Clinical Science (1991)80, 167-176
167
Reassessment of the single intravenous injection method with inulin for measurement of the glomerular filtration rate in man L. F. PRESCOTT, S. FREESTONE
AND
J. A. N. McAUSLANE*
University Department of Clinical Pharmacology, The Royal Infirmary, Edinburgh, U.K.
(Received 8 May/20 August 1990; accepted 14 September 1990)
SUMMARY 1. Factors influencing the total body and renal clearances of inulin were investigated in a total of 37 healthy adult volunteers and 10 patients with stable chronic renal failure after the single intravenous injection of a dose of 70 mg/kg given over 5 min. 2. The elimination of inulin was highly concentrationdependent, and in healthy volunteers the renal clearance fell from 103.7 k 14.4 ml min-' 1.73 m-2 during the first hour after administration to 49.1 k 20.9 ml min-' 1.73 m-2 over the period 6-8 h. In the patients with renal failure the renal clearance fell correspondingly from 39.7 k 16.5 to 26.6 k 8.6 ml min-' 1.73 m-'. There were no changes in the simultaneously measured clearances of creatinine. 3. The values obtained for the total body clearance of inulin after a single injection depend critically on dose, the number and timing of blood samples, the choice of pharmacokinetic model, the number of data points chosen for estimation of the slope of the terminal elimination phase for analysis by the methods of residuals, and the weighting used for curve fitting by non-linear regression analysis. 4. With standardized conditions of sampling from 0 to 2 h and weighted non-linear regression analysis of the plasma concentration-time data, the total body and renal clearances of inulin were almost identical in subjects with normal renal function at 105.2 k 10.2 and 102.9f 13.0 ml min-' 1.73 m-2. In the patients with chronic renal failure sampling was continued for 3 h and the corresponding clearances were 40.4 k 15.3 and 38.9k 15.7 ml min-I 1.73 m-*. *Present address: Centre for Medicines Research, Woodmansterne Road, Carshalton, Surrey SM5 4DS,U.K. Correspondence: Professor L. F. Prescott, University Department of Clinical Pharmacology, The Royal Infirmary, Edinburgh EH3 9YW, U.K.
5. The 0-2 h total body and renal clearances of inulin were measured by the single injection method and the renal clearance was measured by the standard constant infusion method on different occasions in 10 healthy volunteers. The respective clearances were similar at 101.4f6.6, 94.9k11.9 and 88.4k12.1 ml min-l 1.73 m-*. 6. The reproducibility of the single injection and constant infusion methods was compared by measuring the inulin clearance with both techniques on three occasions in separate groups of eight and nine healthy volunteers. The mean coefficient of variation for the total body clearance with the single injection method was only 3.9% compared with 9.5% for the renal clearance determined the same way and 12.0% for the renal clearance during constant infusion. 7. Urine collection and fluid loading are not required for the single injection technique, and it is more reproducible and less demanding than the constant infusion method. With simple precautions, the single injection method with inulin is suitable for routine estimation of the glomerular filtration rate.
Key words: constant infusion, errors of analysis, glomerular filtration rate, inulin, renal clearance, reproducibility, total body clearance. Abbreviation: AUC, total area under the plasma concentration-time curve.
