Intracerebral microdialysis: I. Experimental studies of diffusion kinetics

lntracerebral ~icrodialysis: Diffusion Kinetics

I. Experimental Studies of

NILS LINDEFORS,GUSTAVAMBERC,AND URBANUNCERSTEDT

fntracerebral microdialysis is a brain perfusion technique in which a tubular, semipermeable membrane perfused with a physiological solution is implanted into a selected brain region. Molecules in the extracellular space diffuse into the perfusate and may be recovered and their concentration determined. Hence, the level of substances such as neurotransmitters may be monitored, and the response to different treatments may be studied. The technique also allows for administration of substances locally to the region of the brain surrounding the perfused tubular membrane. Basic principles of the microdialysis technique are described, and the results from methodological experiments are examined. It is concluded that there is a direct linear relation between the concentration of a molecule in the medium surrounding the dialysis membrane and the concentration measured in the collected perfusate. Relative changes of molecular concentration in brain extracellular space may be calculated even when the molecular diffusion rate is unknown. In addition, a method is presented for calculating the real concentration of a substance in the extracellular space from its concentration in the perfusate. Applied in striatum of rat brain using microdiatysis in vivo, the average extracellular concentration of the following substances is estimated to be: substance P, 0.9 nM; dopamine, 1 p,M; and dihydroxyphenylacetic acid, 0.05 mM. Key Words:

Diffusion;

Extracellular concentration;

Microdialysis;

Release

INTRODUCTION

A novel brain perfusion technique was developed to make possible measurements of neurotransmitter release in vivo Wngerstedt, 1984). A thin, semipermeable tubule, perfused with a physiological solution, is stereotaxically implanted in a selected part of the brain (Figures 1 and 2). Exchange by diffusion of neurotransmitters and other molecules between the brain and the perfusate allows for chemical monitoring of the extracellular space. After recovery of the perfusate, the content of a substance may be measured. Microdialysis also allows for administration of substances via the tubule to the brain tissue around it. Continuous measurement of the extracellular concentration of a neurotransmitter presents the possibility of temporally discriminating pharmacological effects and physiological events in the intact From the Department of Pharmacology, Karolinska lnstitutet (N.t., U.U.), and the Department of Hydromechanics, Royal Institute of Technology (G.A.), Stockholm, Sweden. Address reprint requests to: Dr. Nils Lindefors, Department of Pharmacology, Karolinska Institutet, Box 60 400, S-104 01 Stockholm, Sweden. Received November 1988; revised and accepted May 1989.

141 Journal of PharmacDl~icai

Methods

0 1989 Elsevier Science Publishing

22,141-156

(19891

Co., inc., 655 Avenue of the Americas, New York, NY 10010

142

N. Lindefors et al. Bregma

1.7 mm

FIGURE 1. Microdialysis probe I in implanted position in a rat brain shown in cross section. The diffusible part of the probe (not shaded and with flow direction indicated) is 3 mm long. This is the position used for probe I when used in vivo in the present study.

brain. Compared to in vivo techniques, intracerebral microdialysis has the advantage of leaving endogenous nutrition and oxygenation, as well as synaptic integration and neuronal impulse flow, largely intact. This method has so far been used to study brain extracellular concentration of several substances, e.g., catecholamines and their metabolites (Ungerstedt and Pycock, 1974; Zetterstrtim et al., 1983; Sharp et al., 1986), amino acid transmitters (Jacobson and Hamberger, 1984; Toss-

Bregma 1.2 mm

FIGURE 2. Microdialysis probe II in implanted position and in cross section. The diffusible part is 3 mm, and the probe diameter is 0.5 mm. The flow direction is indicated with an arrow. This is the position of probe II when used in vivo in the present study.

