Deep brain stimulation electrodes used for staged lesion within the basal ganglia: experimental studies for parameter validation

Transcription

1 J Neurosurg 107: , 2007 Deep brain stimulation electrodes used for staged lesion within the basal ganglia: experimental studies for parameter validation Laboratory investigation SYLVIE RAOUL, M.D., PH.D., 1 DOMINIQUE LEDUC, PH.D., 2 THOMAS VEGAS, M.S., 2 PAUL SAULEAU, M.D., 3 ANDRES M. LOZANO, M.D., PH.D., 4 MARC VÉRIN, M.D., PH.D., 3 PHILIPPE DAMIER, M.D., PH.D., 5 AND YOUENN LAJAT, M.D. 1 1 Department of Neurosurgery, Centre Hospitalier Universitaire de Nantes; 2 Faculté des Sciences, Université de Nantes, Nantes Atlantique Universités, Institut de Recherche en Electrotechnique et Electronique de Nantes Atlantique; 3 Department of Neurology, Centre Hospitalier Universitaire de Rennes; 5 Department of Neurology, Clinical Investigation Center, Institut National de la Santé et de la Recherche Médicale UMR 643, Centre Hospitalier Universitaire de Nantes, France; and 4 Department of Neuroscience, Division of Neurosurgery, Toronto Western Hospital, University of Toronto, Canada Object. Deep brain stimulation (DBS) has been shown to be an effective treatment for various types of movement disorders. High-frequency stimulation is applied to specific brain targets through an implanted quadripolar lead connected to a pulse generator. These leads can be used for creating lesions in the brain. The experimental study reported here was designed to examine the electrical parameters that could be used to create reproducible therapeutic lesions in the brain. Methods. Egg whites were used to measure the relationship between the electrical parameters (current and voltage) applied through the DBS electrode and the size of coagulum. The authors measured current spread from the electrode contact used for lesioning to the adjacent contact. Similar studies were performed in the pallidum or the thalamus of human cadavers. Modeling of the lesion size was performed with simulation of current density and temperature. The ultrastructure of the electrodes after lesioning was verified by electron microscopy. Results. Coagulation size increased with time but reached a plateau after 30 seconds. For a given set of electrical parameters, reproducibility of the size of lesions was high. Using constant voltage, lesions were larger in egg whites than in cadaveric brains with a mean length of mm in egg whites at 40 V, 125 ma, impedance 233 ; and mm in cadavers at 40 V, 38 ma, impedance Computer modeling indicated negligible current flow to the adjacent, unused electrodes. The electrodes showed no structural alterations on scanning electron microscopy after more than 200 lesions. Conclusions. Results of this study demonstrate that DBS electrodes can be used to generate lesions reproducibly in the brain. The choice of lesioning parameters must take into account differences in impedance between the test medium (egg whites) and the human brain parenchyma. (DOI: /JNS-07/11/1027) KEY WORDS cadaver deep brain stimulation experimental lesion Parkinson disease thermocoagulation R ADIOFREQUENCY lesions have for many years been used to make lesions in specific nuclei in the brain to treat essential tremor, Parkinson disease, chronic pain, and psychiatric disorders. 1,10,11,13,20 Briefly, the technique consists of producing a localized elevation of temperature through an implanted electrode. The size of the lesions depends on the electrical parameters (voltage and Abbreviation used in this paper: DBS = deep brain stimulation. current) applied through the electrode. 19 Since the late 1980s, DBS has been proposed as an alternative treatment to lesioning for tremor and Parkinson disease. 2,16 A quadripolar lead is stereotactically implanted in the targeted nucleus and connected through an internalized cable to a pulse generator. The technique has the advantage of the effects being reversible and the electrical parameters being adaptable according to the patients. It is, however, expensive due to the cost of the hardware, particularly the pulse generator. Furthermore, the use of implanted hardware in- 1027

2 S. Raoul et al. volves a risk of long-term adverse effects, such as infections and skin erosions, and mechanical failure, and regular battery replacement is required. We recently showed that electrodes used for DBS could be implanted, left in place, and used to make staged radiofrequency lesions adapted to the symptom progression. 