Microdialysis Sampling Membrane Performance during in Vitro

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Anal. Chem. 2006, 78, 6026-6034

Microdialysis Sampling Membrane Performance during in Vitro Macromolecule Collection Xiangdan Wang and Julie A. Stenken*

Department of Chemistry and Chemical Biology, Center for Biotechnology and Interdisciplinary Studies, 4215 Biotech Building, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590

Microdialysis sampling is well-established for sampling small molecules. Recently, there has been an increased interest toward collecting macromolecules using microdialysis sampling. In this work, fluorescein isothiocyanatelabeled dextrans (FITC-dextrans) with molecular weight between 10 and 70 kDa were chosen as representative molecules to study analyte mass transport properties during microdialysis sampling using different lengths (2 and 10 mm) of 100-kDa MWCO polyethersulfone membranes. Experiments were performed in both well-stirred and quiescent phosphate-buffered saline solutions as well as in a 0.3% agar solution. Different fundamental parameters affecting microdialysis sampling of macromolecules, including effective membrane diffusion coefficients, were evaluated. The applicability of the most-often-cited Bungay et al. mass transfer model was compared to experimental data for the FITC-dextrans. For the larger macromolecules, the membrane provides a significant mass transport resistance most likely caused by hindered diffusion. These experimental aspects that are critical to microdialysis sampling of macromolecules are presented. Microdialysis sampling is an established technique based on diffusive analyte mass transfer through a semipermeable membrane to allow collection of analytes from various media. Microdialysis sampling has been extensively used for drug metabolism,1,2 neuroscience,3-5 and pharmaceutics applications.6-8 A typical microdialysis probe consists of a semipermeable membrane (length 1-10 mm, o.d. 0.5 mm) with inlet and outlet tubing attached to the membrane. A perfusion fluid is then passed through this tubing at flow rates in the typical range of 1-2 µL/min. Commercially available microdialysis probes have polymeric membranes (cuprophan, polyacrylonitrile, and polyethersulfone) with molecular weight cutoff (MWCO) values that range between 5 and 100 kDa. Analytes smaller than the membrane pores diffuse into the inner fiber lumen and are carried by the continuously flowing perfusion fluid through the probe. Larger analytes will be completely rejected by the membrane pores or their diffusion will be slow enough to cause their recovery into the perfusion fluid to be negligible. The successful application of microdialysis sampling to allow in vivo collection of small hydrophilic molecules has sparked an interest in using it for collection of macromolecules including cytokines and growth factors.9,10 Microdialysis sampling was * Corresponding author. Phone: (518) 276-2045. Fax: (518) 276-4887. E-mail: [email protected].