Microdialysis-Experimental

Studies

man and Ungerstedt, 1986), purines (Zetterstrom et al., 1982), and neuropeptides (Lindefors et al., 1985; Lindefors et al., 1987). Studies of the biochemistry of the extracellular space in vivo with a perfusion technique are also made using pushpull cannulas. This technique has been extensively and successfully used by Glowinski and collaborators (1979). Diffusion is a random process, and diffusion along a concentration gradient is always paralleled by minor molecular movements in the direction opposite to the gradient (Figure 3). As the concentration gradient is decreased, the more similar the molecular movements in both directions will be found. The diffusion is finally eliminated when the molecular movements become uniform, at equilibrium. The rate at which a molecule the size of an ordinary neurotransmitter is transported during diffusion in a pure liquid is on the order of several seconds for 0.1 mm and a quarter of an hour or more for 1 mm (Macey, 1980). Transport in tissue (e.g., the extracellular space in the brain) has a speed less than half that in a pure liquid (Nicholson and Phillips, 1981; Rice et al., 1985). Diffusion with molecular transport may occur as an effect of a concentration gradient (i.e., chemical potential gradient) between the two sides of a permeable membrane (Cussler, 1984), in this case the tissue and the perfusate in the dialysis probe. Other causes of net molecular transport may be differences in solubility, temperature gradients, or pressure drop (Cussler, 1984). Artificial cerebrospinal fluid with a physiological pH, perfused at a low pressure, is used in this study to preserve homeostasis and to eliminate causes of diffusion other than a concentration gradient. Diffusion is described by Ficks law: j = -D+Vc

SEMIPERMEABLE MEMBRANE

CONCENTRATION GRADIENT

C,”

(1)

MOLECULAR MOVEMENT

. . . . .t . . . . . . I) . .

c,

c,

’

c,

c,

=

c,

DIFFUSION

:$ . .

: NO.NE . .

FIGURE 3. Description of the concept of diffusion and its relation to molecular movements between tvvo compartments on each side of diffusible membrane. C denotes the concentration of a molecule that is freely diffusible through the membrane. A C, that is higher than C2 implies a diffusion along the concentration gradient in relation to the size of the gradient. When C, = Cz, the molecular movement in both directions is equal, and the diffusion terminates.

143

144

N. Lindefors et al.

It states that the fluxj is proportional to the concentration gradient Vc. If c denotes the number of molecules per volume, then j is the number of molecules per unit time that cross a unit area perpendicular to the vector j. The proportionality constant D, or the diffusion coefficient, is the parameter that determines how “fast” the diffusion is. C$is the porosity, the fraction of the total volume that is diffusible, e.g., the extracellular space. An inflow, j, into a certain volume is accompanied by an increase in concentration there. This is expressed by: dC -

at

=

D.Vzc

and in essence, this equation states that the equilibrium rate (change in concentration) is more rapid the larger the concentration gradient is. This is analyzed in detail for the intracerebral microdialysis technique in part II of this report (Amberg and Lindefors, 1989). The study of molecular movement during microdialysis entails several difficulties. Some molecules diffuse around and some through the cells, some will be actively taken up into cells, and some will rapidly be removed by degradation. Six substances were chosen for the in vitro and in vivo studies: sucrose, since it is the same size as neurotransmitters (e.g., monoamines and amino acids) and since sucrose is considered to be inert and to diffuse mainly in the extracellular space; potassium, known to be rapidly taken up by and transported inside the cells of the brain when present in increased concentration (Gardner-Medwin, 1983); sodium, which is localized and transported mainly in the extracellular space; and substance P, an endogenous mammalian neuropeptide assumed to diffuse extracellularly after being released. Dopamine, a presumed neurotransmitter, and one its metabolites, dihydroxyphenylacetic acid, were used in addition to substance P as examples of the application of formula (II) (see below). The first compartment to consider when analyzing the microdialysis process is the extracellular space of the tissue in which the probe is implanted. The rate of diffusion in a tissue is lower than that in a liquid. A limiting factor for diffusion in tissue such as brain is the tortousity, A, (Nicholson et al. 1979) and the limited volume fraction of the extracellular space, +. Both factors lower the measured diffusion. Effective diffusion measured in tissue (Dbr) is related to diffusion in a liquid (D,) according to the following formula (Nicholson and Phillips, 1981): &

= DPlX2

(3)

D, and Dbr are the diffusion coefficients in a liquid (e.g., the perfusate) and in the brain, respectively. A is a tortuosity factor representing the increased path length of a diffusing particle in a complex medium compared to a simple medium. A has a value on the order of 1.6 or more in the rat brain (Nicholson and Phillips, 1981; Rice et al., 1985). This implies that diffusion is at least two and a half times slower (< 1.6C2) in rat brain than in a liquid, due to tortuosity. In addition, interaction with macromolecules may slow down the extracellular diffusion even more (Rice et al., 1985). The volume fraction of the extracellular space of the rat brain is ap-