18 In this experimental study, we analyzed the relationship between the radiofrequency parameters and the size of the coagulum to optimize the conditions needed to make localized lesions in the human brain through a DBS electrode. We also assessed the safety of the method by measuring current diffusing to the electrode adjacent to the one used for applying radiofrequency and by analyzing the ultrastructure of the electrode after radiofrequency lesioning. Materials and Methods Experimental Studies in Egg Whites and Cadavers Analysis in Fresh Egg Whites. Forty milliliters of fresh egg whites was placed in a square glass container. The quadripolar Medtronic lead (model 3387 or 3389; Medtronic, Inc.) was inserted into the egg whites in such a way that all four distal electrodes were completely immersed. The four proximal electrodes were held in the air by a mechanical support and two of them were connected to the Radionics radiofrequency generator to apply the voltage between the corresponding distal electrodes. The part of the lead to be immersed was first carefully cleaned before each lesion and then placed inside the egg whites. We then measured the impedance of the medium with an ohmmeter (Radionics). When this impedance was greater than 500, the lead was cleaned again. The next step was to apply the voltage. This was done in 1 to 3 seconds until the tension measured by a voltmeter (Radionics) had reached the desired value. The duration of the stimulation, previously programmed, was controlled by a clock (Radionics). During the lesioning process, we monitored the current with an amperemeter (Radionics) and kept its higher values as the measure of the current. Finally the lead was removed from the egg whites, and the size (length and width) of the lesion was measured. The different experiments are summarized in Table 1. Analysis in Cadavers. The same experimental procedure was used in six human cadavers. Cadavers were maintained at 37 C in a water bath. Electrodes were implanted in the thalamus and pallidum. Part of the skull was removed, and transverse sections were made to expose the pallidum, the caudate nucleus, and the thalamus. The size of the coagulum was measured (length and width) under the microscope (Zeiss). When a lesion was obtained in the basal ganglia, the color of the coagulum was quite different (yellow/white) from the normal color of the thalamus or pallidum in cadavers (gray/purple) (Fig. 1). For some lesions, histological analysis was done to determine more precisely the size of the lesions. Experimental Setup. In fresh egg whites, a 250-kHz current was applied at various intensities, with increments of 10 ma from 10 to 230 ma (corresponding to voltages with increments of 4 V from 2 to 50 V). For each increment, 10 lesions (that is, a total of 250 lesions) were made. During the first part of the study the current was applied for 60 seconds. In the second part of the study we used various durations (30, 60, 90, 120, and 180 seconds; and 5 and 10 minutes) at a constant voltage (40 V). For each duration, 10 lesions were made. In human cadavers, 60 lesions (10 in the pallidum and 50 in the thalamus) were measured using currents of 10 to 170 ma with increments of 10 ma (corresponding to V with increments of 4 V). The impedance, electrode combination, localization, size of lesions, current, voltage, and time were recorded for each bipolar lesion. New DBS Medtronic leads (one was model 3389 and three were model 3387) were used for the experimental studies. The coagulum size (length and width) was measured using the scale on the microscope stage. Various times (10, 20, 30, and 60 seconds) were applied in human brain tissue. Electron Microscopy Study. The ultrastructure of the DBS electrode after radiofrequency lesioning was analyzed with a scanning electron microscope at the end of the experimental study in fresh egg whites. Computer Modeling of the Lead and the Coagulation Measurements of current to the electrode contacts not used for lesioning were performed directly through a resistance of 100 to 10,000 placed between the unused electrodes. We simulated the coagulation process using the finite elements method. We assumed the following mechanism of lesion: the potential difference between active contacts induces a current and the electrical power produced is dissipated in the brain, the temperature of which increases until coagulation. The first step is to calculate the electrical potential distribution, V, around the electrode. This is done by solving the Laplace equation, 3,4 which depends on the electrical conductivity of the brain. The current density is deduced from the potential distribution. At any given point in the brain, a certain amount of electrical power is dissipated, giving rise to a heat flow, Q. To determine the corresponding temperature elevation and spread, one has to solve the bioheat transfer equation, 17 which depends on brain density, ; thermal capacity, C p ; and thermal conductivity, k. To solve the Laplace and bioheat transfer equations at every point, we used Femlab software (Cosmol AB), which is based on the finite elements method. Because of the axial symmetry of the problem, the workspace is reduced to two dimensions. The gray matter is assumed to be uniform. Its physical characteristics were found in the