Nephrol Dial Transplant (2007) 22: 3166–3173
doi:10.1093/ndt/gfm411
Advance Access publication 3 August 2007
Original Article
GFR determination in adults with a single-sample iohexol plasma
clearance method based on the mean sojourn time
Margareta Gref and Kjell Karp
Department of Clinical Physiology, Institution of Surgical and Perioperative Sciences, Umeå University, Umeå, Sweden
Abstract
Background. Glomerular filtration rate is a key
parameter in kidney disease. The Radionuclides in
Nephrourology Committee has recommended a singlesample method with 99mTc-DTPA based on the mean
sojourn time. This study was done to develop the
method for use with iohexol making the method more
available.
Methods. The single-sample formula was derived for
group I (n ¼ 48, Cl ¼ 8–188 ml/min) and applied on
group II (n ¼ 47) and on group III (n ¼ 123). In groups
I and II, reference clearance was determined according
to Sapirstein and in group III according to BrøchnerMortensen.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Results. The formula ClS ¼ ðb þ b2 4acÞ=ð2aÞ
(a ¼ (6.49 106 t þ 8.85 104)t, b ¼ 1.143 t
and c ¼ ln[(C(t))(ECV/Q0)](ECV ) was derived for
patients with estimated Cl > 30 ml/min with the best
result if the single sample was obtained between 4 and
5 h. Extracellular volume was estimated as ECV ¼
9985 BSA 3431.
The formula ClS(24 h) ¼ ln[(C(t))(ECV/Q0)](ECV)/(t)
was developed for patients with estimated
Cl <30 ml/min with a single sample at 24 h. With this
combined approach SDdiff was 2.7 ml/min in group II
and 3.1 ml/min in group III.
Conclusions. An accurate determination of iohexol
clearance can be obtained from a single plasma sample
applying the mean sojourn time approach. A separate
formula must be used for patients with low clearance
values. Body surface area (BSA), injected amount of
iohexol (Q0), time when the single sample is drawn (t)
and the concentration of iohexol [C(t)] in the sample
are needed for the calculations.
Keywords: glomerular filtration rate; iohexol
clearance; renal function; single sample; 24 h sample
Correspondence and offprint requests to: Margareta Gref,
Department of Clinical Physiology, Norrland University Hospital,
S-901 85 Umeå, Sweden. Email: [email protected]
Introduction
Glomerular filtration rate (GFR) is a valuable parameter in many clinical conditions. Iohexol, 51Cr-EDTA
and 99mTc-DTPA are commonly used tracer substances for the estimation of GFR. Several methods
for calculating GFR from a single plasma sample
following a single injection of tracer substance are
available and have been compared in independent
studies [1–8]. The mean sojourn time-based method
applied by Christensen and Groth [8] for plasma
clearance of 99mTc-DTPA has been recommended by
the Radionuclides in Nephrourology Committee on
Renal Clearance [9] for use in adults when GFR is
estimated to be 30 ml/min. Direct application of the
formula for 99mTc-DTPA was found to overestimate
clearance with 51Cr-EDTA and a modified formula for
51
Cr-EDTA was developed in a study by Mårtensson
et al. [10]. Neither the formula for 99mTc-DTPA
clearance nor the one for 51Cr-EDTA is recommended
for use in patients with severe renal failure.
The purpose of this study was to derive a singlesample formula for the calculation of iohexol plasma
clearance in adults, based on the mean sojourn time
method, including also patients with severely reduced
renal function.
Subjects and methods
Patients
Groups I and II. Ninety-six adult patients were included,
all participating in a GFR study at the Department of
Clinical Physiology, University Hospital of Northern
Sweden, Umeå, Sweden. Prior approval of the study was
obtained from the local Ethical Committee. Patients with
pronounced oedema and patients allergic to iodine were
excluded. One patient was later excluded due to the finding
of residuals of iohexol in the blank sample. Efforts were
made to include patients with normal as well as moderately
to severely reduced renal function. The patients were
randomly divided into two groups of equal size. Data
obtained from group I were used to derive a single-sample
ß The Author [2007]. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.
