Mannitol was infused after the bromide and iohexol measurements had been completed. The ECFo expanded by this fluid was 13.7 (3.4) L when the curve-fitting procedure estimated both ECFo and kr. When kr was determined by the urinary excretion, which amounted to 719 (221) mL with a sodium concentration of 63 (27) mmol/L, the corresponding volume was 14.9 (3.5) L (Fig. 2). The results of the two methods of calculating ECFo were very similar but the one based on the measured urinary excretion, which rests on fewer assumptions, was used in further comparisons.
There were no statistically significant differences among the results of the 3 methods (analysis of variance). Instead, the Vd for the three techniques correlated well, the r = 0.84 for sodium dilution versus iohexol, r = 0.88 for bromide (at 60 min) versus iohexol, and r = 0.64 for bromide versus sodium (Fig. 3 a–c, left). Bland-Altman plots for the agreement among the techniques showed that sodium dilution yielded a 0.7 L lower mean value than iohexol, whereas bromide was 0.7 L higher than iohexol. Finally, sodium was 1.4 L lower than bromide (Fig. 3 a–c, right).
The Vd increased with body weight for bromide (r = 0.84, P < 0.01), for iohexol (r = 0.94, P < 0.001), and for the sodium dilution (r = 0.68, P < 0.05). The Vd was 18.3% (3.1%) of the body weight when measured by sodium dilution, 19.6% (1.0%) when obtained using iohexol, and 20.5% (1.1%) when obtained using bromide (Fig. 4).
Our aim was to compare volume kinetics and iohexol with a conventional method for measuring the ECF space in volunteers. None of the methods involved radioisotopes. Bromide dilution has been used as a standard procedure, but slow elimination makes daily measurements questionable. The more rapid elimination of the tracer used in the iohexol and volume kinetic techniques makes daily repetition of these techniques more feasible (5). Kinetic analysis must then be applied to obtain a valid result, but this has become less problematic with the availability of personal computers.
We chose isotonic mannitol solution for the volume kinetic technique, as it is well tolerated and does not contain any sodium ions. The infusion implied administration of nearly pure water, which diluted the ECF space. The resulting dilution of the serum sodium concentration is the result of both the water Vd and the equilibration of sodium ions throughout the ECF space. Previous work using volume kinetics has been focused on the distribution of the infused fluid volume, which can be obtained by applying the kinetic models to the blood Hb, plasma albumin, or blood water concentrations (16). Thus, the method seems quite practicable in the clinical setting using standard laboratory methods, provided that the patients can tolerate volume expansion. A good curve fit was obtained using a one-volume model, the simplest of the models developed.
The ECF space was 6%–13% smaller (depending on the kinetic model used) with volume kinetics as compared with iohexol. The latter is a small hydrophilic solute with properties similar to those of inulin or Cr-EDTA. The reasons why the volume kinetic model indicates a smaller space are not clear. However, the method rests on measuring as precisely as possible a decrease in serum sodium of only 6–10 mmol/L. Moreover, the result should be corrected for the urinary excretion of both sodium ions and water, which could be more precisely quantified over time than we did.
Besides the potential bias involved in how the measurements were performed, one must also consider that fluid and sodium might not equilibrate as perfectly in the ECF space as is commonly believed. At the tissue level, the interstitium is complex and inhomogeneous. There is a framework of collagen, with a gel phase of glycosaminoglycans, plasma proteins, and a crystalloid solution. The macromolecules are held to be mutually exclusive, i.e., not all of the interstitial space is available to proteins. The hydraulic conductive properties of the tissues are affected by overhydration or fluid depletion. With regard to fluid plasma-to-lymph passage times in different tissues, there are considerable variations in path length, linear velocity, and Vd (19). The volume expansion attained by the infusion of mannitol solution must involve readjustments in all or some of these variables, and the possibility remains that the fluid distributes inhomogeneously, within “preferential fluid spaces.”
The volume kinetic model as used here also reflects the capacity of the ECF space to equilibrate the sodium concentration. The process of equilibration might be complex and may require some time, as poorly perfused areas of the body are reached with smaller amounts of infused fluid than are well-perfused areas. Therefore, organ aspects need to be considered. In animal studies and in humans, plasma volume expansion with crystalloid fluid induces a differential loss of water and small solutes from the circulation (20). Moreover, the infused solution does not distribute according to organ weight and presumed ECF space, and there seems to be a preponderance of skin and viscera and an underexpansion of skeletal muscle (21). Such incongruencies in distribution, and the fact that the sodium technique reflects two processes instead of one, may explain the slightly lower value for the ECF space indicated by this approach.
