man skulls with different structures. From application points of view, localization of neural sources on EEG and the electrical impedance tomography (EIT) are ...
2286
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 9, SEPTEMBER 2008
Correlation Between Structure and Resistivity Variations of the Live Human Skull Chi Tang, Fusheng You, Guang Cheng, Dakuan Gao, Feng Fu, Guosheng Yang, and Xiuzhen Dong∗ , Member, IEEE
Abstract—A study on correlation between structure and resistivity variations was performed for live adult human skull. The resistivities of 388 skull samples, excised from 48 skull flaps of patients undergoing surgery, were measured at body temperature (36.5 ◦ C) using the well-known four-electrode method in the frequency range of 1–4 MHz. According to different structures of the skull samples, all the 388 samples were classified into six categories and measured their resistivities: standard trilayer skull (7943 ± 1752 Ω·cm, 58 samples), quasi-trilayer skull (14471 ± 3061 Ω·cm, 110 samples), standard compact skull (26546 ± 5374 Ω·cm, 62 samples), quasi-compact skull (19824 ± 3232 Ω·cm, 53 samples), dentate suture skull (5782 ± 1778 Ω·cm, 41 samples), and squamous suture skull (12747 ± 4120 Ω·cm, 64 samples). The results showed that the skull resistivities were not homogenous and were significantly influenced by local structural variations. The presence of sutures appeared to decrease the overall resistivity of particular regions largely and dentate suture decreased the resistivity more than squamous suture. The absence of diploe appeared to increase skull resistivity. The percentage on thickness of diploe would be the primary factor in determining the resistivity of the skull sample without suture. From resistivity spectra results, an inverse relationship between skull resistivity and signal frequency was found. Index Terms—Diploe, resistivity, skull, structure, suture.
I. INTRODUCTION HE RESISTIVITY of human skull is an important physical parameter, which has a great influence on the studies of bioelectricity of the head, the biological effects of electromagnetic field, and the establishment of a physical model of the human head. The resistivity and thickness of human skull are inhomogenous because of the variation of structure at different positions [1]–[3]. However, most previous studies simplified the skull as a layer of homogenous resistivity and thickness. Up to now, there is no accurate study on the resistivities of live human skulls with different structures. From application points of view, localization of neural sources on EEG and the electrical impedance tomography (EIT) are receiving wide interests. In these techniques, a volume conductor model that is based on actual resistivity and geometry of the head is needed to describe
T
Manuscript received October 24, 2007; revised January 30, 2008. This work was supported in part by the National Science Foundation (NSF), China, under Grant 50337020 and in part by the Ministry of Science and Technology (MOST), China, under Grant 2006BAI03A14. Asterisk indicates corresponding author. C. Tang, F. You, F. Fu, and G. Yang are with the Department of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China. G. Cheng and D. Gao are with the Department of Neurosurgery, Xijing Hospital, Fourth Military Medical University, Xi’an 710032, China. ∗ X. Dong is with the Department of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, China (e-mail: dongxiuzhen@fmmu. edu.cn). Digital Object Identifier 10.1109/TBME.2008.923919
the electrical characteristic of the head accurately [4], [5]. In this volume conductor model, brain (white matter and cortex), cerebrospinal fluid (CSF), scalp, and skull (bones of cerebral cranium) are involved. Because the resistivity of the skull is evidently high compared to that of other tissues, only a very small fraction of the current can penetrate through the skull eventually. Thus, the resistivity of the skull plays the most important role in the model, and misspecification of the skull resistivity can lead to a significant error in electromagnetic calculation and source localization [6]–[8]. Therefore, it is necessary to study the resistivity variation of human skull and the correlation between the skull resistivity and structure, in order to obtain more accurate physical parameters related to skull resistivity and improve the accuracy of studies on bioelectromagnetic effects of the head. Several studies have been performed on skull resistivity (or conductivity that has been converted to resistivity for unification in this paper). In 1996, Gabriel et al. [9]–[11] summarized the previous literature of the dielectric properties of biological tissues including some results of animal skull. In 1968, Rush and Driscoll [12], [13] found that the resistivity ratio of the permeating fluid to the immersed skull was 1/80 by measuring impedance of a dry half-skull in fluid. Then, they used the ratio 1:80:1 for the resistivity of scalp:skull:brain in a concentric sphere model to study the sensitivity of an EEG electrode. Since then, this ratio value has been commonly used in neural source localization. In 2000, Oostendorp et al. [14] questioned the ratio and obtained a new ratio 1:15:1 both