1 Department of Anaesthesia, Söder Hospital, S-118 83 Stockholm, Sweden. 2 Department of Anaesthesia, Karolinska Institute, Stockholm, Sweden
Corresponding author. E-mail: Robert.hahn@anest.sos.sll.se
Accepted for publication: January 7, 2003
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Abstract |
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Methods. Six male volunteers received four separate infusions of glucose 2.5%: 10 ml kg1 and 15 ml kg1 over 30 min, and 15 ml kg1 and 25 ml kg1 over 60 min. The kinetic model was fitted to measurements of plasma glucose concentration and haemodilution.
Results. The mean volume of distribution for the glucose was 9.2 (SEM 0.4) litres while the infused fluid expanded a central body fluid space (V1) of 3.1 (0.3) litres. Increasing the amount of infused fluid, but not the infusion rate, resulted in a proportional increase in the area under the curve for plasma glucose and plasma dilution, the only confounder being glycosuria. The bias of computer simulation was slightly increased by rebound hypoglycaemia, which could occur with the highest infusion rates, but the accuracy was almost identical regardless of whether the kinetic parameters from all 24 experiments or from any of the subgroups were used.
Conclusion. The volume kinetic model for glucose 2.5% is linear and can therefore be used for computer simulation as long as marked glycosuria does not occur.
Br J Anaesth 2003; 90: 6007
Keywords: fluids, i.v.; blood, haemodilution; pharmacokinetics; metabolism, glucose
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Introduction |
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Glucose is usually supplied as a 5% solution, although 2.5% might be more useful in the surgical patient.6 7 Recently, a volume kinetic model in which the glucose metabolism is considered was used to analyse the distribution and elimination of these fluids.8 The proposed model enabled separation of osmotic-driven translocation of fluid, which is affected by diabetes and postoperative insulin resistance, from dilution-dependent elimination, which also becomes impaired by surgery9 and blood loss.10
In the present study we evaluate whether the kinetic model proposed for glucose solutions is linear, that is, whether the kinetic analysis shows the same result regardless of how fast and how much of the fluid is infused. Linearity is required for the kinetic model to be used to simulate the outcome of experiments not performed. For this purpose, glucose 2.5% was infused at four different rates in six male volunteers. The volumes were differentiated by continuing the infusions for 30 or 60 min.
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Materials and methods |
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The infusion programme was chosen to disclose differences in kinetics by varying the rate of administration (15, 20, 25 and 30 ml kg1 h1) and the infusion time (30 and 60 min) while still aiming at avoiding glycosuria (Table 1).
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The plasma glucose concentration was measured in single samples using the GLU Gluco-quant reagent (Roche Diagnostic Inc., Mannheim, Germany) on a Hitachi 917 (Hitachi Co., Naka, Japan). The blood haemoglobin (Hb) concentration, the red blood cell count (RBC) and the mean corpuscular volume (MCV) were measured in single samples and the baseline in triplicate samples, using a Technicon Advia 120 (Bayer, Tarrytown, NY, USA). Hb was obtained by colorimetry at 546 nm and RBC and MCV were measured by light dispersion at two angles using a helium neon laser. The coefficient of variation, as calculated from the baseline samples, was 1.0% for Hb, 1.2% for RBC and 0.5% for MCV. The serum concentration of insulin was measured using a Mercodia insulin ELISA kit (Mercodia AB, Uppsala, Sweden) with a coefficient of variation of 5% for the baseline level and 4.4% for the higher concentrations in the study.
The subjects voided just before the infusions started and, in the recumbent position, whenever necessary during the study. All volunteers also voided at the end of the study. The urine volume and its concentration of glucose, sodium and potassium were measured using a Hitachi 917 System (Hitachi Co., Naka, Japan).