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originally used as a device that provided an essentially proteinfree or “clean” sample using membranes with MWCO values between roughly 5 and 30 kDa. To enable microdialysis sampling for larger molecules, the use of membranes with a larger MWCO became necessary. The most common membrane used for macromolecule collection is the 100-kDa MWCO polyethersulfone membrane marketed by CMA.11,12 The 100-kDa MWCO membranes can often exhibit low recovery for many proteins. For this reason, other researchers have tried a 3000-kDa MWCO membrane with an in-house-prepared dialysis probe for cytokine collection, since these important signaling proteins have molecular weight ranges between 6 and 80 kDa.13,14 The heterogeneous charge distribution, shapes, and sizes of proteins causes them to be quite dissimilar during dialysis sampling, as compared to small hydrophilic analytes. Additionally, aqueous diffusion coefficients are smaller for large macromolecules >10 kDa (10-7-10-8 cm2/s) than for smaller molecules ∼10-6 cm2/s.15 This reduction in aqueous diffusivity between proteins and small molecules will significantly affect microdialysis sampling recovery, since this sampling method is dependent upon analyte diffusivity. Second, the macromolecular size and shape (tertiary structure and radius of gyration) may approach that for the heterogeneous membrane pores, thus causing restricted diffusion through the water-filled pore, which typically does not occur for small molecules during microdialysis sampling. Despite this recent interest in protein collection using microdialysis sampling, there have been few studies to truly test the performance of this methodology for these applications.16 In particular, the response time of the probe during recovery studies (1) Muller, M. Adv. Drug Delivery Rev. 2000, 45, 255-269. (2) Verbeeck, R. K. Adv. Drug Delivery Rev. 2000, 45, 217-228. (3) Bito, L.; Davson, H.; Levin, E. J. Neurochem. 1966, 13, 1057-1067. (4) Robinson, T.; Justice, J. B., Jr. Microdialysis in the Neurosciences; Elsevier: Amsterdam, 1991. (5) Kehr, J. J. Neurosci. Methods 1993, 48, 251-261. (6) Hansen, D. K.; Davies, M. I.; Lunte, S. M.; Lunte, C. E. J. Pharm. Sci. 1999, 88, 14-27. (7) Elmquist, W. F.; Sawchuk, R. J. Pharm. Res. 1997, 14, 267-288. (8) Garrison, K. E.; Pasas, S. A.; Cooper, J. D.; Davies, M. I. Eur. J. Pharm. Sci. 2002, 17, 1-12. (9) Clough, G. AAPS J. 2005, 7, E686-E692. (10) Ao, X.; Stenken, J. A. Methods 2006, 38, 331-341. (11) Phillips, T. M. Luminescence 2001, 16, 145-152. (12) Ao, X.; Sellati, T. J.; Stenken, J. A. Anal. Chem. 2004, 76, 3777-3784. (13) Sopasakis, V. R.; Sandqvist, M.; Gustafson, B.; Hammarstedt, A.; Schmelz, M.; Yang X.; Jansson, P. A.; Smith, U. Obes. Res. 2004, 12, 454-460. (14) Winter, C. D.; Iannotti, F.; Pringle, A. K.; Trikkas, C.; Clough, G. F.; Church, M. K. J. Neurosci. Methods 2002, 119, 45-50. (15) Klein, E.; Holland, F. F.; Eberle, K. J. Membr. Sci. 1979, 5, 173-188. 10.1021/ac0602930 CCC: $33.50

© 2006 American Chemical Society Published on Web 08/04/2006

Figure 1. Schematic diagram of the microdialysis probe. rR, rβ, and ro are the radii of the outer cannula surface, inner membrane surface, and outer membrane surface, respectively; L is the length of the membrane.

has not been performed to determine if expected or unexpected differences between small molecule vs macromolecule sampling with microdialysis probes exist. A particular focus for this work is to highlight and explain the differences with respect to microdialysis sampling of macromolecules as compared to small molecules. This comparison is important and necessary to achieve better design, interpretation, and understanding of microdialysis sampling experiments involving macromolecules. THEORY Microdialysis Sampling. Microdialysis sampling extraction efficiency for any analyte is controlled by diffusive mass transport, with the driving force being the concentration gradient between the perfusion fluid and external sample medium. The sampling effectiveness for a microdialysis sampling device can be calculated via the extraction efficiency (EE) shown in eq 1,

EE )

Cd - C i Ce - Ci

(1)

where Cd, Ce, and Ci stand for the concentration of analyte in dialysate, external sample medium, and perfusion fluid, respectively. For the recovery mode, that is, Ci ) 0, the extraction efficiency is often referred to as the relative recovery (RR) and is defined as the ratio of concentration of analyte in dialysate and external sample medium. Diffusive and kinetic sample parameters greatly influence RR during microdialysis sampling. Bungay et al. have developed a mathematical framework to predict the microdialysis RR at steady state shown in eq 2.17

(

RR ) 1 - exp Rd )

)

1 Qd(Rd + Rm + Re)

13(rβ - rR) ln({r0}/{rβ}) ; Rm ) ; 70πLrβDd 2πLDmφm Re )

1 2πDeφex2roL

(quiescent medium) (2)

Although this equation and model system have been recently updated to include a trauma layer, the original framework focused on mass transport resistances through different regions still remains.18 In their work, the mass transport resistances for the (16) Schutte, R. J.; Oshodi, S. A.; Reichert, W. M. Anal. Chem. 2004, 76, 60586063. (17) Bungay, P. M.; Morrison, P. F.; Dedrick, R. L. Life Sci. 1990, 46, 105-119.