Microdialysis-Experimental

Studies

proximately 0.2, i.e., only a fifth of the total volume is accessible for extracellular diffusion. The tubular membrane wall of the probe is the second compartment to consider. The path length of transport through the probe (0.1 mm) is shorter than that in the brain (up to 1 mm). Hence, the membrane may be of minor importance in the limitation of molecular exchange between the probe and the brain. This should hold if the diffusion rate through the probe is not much slower than through the brain. The third compartment of interest is the perfusate within the probe. Diffusion in the perfusate is not important for our calculations because of its continuous flow (see also part II). The continuous flow of the perfusate stirs it, and thus most molecules that reach the perfusate are quickly removed from the vicinity of the diffusible membrane and remain in the perfusate. However, slow flow rates will increase the importance of this variable (i.e., the diffusion in the perfusate), and the limitations of this will be investigated. The net amount of molecules that enter the dialysis probe during perfusion is denoted recovery. The recovery may be calculated as total recovery, the total number of molecules entering per time unit, or as relative recovery, the relative concentration of a molecule in the perfusate compared to the concentration in the surrounding medium (Ungertedt, 1984). Recovery in the text refers to relative recove ry . The aims of this study were: to describe the microdialysis method, to present a method to study microdialysis in vitro and to compare these findings with results from in vivo experiments, to experimentally evaluate some mathematical statements of microdialysis, and to present a method to determine the extracellular concentration of a substance from its concentration in the perfusate. MATERIALS Dialysis

AND

METHODS

Probes

Two probes, I and II, are used in this study (Figures 1 and 2). For probe I, a tubular membrane is threaded on a tungsten wire with a diameter of 0.2 mm, to guide it during implantation. One end of the tubule is glued into a steel cannula (inner diameter, 0.3 mm; outer diameter, 0.6 mm; and length, 10 mm) to make connection to a perfusion pump possible. The total length of the probe is 50 mm, not counting the tungsten wire. Selected parts of the tubule are coated with epoxy to allow diffusion over only a specific area of the membrane located in a discrete part of the brain. The tungsten wire is taken out before perfusion. The semipermeable membrane (acrylic copolymer, Vita fiber; Amicon, MA) has an outer diameter of 0.3 mm, an inner diameter of 0.2 mm, and a cut-off at 5*104 dalton, as specified by the manufacturer. For probe II, a tubular membrane is glued to a cannula (diameter, 0.6 mm) at one end and is sealed with glue at the other end. The perfusate is brought to the tip of the tubule inside a fine cannula (diameter, 0.3 mm) in the center of the probe, flows back between the membrane and the inner cannula, and is collected at the outlet

145

146

N. Lindefors et al. of the probe. Diffusion is limited by the total length of the membrane. The membrane (polycarbonate, Cambrane; Cambro, Hechingen, West Germany) has an outer diameter of 0.6 mm, an inner diameter of 0.4 mm, and a cut-off at 2.104 dalton. This indicates that at least molecules on the order of 2.103 dalton or less may diffuse freely through the membrane. During the implantation, the probes were held by the micromanipulator of a stereotaxic instrument. Probe I was put together in our laboratory and probe II was provided by Carnegie Medicin AB, Stockholm. Biochemical

Measurements

Dopamine and dihydroxyphenylacetic acid were measured using a reversedphase HPLC system (Sharp et al., 1986). Substance P was measured using a radioimmunoassay with a specific C-terminal-directed antiserum (Lindefors et al., 1987). Potassium was measured with a conductiometric cation chromatography system (Fritz et al., 1980). Microdialysis

in vitro

Dialysis probes were mounted in a cylindrical polyethylene chamber with an inner diameter of 25 mm and a height of 50 mm. The dialysis probes were continuously perfused, and the chambers were subsequently filled with either Krebs-Ringer solution or 0.6% agar (Bacto Agar, Difco Laboratories, Detroit, Ml) in Krebs-Ringer solution. In vitro microdialysis experiments were performed in order to either measure molecular recovery of different substances from the outer medium (perfusate containing only Krebs-Ringer solution) or to measure the molecular loss to the outer medium (perfusate containing Krebs-Ringer solution to which the substance was added to a known concentration). The former will be referred to as out-in, and the latter as in-out, experiments. Microdialysis

in vivo

Male Sprague-Dawley rats (b.w., 190-210 g) were used in the in vivo microdialysis experiments. Each animal was anesthetized with halothane, and the skull was fixed in a stereotactic frame. Holes (2 mm in diameter) were drilled bilaterally in the temporal bones (probe I) or unilaterally in the left frontal bone (probe II). Probe I was inserted through a hole in the temporal bone on the right-hand side, passed horizontally through the brain and out through a hole in the opposite temporal bone (Figure I). Probe II was inserted through a hole in the left frontal bone and implanted in the left striatum (Figure 2). In some rats (n = 4), the probes (type II) were fixed to the skull with dental cement to allow for sampling of perfusate in rats freely moving and not anesthetized. The tubules were always implanted in the rostra1 striatum (locations are indicated in Figures 1 and 2). The implanted probes were perfused with an artificial cerebrospinal solution (Lindefors et al., 1987) during microdialysis, and samples were collected for further measurements. The animals were killed after the experiments, the brains dissected out, and the position of the dialysis tubule determined.