Glucose kinetics and uptake
The WinNonlin Standard 1.5 program (Pharsight Corp., Mountain View, CA, USA) was used to calculate the volume of distribution (Vd), area under the curve (AUC), clearance (CL) and half-life (T1/2) of the infused glucose. The input was the glucose concentration above baseline, and the kinetic analysis was ended when the concentration had returned to baseline. Weights inversely proportional to the predicted concentration were applied. When analysing the results statistically using the F-test, the one-compartment open model was consistently justified.8
Since glucose requires active transport to enter the cells, a decreasing amount of glucose in Vd corresponds to the uptake of glucose into a peripheral compartment that does not equilibrate with venous plasma. The net uptake of glucose into this remote compartment was calculated for each sampling interval as the product of Vd and the incremental change in plasma glucose concentration. During the infusion, the calculation of the incremental net uptake also took account of the amount of glucose added to the system. The equations used for the kinetic analysis and for calculating glucose uptake were given in a previous study.8
Volume kinetic models
The distribution and elimination of infused fluid was studied by volume kinetic analysis810 (Fig. 1). An i.v. infusion given at a constant rate (ki) enters a central body fluid space having the volume (v1) which strives to be maintained at the baseline volume V1 by allowing fluid to leave the space at a controlled rate proportional by a constant kr to the deviation of v1 from V1 and at a low basal rate (kb, fixed rate). Osmotic fluid shifts take place between V1 and a more remote fluid space, V3, and have the strength f(t). As all infused fluid was isotonic, f(t) is governed in the absence of glycosuria by the net uptake of glucose into the remote compartment and the osmotic pressure of glucose; 3.6 ml water was translocated to v3 per mmol glucose taken up by V3. As water must accompany glucose in order to maintain equal osmolality inside and outside V3, the factor 3.6 was obtained from the osmolality of glucose (50 g litre1 or 278 mmol litre1 being isotonic). In the model, fluid also returns from v3 to v1, which occurs at a rate proportional by a constant (k31) to the dilution of V3. The starting estimate for V3 in the curve-fitting procedure was 40% of the body weight,11 but the kinetic output is presented as k31/V3 (i.e. the slope for the dilution of V3) as its volume could not be determined with confidence.
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Calculations of fluid distribution
The dilution of the plasma in the cubital vein was used to quantify the water load. As the sampled plasma is a part of V, we obtain:
at the time t of the experiment. The dilution of the RBC count was calculated in the same way as for Hb and the mean value of the two was used after correction for changes in cell volume as indicated by MCV. Furthermore, a correction of the dilution was always made for the withdrawn amount of erythrocytes based on the baseline blood volume, as estimated according to a regression formula based on the height and weight of the subjects.8 A kb of 0.8 ml min1 was used, which represents the sum of the insensible fluid loss of 0.5 ml min1 and the amount of extracellular fluid withdrawn during blood sampling.3
The model parameters were calculated on a computer using Matlab version 4.2 (Math Works Inc., Natick, MA, USA), in which a non-linear least-squares regression routine based on a modified GaussNewton method was used. Weights inversely proportional to the predicted dilution plus 0.1 were applied.
Predictive performance measures
Computer simulations were made to assess the linearity of the kinetic systems. The residual error between the measured data points in each experiment and the computer-simulated (predicted) values for the group, based on the best parameter estimates according to Tables 2 and 3, was used to describe how well the kinetic model fitted the data. The results were expressed as the median residual error, which shows whether the measured data points are systematically higher or lower than the predicted ones (i.e. the bias), and the median absolute residual error, which reflects the degree of deviation of measured from predicted data points (i.e. the inaccuracy).
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After the infusion, it is:
where T is the infusion time. The resulting osmotic strength, f(t), and the dilution of V1 were simulated using solutions to the differential equations described previously.8
Statistics
The results are expressed as the mean (SEM). Data showing a skewed distribution were given as the median and the 2575th percentile range. The AUC for the plasma glucose and plasma dilution were calculated by the linear trapezoid al method for as long as the data points exceeded baseline. Differences between and during the experiments were evaluated by repeated-measures ANOVA. Correlations between parameters were studied by simple and multiple linear regression; P<0.05 was considered significant.
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Results |
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Fluid kinetics, area approach
The AUC of the dilutiontime profile increased with the volume of infused glucose solution (Fig. 4A). The AUC response to infused fluid tended to change for higher infusion rates, but this relationship was not statistically significant (Fig. 4B). This lack of linearity could be accounted for by glucosuria, which reduced the AUC (r=0.51, P<0.01).
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For all 24 experiments, the median residual error was 0.009 (SEM 0.005) dilution units. Most of this error could be attributed to the inability of the glucose simulation program to predict concentrations below baseline; the dilution of V1 was therefore slightly overestimated during the late stages of the experiments. This error was reduced to 0.003 (0.006) on considering only the data obtained during infusion and 30 min after infusion.
