Professor Pietro Palatini Dipartimento di Farmacologia, Università di Padova, Largo E. Meneghetti 2, 35131 Padova, Italy.
Aims Determination of systemic inulin clearance by the standard technique of constant intravenous infusion has long been accepted as a reliable method for measuring glomerular filtration rate (GFR) without urine collection, except in oedematous patients. However, recent studies using standard clearance techniques have claimed that systemic inulin clearance is significantly greater than renal clearance and therefore overestimates GFR. The main purpose of this investigation was to re-evaluate the relationship between systemic and renal inulin clearance using a different technical approach. A reassessment was also made of inulin disposition kinetics.
Methods Systemic and renal inulin clearances were simultaneously evaluated, in healthy subjects and patients with oedema and ascites, by analysis of the total area under the plasma concentration-time curve (AUC) following bolus intravenous injection. Renal clearance was calculated as the ratio of the total amount recovered in the urine to the AUC, and systemic clearance as dose/AUC.
Results Inulin disposition kinetics were best described by a tri-exponential model. In healthy subjects the volume of the central compartment (mean (s.d.) value 3.86 (1.00) 70 kg−1 ) was slightly greater than the plasma volume; steady-state volume of distribution was 11.00 (1.21) l 70 kg−1, in accordance with the tenet that the inulin space is somewhat smaller than the extracellular fluid volume. The values of systemic and renal inulin clearances were very similar (96.1 (10.0) and 94.6 (12.5) ml min−1 70 kg−1, respectively, in healthy subjects; 104.6 (16.3) and 102.6 (18.5) ml min−1 in ascitic patients). They were also highly correlated to each other in both healthy subjects (r=0.96, P<0.001) and patients with ascites (r=0.98, P<0.001).
Conclusions The method described here constitutes a simpler and more precise technique for measuring renal inulin clearance than the standard method, which is based on constant infusion and timed collections of urine samples, since it avoids errors connected with short successive urine collections. By the present method we demonstrated that renal and systemic inulin clearances are virtually identical in both healthy subjects and patients with expanded extracellular fluid volume. Determination of systemic inulin clearance by the presently described technique is therefore a method of general validity for measuring GFR without urine collection.
Measurement of glomerular filtration rate (GFR) is necessary in both clinical practice and research fields for assessing renal function. The renal clearance of inulin is accepted as one of the reference standards for GFR estimation [ 1]. The classical method for determination of inulin clearance, which requires constant intravenous infusion and timed collections of urine samples, is impractical and particularly inconvenient for patients. Therefore, alternative clearance techniques have been developed. Since there is general consensus that inulin is eliminated exclusively by renal excretion, Earle and coworkers [ 2, 3] proposed to determine systemic inulin clearance in place of renal clearance. This technique, which obviates the need for urine collection, has since been shown to be a valid and convenient substitute for measurement of renal clearance, except in patients with expanded extracellular fluid volume because of oedema and/or ascites [ 1, 3]. This practice has been questioned by three recent studies [ 4–6], which found systemic inulin clearance values significantly higher (up to 20%) than those of renal clearance. According to van Acker et al. [ 6] this was attributable to ‘extrarenal clearance or to storage in a compartment that is characterized by slow diffusion’. In these studies, renal clearance was measured by means of the classic UV/P method, i.e. from the ratio of renal excretion rate to plasma inulin concentration, following either constant intravenous (i.v.) infusion [ 4, 6] or bolus i.v. (‘single-shot’) injection [ 5]. However, with either administration technique, this method has technical drawbacks. If it is based on short, successive urine collections, variations in the completeness of bladder emptying produce substantial errors in the evaluation of the renal excretion rate [ 1]. Bladder catheterization, that would ensure more precise determinations of the excretion rate, may cause bladder infections and is not considered acceptable in volunteers. If observations are performed over an extended period of time, wide fluctuations (up to 50%) may occur in plasma inulin concentration, probably due to the circadian rhythm of renal function [ 6]. Therefore, the customary determination of a single plasma concentration at the mid-point of the urine collection period may either grossly overestimate or underestimate the average plasma concentration. The UV/P method after bolus i.v. injection has recently been shown to provide a poor estimate of inulin clearance [ 7].
The main aim of this study was to compare systemic and renal inulin clearances in healthy subjects and patients with ascites. Accordingly, both clearance parameters were determined by the area method [ 8], after bolus i.v. injection. The disposition kinetics of inulin was also reassessed, since discrepant results regarding the distribution characteristics of inulin have been obtained by two recent studies [ 7, 9].
Sixteen healthy male volunteers (mean (s.d.) age 54 (7) years, weight 73 (8) kg, height 170 (6) (cm) and eight male patients with decompensated liver cirrhosis (mean (s.d.) age 50 (7) years, weight 77 (10) kg, height 173 (5) cm) gave their informed written consent to participate in this study, which was approved by the local Ethics Committee. Healthy subjects were recruited from outpatients attending the hospital for routine laboratory tests. Criteria for their selection were that they did not require any regular medication and had no history of allergy to drugs. They were diagnosed as being healthy by means of a thorough clinical examination, including medical history, physical examination and standard clinical laboratory tests. All cirrhotic patients had ascites and oedema of the lower extremities, and could be categorized as Child’s class C. Apart from the biochemical indices of liver function, all patients had normal laboratory test values, including glycaemia. Patients were excluded from this study if they had a recent history of gastrointestinal bleeding, severe encephalopathy or refractory ascites. Creatinine clearance of healthy subjects and patients ranged from 85–134 and 77–144 ml min−1, respectively. During the period of investigation all participants abstained from alcohol and tobacco and took no drugs, apart from those used for the treatment of cirrhosis (spironolactone or canrenone and vitamin supplements).
