Simulation studies of in vivo electrochemistry

compyILT3 & chemirlry vol. 4,PP. 19-26 PnssLtd.. 1980. Printed in Great Britain Pcrgamon

SIMULATION

STUDIES OF IN VIVO ELECTROCHEMISTRY

W. S. LINDSAY and .I. B. JUSTICES Department of Chemistry, Emory University, Atlanta, GA 30322, U.S.A

and JOHN SALAMONE Department of Psychology, Emory

University, Atlanta. GA 30322. U.S.A.

(Received 23 July 1979) Abstract-A computer program which simulates irt uiuo chronoamperometry is described. Several simulations of chemical and electrical stimulation of the brain are presented to demonstrate the relationship of the observed response to the experimental parameters. Pulse width, time between pulses and electrode geometry are varied and the effect on electrode response illustrated INTRODUCTION

Within the past few years several investigators have reported results obtained from the in uiuo monitoring of brain catecholamines and their metabolites by conventional electroanalytical techniques. Adams’ group at the University of Kansas has used chronoamperometry extensively while Lane and Hubbard at the University of California at Santa Barbara have oublished data obtained from both differential and semi-diffeiential pulse voltammetry (Adams, 1976, Conti et al., 1978; Lane ef al., 1978; Huff et al., 1979; Lane et al., 1979). The theories of such electrochemical methods are discussed in detail elsewhere (Parry & Osteryoung, 1%5; Goto & Ishii, 1975; Galus. 1976; Alford et al., 1977). A typical in viuo experiment consists of the following: (i) stereotaxically placing the standard three electrode cell into the desired brain region of an anesthetized rat: (ii) obtaining a constant baseline electrochemical signal ; (iii) causing an increase in catecholamine level by the injection of an appropriate drug or by electrical stimulation of a particular brain region; and (iv) monitoring the return to baseline after the effect of the drug or stimulation has ended. Typical results of an in uiw experiment conducted in rat striatum are shown in Fig. 1. At point A the rat stopped breathing but was revived just prior to the measurement at B. The signal obtained at the next measurement was 3 times greater than that at B. Successive measurements, thereafter, showed a decline to baseline level very similar to that obtained before ‘stimulation.’ Although the techniques employed for in uiuo measurements are identical to that for the bulk solution, there are some significant differences in the pattern of the obtained response. In the bulk solution the first measurement and all subsequent ones are constant within experimental error: whereas successive responses obtained in uiao decrease until a steady baseline is observed as in Fig. 1. In a recent paper, Cheng ei af. have

derived an Eq. (I) to explain this phenomenon and have shown two results obtained via chronoamperometry simulation (Cheng et al., 1979). c”

=

C”_,

331”.

C”_,

+f

L,(C,-

C.-J.

(1)

The equation was derived by assuming that a small volume of extracellular fluid exists at the tip of the electrode. Electrochemical oxidation lowers the concentration of electroactive species in this space which are then replaced by mass trartsport from the surrounding extracellular fluid. When the rate of depletion equals the rate of replacement, a steady state exists which yields a stable baseline chronoamperometric signal. An increased influx of oxidizabie material will result in an increase in electrochemical signal. If the influx occurs over a very short period of time, as for the period of less than or equal to one measurement, as might occur during brief electrical stimulation, the electrochemical response will show a sharp increase followed by a slow decay to baseline. This will continue untit electrochemical depletion lowers the concentration of the fluid compartment at the electrode tip to pre stimulation levels. The reader is referred to the appropriate article for details of the derivation, but for the sake of clarity the variables in the equation will be defined using the definitions of Cheng et al., C,, = ‘inside’ concentration of fluid compartment; C,,_, = previous concentration of the fluid compartment; D = diffusion coefficient for the measured species; K = a mass transport coefficient; L = thickness of the fluid compartment; t, = duration of a single chronoamperometric pulse; t, = time between successive pulse applications, and Co= endogenous (‘outside’) concentration in the neural tissue. Values of D and K were 1.0 X 10T6cm’lsec and 1.25 X lo-’ cmlsec, respectively. In the work reported here extensive computer simulations of in uiuo el&trochemistry experiments have been conducted in order to better understand the relationship of the observed response to the independent variables.

tAuthor to whom requests for reprints should be sent. 19

20

W. S.

LINDSAY et al.

1800

1200

nAmps 1000

800

400

ab

200

30

60

TIME

(

mid

90

120

Fig. 1. Typical response for successive in viva chronoamperometric measurements in rat striatum. t, = I set, t, = 180sec. Teflon sheathed carbon paste electrode, teflon tubing = 0.6 mm DD. METHOD

A FORTRAN computer program (Appendix 1) was written to simulate in vim chronoamperometry based on Eq. (1). The program has the capability of simulating a complete in vim experiment, i.e. initial decay to baseline, signal increase upon drug injedtion or electrical stimulation and return to baseline after the induced effects have subsided (see Fig. 2). The program shown in Appendix I was written for drug injection simulations using a square wave drug profile, but it can be easily modified to simulate electrical stimulation responses. The user inputs values for t,. pulse width, r,, time delav between pulses and L. length of fluid volume from elecirode surface to surround&tissue. After execution, the program outputs C,/C, values which are directly proportional to successive i t’” values which are in turn proportional to the concentration of the electroactive species. In the graphs that are shown below, the ‘outside’ concentration, C, is increased to 2C0 at the indicated time for drug induced changes and is pulsed to 10C0 for only one measurement in the electrical stimulation case. The simulations shown here were conducted using fixed values for the number of pulses to apply before stimulation, during approach to maximum, and during return to baseline-(26,-U, 15, respectively, for the drug simulations and 20. 1. 15. respectively. for the electrical stimulation simulations).~ These pulse. numbers can be made variable by simply making the final size of the three DO LOOPS in Appendix 1 an integer variable which could be input at the beginning of each simulation run.