Small hydrophilic solutes, cleared exclusively by glomerular filtration, can be used to determine the GFR. Examples of such exogenous substances are inulin, Cr-EDTA, and some radiograph contrast media, such as iohexol. One reason is that it can easily be assayed in plasma or urine by high-performance liquid chromatography or radiograph fluorescence methods, and another is that simplified approaches, such as GFR assessments from one or a few plasma samples, have become available (22). Iohexol has a very low extrarenal clearance, as determined in anephric pigs (23) and in anuric patients (24); it is not handled by the renal tubules or bound to plasma proteins, and it does not influence the GFR. Although inulin and CrEDTA are established tracers for measuring ECF volume, iohexol has only recently been used for this purpose (5).
In view of the kinetic properties of iohexol, it would be an excellent tracer for the ECF volume. Pharmacokinetic models, including up to three compartments, have been validated (25). Our data yielded good curve fits using a two-compartment model. The appearance of the distribution (α) phase varied greatly among the volunteers, resulting in the high sd for k12 and k21 shown in Table 1. Poor delineation of the α phase leads to uncertainty in the parameter estimation process, which is reflected by the standard deviations presented in the Appendix. However, the computer program used for pharmacokinetic analysis separately specifies the uncertainty inherent in the estimation of each parameter in each volunteer. The uncertainty (sd) for Vss averaged 1.0 L (6%), which shows that, overall, the individual Vss was still estimated with acceptable precision. Kinetic analysis of the concentration-time profile of iohexol also offers a state-of-the-art determination of GFR. In the set of kinetic parameters shown in Table 1, the size of the ECF space is given by Vss, and GFR is represented by the clearance. The rapid elimination of iohexol is captured by the half-life, which is obtained as the logarithm for 2 (0.693) divided by k10. This averaged 58 minutes in our study.
There are several reasons why bromide is an imperfect tracer for measurements of the ECF space. It is enriched in the skin, red cells, connective tissue, and secretory organs. The intracellular distribution is 20%–25% and, as illustrated in the present study, its Vd increases with time. In rats, equilibrium occurs at 28–32 hours, reflecting delayed distribution into the connective tissue, skeleton, transcellular water, and central nervous system (8). The Vd for bromide is probably best calculated using kinetic resolution of the time-concentration curve, as it is for the other two methods, but this is not routine. The changing distribution of the tracer and its time course are not well documented in pathological conditions but may be altered. Such deviations would be difficult to trace on the basis of plasma concentration data alone. In our experiments, Vd for bromide increased by up to 10% from 2 hours onward, compared with the 60-minute value. We chose to focus on the Vd obtained at 60 minutes, as there is little decay in plasma concentration after that time in healthy subjects (11). Given the imperfections of the bromide method, our data will serve mostly as an approximation of the ECF volume and a background for the measurements with the other methods.
The study has some limitations. The number of subjects included was quite small. Although volunteers were studied, the methods are intended for use in intensive care patients. Therefore, the present work must be followed by other studies that test the clinical utility of the methods in critically ill patients. Although a reasonable steady state in fluid balance must be maintained during the measurement period, we believe that tracers with a fairly rapid elimination rate have a better chance to guide the clinician because they allow repeated use. The complexity of elimination and distribution of tracers can usually be resolved by pharmacokinetic analysis of the data. A drawback is that adequate separation of the parameters in the kinetic model requires that a series of samples from body fluids be taken. To measure the steady-state dilution of a tracer such as bromide, lower sampling intensity is required. Finally, although venous samples were used for all measurements, arterial blood would have better delineated the distribution phase of the iohexol kinetics and perhaps also revealed a distribution phase for the sodium dilution (14). The use of arterial sampling would modify the estimates of the Vd.
In conclusion, the three methods used in this study gave slightly different estimates of the ECF volume. The bromide method rests on insecure theoretical foundations and measured a larger space than the others. The iohexol method is appealing because it yields both the size of the ECF volume and the GFR. Moreover, the analytical equipment necessary for this tracer is increasingly available. The volume kinetic approach is also applied to a nonsteady-state situation but showed slightly lower values than iohexol.