Microdialysis-Experimental

Studies

Definitions The physical data of the probe and the surrounding

medium are defined as:

R= L= d=

outer probe radius (m) length of the diffusible part of the probe (m) thickness of the membrane wall (m) radius of the solid core in probe II (m) b= volume flux of perfusate through the tubule (m3/sec) q= c= extracellular concentration cp = perfusate concentration before probe passage perfusate concentration after probe passage C O”t = extracellular concentration at large distances or concentration Cbr = medium in in vitro experiments D, = diffusion coefficient in the perfusate (m’/sec) D, = diffusion coefficient in the membrane wall Dbr = effective diffusion coefficient in the brain 4ll = porosity of the membrane $br = porosity of the brain

in the outer

Some nondimensional variables were formed from the physical parameters to be used in formulas for recovery of microdialysis probes (see part II). These nondimensional variables are:

6 = dlR The relative recovery (i.e., diffusible capacity of the membrane) in outdin experiments, measured as the concentration in the perfusate in relation to the concentration in the outer medium is: Gm

recovev =cb r

The relative recovery in in+out experiments can be calculated indirectly by comparing the concentration in the perfused solution before and after perfusion: recovery

=

CP

-

G.ut CP

(5)

147

148

N. Lindefors et al.

This calculation (5) does not discriminate between what is really transported through the membrane and what may be stuck to the membrane. RESULTS Microdialysis

in vitro

Experiments using “Na, 3H-sucrose, or ‘25J-substance P in the outer medium (outdin experiment) revealed a linear relationship between flow rate and the inverted value of relative recovery, in the flow rate range between 2 and 15 pl/min (Figure 4 and Table 1). Similar results were obtained using either probe I or probe II (only results using probe I are shown). To test the recovery formulas [see part II and formulas (6) and (7) below], the recovery was measured with probes having two different diffusible areas. It was found that a doubling of the area (doubling of L) gave close to two (1.7-1.8) times better recovery (of **Na, 3H-sucrose, and 125Jsubstance P), as long as the recovery was less than 0.25-0.30, and this was independent of the substance used. Low flow rate, < 2 Fl/min, gave a higher recovery (0.5 or more) for “Na and 3H-sucrose, and the increase in recovery due to increased diffusible area was less (1.3-I .6). Using **Na in vitro experiments with probe I, no direction dependence of diffusion was found, i.e., the loss from the perfusate during dialysis with **Na in the

60 -

0

5

10

15

FLOW RATE ( pl/min) FIGURE 4. Reciprocal values of relative recovery, (co&~,) -’ as a function of flow rate during an out+in experiment (see also Table 1). Values for ‘25J-substance P, ‘H-sucrose, and =Na (sodium) using an 4-mm probe I (S.E.M. 5 lo%, n = 4) are indicated. Note the inverse proportional correlation between flow rate and relative recovery in the interval from 2 to 15 Pl/min.

Microdialysis-Experimental TABLE 1 Relative Recovery (c,.&,,) Function of Flow Rate FLOW

‘Z5J-SuBsTANC~

P

2

0.39 f 0.04 (1.5)

0.22 f 0.02 (1.7)

0.060 f 0.007 (1.7)

5

0.18 k 0.02 (1.7)

0.11 2 0.01 (1.7)

0.028 2 0.003 (1.7)

10

0.10 + 0.01 (1.7)

0.061 2 0.008 (1.7)

0.017 2 0.002 (1.7)

15

0.075 " 0.007 (1.7)

0.040 '- 0.005 (1.8)

0.011 2 0.001 (1.8)

I

is used, and the length

and n = 4. Agar was used diffusion

3H-Sucrose, and ‘%J-Substance P as a

"NA

RATE ((Ll/min)

Probe

of “Na,

Studies

only.