dialysate (Rd), membrane (Rm), and quiescent external medium with no kinetic uptake or metabolism processes (Re) are additive, and RR can be calculated using eq 2, where Qd is the volumetric flow rate of the perfusion flow rate; rR, rβ, and ro are the radii of the outer cannula surface, inner membrane surface, and outer membrane surface, respectively (Figure 1); Dd, Dm, and De are the analyte diffusion coefficient in dialysate, membrane, and external fluid; L is the length of the membrane; φm is the volume fraction of the membrane; and φe is the accessible volume fraction in the extracellular phase (tissue). Equation 2 can be linearized by rearranging and taking the natural logarithm to yield eq 3.

ln(1 - RR) )

1 -1 Rd + R m + R e Q d

let

1 ) Rd + R m + R e

1

∑R

(3)

Equation 3 indicates that for any given microdialysis sampling system at steady state (including membrane and sample medium), the value of 1/ΣR will be a constant and a plot of (-ln(1 - RR)) vs 1/Qd should ideally be a straight line with a slope of 1/ΣR. The use of well-stirred conditions effectively reduces Re to a value that approaches 0. By knowing the geometry of the probe and the aqueous diffusion coefficient for the targeted analyte, the value for the dialysate resistance, Rd can be estimated using eq 2. The value of Rm can be obtained via subtraction. Since Rm is an intrinsic characteristic of a dialysis polymeric membrane at any given temperature and specified length, it remains constant for the targeted analyte. Once Rd and Rm are known, Re can be determined experimentally. FITC-Dextran Aqueous Diffusion Coefficient Estimation. For these studies, the aqueous diffusion coefficient values for each of the FITC-dextrans are necessary to calculate the microdialysis sampling resistance. Diffusion coefficients for FITC-dextrans in different solutions can be estimated by the Stokes-Einstein equation,

D)

kT 6πηrs

(4)

(18) Bungay, P. M.; Newton-Vinson, P.; Isele, W.; Garris, P. A.; Justice, J. B. J. Neurochem. 2003, 86, 932-946.

Analytical Chemistry, Vol. 78, No. 17, September 1, 2006

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Table 1. FITC-Dextran Diffusion Coefficients Daqb (cm2/s)

Dagarb (cm2/s)

FITC-dextran

MWa

rsa (nm)

calcd

meas19

calcd

meas20

FD-10 FD-20 FD-40 FD-70

9 850 19 400 43 000 77 000

2.3 3.3 4.5 6.0

14.5 × 10-7 10.1 × 10-7 7.4 × 10-7 5.6 × 10-7

16.1 × 10-7 N/R 10.2 × 10-7 8.9 × 10-7

6.8 × 10-7 4.7 × 10-7 3.5 × 10-7 2.6 × 10-7

13.5 × 10-7 N/R 4.2 × 10-7 3.8 × 10-7

a The molecular weight and the Stokes radius (r ) for the FITC-dextrans were provided by the manufacturer. b For the calculated values of D s aq and Dagar, eq 4 was used. Values for η of 0.68 cP for water with agar found to be experimentally 2.13 times greater were used for the calculation. The solution and agar experimental diffusion coefficients have been reported in refs 19 and 20. N/R indicates the value was not reported.

where k is the Boltzmann coefficient, η is the dynamic viscosity (measured with an Ostwald viscometer) of the sample medium, rs is the radii of the FITC-dextrans, and T is the temperature. For the FITC-dextrans used in this study, FITC-Dextran 10 kDa (FD10), FD-20, FD-40, and FD-70, the estimated Daq (diffusion coefficient in aqueous solution) values are similar to measurements and separate calculations performed by Hosoya et al. and agar measurements (Dagar) described by Nicholson (Table 1).19,20 Diffusion through Membrane Pores. A macromolecule diffusing through a membrane pore with size comparable to the solute diameter combined with friction from the wall of the pore it passes through will cause the solute to incur additional hydrodynamic drag. This diffusive hindrance has been of interest to many membrane science researchers who have posed different empirical equations for defining a hindrance factor (Dm/Daq).21 Generally, a ratio of solute radius to pore size radius, λ, can be defined as rs/rp, where rs and rp are the radii of the molecule and the membrane pore, respectively. This ratio can be calculated using the hydrodynamic radii for the FITC dextrans shown in Table 1 combined with the approximate membrane pore diameter (9 nm) provided by the dialysis probe manufacturer. The solute flux (N) through porous membranes includes convective and diffusive components, as shown in eq 5,

dC N ) KCVCs - KDD∞ dz

(5)

where Kc (convective hindrance factor), V (average fluid velocity), and Cs (average concentration in the pores) are terms to describe the convective forces.22 During microdialysis sampling, a fundamental underlying assumption is that analyte mass transport through the membrane pores is driven by diffusion. Therefore, focusing on the diffusive portion of eq 5 by setting the convective force to a value of 0 leads to a simplified version (eq 6).