INTRODUCTION The renal clearance of inulin at steady state during a constant intravenous infusion has been established as the definitive measure of the glomerular filtration rate for more than half a century [ 11.Unfortunately, this technique is too inconvenient and time consuming for routine clinical use, and the need for water loading and bladder
168
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catheterization to obtain accurate short timed urine collections is a further disadvantage [2]. An alternative approach is to calculate the total body clearance of a suitable test compound from serial measurements of its plasma concentrations after a single rapid intravenous injection. Urine collections are not necessary but if excretion data are available the renal clearance can be determined as well. If the compound is removed from the body solely by renal excretion and is filtered freely at the glomerulus without tubular secretion or reabsorption, its total body clearance and renal clearance will be the same and equal to the glomerular filtration rate. In recent years this pharmacokinetic approach has been developed for estimation of the glomerular filtration rate from the time-decay curves of radioactivity in plasma after the single intravenous injection of radiolabelled tracers [3-61. These techniques are easier on the patient and investigator, but the use of radioactive materials is undesirable, especially in children. Inulin remains the reference standard for measurement of glomerular filtration rate and although attempts have been made over the years to measure its clearance after a single intravenous injection [7-211, the technique has not been properly validated in adults and it has not been adopted for clinical use. With many of the single injection techniques there have been problems with the methods of pharmacokinetic analysis, and it has not been generally appreciated that the values obtained for clearance may depend critically on dose, the timing and duration of sampling, the choice of pharmacokinetic model and the weighting of data for non-linear regression analysis and curve fitting. There are further complications with inulin because its renal excretion is concentration-dependent and its elimination kinetics are non-linear [9-12, 221. Little attention has been given to these problems. In this report we reassess the single intravenous injection technique for inulin and draw attention to some important factors which can have a significant effect on the values obtained for its clearance. We also compare the single injection and standard constant infusion methods for measurement of the inulin clearance and glomerular filtration rate.
METHODS
Subjects Normal male and female volunteers were recruited by advertisement and were healthy as judged by physical examination and normal values on routine haematological and biochemical screening. None took drugs (other than oral contraceptives in the case of females) or drank excessive amounts of alcohol regularly. Single injection studies. Single injection studies were carried out in a total of 27 healthy male and 10 healthy female volunteers with a mean age and body weight of 26.8 f 6.1 years and 69.2 f9.5 kg, respectively. Single injection studies were also performed in eight male and two female non-oedematous patients with stable chronic
renal failure due to hypertension (five),glomerulonephritis (two), renal artery stenosis (one), polycystic kidneys (one)and chronic pyelonephritis (one).Their mean ( k SD) age and body weight were 60.5 f7.0 years and 75.3 _+ 7.8 kg, respectively, and their mean ( fSD) creatinine clearance was 44.9f 14.9 (range 26-74) ml min-' 1.73 m- 2. Comparison of single injection and constant infusion methods. The total body and renal clearances of inulin were measured by the single intravenous injection method and the renal clearance was measured by the constant infusion method on separate occasions in 10 healthy male volunteers with a mean ( fSD) age of 26.1 f 8.2 years and a body weight of 73.4 f6.0 kg. The methods were used in random order using inulin obtained from the same source (Kerfoot, Bardsley), and the interval between studies did not exceed 14 days. Reproducibility of the single injection and constant infusion methods. Reproducibility was assessed by measuring the clearances of inulin by both methods on three separate occasions in two different groups of healthy male volunteers. The total body and renal clearances of inulin were determined three times after single intravenous injection in eight volunteers with a mean ( ~ S D age ) of 27.4f 2.7 years and a body weight of 70.0 f 8.6 kg. The interval between the studies did not exceed 22 days. The constant infusion studies were repeated on three occasions in nine volunteers with a mean age of 30.0 f4.9 years and body weight of 68.8f6.7 kg. The maximum interval between studies was 28 days, except in one case where the second study was delayed for 5 months. Informed consent was obtained in all cases and the studies were approved by the local Ethics of Medical Research Committee.
Measurement of inulin clearance The fasting subjects reported to the unit at approximately 08.30 hours. The healthy male volunteers and the patients with renal disease drank 500 ml of water 1 h before the clearance studies began at 09.00 hours after which they took 100-130 ml every half hour for the duration of the study. The subjects remained supine for at least 4 h after dosing and they were then allowed a light lunch without drinks containing caffeine. For measurement of the total body and renal clearances by the single intravenous injection technique, inulin (70 mg/kg) was infused at a constant rate over 5 min by a pump and the infusion line was then flushed through with saline solution (150 mmol/l NaCI). In most experiments, polyfructosan (Inutest; Laevosan Gesellschaft, Linz, Austria) was used. Venous blood was sampled from the opposite arm at 0, 3,5, 10, 15,20, 30,40, 50,60,75,90, 120, 180, 240, 360 and 480 min after the start of the injection, and urine was collected from 0 to 1, 1 to 2 , 2 to 3, 3 to 4,4 to 6,6 to 8 and 8 to 24 h. In the normal female volunteers, water loading was not carried out and blood and urine were sampled for 2 and 8 h, respectively.
