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ENDOCRINE AND DIABETES
Departments of Chemical Endocrinology (H.A.R., J.J.W., F.C.G.J.S.), Endocrinology (H.A.R.), and General Internal Medicine (P.J.v.G., J.W.M.L., C.J.T.), Radboud University Nijmegen Medical Centre, Nijmegen, The Netherlands
Received June 21, 2006; accepted August 9, 2006.
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Abstract |
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For example, measurement of norepinephrine in interstitial fluid of muscle and subcutaneous fat tissue provides a means to assess local (regional) sympathetic neuronal function in humans (Bruce et al., 2002
). To provide reliable information regarding "true" interstitial norepinephrine concentrations, the issue of in vivo recovery needs to be resolved.
There are a number of methods to determine recovery. The "no net flux" method (Lonroth et al., 1987; Wang et al., 1993; De Lange et al., 2000) is a theoretically valid approach to measure in vivo recovery, but it is cumbersome to perform, because it requires multiple changes of perfusate concentration. Moreover, physiologically active substances such as norepinephrine (NE) cannot be infused without affecting the process of interest. Alternatively, an extremely low perfusion rate (Rosdahl et al., 1998) results in dialysate concentrations that are virtually equal to in vivo concentrations, but it yields such small volumes that only analytes in higher concentration or for which there are very sensitive assay methods are suitable for this technique. Approaches that are based on the measurement of in vitro recovery and extrapolating to the in vivo situation by adjustment of a number of physicochemical parameters introduce much uncertainty (Scheller and Kolb, 1991). Finally, the application of an internal standard in retrodialysis seems to be straightforward and relatively user-friendly. This principle is based on the assumption that the relative loss of perfused internal standard from the dialysate to the outer compartment equals the relative gain of the analyte from the outer compartment into the dialysate (Scheller and Kolb, 1991; Wang et al., 1993; Bouw and Hammarlund-Udenaes, 1998; Alberts et al., 1999; De Lange et al., 2000). Obviously, a key assumption is that analyte and internal standard must have similar physicochemical properties. However, the internal standard must not be too similar, because it may mimic or antagonize the biological effects or turnover of the analyte. Until now, no verifiable theoretical model has been proposed that accounts for the observed differences between in vitro and in vivo (retro)recoveries and that defines the conditions that must be fulfilled to gain confidence that the principle equally holds for the in vitro and in vivo situations. We used the principle of retrodialysis with salicylate (Sal), an agent not applied for this purpose so far, to determine in vivo NE recovery. We used Sal for retrodialysis because, owing to its molecular size, it has similar diffusion properties, but it can be considered as not to interfere with NE action and turnover. In the present study, we validate a mathematical model that comprises a simple relationship between recovery and perfusion rate, a mathematical basis for the validity of the retrodialysis concept, and the possibility of identification of the rate-limiting step in in vivo microdialysis, using measurements of NE and Sal in microdialysates obtained from in vivo and in vitro experiments.
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Materials and Methods |
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 | (1) |
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The following simple linear relations between dialysate concentrations of analyte or internal standard and perfusion rate can be derived:
 | (2) |
 | (3) |
Subjects. Nine healthy volunteers, five males and four females [21.3 ± 1.9 years (mean ± S.D.) of age] gave their written informed consent for participation in this study. Intramuscular and subcutaneous perfusion with sodium salicylate was approved by the hospital's ethical committee.
In Vitro Microdialysis. After the in vivo experiment (see below), the microdialysis probe was immersed in a beaker containing 300 ml of 400 ng/l (2364 pM) norepinephrine, dissolved in Ringer's solution. The beaker's contents were kept at 37°C with continuous stirring. The probe was perfused with a 175-mg/l solution of sodium salicylate at 2 or 5 µl/min. The dialysate was collected as below in prechilled microvials.