RESULTS AND Dl!XUSSION

In the type of in uiuo study outlined in the Introduction, one is interested in achieving a stable baseline response in a minimum amount of time and acquiring a maximum signal increase upon drug injection or electrical stimulation. The experimenter has little control over L, for its value is dependent upon the size, geometry, and location of the working electrode (Cheng et al., 1979). However, t, and f, can readily be manipulated. Thus, in the simuliitions reported here, unless stated otherwise, L is fixed at 0.05 mm (Cheng er ai., 1979) and 1, and t, are varied. In Fig. 3(a), which simulates a drug injection experiment, t, is fixed at 180 set and L at 0.05 mm with tl being varied, between 0.5 and 10.0 sec. This graph indicates that the time required to obtain an initial stable baseline decreases with increasing values of t. and ranges from 60min for t. = 0.5 set to 20 min for I, = lO.Osec. Also, the increase in response after a drug injection decreases with increasing values of rr These increases in Fig. 3(a) range from 0.2 units for r, = 0.5 set down to 0.07 units for t, = 10 sec. Fii 3(b) represents data from an electrical stimulation simulation with values for t, and L identical to those of Fig. 3(a). Here again one sees the same pattern in the observed response which was seen in Fig. 3(a) (i.e. larger increases in signal but longer experiments with decreaseing t, values). Figure 4 demonstrates the dependence of the response on t,, the time between pulses, for given values of t. (I set) and L (0.05 mm). In Fig. 4(a), t, is varied between

Simulation studies of in uivo electrochemistry

21

STIMULATION

APPLY

FOR

PULSE

Ts

I

APPLY PULSE FOR Ts

INCREASE Co

I

Fii. 2. Flowchart for simulation program 60 and 300 sec. A stable baseline is achieved most quickly ( = 20 min) with the smallest t,, while the slowest decrease to stable baseline ( = 75 min) is observed with the largest t,. For I, = 300 set the increase in signal after drug stimulation is 0.25 units; whereas the increase for t, = 60 set is only 0.06 units. The results of an electrical stimulation simulation in which the external concentration is increased by lCW% for one pulse for r, = 1 set, L = 0.05mm, and various t, values are shown in Fig. 4(b). In this case, the increase in the observed response also increases with increasing values of L,,. The increase ranges from 0.14 units for t, = 60 see to 0.67 units for t, = 300 sec. The importance of electrode geometry and hence L is shown in Fii. S-The results obtained from the simulation of an electrical stimulation experiment with fixed values of t, (1 set) and t, (300set) clearly demonstrates that small L values yield both a large increase in response and a quick decay to baseline after a purposeful stimulation (Fig. 5b). For L =0.02 mm a stable baseline response is observed in 25 min along with an increase in signal of 1.7 units after stimulation; whereas for L = 0.1 mm a stable baseline is not obtained within 100 tin and results in a signal increase of only 0.3 units. L values are best varied by changing the size and shape of the working electrode, but a determination of the size of L is not straightforward. Perhaps one of the

best ways to quantitate L is to use collected data and solve Eq. (1) for L. For graphite paste electrodes packed in the tip of 30 gauge teflon tubing fitted over stainless steel wire (Conti et al., 1978), we obtained values of L ranging from 0.07 to 0.45 mm, with an average value of 0.24mm for 9 rats. This is approx. 5 times the value reported by Cheng et al., who used glass capillaries packed with graphite paste as electrodes (Cheng et ai., 1979). The difference may be the result of greater tissue damage caused by the larger electrodes used by us. The outside diameter of the teflon electrodes is 0.6mm as opposed to 0.2 mm for the glass capillary electrodes. In choosing values for r, and t, one must bear in mind the time requirements for the experiment. Thus, assuming an L value of 0.05 mm, an entire in vim drug experiment cari bc completed in about 3 hr with t, = 180 set and t, = 1.0 sec. Under these conditions the maximum signal increase after a drug .injection is 0.15 units. As can be seen from Fig. 3(a) slightly larger increases in signal result for f, = 0.5 set with total experimental time approximately equal to that for t. = 1 sec. However, we have found it difficult when using conventional electrochemistry systems (PAR 170) to read the obtained i t’” value for pulse times less than 1 sec. If one is using a computer controlled system, then Z, values less than 1 set pose no problem. In conclusion, the results of this simulation study

W. S. LlmsAY el al.

Simulation studies of in uivo electrochemistry

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CAC Vol. 4, No. 1.-D

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w. s. LINDSAY et Af.

