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The compartment model for chronically implanted voltammetric electrodes in the rat brain
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U O ~ tTs-tso Pu~lreimd
I,TS
Ltd.
THE COMPAggMENT MODEL FOR CHRONICALLY IMPLANTED VOLTAMMETlUC ELECTRODES IN THE~RAT BRAIN
W.J. ALBERY', M. FILLENZ* and R.D. O'NEILL
University Laboratory of Physiology, South Parks Road, O~ord OX! 3PT and IDepurtment o f CIx,mistry, Imperial College, London SW7 2A g (U.K.) (Rca:eived February 17th, 1983; Accepted April 18th, 1983)
Key words: linear sweep voltammetry - rat brain - acute and chronic - theoretical treatment - compartment model
Experimental properties of the peaks obtained with carbon paste electrodes and microprocessor-hased linear sweep voltammetry in the rat brain have been compared with those predicted by a theoretical treatment of the problem which we have recently developed. This c o - - s o n indicates that the electrodes are situated in a restricted compartment and that the oxidation of ascorbate under these conditions is ineversible. Examples of how this situation has been exploited to improve the voitammograms obtained are given.
Linear sweep voltammetry with carbon paste electrodes is a powerful technique for simultaneomly monitoring changes in the extracellular concentration of a wide variety of compounds in the brain of freely movinlg animals [I, 5-10]. The recent application of microprocessor technology to the acquisition and analysis of the c~ata [71 had made possible the precise measurement of the shape of the voltammetric peaks obtained in brain tissue, in this paper we show that, followins implantation of the electrodes, there is a Ipradual change in the shape of the voltammolprams. We propose that these changes represent the transition from the electrodes sampling a semi-infinite linear diffusion field, such as observed in experiments in a beaker, to sampling a restricted compartment. In a semi-infinite diffusion field there is a continuous supply of the electroactive substrate to the electrode; once the oxidation potential is reached, the rate of oxidation is limited by the rate of diffusion. This gives rise to a broad asymmetric peak whose shape is improved by semidifferentiation [4, 6]. In a restricted compartment, when the voltage is swept through the oxidation potential of a particular substance, all of that species present in the compartment is oxidized. The effect on the peak shape of this restriction of the supply of oxidizable material to the electrode is similar to the effect of semidifferentiation. A * Author for correspondence.
0304-3940/83/$ 03.00 © 1983 Eltevier Scientific Publishers Ireland Ltd.
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Fig. I. The effect of increasing the level of brain ascot-bate on the voltammolgrams recorded there between - 200 and M0 mV at 10 mV/$. Before (o) and after (*) injection; the difference is shown without symbols (curves a. b and c. respectively). The current scale on the right for the difference voltammograms has the same magnitude as that on the left. The abscissa is the same for A. B and C. A: the semidifferentiated currem recorded from an anaesthetized rat. using an electrode implanted for a few hours. B: the semidifferentiated current recorded from an unanaesthetized rat several weeks after the electrode had been implanted. C: the direct current recorded with conditions as in B. See text for fuller description and conclusions.
177
l i m ~ compartment model has implications for the shape of the voltammograms under different recording conditions, and can be made use of to further increase the sensitivity of the recording method. A compartment model, based on resu~s obtained r~
previously [10]. The recording apparatus consisted of a 380Z microprocessor (Research Machines Ltd., Oxford) linked to an interface (designed by Dr. N.J. Goddard, Imperial College, London). Voltammograms were recorded between - 2 0 0 and ~ 0 mV at sweep rates of 2.S, 5, l0 and 20 mV/s. Values of the current were stored on magnetic disc at 10 mV intervals for sweep rates of 2.5-10 mV/s and at 20 mV intervals for the 20 mV/s rate. All potentials are reported with respect to the
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Fig. 2. The effect of varying the sweep ram on the position, F.~ in mV, and height, h in hA, of peak I recorded in brain tissue several days after the implantation o f the electrodes, o = 20 mV/s (Era = 248 ± 7, h = 2.4 ± 0.2);* = 1 0 m V / s ( E m = 173 ± 6, h = 1.2 ± 0.1); x = 5 m V / s ( E m = 123 ± 7, h = 0.5 ± 0.0S); + = 2.5 m V / s 0 ~ , = SO ± 7, h = 0.IS ± 0.01). Direct current. Mean ± S.E.IV,. (4 electrodes).