At 08.00 h, after an overnight fast, 5 g of inulin (InutestR, Laevosan GmHB, Linz, Austria) were infused at a constant rate over 1 min by a precise volumetric infusion pump. Inulin vials used throughout the study were from the same batch. Blood samples (4 ml) were taken from a cannula placed in an antecubital vein of the opposite arm at 0 (predosing), 2, 5, 10, 15, 20, 30, 45, 60, 90, 120, 150, 180, 210 and 240 min after the end of the infusion. Blood was drawn into heparinized plastic tubes and centrifuged immediately. Plasma samples were stored at −40° C until assayed. Urine was collected before and from 0−4 and 4–12 h after dosing. Serial determinations in the urine of the first four subjects (two healthy subjects and two ascitic patients) had shown that inulin was no longer detectable or present in traces after 12 h. Mean urinary recovery was 98 [ 5]% of the injected dose. Before starting the determination of inulin clearance, all subjects received oral hydration with 10 ml kg−1 of tap water. To maintain diuresis, urinary losses were replaced by equal amounts of water.
Inulin in plasma and urine was determined by means of the anthrone method, after removal of glucose, essentially as described by Jung et al. [ 10]. Briefly, 0.3 ml of plasma or urine, appropriately diluted, were mixed with 0.05 ml of the glucose-removing reagent (300 IU of glucose oxidase (Sigma, St Louis, MO, USA) and 30000 IU of catalase (Boehringer, Mannheim, FRG) in 1 ml of 100 mm triethanolamine-HCl buffer, pH 7.0) and incubated at 37° C for 4 h. Control experiments showed that the addition of glucose up to 10 mm (about twice the physiological concentration) to inulin samples had no effect on the determinations. After incubation was completed, 0.35 ml of 10% trichloroacetic acid were added and the mixture centrifuged at 12000 g for 10 min. One ml of 5.15 mm anthrone (Sigma) in sulphuric acid was then added to 0.4 ml of supernatant and the mixture incubated at 37° C for 60 min. All samples were run in duplicate. Absorbance was read at 623 nm. For each assay, inulin concentration was calculated from a calibration curve obtained by dissolving inulin in water. Preliminary experiments had shown that identical calibration curves were obtained if inulin was dissolved in plasma or urine. The assay was linear (r2>0.99) up to 250 mg l−1. The detection limit in plasma and urine was 2 mg l−1. The intra- and inter-assay coefficients of variation (n=10), determined at 20 and 200 mg l−1, were below 7 and 5%, respectively.
The data were modelled by using the GraphPad Prism 2.0 software. The inulin decay curve of each subject was analysed by using a bi- or a tri-exponential equation. Initial estimates of the coefficients and exponents of the equations were obtained by a numerical technique. These estimates were then refined by iterative nonlinear regression analysis with a weighting factor of 1/C2. Comparison between competing models was made by means of the F-test.
The total area under the plasma concentration-time curve (AUC) was calculated from the coefficients and exponents of the equation which better fitted the data. Renal clearance (CLR ) was then calculated either as Ae (∞)/AUC, i.e. from the ratio of the total amount recovered in the urine to total AUC, or as Ae (0–4)/AUC (0–4), (that is from the ratio of the amount excreted during the first 4 h to the corresponding AUC). Systemic clearance was calculated as dose/AUC. Systemic clearance was also obtained from a limited number of data points (at 2, 15, 30, 60, 120 and 240 min) using the logarithmic trapezoidal rule with extrapolation to infinity. The other pharmacokinetic parameters, defined in Table 1, were calculated from standard equations [ 11].
Table 1. Mean (s.d.) pharmacokinetic parameters of inulin. Values of clearance and distribution volumes are normalized to 70 kg of body weight.
A power analysis (CSS power assessment procedure; CSS,Statsoft Inc, Tulsa OK, USA, 1991) based on the coefficients of variation obtained by Buclin et al. [ 7] for renal clearance of inulin indicated that the sample sizes used in this study should be sufficient to detect differences of 10%, with a significance level (α) of 0.05 and a power (1- β) of 0.91. Intragroup differences in inulin clearances were evaluated by means of Student’s two-tailed paired t-test, whereas Student’s nonpaired t-test was used for comparison of pharmacokinetic parameters between different study groups. Correlations were examined by linear regression analysis. Probability values <0.05 were considered statistically significant.