In Vivo Microdialysis. Before catheter insertion, the skin was superficially anesthetized with lidocaine. In each subject, CMA 60 microdialysis catheters (CMA/Microdialysis, Solna, Sweden; dialyzing polyamide membrane 30 x 0.6 mm; molecular mass cutoff of 
20,000 Da) were inserted percutaneously into resting skeletal muscle of the quadriceps of the right leg and into peri-umbilical subcutaneous adipose tissue. The inlet of the dialysis chamber was connected to a high-precision perfusion pump (model 106/7; CMA/Microdialysis) that continuously perfused at fixed rates of 2 or 5 µl/min with Ringer's solution containing 175 mg/l Sal. The dialysate was collected in timed fractions (2 µl/min, 75 min; 5 µl/min, 30 min) in closed micro vials, to which 1.2 µl of a solution of 0.5 M glutathione and 0.625 M EGTA had been added, on melting ice. Two consecutive dialysate samples were collected at 5 µl/min. The first hour after insertion of the probes and the first 0.5 h after changing the flow rate, the dialysate was collected, but it was not used for further analyses. After the second collection at 5 µl/min, lower body negative pressure (LBNP) was applied for 30 min during which again dialysate was collected at the same flow rate. A final portion of dialysate was collected during 30 min after termination of LBNP.
Assays. NE was measured by high-performance liquid chromatography with fluorometric detection as described previously (Willemsen et al., 1995) in 90-µl aliquots of dialysate, with a few modifications. The extraction was performed only once, and a Waters 2475 detector was used. For plasma, within-run precision ranged from 2.2 to 4.6%, and between-run precision was 8.5% at a level of 1 nM.
Sodium salicylate was measured in 60-µl aliquots of dialysate by means of fluorescence polarization immunoassay (Abbott Diagnostics Division, Hoofddorp, The Netherlands), run on an Abbott TDX analyzer. Gentisic acid (2,5-dihydroxysalicylic acid) cross-reacts in this assay. This would only be of importance if a significant proportion of salicylate would be converted to this metabolite and if crossreaction considerably exceeds 100%. Because its plasma level is only 1% of total salicylate (Woodbury and Fingle, 1975), i.e., after salicylate ingestion through the gastrointestinal tract, considering that it is confined to the interstitial space, no relevant interference is expected by this derivative. Within-run precision is reported to range from 1.8 to 3.8%, and between-run precision ranges from 3.2 to 7.4%. Operational precision, i.e., the precision that is relevant to the power of the present experiments, is evaluated for both assays under Results.
Calculations. Regression analysis of measurements of concentration versus concentration was performed while taking into account residual variation in both variables. Classic least-squares regression analysis was performed for reciprocal concentration versus (reciprocal) perfusion rates. Relative residuals, expressed as percentage of the measurement range, were calculated for each individual curve and subsequently averaged for each value of the perfusion rate. The standard deviation of the averaged relative residuals was defined as a measure of "(non)linearity." A 90% confidence interval for this statistic was calculated from the variances of the residuals. Relationships were considered as linear, when the percentage of nonlinearity was less than its expected upper 90% confidence limit and if this limit did not exceed 5%. This latter criterion was added to prevent second-order error. We defined retrorecovery as 100% – actual recovery (%), so that NE recovery and Sal retrorecovery can be directly compared.
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Results |
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In Vivo Microdialysis. NE concentrations in dialysates of muscle tissue ranged from 322 to 593 pM (mean 414 pM) at 2 µl/min and from 153 to 471 pM (mean 243 pM) at 5 µl/min. In dialysates from fat tissue NE concentrations ranged from 244 to 427 pM (mean 312 pM) at 2 µl/min and from 101 to 287 pM (mean 185 pM) at 5 µl/min. NE concentrations in dialysates from muscle were higher than in dialysates from fat tissue (p < 0.05). The in vivo recoveries, as calculated from Sal retrorecoveries, showed the opposite outcome: 41 to 67% (mean 52%) and 22 to 39% (mean 28%) for muscle at 2 and 5 µl/min, respectively, and 18 to 58% (mean 39%) and 10 to 40% (mean 22%) for fat tissue at 2 and 5 µl/min, respectively. As a result, the calculated NE concentrations at 2 and 5 µl/min in muscle and fat interstitial fluid did not differ (ratio NE 2 µl/min/NE 5 µl/min for muscle, 1.02 ± 0.115; for fat, 1.11 ± 0.121). A common range of 345 to 1857 pM was observed. In addition, muscle and fat NE levels were found to be significantly correlated between subjects (r = 0.75; p < 0.05).