178
implanted AIg-AgC'I reference electrodes. Further details of the equipment and recording methods have been ~ven elsewhere 171. Fis. IA shows semidifferenfiated linear sweep voltammograms in an anaesthetized rat using an decxrod¢ which had been implanted for a few hours. Voltama s c o r l i g beside the electrode; curve c is the d i f f a I betwc~'n a and b. In this case semi.diffaemiation 1111produces a reasonable ascorbate peak (curve c) and we conclude that the electrode is still sensing a semi-inf'mite diffusion field. The voltammolrams in Fig. IB are similar semidiffercntiated currents to those in Fig. IA except that now the electrode has been implanted for several weeks. The difference voltammolgram (curve c) shows a large nqgadve excursion. This result is typical of electrodes which have been implanted for more than a day or two. Fig. IC shows nonsemidifferentiated recordings of changes in ascorbate similar to those illustrated in Fig. I B; here the difference voltammogram for the added ascorbate (curve c) consists of a simple peak. We conclude that, after the electrode has been implanted for a day or more, semidifferentiation is not appropriate and that it is better to analyze the simple curves shown in Fig. IC. in contrast, in experiments in vitro [4] or recordings from anaesthetized animals with recently implanted electrodes [6], well defined peaks are obtained only after semidifferentiation of the linear sweep voltammolrams. Histological examination of brain sections show the recording electrode to be surrounded by an area of fgliosis. It seems likely thai the gradual accumulation of llial cells is responsible for the development of a restricted compartment around the electrode tip. We have presented elsewhere 121 the theory for the shapes of the peaks for reversible and irreversible electrochemical systems under these conditions and have shown that well behaved peaks as shown in Fil. 1(2 will be observed.
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Fig, 3. A: the values of peak position. Em in mV, for p-~k I. plotted against Ioge of sweep rate. The value of ~ is 0.45 _+ 0,03 (n = 4, number of electrodes). B: a plot of loF, of the height of peak I, h in nA, versus Iog~ of sweep rate. The slope is !.2 _+ 0. I (n = 4. number of electrodes).
179 For an irreversible system, our theoretical analysis of the compartment model describes the shift of the peak voltage, Era, with sweep rate aEm F / R T = ln(aV F / R T A k~) + ln(dE/dt) where V is the volume o f the c o m p ~ m e n t , A is the area of the electrode, k~ is the electrochemical rate constant, and a is the transfer coefficient. Fig. 2 shows typical results f o r the shift o f the ascorbate peak(peak 1) with sweep rate. After correcting for the filter [2], the results are plotted in Fig. 3A. A good straight line is obtained giving a value for a of 0.45 :l: 0,03 (n = 4 ) which is a reasonable value for an irreversible system. For the compartment model the peak height, h, should be a linear function of sweep r~te [2]. The plot of In(h) versus In(dE/d0 from Fig. 2 (see Fig. 3B) has a slope of 1.2 ± 0. I (n = 4) and shows that theory and experiment are in good agreement. Furthermore, our analysis shows [2] that the shape of an irreversible peak should be asymmetric with a width at half height of (65/c0 mV. For a value of a of 0.45 the predicted width is 144 ± 7 mV and is in good agreement with the observed value of 130 ± 3 mV (n = 10). The asym-
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Fig. 4. An example of the implications of an electrode sampling a restricted compartment. By scanning continually, the electrochemical species present in the compartment can be effectively depleted. The voltammograms recorded under these conditions measure the background current of the electrode. Recording at 12 min intervals allows time for the levels to recover. Subtraction produces a difference voltammogram(shownabove) whosecurrent is due entirelyto the oxidation of compounds in the vicinity of the electrode tip. Recorded in the slriatum, peak t is due to ascorbate, peak 2 principally to 5-hydroxyindoleaceticacid, and peak 3 mainly to homovanillic acid.