literature as follows: 9,21 k = W/m/K,C p = 3700J/K/kg, and = 0.18 [1 0.02(T 310)]S/m, where denotes the electrical conductivity, T indicates temperature, and S denotes Siemens. The lead is represented by its fingerprints. Because the lead is coated with insulator material, this surface is not involved in the calculation but rather the areas corresponding to the titanium electrodes. The boundary conditions are contact 0, potential 0 V; contact 1, potential V eff. Contacts 2 and 3 are insulated which means that the current can flow inside these contacts but it cannot pass through them, as in the experiments. The last step was to simulate the coagulation. Results of experimental studies have shown that when the brain coagulates, the current decreases abruptly. This means that gray matter conductivity falls to zero after the coagulation. To reproduce this behavior, we assumed a coagulation temperature threshold, T c, and introduced a phenomenological decay of the conductivity at a given position as TABLE 1 Experimental settings in egg whites and cadavers voltage (V) for constant duration of 60 secs (no. of experiments) egg white 2 (10) 4 (10) 8 (10) 12 (10) 16 (10) 20 (10) 24 (10) 30 (10) 40 (10) 50 (10) cadaver 12 (10) 14 (10) 18 (10) 21 (10) 30 (10) 36 (10) 40 (10) 46 (10) 50 (10) duration of stimulation (in secs) for constant applied voltage of 40 V (no. of experiments) egg white 30 (10) 40 (10) 60 (10) 90 (3) 120 (3) 180 (3) 300 (3) 600 (3) cadaver 10 (10) 20 (10) 30 (10) 60 (10) 1028

3 Experimental studies of DBS electrodes used for staged lesion FIG. 1. Photographs of coagulum in egg whites (A and B) and in human cadavers (C). soon as the temperature exceeded the temperature threshold at this position. The temperature threshold and the rate of conductivity decrease are free parameters of the simulation. The best results were obtained at a temperature threshold of 60 C. 3 Results Results in Egg White and Cadaver Experiments Effects of Radiofrequency Stimulation Applied to Fresh Egg Whites. The first step was to study the effect of voltage (or current) on the size of coagulum. There was a clear threshold (15 V or 90 ma) to obtain coagulation in egg white. Above this threshold, the size of the lesion increased with increasing voltage or current (with homogeneous and constant impedance) until a plateau was reached (Fig. 2). At 40 V, 200 ma, applied during 60 seconds, the mean size ( standard deviation) of 25 lesions was as follows: length mm and width mm. In this experimental setup, we observed that after the threshold of coagulation had been reached the coagulation process occurred rapidly (in 20 seconds). The current increased during 1 second with a constant voltage and then fell abruptly. Around the threshold of coagulation, the current was not sufficient to make stable lesions. With a stimulation of 40 V, 200 ma, the mean lesion size was mm long and mm wide after a stimulation duration of 30 seconds, mm long and mm wide after a duration of 40 seconds, and mm long and mm wide after a duration of 60 seconds (Fig. 3). When the duration of the stimulation is multiplied by 2 (from 30 to 60 seconds) the size of the lesion is only increased by about 10%. This means that the duration of the stimulation is not a critical parameter, as the major part of the lesion is made during the first moments. Effects of Radiofrequency Stimulation Applied to Cadavers. The impedance of human brain tissue measured by the Radionics Generator was usually close to The threshold to obtain a coagulum was in this case 22 V (~ 20 ma) (Fig. 4). Beyond this threshold, the size of lesions increased until a plateau level was reached. The lesion sizes in the thalamus produced with a duration of 60 seconds are shown in Table 2. There was no difference between the thalamus and the pallidum. It took about 15 seconds to create a coagulum in the human brain and, thereafter, the size of the lesions did not increase significantly with increasing stimulation duration (Fig. 5). Recorded sequences during coagulation in eggs and in cadavers showed that a maximum size of coagulation was reached after approximately 15 seconds. As coagulation proceeded, the current decreased abruptly from 40 to 0 ma FIG. 2. Diagrams showing the coagulum size versus voltage (upper) and current (lower) in egg whites. 1029