in vitro and in vivo. They believed that the true value of the ratio of brain to skull resistivity is much closer to 1:15 to 1:80. In 1993, Law [1] showed a considerable variation in skull resistivity in samples obtained from various regions of a dry human cadaver skull that was soaked with 0.9% saline. The study suggested that skull resistivity might be determined by its thickness and structural variation such as sutures and bone formations. Although this study is valuable and instructive because of its description of the relationship between thickness and skull resistivity, the reported resistivity may be different from the resistivity of live human skull. In 2000 and 2002, Akhtari et al. [15], [16] measured the resistivity of each of the individual layers of the trilayer skull separately on postmortem skulls as well as on small pieces of skull flaps freshly obtained from patients undergoing intracranial surgery. Their study indicated that the three layers of the skull have distinct resistivities, and each layer, in turn, can be inhomogenous. Furthermore, the resistivities of all layers are higher in live skull than in cadaver skull, and there is a weak relationship between resistivity and thickness in different
0018-9294/$25.00 © 2008 IEEE
TANG et al.: CORRELATION BETWEEN STRUCTURE AND RESISTIVITY VARIATIONS OF THE LIVE HUMAN SKULL
2287
TABLE I RESISTIVITIES OF HUMAN SKULL REPORTED IN THE LITERATURES IN V ITRO AND OUR RESULTS
layers. In 2003, Hoekema et al. [17] pointed out the drawbacks of previous studies on skull resistivity such as the selection of postmortem skull material, exposure to air, and lack of temperature control. In order to avoid these drawbacks, they measured the mean resistivity of live human skulls that were temporarily removed during epilepsy surgery under controlled condition of 37 ◦ C and relatively high humidity. These conditions are crucial for accurate measurements of skull resistivity. All the earlier reported values of the specific resistivity of human skull are summarized in Table I. Our review of literatures did not reveal any report in which the resistivity variation of the live human skull with different structures had been studied. Furthermore, previous studies could not draw a widely acknowledged statistically significant conclusion about skull resistivity because of small number of samples, narrow frequency range, and variations of measurement methods and condition controls. This report is intended to shed light on the relationship between resistivity and structure of live human skull, and obtain more accurate parameters related to resistivity of human skull in a wide frequency range to facilitate further related studies. In this study, we measured 388 skull samples excised from 48 live human skull flaps to determine: 1) the relationship between structure and resistivity variation of live human skull; 2) more accurate resistivity of live human skull at body temperature (36.5 ◦ C); and 3) the resistivity spectrum of live human skull in the frequency range of 1–4 MHz. II. MATERIALS AND METHODS A. Materials Measurements of resistivity were performed on skull flaps excised from patients who were operated on intracranial surgery and not suffered from primary bone diseases. These skull flaps were not needed for replacement any more, due to clinical considerations. Risks and benefits of the experimental procedure
were explained to the patients by the attending neurosurgeon. All patients gave their informed consent. The study was approved by the Medical Ethics Committee of the Fourth Military Medical University. A total of 48 skull flaps from 48 patients (Xanthoderm, 10 females and 38 males, 20–74 years old, mean age 47.6 years) were studied. The positions of these skull flaps were mainly on frontal–temporal–parietal region (46 samples). In this region, coronal suture and squamosoparietal suture are usually included. Furthermore, two skull flaps were excised from parietal– occipital region where the lambdoid suture was included. Immediately after removal of the skull flap, it was kept in gauze soaked with physiological saline to prevent from air drying. Skull plugs, at interested sites, were drilled perpendicular to the outer and inner surfaces of the skull flaps using a trephine with a 14-mm inner diameter. During the waiting periods for measurements, skull plugs were conserved in salinesoaked gauze. B. Samples Category Skull (bones of cerebral cranium) is a layer of irregular flat bone that is mainly composed of three layers: outer compact bone, diploe, and inner compact bone. At different positions, the structure and thickness of the trilayer skull are not homogenous mainly because of the variation of diploe. Bones of cerebral cranium is an ellipsoid composed of eight bones. Sutures, unossified structure, are present at the joints of bones. Due to different structures, sutures can be separated into dentate suture and squamous suture. According to different structures of skull plugs, we classified all the skull samples into six categories as follows. 1) Standard trilayer skull: the percentage on thickness of diploe (PTD) is much higher than that of compact bone. 2) Quasi-trilayer skull: PTD is similar or less than that of compact bone.