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metry of peak I is also in reasonable agreement with that predicted from the theoretical analysis. The existence of the restricted compartment is further confirmed by the removal
dings, ~ may M clmmed of all t k interfering agorbate and this allows one to obtain more ~ measurements for the rcmaini~ neuroregulators [9]. By continuous ~ of the compartment, all the electroactive species present may be removed and hence a backlpround current can be obtained. The subtraction of this backlpround current from the voltammograms gecorded at 12 rain intervals, which is now a routine part of the analysis, yields voltammouams consisting of 3 well resolved peaks. Fig. 4 shows typical results for the striatum. Peak I is due to ascorbate, peak 2 principally to 5Atydroxyindoleacetic acid, while homovanillic acid is mainly responsible for peak 3 [7, 8, 10]. Using microprocessor-basedlinear sweep voltammetry and carbon paste electrodes together with the compartment model, we are now able to monitor continuously the concentrations of these substances for periods of 6 months or more in the same rat. We thank the MRC for financial support, Mr. R.A. Griinewald for implanting the electrodes, and Dr. N.J. Goddard for designing and constructing the microprocessor-based equipment. I Alhery, W.J., Fillen/, M., Cioddard, N.J., Mclntyre, M.E. and O'Neill, R.D., ChanlleS in brain dopamine metabolites usintt microprocessor-controlled voltammetry in the rat, J. Physiol. (Lond.), .lJ2 (1982~ 107P. 2 Albery, W.J., Beck, r.W., Fillent, M., G(~Jdard, N.J. and O'Neill, R.D., Theoretical and experimental studi~,.'sof linear sweep voltammetry in the rat brain, J. electroanalyt. Chem., submitted. 3 Cheng, ll.-Y., .~henk, J., Huff. R. and Adams, R.N., In vivo electrochemistry: hehaviour of microelectrodes in brain tissue, J. ele~roapalyl. Chem., 100 (1979) 23-31. 4 Goto, M. and lshii, D., Semidifferenlial electroanalysis, Electroanalyt. Chem. Interfac. Electrochem., 61 (1975) 36i-365. 5 Kissinger, P.T., Hart, J.B. and Adams, R.N., Voltammetry in brain tissue - a new neurophysiological measurement, Brain Reg., $5 (1973) 209-213. 6 Lane, R.F., tlubbard, A.T. and Blaha, C.D., Application of semidifferential electroanalysis to studies of neurotransmitters in the central nervous system, J. eleclroanalyl. Chem., 9~f (19"/9) i 17_1"~) 7 O'Neill, R.I)., Fillenz, M., Albe~', W.J. and Goddard. N.J., The monitoring of ascorbate and monoamine transmitter metabolites in the striatum of unanaeslhetised rats using microprocessorba.~-d voltammetry, Nenroscienee, 9 (1983) 87-93. 8 O'Neill, R.D. Fillenz, M. and Alhery, W.J., Circadian changes in homovanillic acid and ascorbate in the rat striatum using microprocessor-controlled voltammelry, Nenrosci. Lett., 34 (1982) i89-103. 9 O'Neill, R.D., Fillenz, M. and Albery, W.J., The development of linear sweep vollammetry with carbon paste electrodes in vivo, J. Nenrosci. Meth., in press. I0 O'Neill, R.D., Grunewald, R.A., Fillenz, M. and Albery, W.J., Linear sweep vollammetry with carbon paste electrodes in the rat strialum, Nenroscience, 7 0982) 1945-1954. I! Oldham, K.B. and Spanier. J., Fra¢lional Calculus, Academic Press, New York, 1074. Ima-.
U O ~ tTs-tso Pu~lreimd
I,TS
Ltd.