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Single-sample iohexol plasma clearance in adults
3167
Table 1. Group I (16 women and 32 men), iohexol clearance, age and BSA
Total
Clearance (ClSM) (ml/min)
Range
Mean
<30
18
30–55
45
55–80
66
>80
109
8–188
66
Age (year)
Range
Mean
31–79
55
42–82
55
38–74
51
22–67
43
22–82
50
Body surface area (m2)
Range
Mean
1.42–2.14
1.84
12
1.54–2.25
1.87
6
1.59–2.22
1.93
14
1.38–2.39
1.95
16
1.38–2.39
1.90
48
No. of patients
Table 2. Group II (18 women and 29 men), iohexol clearance, age and BSA
Total
Clearance (ClSM) (ml/min)
Range
Mean
<30
20
30–55
46
55–80
68
>80
106
16–163
62
Age (year)
Range
Mean
37–83
61
32–73
53
37–72
54
26–74
50
26–83
54
Body surface area (m2)
Range
Mean
1.60–1.96
1.80
1.22–2.54
1.97
1.56–2.19
1.90
1.62–2.30
1.93
1.22–2.54
1.91
9
15
10
13
47
No. of patients
Table 3. Group III (62 women and 61 men), iohexol clearance, age and BSA
Total
Clearance (ClBM) (ml/min)
Range
Mean
<30
19
30–55
44
55–80
70
>80
102
8–158
62
Age (year)
Range
Mean
46–84
68
34–83
59
31–76
56
18–70
51
18–84
58
Body surface area (m2)
Range
Mean
1.40–2.37
1.78
1.40–2.32
1.84
1.56–2.50
1.91
1.56–3.03
2.00
1.40–3.03
1.89
31
23
33
36
123
No. of patients
formula for iohexol clearance by the approach previously
described for 99mTc-DTPA [8] and 51Cr-EDTA [10].
The resulting formula was then tested on group II. Sex,
age and BSA distribution for groups I and II are shown in
Tables 1 and 2.
Group III. Group III was included to be able to apply the
single-sample method on a larger clinical material examined
according to standard procedure at our hospital.
These patients (n ¼ 123) were referred for iohexol clearance by the Brøchner-Mortensen’s final slope method [11].
Some patients underwent repeated clearance measurements
during the time period November 2000–May 2005. In the
case of repeated measurements only the last one was
included. Sex, age and BSA for group III patients are
shown in Table 3.
Procedure
Group I and II. An intravenous catheter with separate
ports for tracer substance injection and blood sampling was
inserted. A blood sample for S-creatinine and blank
measurements was obtained. Iohexol of 5 ml (Omnipaque
300 mg I/ml, Amersham Health) was given as a single
injection. The catheter was flushed with 20 ml of 0.9%
saline. Blood samples were obtained at 5, 10, 15, 30, 45, 60,
90, 120, 150,180, 210, 240, 270 and 300 min after the iohexol
injection. In group II, no blood samples were obtained
between 60 and 150 min. An additional sample was obtained
after 24 h from patients having an estimated creatinine
clearance <50 ml/min calculated from the S-creatinine
value according to Siersbaek-Nielsen et al. [12]. The sampling
times were registered and the amount of iohexol injected
was determined by weighing the syringe before and
after injection.
Group III. In 87 patients, 10 ml of iohexol was injected and
three blood samples were obtained at 180, 225 and 270 min
and in 36 patients, 5 ml of iohexol was injected and four to
five samples were obtained between 180 and 300 min after the
injection. In patients with an S-creatinine >200 mmol/l, an
additional sample was obtained after 24 h according to the
standard procedure at our hospital.
3168
M. Gref and K. Karp
Table 4. Difference ClSM ClS (group II), if Cl <30 and >30 ml/min with single sample taken at different times
Mean
SD
Cl530; n ¼ 9
Mean
SD
Cl430; n ¼ 38
180 min
210 min
240 min
270 min
300 min
24 h (11)
24 h (7)
4.3
7.8
4.5
6.4
4.1
5.7
3.4
5.2
3.3
4.8
0.04
1.2
0.48
1.2
0.4
3.3
1.1
2.9
1.0
2.9
0.9
2.5
0.05
4.1
Iohexol concentrations in plasma samples were measured
by high performance liquid chromatography (HPLC)
according to the method of Krutzén et al. [13]. In brief,
plasma samples were deproteinized by adding 100 ml
plasma to 400 ml 0.33 M perchloric acid. After centrifugation
20 ml of the supernatant were used for the HPLC analysis.
The separation was carried out on a reversed phase
column, Nucleosil 5 C18, 200 4.6 mm (Macherey–Nagel,
Germany). Iohexol was detected at 253 nm by an UV
absorbance detector (Pye Unicam, England). The mobile
phase was a mixture of water/acetonitrile (97 : 3 by volume,
adjusted to pH 2.5 with phosphoric acid). Plasma blank
samples were always analysed. In case of interfering
compounds eluting close to iohexol, the acetonitrile concentration in the mobile phase was lowered to achieve good
separation.