2288
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 9, SEPTEMBER 2008
Fig. 1. Skull samples of trilayer and compact skull. (A) Standard trilayer skull (axial views, top row, left to right). (B) Quasi-trilayer skull (bottom row, left to right). (C) Standard compact skull. (D) Quasi-compact skull.
Fig. 3. Measurement system of skull resistivity. (a) Round current electrodes. (b) Acicular voltage electrodes. (c) Physiological saline. (d) Skull sample.
Fig. 2. Skull samples with sutures. Planar views of top surface (top row). Axial views (bottom row). (A) Dentate suture skull. (B) Squamous suture skull.
3) Standard compact skull: pure compact bone without any diploe. 4) Quasi-compact skull: approximate pure compact bone with sporadic diploe. 5) Dentate suture skull: the samples with dentate suture, mainly from coronal suture and lambdoid suture. 6) Squamous suture skull: the samples with squamous suture, mainly from squamosoparietal suture. Trilayer and compact skull samples are shown in Fig. 1 and suture skull samples are shown in Fig. 2. C. Measurement System and Methods The measurement system of skull resistivity is shown in Fig. 3. It was based on an impedance analyzer (Schlumberger, Solartron SI1260) that could perform impedance and frequency response measurements over the frequency range of 10 µHz– 32 MHz. System control and data input/output are possible through a general-purpose interface board (GPIB) that connects the SI1260 to a computer. The precision of the system in the frequency range of 1–4 MHz is proved higher than 0.1% for the impedance range of 100 Ω–10 kΩ by measuring many precision resistors. In order to control the experimental conditions, an infant incubator was used to maintain the temperature at 36.5 ◦ C. Measurements of skull resistivities were performed using the four-electrode method that was widely used to measure the impedance of biological tissues [18]. In this technique, the two outer electrodes pass the current across the sample and the two
Fig. 4.
Four-electrode assembly for in vitro measurement.
inner electrodes measure the voltage difference. Due to the separation of current and voltage electrodes, this method eliminates problems associated with electrode polarization and contact resistance effectively. The assembly is made of nonconducting plexiglass and is shown in Fig. 4, which is very similar to the reported assemblies [1], [14]. The skull plug was located between two cylindrical containers filled with physiological saline. The inner diameter of the cylindrical containers was the same as the skull plug diameter and the electrode material was silver. Round current electrodes, one on either extreme end, were placed 40 mm from the skull plug. Acicular voltage electrodes, at both sides of the junction between the containers, were fitted at 15 mm from the junction. Water-tight integrity was maintained by nonconducting rubber rings that have the same inner diameter as the skull plug diameter. D. Measurement and Data Processing We measured the complex impedance spectrum (include real part and imaginary part) of each skull plug sample, with 0.5 mA drive current in sweep frequency mode, in the frequency range of 1 Hz–4 MHz. Each sample was measured three times
TANG et al.: CORRELATION BETWEEN STRUCTURE AND RESISTIVITY VARIATIONS OF THE LIVE HUMAN SKULL
continuously and the average was calculated to decrease measurement error. The skull plugs wrapped with saline-soaked gauze were placed in the infant incubator, set at 36.5 ◦ C (body temperature), at least half an hour to warm up before measurements. The thicknesses and diameters of the skull samples were measured by a caliper (precision: 0.02 mm). Due to the curved surface of the skull, especially the inner surface, the thickness was generally not uniform. The average thickness was determined by taking thickness measurements of the center and four orthogonal edges [1]. At the same time, in order to study the influence of component percentage of diploe on the resistivity of trilayer skull, we also measured the diploetic thicknesses of 68 trilayer skull samples by the caliper to calculate the PTD. Because the nonuniformity of the skull thickness was mainly due to the variation of diploetic thickness and the thicknesses of the two compact layers were relatively uniform, we first measured the thicknesses of the two compact layers, respectively, and then obtained the diploetic thickness by subtracting the thicknesses of the two compact layers from the bulk thickness of the skull plug. Resistivities of skull plug samples were calculated by ρ=