N ) -KDD∞

dC dz

(6)

In this equation, KD is defined as the hindrance factor for diffusive transport, and D∞ is the diffusion coefficient for the analyte in the bulk solution. (19) Hosoya, O.; Chono, S.; Saso, Y.; Juni, K.; Morimoto, K.; Seki, T. J. Pharm. Pharmacol. 2004, 56, 1501-1507. (20) Nicholson, C. Rep. Prog. Phys. 2001, 64, 815-884. (21) Davidson, M. G.; Deen, W. M. Macromolecules 1988, 21, 3474-3481. (22) Mochizuki, S.; Zydney, A. L. J. Membr. Sci. 1992, 68, 21-41.

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The hindered diffusion of both rigid spherical and nonspherical macromolecules through membranes with symmetric pore structure has been well-studied.22-26 Quantitative expressions to obtain the hindrance factor for nonspherical macromolecules, such as the dextrans, through membranes with asymmetric pores are not widely available. However, estimation for these values can be obtained using a combination of previous work. Bungay and Brenner have described KD as shown in eq 7 where Kt is denoted as a hydrodynamic function of λ and KD is applicable for all values of λ.27

KD )

6π Kt

(7)

The equation for Kt is an expansion expression that has been previously published along with the appropriate coefficients to solve for Kt as a function of λ.22,28 Morti and Zydney have defined the solute effective membrane diffusion coefficient, Dm (eq 8),

Dm ) φKDD∞

(8)

where  is the porosity of the membrane, defined as the fraction of the membrane volume accessible to water, which is equivalent to Φm in eq 2.29 For a 100-kDa MWCO PES membrane, the approximate value for the membrane porosity is  ) 0.51.29 The symbol φ denotes the solute partition coefficient between the membrane and the solution. Giddings et al. have provided an equation (eq 9) for calculating φ, which is independent of solute size and useful for different pore geometries governed by the effective size ratio, λ*, shown in eq 10, and has been shown to be in good agreement with rigid nonspherical solutes in several different pore geometries.30,31

φ ) exp(-2λ*)

(9)

λ* ) r*/2s

(10)

(23) Deen, W. M. AIChE J. 1987, 33, 1409-1425. (24) Shao, J.; Baltus, R. E. AIChE J. 2000, 46, 1149-1156. (25) Davidson, M. G.; Deen, W. M. Macromolecules 1988, 21, 3474-3481. (26) Robertson, B. C.; Zydney, A. L. J. Membr. Sci. 1990, 49, 287-303. (27) Bungay, P. M.; Brenner, H. Int. J. Multiphase Flow 1973, 1, 25-56. (28) Opong, W. S.; Zydney, A. L. AIChE J. 1991, 37, 1497-1510. (29) Morti, S.; Zydney, A. L. AIChE J. 1998, 44, 319-326 (30) Giddings, J. C.; Kucera, E.; Russell, C. P.; Myers, M. N. J. Phys. Chem. 1968, 72, 4397-4408. (31) Limbach, K. W.; Nitsche, J. M.; Wei, J. AIChE J. 1989, 35, 42-52.

Table 2. Hindrance Factor Parameters FITC-dextran

rs (nm)

λ (rs/rp)a

λ*

φ

λ¢

KD

Dm(C)b × 107 cm2/s

DmΦm(E)b × 108 cm2/s

Rm(C)b

Rm(E)b

Rm(E)/RmC)

FD-10 FD-20 FD-40 FD-70

2.3 3.3 4.5 6.0

0.51 0.73 1.00 1.33

0.24 0.34 0.46 0.62

0.62 0.51 0.40 0.29

0.21 0.29 0.37 0.46

0.57 0.44 0.32 0.21

2.64 1.15 0.47 0.17

4.15 2.14 0.60 0.18

28.0 64.6 157.5 438.5

178.3 345.3 1300.5 4009.8

6.4 5.4 8.3 9.2

a The value for the pore radius is 4.5 nm. b The symbols E and C denote experimentally determined and calculated values for each resistance term.