Attainment of a steady state was ascertained by comparison of Sal and NE concentrations of the first 5-µl/min sampling with the second. No difference could be detected either for Sal or NE. However, the variability in the NE levels was much higher. The mean difference between first and second sampling was 0.6 ± 1.6% (mean ± S.E.M.) for Sal and 4.9 ± 6.0% for NE. From the variation of the differences, the operational S.D. values (which encompass all error sources within one experiment) were derived: 6.2 mg/l at a mean level of 129 mg/l for Sal and 39 pM at a mean level of 214 pM for NE.
The validity of the assumption that NE recovery equals Sal retrorecovery in vivo (also see eq. A3 in the Appendix), is illustrated in Fig. 2. A plot of NE versus Sal results in a straight line, intercepting on the Sal axis at the perfusate level of Sal of 175 mg/l. The y-intercepts correspond to the NE concentrations when dialysate Sal concentration is reduced to 0 (i.e., 100% retrorecovery) and thus is an estimate of the true NE concentration in interstitial fluid in the various subjects. These estimates are used in subsequent tests to calculate NE recoveries at 2 and 5 µl/min. Nonlinearity was 1.5% (with 4.8% as upper 90% confidence limit) for muscle and 3.6% (with 4.9% as upper 90% confidence limit) for fat.
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Values of Q = 1/F0 + 1/P were evaluated from the slope and intercept. For Sal, Q in muscle was 0.47 ± 0.061 and in fat was 1.07 ± 0.26; for NE, Q was 0.50 ± 0.069 in muscle and was 0.84 ± 0.24 min/µl in fat. The value of 1/P was obtained from the in vitro experiment described above: 1/P = 1/30.2 = 0.033 min/µl. Although, in fact negligible, values of F0 were obtained taking the permeability into account. Thus, for Sal, the value for F0 in muscle was 2.80 ± 0.48 and in fat was 1.55 ± 0.32. For NE, F0 in muscle was 2.58 ± 0.44 and in fat was 2.00 ± 0.40 µl/min. Estimates of F0 also can be made from retrorecovery measurements at a single flow rate. This was applied for the samples obtained during and after LBNP. Application of LBNP induced a significant decrease of F0 by 20% in muscle, but not in fat. The reduction of F0 in muscle persisted after termination of LBNP. The consequences of these changes for the estimates of interstitial NE are shown in Table 1.
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Discussion |
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; Bungay et al., 1990; Rosdahl et al., 1998; De Lange et al., 2000), only few attempts have been made to propose a mathematical model for this relationship (Jacobson et al., 1985; Bungay et al., 1990). Moreover, these approaches have not been followed in later years. The present report provides a simple and robust model and its stepwise validation for the measurement of subcutaneous NE levels, using Sal as internal standard of which the retrorecovery is used for correction of measured NE levels. The suitability of Sal was investigated in an in vitro experiment, which showed that NE recovery was equal to Sal retrorecovery. This was not completely true for a perfusion rate of 2 µl/min, but the slight difference probably originates from the fact that Sal values in the dialysate under those conditions approach zero, whereas dialysate NE level approaches, and due to assay variability, sometimes slightly exceeds the total concentration in the large volume surrounding the probe. The model is based on the assumption of steady-state conditions. This implies that the flow around the probe must not change during measurements. Steady state was confirmed by collecting two consecutive samples at 5 µl/min. It is assumed that if steady-state conditions hold for this relatively high perfusion rate, it most certainly will hold for lower flow rates as well. The model predicts that recovery and retrorecovery of substances will be equal when transport rates to, from, and through the membrane are equal, thus providing a theoretical base for what has until now just been a consensus assumption. Irrespective of the actual perfusion rates, this equality can be tested by plotting dialysate concentrations of NE versus Sal (Fig. 2). It also provides an estimate of the interstitial NE concentration that subsequently forms the basis for calculating NE recoveries in testing the relationship between (retro)-recovery and perfusion rate. The requirements of p > 0.1 and a 90% confidence interval of the percentage of nonlinearity being below 5%, although somewhat arbitrarily, provide fair evidence for the linearity of the inverse relationship between dialysate concentrations of Sal and NE as depicted in Fig. 2, at least within the range of measurement. Already in this graph, the difference in recovery between muscle and fat becomes apparent by the different positions of the points on the regression line, but it is demonstrated more clearly in Fig. 3 by plotting reciprocal