Reciprocal

used to calculate recovery of the probe

is doubled

of the diffusible

in the outer

medium

values are shown

in Figure

for these substances (i.e.,

from

membrane to assure

(L) is 4 mm; that molecular

4. Values

at the flow

mean 2 S.E.M. transport

in parentheses

rates indicated,

is indicated,

occurred

show factors

through

that may be

if the length of the membrane

4 to 8 mm).

perfusate equaled the recovery from the outer medium when the “Na was there. However, for 3H-sucrose the recovery from the outer medium was 0.7 times the loss when the 3H-sucrose was in the perfusate. To measure possible net fluid exchange during microdialysis, both probes I and II, implanted in chambers containing Krebs-Ringer solution, were perfused with 2 and IO t.r,l/min for 200 min to determine any loss of fluid during dialysis. The difference between the mass of the fluid before and after perfusion was less than 0.1% for both membranes used (probes I and II). The temperature dependence of diffusion was measured during microdialysis, and a 40% higher recovery was found at 37°C than at 20°C. The substrate used was 3H-sucrose, and the measurements were made at 2,5, and 10 kl/min. These findings are in accordance with findings of temperature dependence of diffusion by Krnjevic and Michell (1960). Microdialysis

in vivo

Results from microdialysis experiments in the rat brain in which loss of perfused sodium and potassium to the brain was measured are shown in Table 2. Similar results were found using either probe I or II if the membranes had a similar diffusible area and if the probes were perfused with a similar flow rate. Using probe I in anesthetized rats measuring substance P (Figure 1; n = 4; flow rate, 10 tJ/min; L = 3 mm), a level of 0.15 2 0.02 fmol/lOO t.~lperfusate (mean ? S.E.M.) was found. Using probe II implanted in rat striatum and fixed with dental cement (Figure 2; n = 11; flow rate, 2 $/min; L = 3 mm), a perfusate level of dopamine of 0.28 & 0.05 pmoV40 t..~land a level of dihydroxyphenylacetic acid of 27 + 5 pmoV40 t.~l were found in awake and freely moving rats. Other awake animals were implanted with a smaller probe (probe II; n = 7; flow rate, 2 tA/min; L = 2 mm), and a level of dopamine of 0.21 + 0.03 pmoV40 PA was measured in the perfusate. Thus, during microdialysis in vivo with similar conditions, a 3-mm probe gave a c,,, of 0.28 pmol/ 40 ~1 compared to 0.21 pmoV40 ,CLIfor the 2-mm probe. This indicates that the in vivo recovery of dopamine increases by a factor of 1.8 if L increases by a factor of 2. However, extracellular concentration may vary along the diffusible membrane of

149

150

N. Lindefors et al.

the microdialysis probe, which makes comparisons somewhat uncertain.

using different

probes in vivo

DISCUSSION

In the discussion below, the microdialysis technique will be evaluated by examination of the basic variables (e.g., perfusion rate, size of diffusible membrane, and the diffusion through the different compartments) that determine the recovery. Mathematical calculations are compared with experimental results, and finally, we will provide a formula by which it is possible to estimate the extracellular concentration of a substance from its concentration in the perfusate. Microdialysis

in vitro

The diffusion of a substance during microdialysis may be studied using a probe implanted in a diffusible medium in vitro. If the medium is an unstirred aqueous solution, simple diffusion alone maintains an exchange of molecules between the medium and the perfusate in the dialysis tubule. However, using only Krebs-Ringer solution as the outer medium, we found unexpectedly high molecular exchange, due to additional convection. One way to eliminate convection is to add agar (polysaccharide) to the Krebs-Ringer solution in the outer medium surrounding the dialysis tubule. Low agar content (< 2%) does not affect diffusion rate much: < 3% for small molecules such as ions and neutrotransmitters and only moderately, < 20%, for large proteins (Schantz and Lauffer, 1962). In vitro experiments using a pure liquid or a 0.6% agar solution as the outer medium indicate that diffusion in the membranes used is not much slower than in water for most substances tested and, thus, is faster than in the brain. The results from these in vitro experiments correpond best with the theoretical calculations (see part II, Figure 7) if the membrane is neglected. In most cases, a hindering effect of the membrane does not have to be considered (relative recovery, < 0.2). It may be concluded from in vitro experiments and mathematical calculations (part II) that the outer medium in most instances is rate limiting for diffusion and for the recovery of a substance. A linear relationship has been found between the concentration of a neuropeptide, neurokinin A, in the medium surrounding the probe and that in the perfusate (Lindefors et al., 1987), i.e., the relative recovery was not concentration dependent. A similar relationship has also been reported for monamine metabolites (Sharp et al., 1986) and for amino acids (Tossman and Ungerstedt, 1986). Hence, changes in concentration in the perfusate during microdialysis experiments are linear projections of the changes in extracellular concentrations. If the recovery is determined, it is also possible to calculate the exact extracellular concentrations in vivo. The direction dependence of the diffusion found for 3H-sucrose but not for 22Na may be explained by an interaction with the membrane. An interaction with the membrane slows down the passage of a substance through the membrane. This is seen if the measurements include the amount of the substance having passed the membrane [equation (4)], but not if only what is leaving the perfusate is measured [equation (5)]. The tendency for a molecule to interact with the membrane may vary

