This study aimed to
develop a nonlabeled method for the measurement of cortisol production
rate to evaluate adrenal function. The cortisol production rate
determination requires that of cortisol clearance, which is not a
parameter but a variable resulting from the saturable binding of
cortisol to corticosteroid-binding globulin (CBG). Our method is based
on evaluation of the plasma clearance of the CBG-free cortisol
fraction. This parameter was evaluated from a pharmacokinetic model of
total plasma cortisol disposition that takes into account specific
binding of the corticoid to CBG in the plasma. We have shown that the
CBG-free cortisol kinetics and CBG-binding parameters thus evaluated
are not statistically different from those obtained by the
radioisotopic method and equilibrium dialysis, suggesting that the
plasma CBG-free cortisol clearance is independent of the total plasma
cortisol concentrations and represents the actual parameter of cortisol
elimination. We validated this modeling approach by using it to
calculate the in vivo entry rate of cortisol mimicked by the perfusion
of cortisol at a known rate.
 |
INTRODUCTION |
ADRENAL FUNCTION has
been evaluated extensively by measuring the cortisol production rate in
physiological and pathological states in humans (3, 10, 12,
13) and in different species, including ewes (17,
18). However, conflicting results have been obtained, depending
on the methodological approach used (5, 24). The method
based on the evaluation of plasma cortisol clearance is hindered by the
nonlinear disposition of cortisol resulting from its specific and
saturable binding to corticosteroid-binding globulin (CBG). In many
species, including ewes, the maximal CBG-binding capacity is of the
same order of magnitude as the maximal plasma physiological cortisol
concentration (6). If it is assumed that only the cortisol
fraction unbound to CBG can be cleared from the plasma, then the
ultradian rhythmicity of cortisol secretion will result in
instantaneous and permanent variations of this metabolizable cortisol
fraction. Thus the plasma cortisol clearance evaluated by radioisotopic
methods is not a parameter but a variable, exhibiting episodic and
circadian fluctuations that will depend on the current total plasma
cortisol concentrations. In contrast, the plasma CBG-free cortisol
clearance (i.e., clearance of cortisol unbound to CBG) will be
independent of the fluctuations in cortisol concentrations and should
represent the actual parameter of cortisol elimination.
In the present paper, we propose to develop and validate a method of
measuring the plasma CBG-free cortisol clearance on the basis of an in
vivo modeling approach that takes into account the specific binding of
cortisol to CBG. This approach enables the CBG-free cortisol
disposition, CBG-binding parameters, and a cortisol production rate to
be determined from the plasma profile of CBG-free cortisol concentrations.
 |
MATERIALS AND METHODS |
General
Nine Lacaune ewes (3-9 yr old), weighing 57.6 ± 6.6 kg, were used. They were kept in a light-sealed room under an
artificial photoperiod (12:12-h light-dark cycle) in individual
metabolism cages and received daily rations of concentrate. Hay and
water were given ad libitum.
Design
Dexamethasone was administered intravenously at 0700, during
each experiment, i.e., 3 h before exogenous cortisol
administration, to suppress endogenous cortisol secretion.
Experiment 1 was designed to evaluate the plasma CBG-free
cortisol kinetics and CBG-binding parameters by modeling the
disposition of exogenous total plasma cortisol concentrations after
intravenous administration of cortisol at 3 dose levels (0.05, 0.2, and
1 mg/kg) in a crossover design involving nine ewes. The blood-sampling schedule was determined from preliminary studies performed in horses
(14) or in ewes (7) that enabled the
pharmacokinetic parameters and predictive concentrations to be
obtained. In addition, peripheral blood samples were collected during a
large period postadministration to guarantee that, for the last
samples, cortisol concentrations were under the level of quantification
of the RIA.
During each treatment, which was separated by a washout period of at
least 7 days, cortisol was administered intravenously at 1000. Peripheral blood samples were collected at 1-h intervals for 3 h
before cortisol administration; at 1, 2, 4, 8, 15, 30, 45, and 60 min;
and then at 1-h intervals until 9 h postcortisol administration.
Experiment 2 was designed to compare the plasma CBG-free
cortisol kinetics and CBG-binding parameters obtained in
experiment 1 (modeling approach) with reference values. The
reference values for plasma CBG-binding parameters were obtained using
equilibrium dialysis. A radioisotopic method was adapted to measure the
control value for plasma CBG-free cortisol clearance. The radioisotopic method was performed with six ewes from experiment 1 3 h after a dexamethasone injection. [3H]cortisol was
administered intravenously at 1000. Peripheral blood samples were
collected at 1-h intervals for 3 h before and after
[3H]cortisol administration at 1, 2, 4, 8, 15, 30, 45, and 60 min and then at 1-h intervals until 12 h postadministration.