concentrations against flow rate (NE) or reciprocal flow rate (Sal). The combined effect of local transport toward and from the dialysis probe and membrane permeability is derived from the slope of these lines. The value obtained for Q = 1/P + 1/F0 is much higher than the estimate of 1/P obtained from the in vitro experiment. Based on this finding, we conclude that it is the local flow carrying NE toward and Sal away from the outer membrane surface, rather than membrane permeability, that determines recovery. This remains the case even when the local flow is increased approximately 3-fold. Obviously, restriction of flow will lower the recovery for any given perfusion rate but will even more be the controlling factor rather than membrane permeability. The observations during LBNP support this conclusion. The decrease of F0 during and after LBNP, an intervention that does not affect membrane permeability, stresses the fact that conditions in the tissue surrounding the probe determine recovery. Therefore, there is no need for in vitro assessment of membrane permeability. Rather, the fact that recovery may change following LBNP stresses the necessity for its assessment under in vivo conditions. Without recovery taken into account, the rise in muscle NE following LBNP is considerably underestimated (Table 1), and it would have been wrongly concluded that NE levels in muscle, both before and during LBNP are significantly higher than in fat. Moreover, the difference in response to LBNP between muscle and fat would have been underestimated.
The values for the virtual flow themselves, being in the order of 2 µl/min, seem to be realistic and fitting to the dimensions of the device and its immediate surroundings. Taking into account that the total outer surface of the membrane is approximately 60 mm2, it can be deduced that a hypothetical unidirectional flow rate along the membrane must be in the order of 0.3 mm/min. In addition, the fact that the F0 value is lower for subcutaneous fat than for muscle, seems plausible because of the higher degree of vascularization of muscle. The lower F0 value in fat and the fact that it seems unaffected by LBNP may be explained by the less pronounced response of fat interstitial NE to LBNP than of muscle NE.
Once the F0 value is known, recoveries at other perfusion rates can be predicted. This will be particularly useful in cases where assay sensitivity is a limiting factor. In those cases, there is a minimal amount of the substance (absolute recovery) that must be collected within a reasonable time. In the case of NE from muscle tissue, it takes at 2 µl/min approximately 1.5 times longer than at 5 µl/min to collect the same amount of NE. With 1 µl/min, it would require 2.5 times longer, which is the reason that in the present study, no lower perfusion rates than 2 µl/min were applied. Thus, low perfusion rates are favorable for NE measurement, but the high relative loss of Sal impairs the precision of its measurement. There are also limitations to the opposite side: at a perfusion rate of 10 µl/min, the relative loss of Sal is only 20%. This is the relative difference between Sal measurements in perfusate and dialysate that must be used for correction of measured NE to estimate the true subcutaneous NE level. The precision of this number is 2.5 times less than if obtained at 2 µl/min when the relative difference is more than 50%.
The model offers the possibility for estimating the interstitial analyte concentration just from estimates at two or more different perfusion rates, without retrorecovery measurements. Comparison of NE values obtained in this way with those estimated according to Fig. 2 seems to confirm this. However, with a NE measurement performed near its limit of detection, this approach is hardly precise enough to draw a firm conclusion. In contrast, the principle was proven with certainty to hold for Sal and probably will work for analytes present in the interstitium for which assay precision is not a limiting factor. Where assay sensitivity is limiting, the application of Sal to measure recovery provides an elegant solution, especially with interstitial NE.
Finally, there is evidence that this model not only applies to the present experimental context. In a recent study (Ekberg et al., 2005), glucose recovery was measured in microdialysates from subcutaneous fat tissue using the same equipment as in the present report, at perfusion rates ranging from 0.3 to 5 µl/min. The authors, being unaware of the relationship underlying the present model, presented corresponding recovery results from which the only semiquantitative conclusion was drawn that the lowest perfusion rate leads to the highest recovery. These independent data, taken from that article, were plotted by us according to the virtual local flow model. A perfectly linear relationship displaying a scatter of less than 3% about the regression line was obtained.