THE COMPAggMENT MODEL FOR CHRONICALLY IMPLANTED VOLTAMMETlUC ELECTRODES IN THE~RAT BRAIN
W.J. ALBERY', M. FILLENZ* and R.D. O'NEILL
University Laboratory of Physiology, South Parks Road, O~ord OX! 3PT and IDepurtment o f CIx,mistry, Imperial College, London SW7 2A g (U.K.) (Rca:eived February 17th, 1983; Accepted April 18th, 1983)
Key words: linear sweep voltammetry - rat brain - acute and chronic - theoretical treatment - compartment model
Experimental properties of the peaks obtained with carbon paste electrodes and microprocessor-hased linear sweep voltammetry in the rat brain have been compared with those predicted by a theoretical treatment of the problem which we have recently developed. This c o - - s o n indicates that the electrodes are situated in a restricted compartment and that the oxidation of ascorbate under these conditions is ineversible. Examples of how this situation has been exploited to improve the voitammograms obtained are given.
Linear sweep voltammetry with carbon paste electrodes is a powerful technique for simultaneomly monitoring changes in the extracellular concentration of a wide variety of compounds in the brain of freely movinlg animals [I, 5-10]. The recent application of microprocessor technology to the acquisition and analysis of the c~ata [71 had made possible the precise measurement of the shape of the voltammetric peaks obtained in brain tissue, in this paper we show that, followins implantation of the electrodes, there is a Ipradual change in the shape of the voltammolprams. We propose that these changes represent the transition from the electrodes sampling a semi-infinite linear diffusion field, such as observed in experiments in a beaker, to sampling a restricted compartment. In a semi-infinite diffusion field there is a continuous supply of the electroactive substrate to the electrode; once the oxidation potential is reached, the rate of oxidation is limited by the rate of diffusion. This gives rise to a broad asymmetric peak whose shape is improved by semidifferentiation [4, 6]. In a restricted compartment, when the voltage is swept through the oxidation potential of a particular substance, all of that species present in the compartment is oxidized. The effect on the peak shape of this restriction of the supply of oxidizable material to the electrode is similar to the effect of semidifferentiation. A * Author for correspondence.
0304-3940/83/$ 03.00 © 1983 Eltevier Scientific Publishers Ireland Ltd.
176 '
A
NA/s~
rb
1
4
0
2
0
12
g
nA/s~ 0
e
3
o
'
G
nA 4
•..100
110 mU
4i0
Fig. I. The effect of increasing the level of brain ascot-bate on the voltammolgrams recorded there between - 200 and M0 mV at 10 mV/$. Before (o) and after (*) injection; the difference is shown without symbols (curves a. b and c. respectively). The current scale on the right for the difference voltammograms has the same magnitude as that on the left. The abscissa is the same for A. B and C. A: the semidifferentiated currem recorded from an anaesthetized rat. using an electrode implanted for a few hours. B: the semidifferentiated current recorded from an unanaesthetized rat several weeks after the electrode had been implanted. C: the direct current recorded with conditions as in B. See text for fuller description and conclusions.
177
l i m ~ compartment model has implications for the shape of the voltammograms under different recording conditions, and can be made use of to further increase the sensitivity of the recording method. A compartment model, based on resu~s obtained r~
previously [10]. The recording apparatus consisted of a 380Z microprocessor (Research Machines Ltd., Oxford) linked to an interface (designed by Dr. N.J. Goddard, Imperial College, London). Voltammograms were recorded between - 2 0 0 and ~ 0 mV at sweep rates of 2.S, 5, l0 and 20 mV/s. Values of the current were stored on magnetic disc at 10 mV intervals for sweep rates of 2.5-10 mV/s and at 20 mV intervals for the 20 mV/s rate. All potentials are reported with respect to the
3.2
2.4
nA
1.6
0.8
0.0 - 90
200
mU
490
Fig. 2. The effect of varying the sweep ram on the position, F.~ in mV, and height, h in hA, of peak I recorded in brain tissue several days after the implantation o f the electrodes, o = 20 mV/s (Era = 248 ± 7, h = 2.4 ± 0.2);* = 1 0 m V / s ( E m = 173 ± 6, h = 1.2 ± 0.1); x = 5 m V / s ( E m = 123 ± 7, h = 0.5 ± 0.0S); + = 2.5 m V / s 0 ~ , = SO ± 7, h = 0.IS ± 0.01). Direct current. Mean ± S.E.IV,. (4 electrodes).