Results
Single-sample formulas derived from group I
Two single-sample formulas were derived. For derivation of formulas see Appendix 1. One general formula
[equation (11) in Appendix 1]
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b þ b2 4ac
ClS ¼
2a
a ¼ ð6:49 106 t þ 8:85 104 Þ t
b ¼ 1:143 t
Calculations
In groups I and II, reference clearance ClSM was calculated
according to a two-compartment kinetic model described
by Sapirstein et al. [14]. The plasma concentration of iohexol
as a function of time is in this model described as the sum
of two exponential functions. Three samples giving the best
fit between 10 and 45 min were used to calculate one
exponential function describing the early fast elimination
from plasma and the other exponential function was fitted
to samples obtained between 3 and 24 h. In patients with a
ClSM <30 ml/min, ClSM was calculated with a 24 h sample,
whereas in patients with ClSM >30 ml/min, ClSM was
calculated from samples obtained between 10 min and 5 h
after injection of iohexol.
In group III, a one-compartment model was used to
calculate reference clearance ClBM. All blood samples
obtained were used to calculate an exponential function
describing the iohexol elimination from plasma. The correction formula by Brøchner-Mortensen for non-immediate
mixing was used [11]. See Appendix 1 for calculation of ClSM
and ClBM.
Distribution of ClSM for group I and II patients is shown
in Tables 1 and 2. Distribution of ClBM for group III patients
is shown in Table 3.
Statistical methods
Linear and multiple regression analysis were used when
appropriate. Agreement between methods was also illustrated with Bland and Altman plots [15]. Means and SDs
were calculated.
ECV
c ¼ ln CðtÞ
ECV
Q0
and one low clearance formula [equation (7) in
Appendix 1] for patients with estimated Cl <30 ml/
min with the single sample obtained at 24 h after the
iohexol injection.
h
i
ln CðtÞ ECV
Q0 ECV
ClSð24 hÞ ¼
t
C(t) is the concentration of iohexol in the plasma
sample t minutes after iohexol injection, Q0 is the
injected amount of iohexol and ECV is the extracellular volume in millilitres estimated from the body
surface area (BSA) as
ECV ¼ 9985 BSA 3431
BSA in square metres, is calculated according to
Haycock et al. [16]. (See Appendix 1 for BSA formula).
Applying the ClS formulas to group II
The single-sample formulas were applied to group II
with ClSM as the reference. ClS was calculated for all
samples obtained between 3 and 24 h after iohexol
injection. Mean value and SD for the differences
ClSM ClS are given in Table 4. A Bland and Altman
plot is shown in Figure 1 with ClS calculated for
t ¼ 180 min, 240 min, 300 min and 24 h using the
general formula.
Single-sample iohexol plasma clearance in adults
3169
Fig. 1. Differences ClSMClS (group II). ClS (general formula) is calculated for t ¼ 180, 240, 300 min and 24 h. Open circles are used if ClSM
<30 ml/min.
For low clearances, Cl <30 ml/min, an accurate
result is only obtained with the 24 h sample. Both
formulas yield good results as seen in Table 4. In the
interval 3060 ml/min, the difference ClSM ClS has a
somewhat greater scatter when calculated from earlier
samples compared with later samples.
A comparison of ClS and ClSM with a single sample
obtained at 270 min if Cl >30 ml/min using the general
formula and at 24 h if Cl <30 ml/min using the formula
for low clearance is shown in Figure 2. This combination with a single sample at 270 min for a clearance
>30 ml/min and at 24 h for a clearance <30 ml/min
gave an SD of 2.7 ml/min and a mean of 0.9 ml/min for
the differences ClSMClS.
Single-sample formula applied to group III
Figure 3A illustrates ClS compared with ClBM with a
single sample at 270 min if S-creatinine <200 mmol/l
and at t ¼ 24 h if S-creatinine >200 mmol/l.
(ClS calculated with the formula for low clearance for
t ¼ 24 h). The SD of the differences ClBMClS was
3.1 ml/min and the mean was 0.3 ml/min.
Figure 3B illustrates low ClS calculated for t ¼ 24 h
compared with ClBM. ClS is calculated using both the
general and the low clearance formula. ClS calculated
using the general formula overestimated the two
highest clearance-values, while the formula for low
clearance produced accurate results.