This ratio, λ*, is found by r* and is the mean projected solute radius, which has been substituted using the Stokes radii (rs) in our study, and s is the ratio of pore volume to pore surface area, which can be calculated using eq 11.

s)

(

)

k1δmLp 

1/2

(11)

For eq 11, k1 is the Kozeny constant and is a function of the detailed characteristics of the porous membrane. On the basis of previous description of a similar PES membrane by Oppong and Zydney, k1 ) 2.28 The membrane thickness, δm, for an asymmetric membrane would be the thickness of the membrane skin layer instead of the entire thickness, which includes the skin and highly porous support layer. Note that δm corresponds to ro in eq 2. Finally, Lp is the membrane hydraulic permeability, which according to the microdialysis probe membrane manufacturer has a value of 67 × 10-4 cm/s bar. A dimensional analysis of eq 11 suggested that this Lp value did not give the appropriate units in meters. In some membrane diffusion studies and in this work, Lp is multiplied by the value for solution viscosity to give the correct dimensions (0.89 cP at 25 °C and 0.68 cP at 37 °C). Table 2 shows the ratio λ (rs/rp) for all the FITC-dextrans. For FD-40 and FD-70, λ g 1, suggesting that these molecules would be too large to fit through the pores to be recovered. To correct for this problem, assuming a spherical solute in a membrane with cylindrical pores, a partition coefficient φ can be calculated using eq 12. From eq 12, Opong and Zydney studied the transport of proteins through asymmetric membranes and altered it to allow λ to be a function of φ, and expressed as λ′ (eq 13).

φ ) (1 - λ)2

(12)

λ′ ) 1 - xφ

(13)

Then, λ′ can be used in the previously published equation and coefficients for Kt. Using all of these equations, the value for Dm can be estimated allowing for concomitant calculation of the membrane resistance, Rm for each of the FITC-dextrans. EXPERIMENTAL SECTION Chemicals. FITC-dextrans with nominal molecular weights of 10, 20, 40, and 70 kDa were purchased from Sigma-Aldrich (St. Louis, MO). Agar was purchased from Sigma-Aldrich (St. Louis, MO) and was prepared using 0.3 wt % in phosphate buffered saline (PBS), pH 7.4, consisting of 137 mM NaCl, 2.7 mM KCl, 8.1 mM Na2HPO4, and 1.5 mM KH2PO4. An Ostwald viscometer was used