Rs A πD2 (R − R0 ) 1 = = σ L 4L
where ρ and σ are the resistivity and conductivity of the skull, Rs is the modulus of complex impedance of the skull sample, R and R0 are the modulus of measured complex impedance with and without skull sample, L is the thickness of the sample, and D and A are the diameter and area of the sample, respectively. III. RESULTS A total of 388 skull plugs drilled from 48 skull flaps were measured. The measurements of resistivity for these samples ranged from 5782 to 26 546 Ω·cm ( f = 1 kHz), which indicated that the variation of skull resistivity was noticeable. Table I and Fig. 5 show that there are significant differences in the resistivities among the skull samples with different structures. Standard compact skull has the highest resistivity, and the resistivity of quasi-compact skull is lower than that of standard compact skull. The resistivity of dentate suture skull, significantly lower than that of squamous suture skull, is the lowest of all. For trilayer skulls, the resistivity of a standard trilayer skull is noticeably lower than that of a quasi-trilayer skull. The thicknesses of skull samples with different structures vary widely. The mean thickness of the dentate suture samples is greater than that of the squamous suture samples. Except for suture samples, the order of mean thickness from the greatest to least is standard trilayer, quasi-trilayer, quasi-compact, and standard compact skull, which is exactly contrary to the order of skull resistivity (Fig. 5). The influence of PTD and thickness on the resistivity of a trilayer skull is shown in Fig. 6. They all have an inverse relationship. However, the absolute value of the correlation coefficient between PTD and skull resistivity (r = –0.917) is much higher than that between skull thickness and resistivity (r = –0.596).
2289
Fig. 5. Histogram of resistivities (left) and thicknesses (right) of skull samples with different structures. The skull resistivities are the results at the frequency of 1 kHz.
The resistivity spectra have shown that there is an inverse relationship between the skull resistivity and frequency in a wide frequency range. Within the frequency interval from 1 Hz to 10 kHz, the resistivities are kept steady. In the range from 10 to 100 kHz, the resistivities decreased gradually. After 100 kHz, the resistivities decreased rapidly. These resistivity loci were calculated from the mean values of data measured on all the samples of each type of skull (Fig. 7). IV. DISCUSSION In order to overcome the drawbacks of previous studies on skull resistivity, such as: 1) the use of postmortem skull materials, 2) lack of temperature control, 3) single frequency or narrow frequency range, 4) small numbers of skull samples, and 5) ignorance of the variation of skull resistivity, we designed and performed the experiments before. In this experimental study, we intended to obtain more accurate skull resistivity values by applying the classical measurement method of skull resistivity [1], [14] on a large number of samples that were cut from many calvaria of live human skulls in the frequency range of 1–4 MHz and in a carefully controlled situation with a stable temperature (36.5 ◦ C), and performed a precise analysis on the relationship between the resistivity and the structure of live human skull. Measurements on freshly excised skull can determine more realistic resistivities due to the presence of vascular tissue and fluids that fill the bone pores. By controlling the measurement temperature at body temperature, we can further approach the condition of in vivo. From the experimental results, we found that the influencing factors on skull resistivity are miscellaneous. A. Influence of Sutures The resistivity range of our results indicates that the variation of skull resistivity, influenced by the structural variation of skull, is noticeable. First of all, the presence of suture lines can significantly decrease the skull resistivity of the particular region. Sutures are unossified and filled with cartilage, chondroid, and vascular tissue, which contain more abundant fluid content of
2290
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 9, SEPTEMBER 2008
Fig. 6. Scatter plot (68 samples). (a) Thickness of trilayer skull versus skull resistivity (correlation coefficient: r = –0.596). (b) PTD of trilayer skull versus skull resistivity (correlation coefficient: r = –0.917).