Fig. 2. Differences ClSMClS (group II) with a single sample
obtained at 270 min (filled circle) if Cl >30 ml/min (general clearance
formula) and at 24 h (open circle) if Cl <30 ml/min (low clearance
formula).
Discussion
This study shows that it is possible to obtain an
accurate determination of iohexol clearance from a
single plasma sample in adults with normal as well as
severely reduced renal function by the mean sojourn
time-based approach.
3170
M. Gref and K. Karp
Fig. 3. (A) Differences ClBMClS (group III) with a single sample obtained at 270 min (filled circle) if S-creatinine <200 mmol/l (general
clearance formula) and at 24 h (open circle) if S-creatinine >200 mmol/l (low clearance formula). (B) Comparison between ClS and ClBM
(group III, low clearance values) with the single sample obtained at 24 h and ClS calculated both from the general clearance formula (filled
circle) and from the low clearance formula (open circle). The line of identity is displayed.
The basis for the methodology used [17], is
transformation of the assumed bi-exponential plasma
time–concentration curve, C(t), into an imaginary
mono-exponential curve with an identical mean
sojourn time, t, and an initial plasma concentration
C(0) ¼ Q0/ECV. The areas under the curves (0 t < 1)
are identical, and if a single plasma sample is drawn at
a time when the curves intersect, the imaginary curve
can be determined and ClS calculated, provided ECV is
known or is possible to estimate. The time of
intersection of the curves occurs earlier when clearance
is higher and later when clearance is low. This time is
not known in advance, but Christensen and Groth [8]
showed that a function, g(t), could correct for this in
patients with Cl > 30 ml/min if the single sample was
obtained at 180 t 300 min.
Irwin et al. [18] tested the formula on low GFR and
concluded that it should not be used in patients with
poor renal function. Our study included patients with
low GFR. When calculating clearance from the plasma
time–concentration curve, extrapolation to infinity is
necessary and blood sampling must not end until the
final slope of the curve is reached. The time needed to
reach the final slope depends on the GFR. When GFR
is assumed to be normal to moderately decreased, the
sampling may end 4–5 h after tracer injection. If GFR
is predicted to be below 20 ml/min, the sampling time
has to be prolonged up to 24–48 h [19,20], otherwise
plasma clearance overestimates renal clearance. When
deriving the single-sample formula in this study, a 24 h
sample was included in patients with clearance <30 ml/
min. The reference clearance, ClSM, was calculated
according to the two compartment model of Sapirstein
with the late exponential function determined from
samples obtained 3–24 h after tracer injection.
A close correlation between ClBM and ClSM was
shown in a previous study [10]. ClS was compared with
ClBM in group III, that included patients referred for
routine clinical GFR determination. ClBM should be
used with care for high clearance, since BrøchnerMortensen’s correction for the early, fast elimination
was done on a material with clearance under 140 ml/
min [11]. In group III, there is only one value over
140 ml/min.
When deriving the single-sample formula for 99mTcDTPA clearance, Christensen and Groth [8] used an
iterative method. Watson [21] showed that this is not
necessary. Rewriting the single-sample formula of
Christensen and Groth, Watson arrived at a quadratic
equation from which Cl could easily be calculated. This
approach was used also in the present study (see
Appendix 1). The accuracy of this single-sample
method for iohexol clearance depends on the estimated
ECV (defined as the distribution volume of iohexol),
the derived correction function g(t)corr and the time t,
when the single sample is collected.
The correlation between the distribution volume of
iohexol and BSA (r ¼ 0.74) was higher than that
reported for 99mTc-DTPA (r ¼ 0.35) by Christensen
and Groth [8] and on the same level as for 51Cr-EDTA
(r ¼ 0.81) by Mårtensson et al. [10]. The estimated
distribution volume of iohexol is larger than the
estimated distribution volume of EDTA calculated
according to Mårtensson et al. [10]. Compared with the
distribution volume of DTPA, estimated according to
Christensen and Groth [8], the distribution volume of
iohexol is larger for individuals with a BSA above
1.83 m2. This implies that a separate formula for the
estimation of ECV should be derived for each test
substance.