Single injection inulin clearance For determination of the renal clearance of inulin by the traditional constant infusion method, an intravenous loading dose of 2.3 g was followed by a constant infusion of 18.1 mg/min for 3 h. After equilibration for 1 h, four timed 30 min urine samples were obtained and venous blood was sampled at the beginning and end of each urine collection period [23]. For this study the maintenance fluid intake was 200 ml every 30 min. In all studies the renal clearance of creatinine was determined at the same time as the inulin clearance using the same samples.
169
(a)
-
150
N
4
E rc)
?
-
3
100
I
.l
3 58
50
B
Analytical methods Plasma and urine were either stored at 4°C and assayed for creatinine and inulin within 72 h, or stored at - 20°C. Inulin was estimated according to Heyrovsky using an automated method [24] and creatinine was determined by a standard autoanalyser technique (Gemstar ElectroNucleonics, Fairfield, NJ, U.S.A.).
0
0-1
1-2
2-3
3-4
4-6
6-8
Time after administration of inulin (h)
(4
Pharmacokinetic and statistical analysis For estimation of the total body clearance of inulin after a single intravenous injection, the individual plasma concentration-time data for different sampling schedules were fitted to a two-compartment pharmacokinetic model with zero-order administration of the dose over 5 min using the 'SIPHAR' curve fitting and modelling program (Centres &Etudes et de Recherches en Statistiques et Informatique MCdicales, Creteil Cedex, France). The method was based on two simultaneous exponential processes with constant rate input as defined by the following equation:
where Y is the plasma concentration of inulin at time t, T is the duration of the infusion and A , a, B and B are the coefficients and exponents of the fast distribution and slower elimination phases, respectively. The parameters of the model were first obtained using the simple method of residuals ('peeling' or 'feathering'). A number of points on the supposedly log-linear terminal slope of the plasma concentration-time curve were chosen to define the elimination phase and its intercept on the y-axis by the method of least squares. The values on the early part of this line extrapolated to the y-axis were subtracted from the corresponding observed concentrations to yield a series of residuals which represented the distribution phase [25].The coefficients and exponents of these two processes were subsequently refined by iterative non-linear regression analysis using the minimization algorithm described by Powell [26] with different weighting factors. The calculations were repeated for comparisons of different sampling schedules and conditions for analysis.The total body clearance of inulin was determined as the administered dose divided by the total area under the plasma concentration-time curve (AUC)
0-1
1-2
2:3
3-4
4-6
6:8
Time after administration of inulin (h)
Fig. 1. Progressive fall in the renal clearance of inulin (m) without a change in the creatinine clearance ( 8 ) after a single intravenous injection in (a) 27 healthy male volunteers and ( b ) 10 patients with chronic renal failure.
according to the model estimates. The data at 3 and 5 min after the start of the inulin infusion were omitted as necessary to obtain the best fit of the curve as indicated by the lowest coefficients of variation of the parameter estimates. The renal clearance of inulin after single injection was determined as the amount excreted in the urine in a given time period divided by the corresponding AUC calculated by the trapezoidal rule [25]. The renal clearance of inulin during the constant infusions was calculated as the amount excreted in each urine collection period divided by the mean plasma concentration. The results for each period were averaged to give a mean value. The creatinine clearance was calculated as the amount excreted in the urine divided by the mean plasma concentration. All clearances were normalized to a standard body surface area of 1.73 m2 as determined by nomogram from the height and weight [271. Results are expressed as means fSD. For standardized comparisons in healthy volunteers, the total body clearance of inulin was calculated by non-linear regression weighted by the reciprocal of the square of the concentra-
L. F. F'rescott et al.
170
Table 1. Total body and renal clearances of inulin on a cumulative time basis after a single intravenous injection in 27 healthy male volunteers and 10 patients with chronic renal failure Valus are means ~ S D Statistical . significance: *P
167
Reassessment of the single intravenous injection method with inulin for measurement of the glomerular filtration rate in man L. F. PRESCOTT, S. FREESTONE
AND
J. A. N. McAUSLANE*
University Department of Clinical Pharmacology, The Royal Infirmary, Edinburgh, U.K.