low resistivity than surrounding bone tissues. Therefore, sutures can provide a path of low resistance for current and decrease the overall resistivity. Our conclusion is in agreement with the earlier study of Law [1], and proves the existence of the influence of sutures on skull resistivity ex vivo. In Law’s study, however, because of dry postmortem skull material, the tissues in the sutures have shrunk for a long time and liquid in measurement assembly can pass through the gaps of sutures more easily, which may explain why our result of suture samples is slightly higher than that of Law [1]. The results of our experiments also showed that dentate suture and squamous suture, with different structures described as their names, have different influences on decreasing the skull resistivity. Dentate suture decreases the skull resistivity more than the squamous suture. There are five suture lines on adult calvarium, coronal, sagittal, and lambdiod suture that belong to dentate suture and two squamosoparietal sutures are squamous suture. Two parts of bone vaults of dentate suture occlude each other as sawtooth and the suture can approximately vertically penetrate the two skull surfaces. Whereas, two parts of bone vaults of squamous suture joint each other as squama and the suture penetrates the two skull surfaces slantingly, which provide a longer path of low resistivity than that of dentate suture at the same bulk thickness. This is clearly shown in Fig. 2(A) and (B). B. Influence of Diploe Except for the influence of sutures, another important influencing factor on skull resistivity is the component percentage of diploe on skull samples. Our results have shown that there is an inverse relationship between them. The diploe is composed of spongy bone that has more pores and cavities than compact bone. Since these pores and cavities of the diploe are filled with tissues of high fluid component and low resistivity such as marrow and vascular tissue, the resistivity of the diploe is obviously lower than that of the compact bone. Therefore, the proportion of the diploe component in skull samples without suture would
Fig. 7. Resistivity spectra of skull samples with different structures in the frequency range of 1–4 MHz.
be the primary factor in determining the overall resistivity of the sample. In our results, the mean resistivity of standard trilayer skulls is significantly lower than that of quasi-trilayer skulls because of the higher component percentage of diploe in standard trilayer skulls. By the same reason, the mean resistivity of standard compact skulls is higher than that of quasi-compact skulls. The skull thickness is not uniform and the diploetic thickness is highly correlated with the total skull thickness [2], [3]. Therefore, some previous studies put more emphasis upon the relationship between skull thickness and resistivity and showed somehow inverse relationship [1], which reflected the influence of component percentage of diploe on skull resistivity indirectly. In our results (Fig. 6), both the skull thickness and the PTD had an inverse correlation with skull resistivity. However, the absolute value of correlation coefficient between skull thickness and resistivity was lower than that between PTD and resistivity, which indicated that the latter should reflect more about the influence of diploe on skull resistivity.
TANG et al.: CORRELATION BETWEEN STRUCTURE AND RESISTIVITY VARIATIONS OF THE LIVE HUMAN SKULL
C. Resistivity Spectrum of Human Skull It should be noted that the skull resistivity is not constant in a wide frequency range. However, the previous studies only measured the skull resistivity in the single frequency or narrow frequency range. The resistivity spectra of our results (Fig. 7) have shown that there is an inverse relationship between skull resistivity and frequency, especially when the frequency is higher than 10 kHz. The skull resistivity decreases 15% from 10 to 100 kHz. In our experiments, we could not obtain ideal values at higher frequencies (above 4 MHz) because of the influence of stray capacitances. Whether it is possible to obtain sufficiently accurate data by impedance measurement at suitably high frequencies is a question for further investigation, because we have to consider the disturbing influence of stray capacitances of the measuring circuits (especially lead wires).
2291
realistic volume conductor model of human head, further investigation must be done to obtain resistivity distribution on bones of cerebral cranium. We hope this paper will be instructive and helpful for the investigation. E. Summary In summary, the resistivities of live human skulls are not homogenous and appear to be influenced greatly by the variation of local structures such as sutures and diploes. First, the presence of sutures can significantly decrease the local skull resistivity, and dentate suture decreases the resistivity more than squamous suture. Second, an inverse relationship between component percentage of diploe and skull resistivity was found. Finally, the skull resistivity decreased as the frequency increased in a wide frequency range, especially when the frequency is higher than 10 kHz.