178
implanted AIg-AgC'I reference electrodes. Further details of the equipment and recording methods have been ~ven elsewhere 171. Fis. IA shows semidifferenfiated linear sweep voltammograms in an anaesthetized rat using an decxrod¢ which had been implanted for a few hours. Voltama s c o r l i g beside the electrode; curve c is the d i f f a I betwc~'n a and b. In this case semi.diffaemiation 1111produces a reasonable ascorbate peak (curve c) and we conclude that the electrode is still sensing a semi-inf'mite diffusion field. The voltammolrams in Fig. IB are similar semidiffercntiated currents to those in Fig. IA except that now the electrode has been implanted for several weeks. The difference voltammolgram (curve c) shows a large nqgadve excursion. This result is typical of electrodes which have been implanted for more than a day or two. Fig. IC shows nonsemidifferentiated recordings of changes in ascorbate similar to those illustrated in Fig. I B; here the difference voltammogram for the added ascorbate (curve c) consists of a simple peak. We conclude that, after the electrode has been implanted for a day or more, semidifferentiation is not appropriate and that it is better to analyze the simple curves shown in Fig. IC. in contrast, in experiments in vitro [4] or recordings from anaesthetized animals with recently implanted electrodes [6], well defined peaks are obtained only after semidifferentiation of the linear sweep voltammolrams. Histological examination of brain sections show the recording electrode to be surrounded by an area of fgliosis. It seems likely thai the gradual accumulation of llial cells is responsible for the development of a restricted compartment around the electrode tip. We have presented elsewhere 121 the theory for the shapes of the peaks for reversible and irreversible electrochemical systems under these conditions and have shown that well behaved peaks as shown in Fil. 1(2 will be observed.
,.oi
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;
1~;0 -
//
/
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/
140
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//
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.-,
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: 0
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....
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Fig, 3. A: the values of peak position. Em in mV, for p-~k I. plotted against Ioge of sweep rate. The value of ~ is 0.45 _+ 0,03 (n = 4, number of electrodes). B: a plot of loF, of the height of peak I, h in nA, versus Iog~ of sweep rate. The slope is !.2 _+ 0. I (n = 4. number of electrodes).
179 For an irreversible system, our theoretical analysis of the compartment model describes the shift of the peak voltage, Era, with sweep rate aEm F / R T = ln(aV F / R T A k~) + ln(dE/dt) where V is the volume o f the c o m p ~ m e n t , A is the area of the electrode, k~ is the electrochemical rate constant, and a is the transfer coefficient. Fig. 2 shows typical results f o r the shift o f the ascorbate peak(peak 1) with sweep rate. After correcting for the filter [2], the results are plotted in Fig. 3A. A good straight line is obtained giving a value for a of 0.45 :l: 0,03 (n = 4 ) which is a reasonable value for an irreversible system. For the compartment model the peak height, h, should be a linear function of sweep r~te [2]. The plot of In(h) versus In(dE/d0 from Fig. 2 (see Fig. 3B) has a slope of 1.2 ± 0. I (n = 4) and shows that theory and experiment are in good agreement. Furthermore, our analysis shows [2] that the shape of an irreversible peak should be asymmetric with a width at half height of (65/c0 mV. For a value of a of 0.45 the predicted width is 144 ± 7 mV and is in good agreement with the observed value of 130 ± 3 mV (n = 10). The asym-
o,s
1
0 .. 6
, A
2 0,4
3 0.2
O.O -100
200
mU
$00
Fig. 4. An example of the implications of an electrode sampling a restricted compartment. By scanning continually, the electrochemical species present in the compartment can be effectively depleted. The voltammograms recorded under these conditions measure the background current of the electrode. Recording at 12 min intervals allows time for the levels to recover. Subtraction produces a difference voltammogram(shownabove) whosecurrent is due entirelyto the oxidation of compounds in the vicinity of the electrode tip. Recorded in the slriatum, peak t is due to ascorbate, peak 2 principally to 5-hydroxyindoleaceticacid, and peak 3 mainly to homovanillic acid.