~icrodialysis-Experimental

Studies

due to chemical characteristics. The “adhesiveness” may be quantified by a capture propability constant (part II). This must be done cautiously since the “capture,” in the case of binding, may be a time-dependent, saturable phenomenon. One factor of possible importance for recovery is the hydrophilicity/lipophilicity of the membrane producing different interactions with different diffusing molecules. The membranes used in this study are hydrophilic, i.e., more permeable for hydrophilic substances. The selection of membranes with different characteristics can be used to attain more selective passage of molecules. No difference has been found in the recovery between probes 1 and II if the membrane size and flow rate of perfusate are similar. This outcome is possible to predict using the mathematical microdialysis model (for calculations, see part II). It may be concluded that the cannula in the center of probe II is of minor importance for the recovery. Bulk flow of the perfusate through the membrane during microdialysis was excluded by the measurement of the liquid mass before and after passage through the probe. moreover, the microdialysis process is shown to be temperature dependent. It is suggested that a good membrane should fulfill the following criteria: (1) diffusible pores significantly bigger than the molecule of interest, (2) no significant interaction between the substance measured and the material of the membrane, and (3) a well-defined diffusible area to simplify calculation of recovery and extracellular concentrations and to eliminate the risk of unexpected obstructions for diffusion. Microdialysis

in vivo

The mathematical

investigations

in part II yield an expression for the recovery:

recovery = 8M3 In the normal situation of an in vivo recovery of < 0.2, the second term containing g(t) may be neglected, The remaining expression is: recovery = 8cxph(t)

(7)

t is the time, normalized as t = t”.D,,lR* (t* is time in set). In equation (7), IY characterizes a direct relation between recovery and diffusion coefficient or membrane length (area) and a reverse relation to flow rate. In equation (6), accumulation of recovered substances in the perfusate is significant. Hence, an already high recovery increases more slowly with increased length of the probe or with decreased flow rate of the perfusate. 01 is on the order of 0.5-0.01 for most applications of microdialysis (De = 0.2-2*10-‘, L = 2-4*10P3, and 9 = 0.167-1.67~10-‘“). p determines the effects of variation of the ratio of the diffusion coefficients in water and in brain, i.e., the recovery from the brain is low if the diffusion in the brain is low for this particular substance (e.g., due to interaction with macromolecules in the extracellular space). Thus, a low recovery in brain indicates a high cb, for a given coUt. h(t) is a function of the nondimensional parameters described above and is

151

152

N. Lindefors et al. shown

in part II, Figure 2. h(t)

ginning of the experiment. due to the development parameter probe.

describing

the

The parameter

numerical

describes

hindering

of recovery

of the membrane

(0.19404). S is a parameter

constant

ratio of the wall thickness

in the be-

determining

membrane,

further

of the microdialysis 0.2 (see part II). A is a

of I

the fluid velocity discussed

radius R. 6 is between

d to the probe

gradient

in part II. 6 is the 0.1 and 0.5 for the

used.

The recovery prime

effect

y turns out to be on the order

on the inner wall of the diffusible probes

the equilibration

h(t) decreases rapidly in the beginning of the perfusion of the concentration gradient outside the tubule. y is a

interest

formulas

(6) and (7) may be used for a number

to be able to tell what the concentration

from a measurement

of the concentration

of purposes.

of a substance

in the probe

perfusate

It is of

is in the brain

after microdialysis.