Simulation studies of in oiuo electrochemistry indicate that for optimum response time of the signal relative to changing endogenous concentration of electroactive species, one should keep the volume of fluid at the electrode tip as small as possible. The size of L determines to a great extent how frequently one may make observations and how closely one may follow rapidly changing levels of the species under study. In this regard, Gonon (Gonon et al., 1978) using carbon fiber electrodes of 8~ diameter, was able to record every 5 set using a pulse width of 200 msec. The price one pays for this increased data rate is a greatly reduced signal amplitude, so that particular attention must be paid to electrical isolation and signal amplification when using very small electrodes.

25 REFERENCES

Adams, R. N. (1976). Anal. Chem. 48, 1128A. Alford, P. D., Goto, M. & Oldham, K. B. (1977). L Electroanal. Chem. 85, I. Cheng, H. Y., Schenk, J., Huff, R. & Adams. R. N. (1979). J. Efectroanal. C/tern. 1tW. 23. Conti, 1. C., StroDe, E., Adams, R. N. & Marsden, C. A. (1978) Life Sciences i3,2705. Galus, 2. (1976), Fundamentals of Electrochemical Analysis. Halsted Press, New York. Gonon. F., Cewualio. R., Ponchon, J. L.,Buda, M. Jouud, M., Adams, R. N: ~Pujol, J.-F. (1978), C. R. Acad. Sci. Paris 286. 1203.

Goto, M. & Ishii, D. (1975) 3. Electroanaf. Huff, R., Adams, R. N., & Rutledge, C. 0. (in press). Lane, R. F.. Hubbard, A. T. & Blaha, troanal. Chem. 95, 117. Lane. R. F.. Hubbard. A. T. & Blaha.

Acknowledgement-Acknowledgement

is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.

f&hem.

Chem. 61, 361. (1980), Brain Research C. D. (1979). J. ElecC. D. (1978). Bioelec-

and Bioene’qet. 5, 506.

Parry, E. P. % Osteryoung,

R. A. (1%5), Anal. Chem. 37, 1634.

APPENDIX 1 Chrononmp simulation THIS

IS

TPE

A

PROGFAM

PROGRAN

THE

C”ENG

ET _I

METRY

SIMULATION.

Tw

AL.

(TIME

THE

OF

RATIO

CENTRATION.

PROGFtAN

THIS

DIMENSION

VIVO

ELECTROCHEMISTRY.

PROCEDURE

IS

TS

RATIO

CAN

(DURATION

DIRECTLY

BE

OUTLINED

THE

OUTPUT

TO

THE

BY

CHRONOANPEROCHANGED

PULSE),

OF

CONCENTRATION IS

IS

FOR

WHICH

COMPARTMENT). NEW

THAT

SPECIFICALLY

VARIABLES

FLUID EACH

IN --

SANE

PULSES],

THE OF

SIMULATE THE

THE

BETWEEN

THICKNESS AS

TO

FOLLOWS

ARE

AND IS

TO

(THE

EXPRESSED

INITIAL

PROPORTIONAL

L

IT

CONl/2

.

C (100)

WRITE(2.9) ‘DURATION

F@RMAT(lX,

OF

SINGLE

CHRONOAMP

N.ZASUREMENT?(O

READ,TS IF

(TS.EQ.O)GO

TO

5

WRITE(2,19) 19

FORMAT(lX,‘TIME READ, co

C

c

IS

SUCCESSIVE

MEASUREMENTS?‘)

Tw

=

THE

BETWEEN

0.50 VPLUE

USED

FOR

CO

WILL

NOT

AFFECT

THE

OUTPUT

CN=CO D=l.OE C

D IS

-06 THE

DIFFUSION

COEFFICIENT

FOR

DOPAMINE.

WRITE(2.39) 39

FORMAT(lX,‘THICKNESS

OF

FLUID

COMPARTMENT?‘)

RFAD,AI. A,K=1.25E C

AK

Is

A

-06 MASS

TRRNSPORT

COEFFICIENT.

A=((2’(D**0.5)*(TS*‘0.5))/(AL*(3.14’*0.5)1)

RATIO

WHICH

TO

STOP)

’)

W. S. LINDSAYct al.

26

B= (AK/AL)

*TW

E=l-A-B F=B*CO C

BASELINE DO

TAKES

PLACE

1=1,20

10

C(I)=tCN’E)+F CN=C(I) RATIO==

(I)

PRINT,

10 C

/CO

RATIO

CONTINUE DRUG

STIMULATION

F=2*F civ=c DO

(20) 20

I=l,lS

C(I)=(CN*E)+F CN=C

(I)

IUtTIO=C PRINT,

(I

) /CO

RATIO

20

CONTINUE

C

RETURN

TO

BASELINE

F=F/Z CN=C(15) DO

30

1=1,15

C(I)=(CN*E)+F CN=C

(I)

RATIO=C PRINT, 30

CONTINUE GO

5

(I) RATIO

TO

STOP END

2

/co

TAKES

PLACE