to determine the viscosity of the 0.3% agar solution.32 Before measurement, the agar solution had been placed in the viscometer in a 37 °C water bath for 3 h. The viscosity of the agar solution was found to be 2.13 times that of distilled water. Microdialysis Setup. A 1000-µL BAS MD-0100 glass syringe (Bioanalytical System Inc., West Lafayette, IN) was controlled by a CMA/102 microdialysis pump (CMA Microdialysis, North Chelmsford, MA). Polyethersulfone (PES) microdialysis probes (length 10 and 2 mm, MWCO 100 kDa, CMA Microdialysis, North Chelmsford, MA) were used for all experiments. According to the manufacturer, the external diameter of the internal cannula is 350 µm, the membrane internal diameter is 420 µm, and the membrane external diameter is 500 µm. The probes were perfused with PBS. Microdialysis probes were soaked in PBS for 0.5 h before starting the experiments. The initial relative recovery experiments were performed by inserting the microdialysis probe into well-stirred and quiescent PBS solutions as well as the agar solution (0.3%) in which the concentrations of FITC-dextrans were prepared to 0.04 mg/mL. Dialysates of each FITC-dextran were collected at five flow rates (at 0.5 and 0.7 µL/min, samples were collected for 40 min; at 1.0, 1.4, and 2.0 µL/min, samples were collected for 30 min). Samples were typically collected from highest, 2.0 µL/min, to lowest flow rate, 0.5 µL/min. To study the approach to steady-state concentrations associated with macromolecules and dialysis sampling, the microdialysis probe was equilibrated by placing it into the 0.3% agar solution containing 0.05 mg/mL FITC-dextrans (FD-10 and FD-20) at 37 °C for 1 h prior to initiating perfusion fluid flow through the microdialysis probe. First, the dialysate samples were collected every 2.5 min at 1.8 µL/min for 1 h after the pump was turned on, then a sequence of wait periods were added, and the pump was turned on for 3 min to collect a sample to ensure maximum response and was turned off for the minutes denoted in the following intervals: 2, 4, 6, 8, 10, 12, 14, 16, 20, 25, 30, 35, 40, 50, and 60 min. The low relative recoveries of FD-40 and FD-70 precluded these molecules from these experiments. Liquid Chromatography System. A size exclusion column, TSK gel G 2000sw, 7.5-mm i.d., 30 cm (Tosohaas, Japan), was used to separate the FITC-dextrans using a Shimadzu LC system, which include an SIL-10ADvp autoinjector, an LC-10ADvp pump, a DGU-14A degasser, a CTO-10ASvp column oven, and an SCL10Avp system controller. Quantitation was achieved using a Shimadzu RF-551 fluorescence detector (λex ) 490 nm, λem ) 520 nm) equipped with an analytical flow cell coupled with a Shimadzu (32) Lawson, G. W. Am. J. Bot. 1954, 41, 212-214.

Analytical Chemistry, Vol. 78, No. 17, September 1, 2006

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Figure 2. Relative recovery values for each FITC-dextran in sample media at 37 °C. Symbols denote 0.3% agar (9), quiescent phosphate buffered saline (b), and well-stirred phosphate buffered saline (2). Note that for FD-10 and FD-20, the scale for recovery is the same, but is reduced for FD-40 and FD-70. Symbols and error bars are mean ( SD (n ) 3).

HPLC system. The flow rate of the mobile phase (NaCl 150mM, phosphate 50mM, pH)6.5) was 1 mL/min. Scanning Electron Microscopy. A JEOL JEM-840 scanning electron microscope was used to observe the structure of the PES membrane. The membrane samples were first dried under high vacuum and then coated with gold and palladium before viewing under the microscope. RESULTS AND DISCUSSION Relative Recovery of FITC-Dextrans. Relative recoveries of FITC-dextrans (FD-10, FD-20, FD-40 and FD-70) for the different flow rates and external media (stirred buffer, quiescent buffer, and agar) are shown in Figure 2. With increasing flow rate from 0.5 to 2.0 µL/min, the RRs of all the four FITC-dextrans studied decreased. Using these conditions, the decrease in RR is related to the increase in the molecular weight (10-70 kDa) for each of the FITC-dextrans. When switching the external medium from agar to quiescent PBS and to well-stirred PBS solutions, all four FITC-dextrans showed increased relative recovery. These results are consistent with the Bungay et al. resistance theory in that analytes that were collected with higher flow rate, possessing higher molecular weight and a greater resistance in the external medium resulted in lower recovery values. 6030 Analytical Chemistry, Vol. 78, No. 17, September 1, 2006

Experimental Mass Transfer Resistance Calculations for Macromolecules. The recovery values for FITC-dextrans were collected using the PES 10-mm microdialysis probe immersed into either agar or PBS solutions. Using the relative recovery data shown in Figure 2 for five different flow rates, eq 3 can be used to find the overall mass transfer resistance for each of the individual FITC-dextrans across the PES membrane. Slope and correlation coefficient values (r2) from the least squares linear regression fit for FD-10, FD-20, FD-40, and FD-70 using eq 3 were determined. For FD-10 and FD-20, the correlation coefficient values were 0.99 or greater for stirred and quiescent solutions. The data for FD-40 gave correlation coefficients of 0.99 and 0.97 for the stirred and quiescent media, respectively. FD-70 in quiescent solution exhibited the lowest correlation coefficient values of 0.95 and 0.91 in the stirred and quiescent media, respectively. These lower values may be due to increased variation in the RR measurement caused by the very low recovery of FD70. For example, for FD-70, at 0.5 µL/min, in quiescent PBS, RR is 1.58%. The experimental data shown in Figure 2 combined with the highly correlated linear fits using eq 3 suggests that even for large macromolecules, eq 2 can be used as a means to estimate microdialysis sampling resistance values. However, as the indi-