To do this, the recovery is calculated according to equation (7) for recoveries up to 0.2 or from equation (6) for recoveries up to 0.4. Formula (6) differs from formula (7) in that it considers g(t)

is the term

Once

the effects of diffusion

describing

the recovery

the hindering

is calculated,

in the tubular

effect

wall and in the perfusate.

of the membrane.

the concentration

in the brain outside

the tubule

is simply: Cbr

Estimation of Diffusion Using

recovery

experiment

where

diffusible

part

amounts. timated,

data,

Coefficients

of the

in vivo and in vitro

is calculated

tubule,

e.g.,

&.

This is done

from the loss during

by using

in equation

03)

recovery

we may also estimate

recovery

All quantities

c0,t

=

(7) except

a radiolabeled

by performing

an

passage through

the

substance

D br are known

in trace

or may easily be es-

and Dt,,. may be computed.

Assuming

a concentration

gradient

[equation

(2)l and simple

(I)] during

in vitro microdialysis

and using recovery

coefficient

for a new substance

may be calculated

comparison

is made with a control

substance

D “l3V =D control .

formulas

diffusion

[equation

(6) and (7), a diffusion

if the recovery

is measured

and

as follows: recovery,ew

(9)

recoverycon~ro~

To reduce the uncertainty introduced by relying heavily on the theoretical model, we may also use equation (6) simply to infer that recovery should be approximately and proportional to Dbr. If Dbr is known and if D, is measured in vitro experiments if both the in vitro and the in vivo experiments are done with the same probe with similar equilibrium time and with the same flow rate in the tubule, we get simply:

recOVeryin

Dbr viva

=

D,

’

+br

.

recoveryi,

(10)

vitro

D, is assumed to be similar in the perfusate and in the outside vitro conditions and is thus denoted D, in formula (10).

medium

during

in

Microdialysis-Experimental

Studies

The Dbr determined from the loss of sodium (=Na) to the brain during microdialysis was found to be of the expected magnitude. Applying equation (IO) and inserting a loss in vivo of 0.074 (Table 2), a loss in vitro of 0.125, and a D, of 1.4~10-g m2/sec (Shantz and Lauffer, 1962), it is found that Dbr = 0.84~10-g m2/sec for =Na. This implies a A of 1.5, if diffusion coefficients are corrected for the temperature difference between in vitro and in vivo conditions. Microdialysis with an increased concentration of potassium in the perfusate, however, resulted in a loss to the brain of 0.17-0.18 (Table 2). A D, of 1.6.10-’ m2/sec (Shantz and Lauffer, 1962) and a recovery in vitro (Lindefors et al., unpublished findings) of 0.11 give Dbr = 2.7.10-’ m2/sec, i.e., larger than in water. This would only be possible with a diffusible extracellular space larger than lOO%, which is futile. A probable explanation is rapid cellular uptake and spatial buffering of increased extracellular concentrations of potassium (Gardner-Medwin, 1983). An effective mechanism for the regulation of the extracellular concentration of a substance, e.g., potassium, maintains the concentration gradient and may be detected as a high concentration in the perfusate. This is clearly seen for potassium, which in relation to sodium is found in unexpectedly high concentrations in the perfusate from brain. Sodium diffuses mainly extracellularly to the probe while potassium, in addition, may be shunted intracellularly (Gardner-Medwin, 1983). A continuous high supply to the perfusate is then supported effectively. The concentration of potassium is not allowed to decrease much around the probe, and hence, we find a high concentration in the perfusate. The phenomenon of limitations in the development of concentration gradients (i.e., significant cellular supply of molecules close to the probe) may occur to a varying extent for, e.g., neurotransmitters. It is speculated that the capacity of stabilize the extracellular concentration in this way may vary not only for different substances but also in different regions of the brain due to differences in the geometry of the extracellular space and a variation in density of releasing or reuptaking sites. Microdialysis seems to be sensitive to homeostatic mechanisms in the brain and may thus be a tool for the exploration of such mechanisms.

of “Nil+ and K+ TABLE 2 Molecular exchange ([c, - c,.&,) during in vivo Microdialysis Using Probe II in Striatum of Rat Brain

SUBSTANCE K+ K+ K+ K+ 22Na+

CONCENTRATION IN PERFUSATE 3mM 50 mM 100 mM 150 mM Trace, in 150 mM NaCl

RELATIVE Loss TO THE BRAIN

n

0 IfI k f 2

6 6 6 16

0.179 0.170 0.176 0.074

0.010 0.010 0.007 0.007

The perfusion rate is 5 &min, and the diffusible length of the membrane is 4 mm. Potassium was determined using a conductometric cation chromatography system (Fritz et al., 1980).