IS0
metry of peak I is also in reasonable agreement with that predicted from the theoretical analysis. The existence of the restricted compartment is further confirmed by the removal
dings, ~ may M clmmed of all t k interfering agorbate and this allows one to obtain more ~ measurements for the rcmaini~ neuroregulators [9]. By continuous ~ of the compartment, all the electroactive species present may be removed and hence a backlpround current can be obtained. The subtraction of this backlpround current from the voltammograms gecorded at 12 rain intervals, which is now a routine part of the analysis, yields voltammouams consisting of 3 well resolved peaks. Fig. 4 shows typical results for the striatum. Peak I is due to ascorbate, peak 2 principally to 5Atydroxyindoleacetic acid, while homovanillic acid is mainly responsible for peak 3 [7, 8, 10]. Using microprocessor-basedlinear sweep voltammetry and carbon paste electrodes together with the compartment model, we are now able to monitor continuously the concentrations of these substances for periods of 6 months or more in the same rat. We thank the MRC for financial support, Mr. R.A. Griinewald for implanting the electrodes, and Dr. N.J. Goddard for designing and constructing the microprocessor-based equipment. I Alhery, W.J., Fillen/, M., Cioddard, N.J., Mclntyre, M.E. and O'Neill, R.D., ChanlleS in brain dopamine metabolites usintt microprocessor-controlled voltammetry in the rat, J. Physiol. (Lond.), .lJ2 (1982~ 107P. 2 Albery, W.J., Beck, r.W., Fillent, M., G(~Jdard, N.J. and O'Neill, R.D., Theoretical and experimental studi~,.'sof linear sweep voltammetry in the rat brain, J. electroanalyt. Chem., submitted. 3 Cheng, ll.-Y., .~henk, J., Huff. R. and Adams, R.N., In vivo electrochemistry: hehaviour of microelectrodes in brain tissue, J. ele~roapalyl. Chem., 100 (1979) 23-31. 4 Goto, M. and lshii, D., Semidifferenlial electroanalysis, Electroanalyt. Chem. Interfac. Electrochem., 61 (1975) 36i-365. 5 Kissinger, P.T., Hart, J.B. and Adams, R.N., Voltammetry in brain tissue - a new neurophysiological measurement, Brain Reg., $5 (1973) 209-213. 6 Lane, R.F., tlubbard, A.T. and Blaha, C.D., Application of semidifferential electroanalysis to studies of neurotransmitters in the central nervous system, J. eleclroanalyl. Chem., 9~f (19"/9) i 17_1"~) 7 O'Neill, R.I)., Fillenz, M., Albe~', W.J. and Goddard. N.J., The monitoring of ascorbate and monoamine transmitter metabolites in the striatum of unanaeslhetised rats using microprocessorba.~-d voltammetry, Nenroscienee, 9 (1983) 87-93. 8 O'Neill, R.D. Fillenz, M. and Alhery, W.J., Circadian changes in homovanillic acid and ascorbate in the rat striatum using microprocessor-controlled voltammelry, Nenrosci. Lett., 34 (1982) i89-103. 9 O'Neill, R.D., Fillenz, M. and Albery, W.J., The development of linear sweep vollammetry with carbon paste electrodes in vivo, J. Nenrosci. Meth., in press. I0 O'Neill, R.D., Grunewald, R.A., Fillenz, M. and Albery, W.J., Linear sweep vollammetry with carbon paste electrodes in the rat strialum, Nenroscience, 7 0982) 1945-1954. I! Oldham, K.B. and Spanier. J., Fra¢lional Calculus, Academic Press, New York, 1074. Ima-.