The extracellular fluid (ECF) volume indicated by bromide ions (Br) is equivalent to the distribution volume (Vd) of this ion at time t after injection of a bolus dose injected at t = 0. The calculation is corrected for the minor urinary losses of Br, measured when the volunteers voided spontaneously at 122 ± 35 min (mean ± sd) of the study:
where 0.9 is the correction factor for intracellular bromide, 0.95 corrects for the Donnan effect, and 0.934 is the correction for the water content of plasma (1,15).
The disposition of iohexol followed a bi-exponential equation in which the concentration C at time t after a bolus dose is described by (20):
where α and β correspond to the initial and terminal slopes, respectively, and A and B represent the intercepts on the y-axis with t = 0. This equation corresponds to the parameters in the kinetic model (Fig. 1, top), as follows (18):
The ECF space corresponded to the total Vd of iohexol at steady-state, Vss, which is the sum of V1 and V2.
The clearance (CL) is given by the dose divided by the area under the curve (AUC) for the entire concentration-time profile. If the latter is unknown, it can be deduced from the equation describing this profile. Hence,
The dilution of the serum sodium (SNa) concentration was used to estimate the dilution of the ECF space. In its simplest from, this relationship can be written as:
where SNao is the serum sodium concentration at baseline (t = 0). Although further calculations per se do not require the assumption of the existence of the ECF space, the correction of dilution for sodium loss does, and ECFo was then initially set to 20% of the body weight. Assuming that the number of sodium ions is constant in the ECF space except for losses that can be measured, we obtain:
The relative expansion of the ECF volume yields the same result as the raw sodium dilution quoted above, but it becomes slightly shifted downward when sodium is lost.
In this study, the urinary excretion of sodium and water was not measured for each blood sample but only as the total amount during the experiment. To mimic the real situation, where more sodium and water are excreted depending on the ECF dilution (19), the losses were graded by calculating a parameter kNa that describes the tendency to excrete sodium for any specific degree of ECF dilution:
This parameter, kNa, multiplied by the ECF dilution and the time (t), then yields the cumulative sodium loss up to any time (t). Hence, by rearrangement:
The disposition of the infused fluid that dilutes the serum sodium concentration is described by the following differential equation (Fig. 1, bottom), in which the dilution is corrected according to the calculations of the expansion of the ECF space (16):
where ki is the infusion rate of mannitol 5%, kb is an evaporation factor which is set to 0.5 mL/min, and kr is a dilution-dependent elimination rate constant (16). During (d) infusion, this differential equation has the following solution:
and after (a) infusion
where w(t) is the dilution (ECFt − ECFo)/ECFo and t1 is the infusion time.
On considering that approximately half of the basal fluid losses were represented by urine excretion, the parameter kr was calculated as the renal clearance for infused fluid, assuming that half of the basal fluid losses appeared as urine:
where T is the total time of the experiment. The kinetic model was first fitted to measured data on SNa with a correction for sodium losses as described above. The computer repeated the analysis 4 times, using progressively more precise estimates of ECFo as input, until the final ECFo was taken as the size of the ECF.
Uncertainty of the Calculations
The kinetic equations used to calculate the ECF volume with the iohexol and sodium methods have no definitive solutions. Therefore, the parameters are estimated with some uncertainty, which can be quantified as an sd. The following list shows the uncertainty of pertinent estimates, described as the mean value for all 10 volunteers.
For the sodium method:
These data of uncertainty serve as an adjunct to the evaluation of how the best estimates of each parameter vary between the volunteers, which is shown in Table 1.
1. Leth A, Binder C. The distribution volume of 82
as a measurement of the extracellular fluid volume in normal persons. Scand J Clin Lab Invest 1970;25:291–7.
2. Kim J, Wang Z, Gallagher D, et al. Extracellular water: sodium bromide dilution estimates compared with other markers in patients with acquired immunodeficiency syndrome. J Parent Ent Nutr 1999;23:61–6.
3. McCullough AJ, Mullen KD, Kalhan SC. Measurements of total body and extracellular water in cirrhotic patients with and without ascites. Hepatology 1991;14:1102–11.