Experiment 3 was performed with the six ewes from
experiment 2 to validate the proposed method of estimation
of cortisol production rate from the values of the plasma CBG-free
cortisol clearance and the area under the plasma CBG-free cortisol
concentration-time curve. For this, the method was applied to an
experimental situation during which the cortisol production rate was
mimicked by the intravenous perfusion of cortisol at a known rate.
During the first trial, ewes received two successive perfusions of
cortisol at the rates of 1.6 and 12 mg/h for 5 h. During a second
trial 8 mo later, the same ewes received three successive perfusions of
cortisol at the rates of 0.27, 2.7, and 18 mg/h for 4 h. The endogenous cortisol secretion was suppressed by the administration of
dexamethasone at 0700, i.e., 3 h before the beginning of the first
perfusion. Peripheral blood samples were collected at 1-h intervals for
3 h before the start of the first cortisol perfusion and at 20-min
intervals during the perfusions.
Protein binding.
Blood samples (50 ml) were obtained by venipuncture of the left jugular
vein before the experiments to measure the in vitro plasma protein
binding of cortisol. The endogenous corticoids were removed from the
plasma by adsorption on charcoal (2). In vitro protein
binding of cortisol was measured at 37°C over a wide range of
concentrations (0.005-2.762 µM) by equilibrium dialysis using a
Dianorm system (CH8135; Langenau, Zurich, Switzerland), as previously
described by Gayrard et al. (6).
Administrations and blood sampling.
All drugs were injected in the right jugular vein via an indwelling
catheter that had been inserted the day before the experiments. Dexamethasone (Cortamethasone; Vetoquinol, Lure, France) was
administered intravenously at a dosage of 0.1 mg/kg. For
experiment 1, cortisol (hydrocortisone; Sigma, l'Isle
d'Abeau Chesnes, La Verpillière, France) was dissolved in DMSO
and ethanol (50:50, vol/vol) to produce respective concentrations of
1.75 (0.05 mg/kg), 7 (0.2 mg/kg), and 35 (1 mg/kg) mg/ml. For
experiment 3, cortisol was dissolved in ethanol and saline
to produce concentrations of 0.09 mg/ml (10:90, vol/vol, 0.27 mg/h),
0.4 mg/ml (10:90, vol/vol, 1.6 mg/h), 0.9 mg/ml (10:90, vol/vol, 2.7 mg/h), and 3 mg/ml (25:75, vol/vol, 12 mg/h). To produce a 6 mg/ml
cortisol solution, cortisol was dissolved in DMSO, ethanol, and saline
(37.5:2.5:60, vol/vol/vol, 18 mg/h).
[1,2,6,7-3H]cortisol was purchased from Amersham
International (Buckinghamshire, UK) in toluene-ethanol (9:1, vol/vol).
The specific activity was 63 Ci/mmol, and the radiochemical purity was
>99%. The solution was evaporated to dryness with nitrogen gas. Five
milliliters of DMSO were added to the residue.
[1,2,6,7-3H]cortisol was administered at a dosage of 5 µCi/kg in DMSO. The precise dose administered to each ewe was
determined by weighing the syringe before and after injection and by
measuring the activity of a 10-µl weighed aliquot of the
[3H]cortisol solution.
Blood samples were obtained from the left jugular vein with an
indwelling catheter inserted the day before the experiments. Blood
samples were collected in heparinized tubes and centrifuged for 10 min
at 1,400 g. The plasma was separated and stored at
20°C
until assay.
Analytical methods.
Cortisol was assayed in duplicate using 50-µl aliquots of plasma and
the RIA method adapted from Gomez Brunet and Lopez Sebastian (8). The level of quantification of the assay was 2 ng/ml. The mean intra-assay coefficient of variation for three plasma levels
(4, 16, and 32 ng/ml) was 13%; the mean interassay coefficient of
variation for these plasmas was 14%. The cortisol specific activity
was measured by coupling HPLC and scintillation liquid counting
techniques as previously described (14).
Data Analysis
In vitro protein binding.