Representative examples of the plasma decay of inulin in healthy and ascitic subjects are shown in Figure 1. With the exception of two ascitic patients, the best agreement between theoretical curves and experimental data points was always obtained using a tri-exponential equation. The pharmacokinetic parameters characterizing inulin disposition are shown in Table 1. The values of the volume of the central compartment and the steady-state volume of distribution in healthy volunteers were very similar to those observed in healthy subjects by Odeh et al. (3.90 and 11.48 l 70 kg−1, respectively; [ 9]) and significantly lower than those observed in ascitic patients. Very similar values were obtained for renal and systemic inulin clearances in both healthy and ascitic subjects. The correlation between the two parameters was highly significant in both groups (r=0.96, P<0.001 and r=0.98, P<0.001, respectively). Determination of renal clearance as Ae (0,4 h)/AUC (0,4 h) yielded values very similar and highly correlated to those calculated from total urinary recovery (97.0 (12.4) and 105.1 (18.6) ml min−1 for healthy and ascitic subjects, respectively; r>0.98 and P<0.001 in either case). Systemic clearance estimates obtained by application of the logarithmic trapezoidal rule to six points (see Methods) were in close agreement with those obtained from pharmacokinetic modelling of the decay curves (93.5 (9.2) and 102.6 (19.6) ml min−1 for healthy and ascitic subjects, respectively) and also showed a close correlation with renal clearance values (r=0.99, P<0.001; r=0.97, P<0.001, respectively). The variability of the clearance estimates was similar with all four methods used. Intersubject coefficients of variation ranged from 10 to 13% for healthy subjects and from 15 to 19% for ascitic patients.
Our results regarding healthy subjects are very similar to those reported by Odeh et al. [ 9]. Like these authors, we found that inulin disposition kinetics are best described by a tri-exponential model. This underlines the inadequacy of the one- or two-exponential models often used to calculate inulin clearance from plasma concentration data (reviewed in 1). The values of V C and V SS found in this study are also in very close agreement with those obtained by Odeh et al. [ 9]. On the contrary, significantly higher estimates were reported by Buclin et al. [ 7]: 7.4 and 13.4 l for V C and V SS, respectively (P<0.001 and P<0.01 compared to our estimates). These discrepancies are most likely due to the fact that these authors used a bi-exponential equation to describe their data. We verified that using a bi-exponential instead of a tri-exponential model yields considerably lower values of C(0) and, consequently, higher V C estimates. Atkinson and coworkers [ 9, 12] interpreted the value of 3.90 l for V C as indicating that the central compartment corresponds to the plasma space and proposed that transcapillary exchange is the rate-limiting step in inulin distribution. However, the observed V C value is about 30% larger than the generally accepted value for plasma volume (3l 70 kg−1; [ 13]). This suggests that part of the extracellular fluid is in rapid equilibrium with plasma. Consistent with this conclusion is the finding that the volume of the central compartment is about twice the plasma volume in ascitic patients. The value of the steady-state volume of distribution obtained in this study is in agreement with various previous estimates (see 6, 9 and references therein) and also in accordance with the tenet that ‘the inulin space is rather smaller than the extracellular fluid volume’, averaging 13l 70 kg−1 [ 13].
Our clearance measurements have shown that, contrary to the continuous i.v. infusion technique, the method based on the analysis of the area under the concentration-time curve following bolus i.v. injection yields virtually identical values of systemic and renal inulin clearances, in both healthy subjects and patients with expanded extracellular fluid volume. In addition, the coefficients of variation of the two clearance parameters proved to be quite similar. This contrasts with the results obtained by means of the UV/P method, which yielded renal clearance estimates much more variable than those of total body clearance [ 5, 7].
A major problem in the determination of systemic inulin clearance by the constant infusion technique is the attainment of a true steady state. Van Acker et al. [ 6] showed that, 6 h after administration of a priming dose and onset of continuous infusion, a steady-state concentration had still not been reached. In two patients they observed a continuous increase in plasma inulin concentration throughout their 30 h study period. According to Hellerstein et al. [ 4], complete equilibration of inulin in the extracellular fluid is a process that requires at least 12–15 h. This process is still longer in patients with expanded extracellular fluid volume. The method described in the present study requires no assumption regarding equilibrium and is therefore of more general applicability. By this method, GFR can be accurately and easily estimated also in oedematous patients from plasma data alone over a relatively short period of time. When, as in routine clinical practice, the above described approach, requiring numerous blood samples for pharmacokinetic modelling, is not feasible, GFR can be estimated by a simplified sampling protocol, without appreciable loss of precision. We have in fact shown that application of the logarithmic trapezoidal rule to only six data points yields essentially equal results, with very similar coefficients of variation.
In conclusion, this study has shown that determination of renal inulin clearance from the ratio of the amount excreted in the urine to the AUC over the corresponding period of time, constitues a simpler and more precise clearance technique than the classic UV/P method, since it avoids errors connected with frequent urine collections. By this method, we have demonstrated that renal and systemic inulin clearances are virtually identical in both normal subjects and oedematous patients. Determination of systemic inulin clearance by the presently described technique represents therefore a method of general applicability for measuring GFR without the need for urine collection.
This work was supported by a grant from MURST (Ministero per l’Università e la Ricerca Scientifica e Tecnologica). The technical assistance of Mr P. Favero is acknowledged.