The overall median absolute residual error was 0.026 (0.003), which did not change on exclusion of the late stages of the experiments. This error was less than 0.01 dilution units higher when any dilutiontime curve was simulated using the average parameter estimates for all 24 experiments, compared with when it was based on its own series of six infusions. These actual differences for the four series of experiments averaged +0.004, 0.003, 0.006 and +0.005 (Table 4).
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As expected, the renal clearance of the infused fluid (urine volume divided by the AUC for dilution) correlated with the elimination rate constant (kr) yielded by the compartment analysis (Fig. 6A).
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The potassium excretion averaged 19 (2) mmol and differed little between the groups. The highest excretion (66 mmol) occurred in the experiment associated with the most pronounced glycosuria.
The systolic and arterial pressures increased slightly during the experiments, from 123 (2) and 72 (1) mm Hg, respectively, at baseline to 127 (2) (not significant) and 76 (2) mm Hg (P<0.001) at 180 min. The heart rate increased from 62 (2) to 64 (2) beats min1 (P<0.001).
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Discussion |
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The kinetic analysis consists of two parts. First, the amount of fluid translocated to the cells by virtue of glucose uptake is estimated using Vd as the calibration factor between the plasma glucose concentration and the amount of glucose that readily equilibrates with the plasma, which mirrors the amount of glucose that has not been taken up by the cells. Secondly, a volume kinetic analysis of the remaining fluid is made. An estimate of the size of the central body fluid space expanded by infused fluid (V1), which is a central concept in volume kinetic theory,9 10 is made possible by the fact that the dilution of the blood with respect to a large macromolecule such as Hb which does not penetrate vessel walls is a measure of the distribution of the infused fluid volume, and not of the macromolecule. In contrast, the concentration of small molecules, such as glucose which easily diffuse across vessel walls is a measure of the distribution of the molecules and not of the fluid volume.
The results confirm previous findings that the net removal of glucose from plasma occurs quite quickly in healthy volunteers.8 The plasma had been cleared of excess glucose 30 min after the infusions ended. The infused water had also been cleared, although the volume of urine measured 90 min later shows that the osmotic fluid shift still retained 38% of the infused fluid in the body. Predictions based on the kinetic data suggested that the excess fluid in V3 was between 0.20 and 0.25 litres at the end of the experiments (figure not shown), which is consistent with the measured urinary excretion provided that we also consider insensible fluid losses. The cellular volume thus seems to remain expanded for a much longer time than V1.
The kinetic analysis indicated that the infused glucose is distributed in a volume three times larger than that of the infused fluid. No expansion of a body fluid space between the small V1 and the remote body fluid space V3 could be supported by adding one more exponent to the equation for the dilutiontime curve. The lack of a V2 can probably be explained by the rapid uptake of glucose, which occurred at a rate similar to the expected time course for distribution of fluid between V1 and V2.10 13 Furthermore, the close correlation between kr derived from the urinary excretion and kr estimated by the curve-fitting procedure (Fig. 6A) supports the theory that fluid was indeed removed from V1 only by urinary excretion or by uptake into V3. In pharmacokinetics, this argument would correspond to the view that a drug is fully eliminated by urinary excretion if the renal CL corresponds closely to the total body CL.
The evaluation of model linearity also consisted of two parts. The first one confirmed that the AUC for glucose increased in proportion to the dose and that CL was virtually the same regardless of the infusion rate (Fig. 3). As concerns the fluid volume, glycosuria reduced the AUC for the plasma dilution and thereby distorted the comparisons (Fig. 4). However, on removing the cases involving glycosuria, the linearity was almost as good for the fluid volume as for the glucose.
The second part of the evaluation of linearity was based on predictive performance measures. This is an alternative to comparing the kinetic parameters for the four groups studied. Kinetic parameters usually show some degree of intercorrelation, and it might be difficult to judge whether the slightly higher Vd and lower CL we observed for higher infusion rates of glucose (Table 2) have any practical meaning, or whether they cancel out when the parameters are used for simulation. The approach used here to assess predictive performance was inspired by a study on infusion pumps,14 although we report absolute instead of relative errors as a long period of late dilution close to baseline is needed for the estimation of k31/V3.