(Received 8 May/20 August 1990; accepted 14 September 1990)
SUMMARY 1. Factors influencing the total body and renal clearances of inulin were investigated in a total of 37 healthy adult volunteers and 10 patients with stable chronic renal failure after the single intravenous injection of a dose of 70 mg/kg given over 5 min. 2. The elimination of inulin was highly concentrationdependent, and in healthy volunteers the renal clearance fell from 103.7 k 14.4 ml min-' 1.73 m-2 during the first hour after administration to 49.1 k 20.9 ml min-' 1.73 m-2 over the period 6-8 h. In the patients with renal failure the renal clearance fell correspondingly from 39.7 k 16.5 to 26.6 k 8.6 ml min-' 1.73 m-'. There were no changes in the simultaneously measured clearances of creatinine. 3. The values obtained for the total body clearance of inulin after a single injection depend critically on dose, the number and timing of blood samples, the choice of pharmacokinetic model, the number of data points chosen for estimation of the slope of the terminal elimination phase for analysis by the methods of residuals, and the weighting used for curve fitting by non-linear regression analysis. 4. With standardized conditions of sampling from 0 to 2 h and weighted non-linear regression analysis of the plasma concentration-time data, the total body and renal clearances of inulin were almost identical in subjects with normal renal function at 105.2 k 10.2 and 102.9f 13.0 ml min-' 1.73 m-2. In the patients with chronic renal failure sampling was continued for 3 h and the corresponding clearances were 40.4 k 15.3 and 38.9k 15.7 ml min-I 1.73 m-*. *Present address: Centre for Medicines Research, Woodmansterne Road, Carshalton, Surrey SM5 4DS,U.K. Correspondence: Professor L. F. Prescott, University Department of Clinical Pharmacology, The Royal Infirmary, Edinburgh EH3 9YW, U.K.
5. The 0-2 h total body and renal clearances of inulin were measured by the single injection method and the renal clearance was measured by the standard constant infusion method on different occasions in 10 healthy volunteers. The respective clearances were similar at 101.4f6.6, 94.9k11.9 and 88.4k12.1 ml min-l 1.73 m-*. 6. The reproducibility of the single injection and constant infusion methods was compared by measuring the inulin clearance with both techniques on three occasions in separate groups of eight and nine healthy volunteers. The mean coefficient of variation for the total body clearance with the single injection method was only 3.9% compared with 9.5% for the renal clearance determined the same way and 12.0% for the renal clearance during constant infusion. 7. Urine collection and fluid loading are not required for the single injection technique, and it is more reproducible and less demanding than the constant infusion method. With simple precautions, the single injection method with inulin is suitable for routine estimation of the glomerular filtration rate.
Key words: constant infusion, errors of analysis, glomerular filtration rate, inulin, renal clearance, reproducibility, total body clearance. Abbreviation: AUC, total area under the plasma concentration-time curve.
INTRODUCTION The renal clearance of inulin at steady state during a constant intravenous infusion has been established as the definitive measure of the glomerular filtration rate for more than half a century [ 11.Unfortunately, this technique is too inconvenient and time consuming for routine clinical use, and the need for water loading and bladder
