can be determined from CT scans. However, for a practical application in individual cases, this would require CT at a resolution (radiation load) which is not realistic. Therefore, an approach in which an individual but single and effective conductivity value is determined, incorporating real skull conductivity, inhomogeneity, and thickness, would be prefereable. Impedance tomography, in which the same volume conductor model is used to estimate an effective conductivity value and to localize the source, may constitute such an approach (Goncalves et al. 2000). In order to establish its validity, however, the method presented here, possibly with an extension to inhomogeneous bone, can provide real reference conductivity values. References Akhtari M., Bryant, H., Mamelak, A., Heller, L., Shih, J., Mandelkern, M., Matlachov, A., Ranken, D., Best, E. and

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