4. Shaffer SG, Ekblad H, Brans YW. Estimation of extracellular fluid volume by bromide dilution in infants of less than 1000 grams birth weight. Early Human Develop 1991;27:19–24.
5. Zdolsek HJ, Lisander B, Jones AW, Sjöberg F. Albumin supplementation during the first week after a burn does not mobilise tissue oedema in humans. Intensive Care Med 2001;27:844–52.
6. Lucas CE, Ledgerwood AM, Rachwal WJ, et al. Colloid oncotic pressure and body water dynamics in septic and injured patients. J Trauma 1991;31:927–33.
7. Hahn RG. Measuring the sizes of expandable and non-expandable body fluid spaces by dilution kinetics. Austral-Asian J Cancer 2003;2:215–9.
8. Bäck S-E, Krutzén E, Nilsson-Ehle P. Contrast media as markers for glomerular filtration: a pharmacokinetic comparison of four agents. Scand J Clin Lab Invest 1988;48:247–53.
9. Pierson RN Jr, Price DC, Wang J, Jain RK. Extracellular water measurements: organ tracer kinetics of bromide and sucrose in rats and man. Am J Physiol 1978;235:F254–64.
10. Thomas LD, Vander Velde D, Schloerb PR. Optimum dose of deuterium oxide and sodium bromide for determination of total body water and extracellular fluid. J Pharm Biomed Anal 1991;9:581–4.
11. Cousins C, Skehan SJ, Rolph SM, et al. Comparative microvascular exchange kinetics of (77
Br)bromide and 99m
Tc-DTPA in humans. Eur J Nucl Med 2002;29:655–62.
12. Rodushkin I, Ödman F, Olofsson R, et al. Multi-element analysis of body fluids by double-focusing ICP-MS. Recent Res Devel Pure Appl Chem 2001;5:51–6.
13. Krutzén E, Bäck S-E, Nilsson-Ehle I, Nilsson-Ehle P. Plasma clearance of a new contrast agent, iohexol: a method for the assessment of glomerular filtration rate. J Lab Clin Med 1984;104:955–61.
14. Cousins C, Bunasekera RD, Mubashar M, et al. Comparative kinetics of microvascular inulin and 99m
Tc-labelled diethylenetriaminepenta-acetic acid exchange. Clin Sci 1997;93:471–7.
15. Cassady G. Bromide space studies in infants of low birth weight. Pediatr Res 1970;4:14–24.
16. Svensén C, Hahn RG. Volume kinetics of Ringer solution, dextran 70 and hypertonic saline in male volunteers. Anesthesiology 1997;87:204–12.
17. Stalberg HP, Hahn RG, Hjelmqvist H, et al. Haemodynamics and fluid balance after intravenous infusion of 1.5% glycine in sheep. Acta Anaesthesiol Scand 1993;37:281–7.
18. Hull CJ. Pharmacokinetics for anaesthesia, 1st ed. Oxford: Butterworth Heinemann, 1991:172–82.
19. Aukland K, Reed RK. Interstitial-lymphatic mechanisms in the control of extracellular fluid volume. Physiol Rev 1993;73:1–78.
20. Berg S, Golster M, Lisander B. Albumin extravasation and tissue washout of hyaluronan after plasma volume expansion with crystalloid or hypo-oncotic colloid solutions. Acta Anaesthesiol Scand 2002;46:166–72.
21. Renkin EM, Rew K, Wong M, et al. Influence of saline infusion on blood-tissue albumin transport. Am J Physiol 1989;257:525–33.
22. Jacobson L. A method for the calculation of renal clearance based on a single plasma sample. Clin Physiol 1983;3:297–305.
23. van Westen D, Almén T, Chai CM, et al. Biliary and total extrarenal clearance of inulin and iohexol in pigs: a source of error when determining GFR as body clearance. Nephron 2002;91:300–7.
24. Sterner G, Frennby B, Månsson S, et al. Assessing residual renal function and efficiency of hemodialysis: an application for urographic contrast media. Nephron 2000;85:324–33.
© 2005 International Anesthesia Research Society
25. Frennby B, Sterner G, Almén T, et al. Clearance of iohexol, 51Cr-EDTA and endogenous creatinine for determination of glomerular filtration rate in pigs with reduced renal function: a comparison between different clearance techniques. Scand J Clin Lab Invest 1997;57:241–52.