D. Comparison With the Previous Studies The skull resistivities of our results were slightly higher than those reported earlier [1], [14], [17]. The discrepancy may be attributed to the differences in the immersion fluid, because bone resistivity is primarily dependent on the resistivity of the fluid perfusing the bone tissue [19], [20]. In Law’s study [1], the skull was soaked in 0.9% saline, whereas in our experiments, the skulls were fresh and thus still filled with its natural liquid content. Wendel and Malmivuo [21] supposed that the natural content was CSF; however, we thought it should be tissue fluid and blood that had higher resistivity than that of CSF. Compared with 0.9% saline, even the resistivity of CSF is still slightly higher at the same temperature. Furthermore, some special treatments on skull sample may result in the variation of impedance characteristic. In Oostendorp et al.’s study [14], the specimen was preserved in a freezer for a few days before the measurement was performed. In Hoekema et al.’s study [17], the results were surprisingly low, because a film of saline on the skull surface may have provided a shunting effect. Most of previous studies emphasized the mean skull resistivity irrespective of location and structure variations [14]–[17], which may be instructive for multilayer concentric sphere model with homogenous resistivities of each layer. Whereas many studies have shown that the simplification of this uniform layer model, especially on the skull layer, produces significant errors on EEG source localization [6]–[8]. Therefore, the variation of skull resistivity and thickness should be incorporated into head model to provide more accurate parameters for researches. Further research should be performed to study the equivalent circuit model by the measured data, which is needed in the study of electrical characteristics of human skull. Due to inhomogenous components of the skull, especially in trilayer skull, anisotropy of resistivity is an actual characteristic of human skull. In this study, we measured the skull resistivity only in the direction perpendicular to the top and bottom surfaces (transverse direction). With the deepening of the research on skull resistivity, the electrical characteristics of compact bone and spongy bone should be studied independently, and the resistivities in other directions should be measured to study the anisotropy of skull resistivity. Finally, in order to establish a
REFERENCES [1] S. K. Law, “Thickness and resistivity variations over the upper surface of the human skull,” Brain Topogr., vol. 6, pp. 99–109, 1993. [2] N. Lynnerup, J. G. Astrup, and B. Sejrsen, “Thickness of the human cranial diploe in relation to age, sex and general body build,” Head Face Med., vol. 1, no. 13, pp. 1–7, 2005. [3] N. Lynnerup, “Cranial thickness in relation to age, sex and general body build in a Danish forensic sample,” Forensic Sci. Int., vol. 117, pp. 45–51, 2001. [4] D. H. Fender, “Models of the human brain and the surrounding media: Their influence on the reliability of source localization,” J. Clin. Neurophys., vol. 8, pp. 381–390, 1991. [5] G. Huiskamp, M. Vroeijenstijn, R. van Dijk, G. Wieneke, and A. C. van Huffelen, “The need for correct realistic geometry in the inverse EEG problem,” IEEE Trans. Biomed. Eng., vol. 46, no. 11, pp. 1281–1287, Nov. 1999. [6] R. Pohlmeier, H. Buchner, G. Knoll, A. Rienacker, R. Beckmann, and J. Pesch, “The influence of skull-conductivity misspecification on inverse source localization in realistically shaped finite element head models,” Brain Topogr., vol. 9, pp. 157–162, 1997. [7] J. O. Ollikainen, M. Vauhkonen, P. A. Karjalainen, and J. P. Kaipio, “Effects of local skull inhomogeneities on EEG source estimation,” Med. Eng. Phys., vol. 21, pp. 143–153, 1999. [8] C. G. Benar and J. Gotman, “Modeling of post-surgical brain and skull defects in the EEG inverse problem with the boundary element method,” J. Clin. Neurophysiol., vol. 113, pp. 48–56, 2002. [9] C. Gabriel, S. Gabriel, and E. Corthout, “The dielectric properties of biological tissues: Part I. Literature survey,” Phys. Med. Biol., vol. 41, pp. 2231–2249, 1996. [10] S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: Part II. Measurements in the frequency range 10 Hz to 20 GHz,” Phys. Med. Biol., vol. 41, pp. 2251–2269, 1996. [11] S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: Part III. Parametric models for the dielectric spectrum of tissues,” Phys. Med. Biol., vol. 41, pp. 2271–2293, 1996. [12] S. Rush and D. A. Driscoll, “Current distribution in the brain from surface electrodes,” Anesth. Analg., vol. 47, pp. 717–723, 1968. [13] S. Rush and D. A. Driscoll, “EEG electrode sensitivity: An application of reciprocity,” IEEE Trans. Biomed. Eng., vol. BME-16, no. 1, pp. 15–22, Jan. 1969. [14] T. F. Oostendorp, J. Delbeke, and D. F. Stegeman, “The conductivity of the human skull results of in vivo and in vitro measurements,” IEEE Trans. Biomed. Eng., vol. 47, no. 11, pp. 1487–1491, Dec. 2000. [15] M. Akhtari, H. C. Bryant, A. N. Mamelak, L. Heller, J. J. Shih, M. Mandelkern, A. Matlachov, D. M. Ranken, E. D. Best, and W. W. Sutherling, “Conductivities of three-layer human skull,” Brain Topogr., vol. 13, pp. 29–42, 2000. [16] M. Akhtari, H. C. Bryant, A. N. Mamelak, E. R. Flynn, L. Heller, J. J. Shih, M. Mandelkern, A. Matlachov, D. M. Ranken, E. D. Best, M. A. Dimauro, R. R. Lee, and W. W. Sutherling, “Conductivities of three-layer live human skull,” Brain Topogr., vol. 14, pp. 151–167, 2002.