168
L. F. Prescott et al.
catheterization to obtain accurate short timed urine collections is a further disadvantage [2]. An alternative approach is to calculate the total body clearance of a suitable test compound from serial measurements of its plasma concentrations after a single rapid intravenous injection. Urine collections are not necessary but if excretion data are available the renal clearance can be determined as well. If the compound is removed from the body solely by renal excretion and is filtered freely at the glomerulus without tubular secretion or reabsorption, its total body clearance and renal clearance will be the same and equal to the glomerular filtration rate. In recent years this pharmacokinetic approach has been developed for estimation of the glomerular filtration rate from the time-decay curves of radioactivity in plasma after the single intravenous injection of radiolabelled tracers [3-61. These techniques are easier on the patient and investigator, but the use of radioactive materials is undesirable, especially in children. Inulin remains the reference standard for measurement of glomerular filtration rate and although attempts have been made over the years to measure its clearance after a single intravenous injection [7-211, the technique has not been properly validated in adults and it has not been adopted for clinical use. With many of the single injection techniques there have been problems with the methods of pharmacokinetic analysis, and it has not been generally appreciated that the values obtained for clearance may depend critically on dose, the timing and duration of sampling, the choice of pharmacokinetic model and the weighting of data for non-linear regression analysis and curve fitting. There are further complications with inulin because its renal excretion is concentration-dependent and its elimination kinetics are non-linear [9-12, 221. Little attention has been given to these problems. In this report we reassess the single intravenous injection technique for inulin and draw attention to some important factors which can have a significant effect on the values obtained for its clearance. We also compare the single injection and standard constant infusion methods for measurement of the inulin clearance and glomerular filtration rate.
METHODS
Subjects Normal male and female volunteers were recruited by advertisement and were healthy as judged by physical examination and normal values on routine haematological and biochemical screening. None took drugs (other than oral contraceptives in the case of females) or drank excessive amounts of alcohol regularly. Single injection studies. Single injection studies were carried out in a total of 27 healthy male and 10 healthy female volunteers with a mean age and body weight of 26.8 f 6.1 years and 69.2 f9.5 kg, respectively. Single injection studies were also performed in eight male and two female non-oedematous patients with stable chronic
renal failure due to hypertension (five),glomerulonephritis (two), renal artery stenosis (one), polycystic kidneys (one)and chronic pyelonephritis (one).Their mean ( k SD) age and body weight were 60.5 f7.0 years and 75.3 _+ 7.8 kg, respectively, and their mean ( fSD) creatinine clearance was 44.9f 14.9 (range 26-74) ml min-' 1.73 m- 2. Comparison of single injection and constant infusion methods. The total body and renal clearances of inulin were measured by the single intravenous injection method and the renal clearance was measured by the constant infusion method on separate occasions in 10 healthy male volunteers with a mean ( fSD) age of 26.1 f 8.2 years and a body weight of 73.4 f6.0 kg. The methods were used in random order using inulin obtained from the same source (Kerfoot, Bardsley), and the interval between studies did not exceed 14 days. Reproducibility of the single injection and constant infusion methods. Reproducibility was assessed by measuring the clearances of inulin by both methods on three separate occasions in two different groups of healthy male volunteers. The total body and renal clearances of inulin were determined three times after single intravenous injection in eight volunteers with a mean ( ~ S D age ) of 27.4f 2.7 years and a body weight of 70.0 f 8.6 kg. The interval between the studies did not exceed 22 days. The constant infusion studies were repeated on three occasions in nine volunteers with a mean age of 30.0 f4.9 years and body weight of 68.8f6.7 kg. The maximum interval between studies was 28 days, except in one case where the second study was delayed for 5 months. Informed consent was obtained in all cases and the studies were approved by the local Ethics of Medical Research Committee.
Measurement of inulin clearance The fasting subjects reported to the unit at approximately 08.30 hours. The healthy male volunteers and the patients with renal disease drank 500 ml of water 1 h before the clearance studies began at 09.00 hours after which they took 100-130 ml every half hour for the duration of the study. The subjects remained supine for at least 4 h after dosing and they were then allowed a light lunch without drinks containing caffeine. For measurement of the total body and renal clearances by the single intravenous injection technique, inulin (70 mg/kg) was infused at a constant rate over 5 min by a pump and the infusion line was then flushed through with saline solution (150 mmol/l NaCI). In most experiments, polyfructosan (Inutest; Laevosan Gesellschaft, Linz, Austria) was used. Venous blood was sampled from the opposite arm at 0, 3,5, 10, 15,20, 30,40, 50,60,75,90, 120, 180, 240, 360 and 480 min after the start of the injection, and urine was collected from 0 to 1, 1 to 2 , 2 to 3, 3 to 4,4 to 6,6 to 8 and 8 to 24 h. In the normal female volunteers, water loading was not carried out and blood and urine were sampled for 2 and 8 h, respectively.