4 S. Raoul et al. FIG. 3. Diagram showing the coagulum size versus increasing time at constant voltage (40 V) and constant impedance (400 ) in egg whites. in 10 seconds, as observed on the amperemeter of the Radionics Generator. This confirmed that a stable lesion had been made. As in egg whites, the size of the lesions in cadavers did not extend beyond two adjacent electrodes. We made 10 lesions in the thalamus at 80 V and 80 ma during 10 minutes; the lesions were mm in length and mm in width. Results of the Scanning Electron Microscopy Study The DBS electrode was made of titanate and a Teflon insulated component. After it was used to make 200 lesions, the electrode showed no clear alterations in its ultrastructure (Fig. 6). Results of Computer Modeling FIG. 4. Diagrams showing the coagulum size versus voltage (upper) and current (lower) in human cadavers. The temporal evolutions of current density, temperature, and conductivity obtained with the numerical simulation of a lesion produced with an amplitude of 40 V are shown in Figs. 7 through 9. At the beginning, the current is concentrated along the electrode, between the two active contacts (Fig. 7A). The temperature rapidly increases in this area (Fig. 8A) and exceeds the coagulation threshold. A coagulum appears in this area, which becomes isolated (Fig. 9A). As the current must circumvent this new obstacle, its path increases and its amplitude consequently decreases (Fig. 7B). However, it remains high enough so that the temperature remains above the threshold (Fig. 8B) and the coagulum grows (Fig. 9B). This mechanism is repeated, until the two contacts are embedded in the coagulum (Fig. 9C) and become isolated. There is now no way for the current to reach the two active contacts, and the current disappears (Fig. 7D). The temperature at this point remains high, but the heat is dissipated and the brain recovers its normal temperature after a few seconds (Fig. 8D). The final length and width of coagulum are in the region of 4 and 3 mm, respectively (Fig. 9D). The key feature of this is that the process is self-limiting. As soon as the coagulum reaches a given width, the coagulation stops. This implies firstly that there is no current flowing to the unused contacts and secondly that the size of the lesions is limited to the area between the two active contacts. TABLE 2 Lesion size produced by a 60-second stimulation at three different voltages in cadaveric brain Lesion Size (mm) Voltage Length Width Summary of Results Discussion This study was performed to assess the range of parameters that could be used in a surgical procedure to create radiofrequency lesions in the brain through DBS leads. The most important result of the experimental study is that the process of coagulation was very simple with a threshold and a plateau level, both in egg whites and in cadaver brains. Computer modeling was performed to assess various parameters that we were unable to measure experimen- 1030

5 Experimental studies of DBS electrodes used for staged lesion FIG. 5. Diagram showing the coagulum size versus increasing time at constant voltage (40 V) and constant impedance (1000 ) in human cadavers. tally, such as current density and temperature. The results of modeling are in agreement with the experimental procedure. Experiments and computer modeling demonstrate that using a DBS lead to create radiofrequency lesions is safe. Authors of clinical studies have shown that it is possible to use this procedure in patients. 15,18 Discussion of Experimental Results Two models (egg whites and cadavers) were used to estimate lesion size and calculate parameter settings. Egg white or albumin solutions are classic models used to study radiofrequency lesions. 8,14,19 This is, however, the first time that coagulation has been studied in cadaver brains. We found some differences between the two models. The impedance in fresh egg white was lower ( ) than in human cadaver basal ganglia ( ). This means that, to produce a given lesion size, less current was needed in human brain than in egg white. When using a DBS electrode to create lesions, the impedance of the brain must be checked before and after lesioning. Human cadavers serve as a good model for radiofrequency lesioning procedures. Nevertheless, there are likely to be modifications in the lesion size in patients because of blood and fluid circulation. Eriksson et al. 7 sought to correlate the size of lesion in egg and on magnetic resonance images after lesioning the brain of pigs. They found a close correlation between the coagulation size and the inner zone seen on magnetic resonance images. 12 Similar results could be expected in humans. Indeed, the size of coagulum (3 5 mm) did not differ greatly from that of the lesions produced in patients 18 using our new surgical procedure. We have proved that lesions cannot extend beyond two active electrodes and that we can create staged, small, and self-limiting lesions in human brains. Another experimental finding was that the DBS electrode was not modified after lesioning. This is an argument in favor of the safety of this surgical procedure in patients. It means that if the electrode used to produce a lesion is left in place it could subsequently be used for DBS. Indeed, this procedure offers various therapeutic alternatives. For example, if tolerance to DBS was observed, lesioning could then be performed after administration of local anesthesia. Discussion of Computer Modeling Several important