Table 3. Calculated and Experimental Mass Transfer Resistancesa resistanceb s/mm3

FD-10

FD-20

FD-40

FD-70

RT (Rd + Rm + Re) Rd(C) Rm Re(E) Re(C)

264.3 6.4 178.3 79.6 456.3

556.6 8.9 345.3 202.4 635.5

1780.4 12.4 1300.5 467.5 926.8

6666.7 17.0 4009.8 2639.8 1223.0

a Samples were collected in a phosphate buffered saline solution at 37°. b The symbols E and C denote experimentally determined and calculated values for each resistance term.

vidual terms in eq 2 are examined more closely, it is apparent that adjustments must be made to these terms to account for macromolecule-hindered diffusion, thus allowing for more accurate estimation or prediction of the experimental RR through dialysis membranes. Macromolecule Dialysis Resistance. The original development of the mass transport resistance model for microdialysis sampling made assumptions about analyte mass transport through the various regions of the dialysis sampling experiment (e.g., sample, membrane, and perfusion fluid). During the sampling process, the analyte diffusion time across the annular region of the cannula shown in Figure 1 is assumed to be less than the time needed for the fluid to pass through the cannula. The equation from ref 17 for the dialysate resistance is shown in eq 14.

Rd )

(rβ - rR) 2πLrβDdϑ

(14)

Using information from the manufacturer combined with the FITC-dextran aqueous diffusion coefficient values, it is possible to calculate Rd for these dialysis experiments. Here, the coefficient ϑ is the ratio of the annulus residence time, TQ (TQ ) π(rβ2 rR2)L/Qd), to the time that is characteristic of transannulus diffusion TD (TD ) (rβ - rR)2/Dd). When TQ > TD, the approximation value ϑ ) 35/13 was used resulting in the expression of eq 2.17 This condition assumes that analyte concentrations within the dialysate equilibrate faster in the annular direction, as compared to the length of time the fluid is passing through the membrane window. In these experiments, each of the FITC-dextrans satisfies this condition of TQ > TD for the 10-mm membrane, except FD70 that has a TQ-to-TD ratio of 1.09. This ratio suggests that for the larger FD-70, its concentration within the fluid is just beginning to reach the inside cannula at the approximate time the fluid exits the probe. This slow diffusivity of the FD-70 causes it to maintain a high concentration at the outer membrane wall due to its slow transannulus diffusion time, resulting in a lower RR. However, despite the smaller aqueous diffusion coefficient values for the FITC-dextrans, the overall mass transport resistance due to the dialysate is still at least an order of magnitude lower than for the membrane or external sample. For each FITC-dextran, Rm and Re can be found from the slope of eq 3 using well-stirred and quiescent conditions. These values are shown in Table 3. In eq 2, Dm and Φm are denoted as separate

Figure 3. SEM analysis of the PES membrane structure: (a) cross section of the PES membrane (original magnification ×1000) and (b) structure of the outer layer membrane (original magnification ×5000).