Single injection inulin clearance For determination of the renal clearance of inulin by the traditional constant infusion method, an intravenous loading dose of 2.3 g was followed by a constant infusion of 18.1 mg/min for 3 h. After equilibration for 1 h, four timed 30 min urine samples were obtained and venous blood was sampled at the beginning and end of each urine collection period [23]. For this study the maintenance fluid intake was 200 ml every 30 min. In all studies the renal clearance of creatinine was determined at the same time as the inulin clearance using the same samples.
169
(a)
-
150
N
4
E rc)
?
-
3
100
I
.l
3 58
50
B
Analytical methods Plasma and urine were either stored at 4°C and assayed for creatinine and inulin within 72 h, or stored at - 20°C. Inulin was estimated according to Heyrovsky using an automated method [24] and creatinine was determined by a standard autoanalyser technique (Gemstar ElectroNucleonics, Fairfield, NJ, U.S.A.).
0
0-1
1-2
2-3
3-4
4-6
6-8
Time after administration of inulin (h)
(4
Pharmacokinetic and statistical analysis For estimation of the total body clearance of inulin after a single intravenous injection, the individual plasma concentration-time data for different sampling schedules were fitted to a two-compartment pharmacokinetic model with zero-order administration of the dose over 5 min using the 'SIPHAR' curve fitting and modelling program (Centres &Etudes et de Recherches en Statistiques et Informatique MCdicales, Creteil Cedex, France). The method was based on two simultaneous exponential processes with constant rate input as defined by the following equation:
where Y is the plasma concentration of inulin at time t, T is the duration of the infusion and A , a, B and B are the coefficients and exponents of the fast distribution and slower elimination phases, respectively. The parameters of the model were first obtained using the simple method of residuals ('peeling' or 'feathering'). A number of points on the supposedly log-linear terminal slope of the plasma concentration-time curve were chosen to define the elimination phase and its intercept on the y-axis by the method of least squares. The values on the early part of this line extrapolated to the y-axis were subtracted from the corresponding observed concentrations to yield a series of residuals which represented the distribution phase [25].The coefficients and exponents of these two processes were subsequently refined by iterative non-linear regression analysis using the minimization algorithm described by Powell [26] with different weighting factors. The calculations were repeated for comparisons of different sampling schedules and conditions for analysis.The total body clearance of inulin was determined as the administered dose divided by the total area under the plasma concentration-time curve (AUC)
0-1
1-2
2:3
3-4
4-6
6:8
Time after administration of inulin (h)
Fig. 1. Progressive fall in the renal clearance of inulin (m) without a change in the creatinine clearance ( 8 ) after a single intravenous injection in (a) 27 healthy male volunteers and ( b ) 10 patients with chronic renal failure.
according to the model estimates. The data at 3 and 5 min after the start of the inulin infusion were omitted as necessary to obtain the best fit of the curve as indicated by the lowest coefficients of variation of the parameter estimates. The renal clearance of inulin after single injection was determined as the amount excreted in the urine in a given time period divided by the corresponding AUC calculated by the trapezoidal rule [25]. The renal clearance of inulin during the constant infusions was calculated as the amount excreted in each urine collection period divided by the mean plasma concentration. The results for each period were averaged to give a mean value. The creatinine clearance was calculated as the amount excreted in the urine divided by the mean plasma concentration. All clearances were normalized to a standard body surface area of 1.73 m2 as determined by nomogram from the height and weight [271. Results are expressed as means fSD. For standardized comparisons in healthy volunteers, the total body clearance of inulin was calculated by non-linear regression weighted by the reciprocal of the square of the concentra-
L. F. F'rescott et al.
170
Table 1. Total body and renal clearances of inulin on a cumulative time basis after a single intravenous injection in 27 healthy male volunteers and 10 patients with chronic renal failure Valus are means ~ S D Statistical . significance: *P