parameters, such as current density or temperature, cannot be directly measured when the lead is embedded in the patient s brain. To overcome this limitation, we performed numerical simulations. This also enabled us to test assumptions on the mechanisms governing the evolution of the lesioning process. Our simulations were based on Laplace and bioheat transfer equations, which state that the temperature increase is due to resistive heating induced by the flow of electrical current between electrodes. The first equation gives the electrical potential distribution. We assumed a quasistatic conduction model because a cell is poorly conductive compared with the surrounding electrolyte at 250 khz. Thus, only the extracellular fluid is available to current flow 9 and capacitive heating is negligible. Moreover, temperature change is much slower than that of the electrical parameters. We can thus assume that the temperature increase is due to the mean electrical dissipated power. The second equation describes the heat spread in the brain, leading to coagulation. In pa- FIG. 6. Scanning electron microscopy photographs obtained when contact was used (left) and when contact was not used (right). 1031

6 S. Raoul et al. FIG. 7. Computer modeling image showing the evolution of the current density (units are given in A/m 2 and shown on the colored bar at left). The times elapsed since the beginning of the stimulation (t) are 0.5 (A), 1.5 (B), 3 (C), and 60 (D) seconds. The workspace (that is, the portion of the brain which is stimulated) is measured on the x and y axes in millimeters. tients, lesions should be smaller because of blood perfusion. 3,4 The simulations establish the upper limit of the lesion size. Experimentally, the current increases at the beginning of the coagulation and then falls abruptly. Conductivity behaves in a similar manner. It is known 6 that collagen becomes glucose at approximately 60 C, the liquids become vapor at approximately 100 C, and tissue charring is initiated at approximately 200 C, yet the microscopic mechanisms underlying the conductivity transformations are not well established. That is why we used the phenomenological description in which the conductivity decreases as soon as the temperature has exceeded a threshold value. This behavior has not been considered before because previous studies 3 6 focused on electrodes specifically designed for radiofrequency ablation, which are regulated to prevent the temperature exceeding a given threshold. The qualitative agreement between experimental results and simulations confirms the validity of our assumptions and insures that the coagulation is a self-limiting mechanism. Practical Guidelines to Create Lesions in Human Brain In patients, we recommend that bipolar lesions are made with a 250-kHz radiofrequency generator at the steady state of the plateau (40 V for 1000 impedance in the brain tissue), given that experiments in fresh egg whites have shown that, around the threshold, the coagulum could be unstable. This could be the same in human brain if the heat is dissipated by the vessels. Time was not a good parameter in this experiment to increase the size of lesions. We recommend using a duration of 30 or 60 seconds in humans. In our experience in using the technique in patients 18 we preferred to use two short durations rather than one long duration to increase the size of the lesion. This was based on the fact that in experimental 1032

7 Experimental studies of DBS electrodes used for staged lesion FIG. 8. Computer modeling image showing the evolution of the temperature (units are given in Kelvins and shown on the colored bar at left). The times elapsed since the beginning of the stimulation are 0.5 (A), 1.5 (B), 3 (C), and 60 (D) seconds. studies lesions were produced in 10 or 20 seconds and after this time no current was observed through the electrodes. We recommend the following precautions when using this procedure in patients: check the impedance before lesioning to adjust setting parameters of coagulation, use a radiofrequency generator that produces 250 khz or more (never less, as the electrode could be damaged and disabling pain could occur), use bipolar rather than monopolar lesions, and use voltage or current but always check that the relationship between these two parameters is consistent with the impedance measured before lesioning. Conclusions In present study we have reported on experimental and numeric studies of lesions made with a DBS lead. Experimental lesions were made in fresh egg whites and human cadaver brains. Similar results were obtained with both media. There is a voltage or current coagulation threshold. Above this threshold, the size of the lesion first increases exponentially, then saturates and remains almost constant. Above the threshold, the lesion reaches its final size within a few seconds. Increasing the stimulation duration does not