variables, but only the product, DmΦm, can be elucidated using these experimental conditions, since the geometry of the probe is known (e.g., membrane radii and length). These experimental results give the sum of Rd and Rm, since it is not possible to create experimental conditions to isolate the dialysate resistance value. Therefore, Rm values denoted in Table 3 were obtained by subtracting Rd (calculated using the empirical diffusion coefficients shown in Table 1) from the total resistance (Rd + Rm) obtained during the well-stirred sample conditions. Table 3 shows that for microdialysis sampling of macromolecules, the membrane provides the dominant mass transport resistance. When a macromolecule is in a pore with size that is comparable to the solute diameter, in addition to the friction from the wall of the pore it passes through, the macromolecule also incurs additional hydrodynamic drag due to its large size. Figure 3a shows an SEM for the PES membrane cross section and illustrates the inner and outer layers of this composite membrane. These structural features are common with dialysis membranes that often contain an inner layer that defines the molecular weight cutoff and an outer support layer. The outer support layer consists of much larger pores that have a diameter of ∼1 µm, as shown in Figure 3b. Additionally, the SEM images indicate that the thickness of the inner layer is ∼10 µm, so ro in eq 2 should be set to a value of 0.22 mm instead of 0.25 mm, where 0.03 mm comprises the outer support layer with much larger pore size. Table 2 shows the values for all the different parameters that are necessary to calculate Dm with eqs 7-11. For FD-40 and FD-70, λ, the ratio between the analyte and pore radii have values >1. Although the hydrodynamic radii for FD-40 and FD-70 are equal to or larger than the membrane pore radius, these analytes are recovered through the microdialysis membrane, indicating that this 9-nm estimation is an average and not homogeneous throughout the inner selective layer of the membrane. Microdialysis collection of some analytes nearly equal to or larger than the membrane cutoff has been previously reported, and as expected, these relative recoveries are extremely low (60 min. This information may be useful in redesign of protein collection experiments using microdialysis sampling. An almost 15-fold increase in recovered concentration for the FD-20 was obtained using the stopped-flow methodology rather than continuous flow. As more and more researchers are interested in microdialysis sampling for protein collection and quantitation, it may be important to consider alterative approaches to increase collected concentrations, and using stopped flow may be one possibility. CONCLUSIONS Microdialysis sampling is increasingly being applied to sample larger macromolecules. The purpose of this study was to provide greater physical insight into the sampling process for larger molecules. The mass transport resistance models provide useful physical insight into the microdialysis sampling process. However, it is critically important to understand how these models are affected by differences in molecular diffusion, especially for aiding the understanding of experimental data obtained in vivo. ACKNOWLEDGMENT We thank CMA Microdialysis, Inc. for providing us with 2-mm PES probes for this study. NIH EB 001441 supported this work.

N)

Qd ) volume flow rate of perfusion fluid RR ) relative recovery Rd ) resistance for the dialysate Rm ) resistance for membrane Re ) resistance for quiescent external medium RT ) total resistance r* ) mean projected solute radius rR ) radius of the outer cannula surface rβ ) radius of the inner membrane surface ro )

radius of the outer membrane surface

rs )

hydrodynamic radius of the solute molecule

rp )

radius of the membrane pore

s)

ratio of pore volume to pore surface area

T)

temperature

Re(E) ) experimentally determined resistance for external medium Re(C) ) calculated resistance for external medium using equation in Bungay theory RR(E) ) experimentally determined relative recovery RR(C) ) calculated relative recovery for external medium using Re(C) TQ ) annulus residence time TD ) transannulus diffusion time V)

average fluid velocity

)

porosity of the membrane, defined as the fraction of the membrane volume accessible to water, which is equivalent to Φm in eq 2

φ)

solute partition coefficient between the membrane and solution

GLOSSARY OF SYMBOLS Cd ) analyte in dialysate

solute flux through porous membranes

Ce ) analyte concentration in external sample medium Ci ) concentration of analyte in the entering perfusion fluid

φm ) volume fraction of membrane

Cs ) average concentration in the pores

φe ) accessible volume fraction in extracellular phase (tissue)

Dd ) analyte diffusion coefficient in dialysate

ϑ)

ratio of the annulus residence time to the transannulus diffusion time

λ)

ratio of the radii of the solute molecule to the membrane pore (rs/rp)

Dm ) analyte diffusion coefficient in membrane De ) analyte diffusion coefficient in external fluid D∞ ) diffusion coefficient for the analyte in the bulk solution EE ) extraction efficiency KC ) convective hindrance factor KD ) hindrance factor for diffusive transport Kt ) hydrodynamic function of λ in Bungay and Brenner’s equation k)

length of membrane

Lp ) membrane hydraulic permeability

6034

ω)

radius of the sphere in the spherical coordination

η)

dynamic viscosity of the sample medium

δm ) membrane thickness

Boltzmann coefficient

k1 ) Kozeny constant L)

λ* ) effective size ratio

Analytical Chemistry, Vol. 78, No. 17, September 1, 2006

Received for review February 16, 2006. Accepted June 30, 2006. AC0602930