One could suspect the regression of ECV on BSA to
differ between males and females. This was tested
merging group I and II patients (n ¼ 95, 61 males and
34 females). The test for a difference in slope
and intercept of the two regression lines for males
and females resulted in a P-level of 0.4 and 0.3,
respectively. The presence of a gender difference was
not verified in the present population. Substituting
Single-sample iohexol plasma clearance in adults
estimated lean body mass based on height and weight
with different formulas for males and females [22]
for BSA did not improve the regression (r ¼ 0.796
compared with r ¼ 0.811 for BSA, n ¼ 95).
Applying the derived general single-sample formula
for iohexol clearance on group II patients yields
accurate results for clearance values > 30 ml/min if
the single sample is collected between 4 and 5 h after
iohexol injection. This implies that the derived correction function g(t)corr corrects for the plasma sample not
being drawn at an optimal time.
When clearance is low, the optimal time for
obtaining the single sample occurs late and g(t)corr
fails to correct adequately, if the sample is collected as
early as 4–5 h after iohexol injection. A 24 h sample
yields accurate results in patients with a clearance
under 30 ml/min. The formula was derived from group
I, only including patients with clearance 8–25 ml/min
where a 24 h sample had been obtained. A formula
should be used with caution outside the range for
which it was developed. This was illustrated for one
patient in group III with a reference clearance outside
the interval from which the formula had been derived
(Cl ¼ 35 ml/min), resulting in an overestimation of ClS
calculated from a 24 h sample.
For t ¼ 24 h, all calculated values of g are close to 1
with a difference <1.5% (Figure A2, Appendix 1).
Using g(t)corr ¼ 1 in these cases allows the use of a
simple formula for calculating low clearances if the
single sample is obtained 24 h after iohexol injection.
To avoid overestimating clearance calculated from a
24 h sample the low clearance formula is recommended
in preference to the general formula. That an overestimation is likely to occur using the general formula
and a 24 h sample for clearance over 25 ml/min can be
seen calculating g(t)corr from equation 8 in Appendix 1.
g(t)corr gives values that are increasingly divergent
below the expected value of 1 resulting in an overestimated ClS in equation 5, Appendix 1. That g(t)corr
approaches 1 using late sampling in patients with a low
clearance has previously been theoretically discussed
by Groth [17].
The decision to obtain a 24 h sample in group III
was based on the S-creatinine value. With a limit of
200 mmol/l, one patient was found with Cl <20 ml/min
and a missing 24 h sample and another patient with Cl
>30 ml/min and a 24 h sample obtained. A decision
made on an estimated creatinine clearance, where
age, weight and sex are taken into account might be
better [23].
Conclusion and recommendations
In adults, an accurate determination of iohexol
clearance can be obtained from a single plasma
sample based on the mean sojourn time. This is
possible not only in patients with normal to moderately reduced renal function as previously described for
99m
Tc-DTPA and 51Cr-EDTA but also in patients with
severely reduced renal function. It is recommended
3171
that the single plasma sample is taken between 4 and
5 h after iohexol injection in patients with an estimated
clearance >30 ml/min and clearance calculated from
the derived general formula. In patients with lower
clearance rates, the single sample should be obtained
around 24 h after injection and the clearance calculated
using the formula derived for low clearance values.
Acknowledgements. The authors are grateful for laboratory and
technical support from the staff at the Department of Clinical
Physiology and for support from the Norrland University Hospital.
Conflict of interest statement. None declared.
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Received for publication: 28.6.06
Accepted in revised form: 31.5.07
Appendix 1
Calculation of clearance, ClSM, according to a
two-compartment model by Sapirstein et al. [14]
ClSM ¼
Q0
R1
0
CðtÞdt
¼
Q0
R1
ðc1 eb1 t þ c2 eb2 t Þdt
Q0
c2
b1 þ b2
¼ c1
0
where
Q0 ¼ amount
of
injected
marker,
C(t) ¼ concentration of marker at time t, b1 and
b2 ¼ disappearance rates of marker and c1 and
c2 ¼ corresponding intercepts, when the plasma time–
concentration curve is described as the sum of two
exponential functions.
Calculation of clearance, ClBM, according to a
one-compartment model with correction for nonimmediate mixing by Brøchner-Mortensen [11]
Cl1 ¼
BSA was calculated according to Haycock et al. [16].
BSA ¼ 0:024265 W 0:5378 H 0:3964
where W ¼ body weight in kilograms and H ¼ height in
centimetres. BSA is received in square metres.