2292
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 9, SEPTEMBER 2008
[17] 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, “Measurement of the conductivity of skull, temporarily removed during epilepsy surgery,” Brain Topogr., vol. 16, pp. 29–38, 2003. [18] J. J. Ackmann and A. S. Seitz, “Methods of complex impedance measurements in biological tissue,” CRC Crit. Rev. Biomed. Eng., vol. 10, pp. 281–311, 1984. [19] J. D. Kosterich, K. R. Foster, and S. R. Pollack, “Dielectric permittivity and electrical conductivity of fluid saturated bone,” IEEE Trans. Biomed. Eng., vol. BME-30, no. 2, pp. 81–86, Feb. 1983. [20] J. D. Kosterich, K. R. Foster, and S. R. Pollack, “Dielectric properties of fluid-saturated bone—The effect of variation in conductivity of immersion fluid,” IEEE Trans. Biomed. Eng., vol. BME-31, no. 4, pp. 369–373, Apr. 1984. [21] K. Wendel and J. Malmivuo, “Correlation between live and post mortem skull conductivity measurements,” in Proc. IEEE 28th Annu. Int. Conf. Eng. Med. Biol. Soc., 2006, pp. 4285–4288.
Chi Tang was born in China in 1977. He received the B.S. and M.S. degrees in biomedical engineering in 2000 and 2005, respectively, from the Fourth Military Medical University, Xi’an, China, where he is currently working toward the Ph.D. degree. He is currently a Lecturer in the Department of Biomedical Engineering, Fourth Military Medical University. His current research interests include biological tissue impedance measurement and detecting and processing of biomedical signals.
Fusheng You received the B.S., M.S., and Ph.D. degrees in biomedical engineering from the Fourth Military Medical University, Xi’an, China, in 1990, 1998, and 2004, respectively. From 1990 to 1995, he was with the Research Center for High Altitude Disease, Lhasa, Tibet. Since 1995, he has been with the Department of Biomedical Engineering, Fourth Military Medical University, where he is currently an Associate Professor. His current research interests include image monitoring by electrical impedance tomography, biomedical signal detecting and processing, and electronic instrumentation for biomedical applications.
Guang Cheng was born in China in 1971. He received the B.S., M.S., and M.D. degrees in medicine from the Fourth Military Medical University, Xi’an, China, in 1995, 2003, and 2006, respectively. He is currently an Attending Doctor and a Lecturer in the Department of Neurosurgery, Xijing Hospital, Fourth Military Medical University. His current research interests include remedy of glioma.
Dakuan Gao was born in China in 1975. He received the B.S., M.S., and M.D. degrees in medicine from the Fourth Military Medical University, Xi’an, China, in 1997, 2000, and 2006, respectively. He is currently an Attending Doctor and a Lecturer in the Department of Neurosurgery, Xijing Hospital, Fourth Military Medical University. His current research interests include remedy of glioma.
Feng Fu received the B.S., M.S., and M.D. degrees in biomedical engineering from the Fourth Military Medical University, Xi’an, China, in 1993, 1996, and 1999, respectively. He is currently an Associate Professor in the Department of Biomedical Engineering, Fourth Military Medical University. His current research interests include bioimpedance measurement and imaging.
Guosheng Yang was born in China in 1946. He received the B.S. degree in automatic control from Harbin Military Engineering University, Harbin, China, in 1969. During 1980, he was involved in research on biomedical engineering. Since 1989, he has been an Associate Professor in the Department of Biomedical Engineering, Fourth Military Medical University, Xi’an, China, where he is currently a Professor. His current research interests include application of microwave in medicine.
Xiuzhen Dong (M’00) was born in China in 1945. She received the B.S. degree in automatic control from Harbin Military Engineering University, Harbin, China, in 1968. Since 1994, she has been a Professor at the Fourth Military Medical University, Xi’an, China, where she has also been a Doctoral Advisor since 1998. She is the author or coauthor of more than 200 papers published in international journals and conferences. Her current research interests include electrical impedance tomography and biomedical signal detection and processing. Prof. Dong is the Deputy Chairman of the Chinese Society of Biomedical Engineering.