increase the size of the lesion. The current increases slightly at the beginning of the stimulation and falls abruptly as the medium coagulates. Taking all these observations together, we assumed that the coagulation process was selflimiting when the coagulum grows it coats the active electrodes which become electrically insulated, and the process then stops. This assumption was confirmed by the numeric study; the model must include a temperature-dependent conductivity that becomes equal to zero when the temperature exceeds a threshold, to reproduce the experimental results. The simulations then show that the current flowing outside the desired zone is negligible. It is thus possible to create localized lesions with DBS leads operating well above the coagulation threshold (typi- 1033

8 S. Raoul et al. FIG. 9. Computer modeling image showing the evolution of the conductivity (units are given in S/m and shown on the colored bar at left). The times elapsed since the beginning of the stimulation are 0.5 (A), 1.5 (B), 3 (C), and 60 (D) seconds. cally 40 V with a radiofrequency generator). The procedure is safe because it is self-limiting. We wish to emphasize that this technique should not replace conventional stimulation but can be used when problems occur with the lead and the pacemaker. Authors of several studies have demonstrated that lesioning can be done with moderate side effects and is stable with time. 1,16 With our technique we can reduce the side effects. References 1. Alvarez L, Macias R, Lopez G, Alvarez E, Pavon N, Rodriguez- Oroz MC, et al: Bilateral subthalamotomy in Parkinson s disease: initial and long-term response. Brain 128 (Pt 3): , Bittar RG, Hyam J, Nandi D, Wang S, Liu X, Joint C, et al: Thalamotomy versus thalamic stimulation for multiple sclerosis tremor. J Clin Neurosci 12: , Chang I: Finite element analysis of hepatic radiofrequency ablation probes using temperature-dependent electrical conductivity. Biomed Eng Online 2:12, Chang IA, Nguyen UD: Thermal modeling of lesion growth with radiofrequency ablation devices. Biomed Eng Online 3:27, Chua E, Gose E, Vinas FC, Dujovny M, Star J: Temperature distribution produced in brain tissue and other media by a radiofrequency hyperthermia generator. Stereotact Funct Neurosurg 72:22 34, Ekstrand V, Wiksell H, Schultz I, Sandstedt B, Rotstein S, Eriksson A: Influence of electrical and thermal properties on RF ablation of breast cancer: is the tumor preferentially heated? Biomed Eng Online 4:41, Eriksson O, Backlund EO, Lundberg P, Lindstam H, Lindstrom S, Wårdell K: Experimental radiofrequency brain lesions: a volumetric study. Neurosurgery 51: , Eriksson O, Wårdell K, Bylund NE, Kullberg G, Rehncrona S: In vitro evaluation of brain lesioning electrodes (Leskell) using a computer-assisted video system. Neurol Res 21:89 95, Foster KR, Schwan HP: Dielectric properties of tissues and biological materials: a critical review. Crit Rev Biomed Eng 17: , Fox JL: Experimental relationship of radio-frequency electrical current and lesion size for application to percutaneous cordotomy. J Neurosurg 33: , Gill SS, Heywood P: Bilateral dorsolateral subthalamotomy for advanced Parkinson s disease. Lancet 350:1224, Hariz MI, Hirabayashi H: Is there a relationship between size and 1034

9 Experimental studies of DBS electrodes used for staged lesion site of the stereotactic lesion and symptomatic results of pallidotomy and thalamotomy? Stereotact Funct Neurosurgery 69: 28 45, Laitinen LV: Psychosurgery. Stereotact Funct Neurosurg 76: , Moringlane JR, Koch R, Schäfer H, Ostertag CB: Experimental radiofrequency (RF) coagulation with computer-based on line monitoring of temperature and power. Acta Neurochir (Wien) 96: , Oh MY, Hodaie M, Kim SH, Alkhani A, Lang AE, Lozano AM: Deep brain stimulator electrodes used for lesioning: proof of principle. Neurosurgery 49: , Okun MS, Vitek JL: Lesion therapy for Parkinson s disease and other movement disorders: update and controversies. Mov Disord 19: , Pennes HH: Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 1:93 122, Raoul S, Faighel M, Rivier I, Vérin M, Lajat Y, Damier P: Staged lesions through implanted deep brain stimulating electrodes: a new surgical procedure for treating tremor or dyskinesias. Mov Disord 18: , Van den Berg J, Van Manen J: Graded coagulation of brain tissue. Acta Physiol Pharmacol Neerl 10: , Yen CP, Kung SS, Su YF, Lin WC, Howng SL, Kwan AL: Stereotactic bilateral anterior cingulotomy for intractable pain. J Clin Neurosci 12: , Zhu L, Diao C: Theoretical simulation of temperature distribution in the brain during mild hypothermia treatment for brain injury. Med Biol Eng Comput 39: , 2001 Manuscript submitted July 9, Accepted March 29, Address correspondence to: Sylvie Raoul, M.D., Ph.D., Service de Neurochirurgie, Hôpital G. et R. Laënnec, Boulevard Jacques Monod, Nantes Cedex 1, France. sylvie.raoul@ chu-nantes.fr. 1035