The results show that the errors associated with simulation were usually quite small. However, the dilution was usually slightly overestimated during the later stages of the experiments when glucose 2.5% was infused rapidly, mostly because the kinetic model could not take account of dilution below baseline. This limited capacity to deal with rebound hypoglycaemia must be kept in mind when simulating an abrupt stop of glucose administration liberal enough to raise the plasma glucose level close to the renal threshold (>12 mmol litre1). The inaccuracy of simulating by computer, expressed as the median absolute residual error, averaged 0.026 dilution units but, more importantly, it was practically the same when the kinetic parameters used for simulation were based on all 24 infusions, as compared with when they were derived from any of the four subgroups. Hence, using the parameter estimates from the pooled series of infusions did not increase the inaccuracy of the simulations.
Slight glycosuria occurred in several volunteers despite the lack of a family history of diabetes. Glycosuria may occur in healthy patients who receive glucose infusions2 and might be difficult to prevent completely.15 As could be expected, however, it mostly occurred in the two groups with the highest infusion rates.6 Glycosuria did not affect the parameters describing glucose kinetics as glucose was cleared from plasma as fast as the fluid volume. The AUC for plasma dilution was reduced, however, which can, from a kinetic point of view, be attributed to less fluid being returned from V3 to V1 after metabolism of the glucose. This probably explains why the estimates of k31/V3 were lower when glucose was infused at the two highest rates. Computer simulations indicated that k31/V3 governed a slight upward shift of the dilutiontime profile of V1 after infusion but otherwise had a quite limited impact on the curve. Variations in glucose kinetics also seemed to have a relatively small influence on V1, which was clearly most affected by kr (figures not shown).
In conclusion, by using an area method and comparing residual errors after simulation, we found linearity for glucose 2.5% when infused at different volumes and rates. Glycosuria and rebound hypoglycaemia appeared to be confounders, however.
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References |
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2 Miller RD. Anesthesia, 5th Edn. Philadelphia: Churchill Livingstone, 2000; 1596, 1938, 2528
3 Thorén L, Wiklund L. Intraoperative fluid therapy. World J Surg 1983; 7: 5819[ISI][Medline]
4 Ljungqvist O, Thorell A, Gutniak M, Häggmark T, Efendic S. Glucose infusion instead of preoperative fasting reduces postoperative insulin resistance. J Am Coll Surg 1994; 178: 32936[ISI][Medline]
5 van der Berghe G, Wouters P, Weekers F, et al. Intensive insulin therapy in critically ill patients. New Engl J Med 2001; 345: 135967
6 Doze VA, White PF. Effects of fluid therapy on serum glucose levels in fasted outpatients. Anesthesiology 1987; 66: 2236[ISI][Medline]
7 Stillström A, Persson E, Vinnars E. Postoperative water and electrolyte changes in skeletal muscle: a clinical study with three intravenous infusions. Acta Anaesthesiol Scand 1987; 31: 2848[ISI][Medline]
8 Sjöstrand F, Edsberg L, Hahn RG. Volume kinetics of glucose solutions given by intravenous infusion. Br J Anaesth 2001; 87: 83443
9 Svensén C, Ponzer S, Hahn RG. Volume kinetics of Ringer solution after surgery for hip fracture. Can J Anaesth 1999; 46: 13341[Abstract]
10 Drobin D, Hahn RG. Volume kinetics of Ringers solution in hypovolemic volunteers. Anesthesiology 1999; 90: 8191[ISI][Medline]
11 Guyton AC, Hall JE. Textbook of Medical Physiology, 9th Edn. Philadelphia: W.B. Saunders, 1996; 1856, 298302
12 Gabrielsson J, Weiner D. Pharmacokinetic/Pharmacodynamic Data Analysis: Concepts and Applications, 2nd Edn. Stockholm: Swedish Pharmaceutical Press, 1997; 645
13 Svensén C, Hahn RG. Volume kinetics of Ringer solution, dextran 70 and hypertonic saline in male volunteers. Anesthesiology 1997; 87: 20412[CrossRef][ISI][Medline]
14 Varvel JR, Donoho DL, Shafer SL. Measuring the predictive performance of computer-controlled infusion pumps. J Biopharm Biopharmaceut 1992; 20: 6394
15 Davidson JK. Clinical Diabetes Mellitus a Problem-oriented Approach, 3rd Edn. New York: Thieme, 1999; 444