153

154

N. Lindefors et al.

Calculation

of Extracellular Concentrations

The extracellular formula (8):

concentration

may, as discussed above, be calculated using the

Cbr

=

tout recovery

The recovery in the brain depends on the diffusion in the brain, as discussed in the introduction, and may be calculated using formula (6) or (7). The extracellular concentrations of neurotransmitters and metabolites are assumed to be related to concentrations in the perfusate in the following way [derived from equations (4) and (7)l: Cbr

=

Gout ’

Q ‘hf

‘&&*h(

t*

(11)

Db,/R2)

The use of this formula may be exemplified by the application to studies of extracellular substance P-like immunoreactivity (SPLI, concentration of peptide measured by radioimmunoassay) in striatum of rat brain. A diffusion coefficient for substance P in water of 0.20 or 0.21~10-g m2/sec may be calculated according to equation (9), using values for recovery (Table 1) and diffusion coefficients (Lindefors et al., unpublished findings) found for 3H-sucrose or 22Na, respectively, and using the diffusion coefficients for sucrose and sodium in water found by Schantz and Lauffer (1962). In order to calculate Dt,, for substance P, we have to assume that equation (3) is applicable, giving a Dbr of 0.09~10-gm/s2 (Dp = 0.2.10-gm/s2 and A = 1.5). In a microdialysis experiment perfusing rat striatum, we found that the tout was around 0.15 fmol in a IOO-t.d sample, the flow rate was IO t.&min, and the diffusible part of the membrane was 3 mm (probe I). Applying equation (II) we get: 1 .67.10-lo Cbr

=

Gout

’

4.7F.3.10-3.0.2.0.0g.~~-~.~,42

=

88

fmol’lOO

IJJ

The extracellular level of SPLI in striatum of rat brain in vivo is thus estimated to 0.9 nM (in equivalents of synthetic substance P). Since SPLI in rat striatum corresponds by more than 95% to substance P at chromatographic characterization combined with radioimmunoassay (Lindefors et al., 1986), SPLI in rat striatal perfusates is considered to represent released substance P. A list of critical values in the calculation of extracellular concentrations of substance P, dopamine, and dihydroxyphenylacetic acid is shown in Table 3. For dopamine, the estimated extracellular concentration in striatum of awake, freely moving rats is 1 .I PM, and the estimated concentration of dihydroxyphenylacetic acid is 49 PM. It must be borne in mind that all our formulas are applicable under restricted conditons. Ultimately, every substance must be examined for interactions with the probe, rate of extracellular diffusion and interaction with extracellular molecules, rate of cellular uptake/release, etc. before a reliable calculation of extracellular concentration may be done. In conclusion, we have described the microdialysis technique and a possible way

~icrodialysis-Experimental

Studies

TABLE 3 Critical Values in Calculations of Extracellular Concentrations (c,,& of Some Substance Collected in Microdialysis Perfusates of Striatum of Rat Brain DIHYDROXYPHENYLACETIC VARIABLE

SUBSTANCEP

tout (pmoWO01.4 o (Pi/min) q (m3/sec)

o.15*10-3 IO l.FIO-‘” 3-10-3 0.9.10-‘O 1.56’ 0.42 88.1o-3= 0.9 nM

L fin) Dbr fm?%ec) t (t = t**D,,,/R2) h(t) (see part II) cbr (pmol/lOO Pi) Cbr

DOPAMINE

0.71 2 3.3.10-‘1 3.10-3 0.68~10-‘0~ 5.96 0.31 53= 1.1 PM

ACID 68 2 3.3*10-” 3.10-3 2.5.10-‘oa 21.6’ 0.24 3,825’ 49 PM

cbr was calculated for substance P using probe I (Figure I) in anaesthetized rats and for dopamine and dihydro~phenylacetic acid using probe II (Figure 2) in awake, freely moving rats. a From Rice et al., 1985. bt*is1.5horS,408s. c Calculated using formula (11).

to determine the dynamics of this method in vitro. Furthermore, we describe a method to calculate the concentration of a substance in the extracellular space in vivo from its concentration measured in the microdialysis perfusate. We are grateful to Anna-Karin Collin, Agneta Eliasson, Ase Hallstrom and ka Schippert for excellent technical assistance and to Dr. Hugh Series for valuable comments. Professor Bengt-Joel Andersson is thanked for the inspiration to the interdisciplinary collaboration that made this study possible. This study was supported by the Swedish Medical Research Council.

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Mass Transfer in Nuid Cambridge University

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