Mean sojourn time, t, for iohexol in its distribution
space, was determined (10) as
t ¼ ECVSM =ClSM
ð2Þ
g ¼ sðtÞ=ð1=tÞ
ð3Þ
The fractions
were calculated for t ¼ 180, 210, 240, 270, 300 min and
24 h with
h
i
SM
ln CðtÞ ECV
Q0
ð4Þ
sðtÞ ¼
t
where C(t) is the concentration of iohexol in the
plasma sample t minutes after iohexol injection and Q0
is the injected amount of iohexol.
Finally, single-sample clearance, ClS, by the mean
sojourn time approach, was calculated as:
h
i
ln CðtÞ ECV
Q0 ECV
ð5Þ
ClS ¼
t gðtÞcorr
ECV was estimated by relating ECVSM to BSA,
(Figure A1). The correlation was significant (r ¼ 0.74,
P < 0.001) and the received regression line with ECV in
millilitres was
ECV ¼ 9985 BSA 3431
ð6Þ
The result of calculating g ¼ sðtÞ=ð1=tÞ from the
iohexol concentrations of plasma samples obtained
at times between 3 and 24 h is shown in Figure A2.
A late plasma sample (24 h) was only obtained
for low clearance values. At this time the calculated
g-value is close to 1 (0.99–1.01). As a result
for low clearances, ClS can be calculated from
Q0
c1
b1
ClBM ¼ 0:990778 Cl1 0:001218 Cl21 where
Q0 ¼ amount of injected marker, b1 ¼ disappearance
rate of marker and c1 ¼ intercept.
Deriving a single-sample formula by the mean
sojourn time approach
Parameters needed to derive the single-sample formula
were calculated as follows:
ECV, defined as the distribution volume of iohexol,
was determined according to Sapirstein et al. [14],
ECVSM, from the same plasma samples used to
calculate ClSM.
ð1Þ
Fig. A1. Correlation between ECVSM and BSA.
Single-sample iohexol plasma clearance in adults
3173
Table A1. Regression analysis of g ¼ sðtÞ=ð1=t Þ on ClSM for different
values of time
Intercept
Slope 104
r
P
g180
g210
g240
g270
g300
g24h
1.09
þ4.0
0.25
0.09
1.16
6.0
0.41
<0.005
1.16
9.0
0.63
<0.001
1.14
9.4
0.70
<0.001
1.15
12.4
0.69
<0.001
1.02
6.8
0.60
<0.05
When g(t)corr is inserted the equation becomes
quadratic in ClS:
a Cl2S þ b ClS þ c ¼ 0
with the solution
Fig. A2. Values of g ¼ sðtÞ=ð1=t Þ calculated for different sampling
times.
equation (5) with g(t)corr ¼ 1, for t ¼ 24 h generating the
formula
h
i
ln CðtÞ ECV
Q0 ECV
ð7Þ
ClSð24 hÞ ¼
t
(t in minutes)
For samples collected between 180–300 min, high gvalues were found in patients with low clearance. This
indicates that ClSM and g are not independent
variables. A regression analysis of g on ClSM was
performed. A correlation with P < 0.001 was found for
t ¼ 240, 270 and 300 min (Table A1). To use the
relationship between g, t and Cl, multiple regression
analysis was performed. Different combinations of t,
Cl, t Cl and t2 as independent variables were tested.
The best result was obtained with Cl and t Cl as
independent variables giving the following g(t)corrfunction:
gðtÞcorr ¼ ð6:49 106 t þ 8:85 104 ÞCl þ 1:143
ð8Þ
Equation (5) can be rewritten according to Watson
(21) as
ECV
Cls t g ðtÞcorr þ ln CðtÞ
ECV ¼ 0 ð9Þ
Q0
ClS ¼
b þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b2 4ac
2a
ð10Þ
ð11Þ
a ¼ ð6:49 106 t þ 8:85 104 Þ t
b ¼ 1:143 t
ECV
c ¼ ln CðtÞ
ECV
Q0
The values a and b are constants for a given time t,
while c is calculated from the measured concentration
of iohexol in the plasma sample at time t, C(t), the
injected amount of iohexol, Q0, and the predicted ECV
from equation (6).
Only the positive value of the square root has to
be calculated. This is obvious since the term –b/2a
in equation (11) is positive and greater than 500 in the
time interval 180–300 min. With the negative value of
the square root calculated, clearance is even higher.
The 24 h sample is only obtained in patients with
severely compromised kidney function with expected
clearance values well below 40 ml/min. For t ¼ 24 h the
negative value of the square root gives a clearance
equal to or greater than 70 ml/min. Therefore, the only
solution of the quadratic ClS equation to be considered
is equation (11).