In summary, a theoretical model for subcutaneous microdialysis has been presented that not only provides a theoretical basis to the assumption of the equality of recovery and retrorecovery but also adequately describes the relationship between (retro)recovery and perfusion rate, permitting optimization of assay precision. In addition, the model permits identification of the rate-limiting step in transfer of the analyte from the interstitium into the dialysate and unveils the fact that membrane permeability plays a negligible role in interstitial microdialysis. Finally, it provides a means to estimate interstitial concentrations of analytes from measurements performed at different perfusion rates, without the necessity of separate estimation of recovery.
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Appendix |
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The analyte concentration at the membrane outside, c1, can be eliminated from these two mass balance equations, leading to the following simple expression for the relation between c2 and c0, the perfusate, and in vivo concentrations of the analyte, respectively:
 | (A1) |
The internal standard is perfused with a concentration c0' and migrates through the membrane into the interstitial compartment, which leads to a lower concentration c1' in the perfusate, leaving the probe toward the collection device. The concentration of internal standard in the interstitial fluid entering the surrounding medium is zero. It leaves the compartment at concentration c2', which is also the concentration at the membrane outside. Applying the mass balance principle again, F0 x c2', P x (c1' – c2'), and F x (c0' – c1') must be equal. The concentration at which the standard leaves the interstitial compartment, c2', can be eliminated, which leads to the expression:
 | (A2) |
Comparison of eqs. A1 and A2 immediately shows under what conditions retrodialysis accurately reflects analyte recovery; membrane permeability P as well as virtual flow F0 must be equal. Of course, the latter would be violated if the analyte was either interstitially produced or metabolized. If analyte and standard had different diffusion coefficients, membrane permeabilities would not be equal. Furthermore, virtual flow might have differed if it in fact depended for an important part on diffusion. This risk is reduced by choosing a standard with physicochemical properties similar to that of the analyte. If these conditions are fulfilled, the estimates of c0 made by applying eq. A3
 | (A3) |
 | (A4) |
This means that when the dialysate concentrations of internal standard (c1') and analyte (c2), as measured at different perfusion rates, are plotted against each other, one should obtain a straight line intercepting the y- and x-axes at c0' and c0, respectively. Moreover, eq. A2 can be applied for different perfusion rates, Fa and Fb, separately. Subsequently, by elimination of 1/P + 1/F0 from the resulting expressions, one obtains
 | (A5) |
If the estimated Fa/Fb matches the quotient of actual applied perfusion rates, this further supports the validity of the model. Furthermore, the model describes and predicts the relation between perfusion rate F and dialysate concentrations of analyte and standard, which may be used to calculate values for 1/P + 1/F0 in different situations. This can be done by rearranging eq. A1 or eq. A2 to a reciprocal form,
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| (A6) |
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| (A7) |
From the plots of 1/c2 as a function of F or 1/c1' against 1/F, independent estimates of Q, c0, and c0' can be obtained. Because a plot of 1/c2 as a function of perfusion rate can be made independent of the retrodialysis measurements, this in principle would obviate the need for applying internal standardization. An in vitro experiment may be conducted under simplifying conditions. The probe is immersed in a large well-stirred volume of a solution of the analyte. The internal standard is perfused through the dialysis probe, allowing to pass the membrane into the surrounding solution where it is immediately carried away from the membrane surface. Thus, the internal standard concentration on the outside is virtually zero and remains negligible when the solution is renewed between experiments. Simultaneously, analyte is taken up from the surrounding solution and carried away in the dialysate without noticeable decrease of the analyte concentration in the outside solution because of its large volume. These conditions are equivalent to those of an infinitely large value for F0, so that 1/F0 is zero. Thus, membrane permeability is rate-limiting, and P, which has the dimension of flow, can be assessed and compared with in vivo estimates of 1/P + 1/F0, thus providing insight into what factor is rate-limiting for the uptake of analyte from the medium surrounding the probe under in vivo conditions.
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Footnotes |
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ABBREVIATIONS: NE, norepinephrine; Sal, sodium salicylate (sodium 2-hydroxybenzoate); LBNP, lower body negative pressure.
Address correspondence to: Dr. Henry Alexander Ross, Department of Chemical Endocrinology, Radboud University Nijmegen Medical Centre, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. E-mail: a.ross{at}ace.umcn.nl
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References |
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