Protein-bound cortisol concentrations were plotted against the unbound
cortisol concentrations. The profiles indicated the presence of
saturable and nonsaturable protein binding, CBG, and albumin. The data
were fitted by use of the following relationship
|
(1)
|
where F and B are the concentrations of free and bound cortisol,
respectively. Bmax (nM) and Kd (nM)
are the CBG maximal binding capacity and the cortisol dissociation
constant, respectively, i.e., the free plasma cortisol corresponding to
half-saturation of CBG. NS is a dimensionless
proportionality constant for the nonspecific binding of cortisol to
albumin. Binding parameters (Bmax,
Kd, and NS) were evaluated by a
computerized nonlinear least squares regression program adapted from
Multi (23).
Kinetic Analysis
Experiment 1.
The following two approaches were used to analyze the total plasma
cortisol concentrations: the statistical moment approach was used to
calculate the total plasma cortisol clearance and the compartmental
analysis to estimate the plasma clearance of CBG-free cortisol and
CBG-binding parameters (Bmax,
Kd CBG-free).
The total plasma cortisol clearance (ClT,
ml · kg
1 · min
1) was
calculated using Eq. 2
|
(2)
|
where AUC (ng · min · ml
1) is the
area under the total plasma cortisol concentration-time curve
calculated from time 0 to the last measurable concentration
(tlast) by use of the arithmetic trapezoidal
rule, and dose (ng/kg) is the dose of cortisol administered.
Plasma total cortisol concentrations were also analyzed using a
compartmental approach similar to that described previously for
inhibitors of angiotensin-converting enzyme (22). A first assumption was that free and albumin-bound cortisol were not
distinguishable from a kinetic point of view. These two fractions were
therefore pooled and named CBG-free cortisol. CBG-free cortisol was
assumed to represent the driving force for processes of distribution, elimination, and binding to CBG.
The model of cortisol disposition was therefore described by the
following equations
|
(3)
|
|
(4)
|
|
(5)
|
where t is time, QCBG-free is
the amount of cortisol not bound to CBG in the central compartment,
Qperiph is the amount of cortisol in the
peripheral compartment, QCBG-bound is the amount of cortisol bound to CBG in the central compartment, A is
the maximal amount of CBG-binding sites in the central compartment, k1 is the second-order rate constant of
association of the cortisol-CBG complex, k2 is
the first-order rate constant of dissociation of the cortisol-CBG
complex, k12 is the first-order rate constant of
transfer from central to peripheral compartment,
k21 is the first-order rate constant of transfer
from peripheral to central compartment, and k10
is the first-order rate constant of elimination from the central compartment.
The second hypothesis of our model was to assume near-instantaneous
equilibrium conditions for cortisol binding to CBG, i.e., dQCBG-bound/dt = 0, which is in
agreement with data concerning the kinetics of the cortisol-CBG
interaction (4). Appendix 1 presents
step-by-step rearrangements of Eq. 3 that can be performed under this assumption. Finally, the model described by Eqs.
3-5 can be reduced to Eq. 4 and Eq. 6
|
(6)
|
where K is equal to
k2/k1 and corresponds to
the equilibrium dissociation constant (with dimension of quantity).
Equations 4 and 6 were used for in vivo data
analysis and parameter estimation. Finally, the estimated parameters
were k10, k12,
k21 (first-order rate constants expressed in
min
1), Vc (volume of the central compartment,
l/kg), A (nmol), and K (nmol).
A fifth-order Runge-Kutta method with variable step size was used to
solve the model numerically. The parameters were obtained using REVOL,
a free-derivative Monte Carlo minimizing algorithm (11).
The goodness of fit of the described model was assessed using
least-square criteria. The data points were weighted using 1/
with
i, the ith fitted
concentration. An F-test was used to select the appropriate
number of compartments (1 or 2), and a bicompartmental model was
selected (Fig. 1).

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Fig. 1.
Physiologically based bicompartmental model for cortisol
disposition. The total plasma cortisol amount actually measured by the
analytical method is the sum of 1) cortisol specifically and
reversibly bound to corticosteroid-binding globulin (CBG; termed
QCBG-bound) and 2) cortisol not bound
to CBG (termed QCBG-free).
QCBG-free represents the fraction eliminated,
according to the first-order rate constant k10,
and exchanged between the central and peripheral compartments with the
first-order rate constants k12 and
k21. k1 is the
second-order rate constant of association of the cortisol-CBG complex;
k2 is the first-order rate constant of
dissociation of the cortisol-CBG complex. On the assumption that
equilibrium conditions for cortisol binding to CBG were achieved, the
equilibrium dissociation constant [which corresponds to the ratio
k2/(k1 × Vc), where Vc is the volume of the central
compartment] and maximal binding (Bmax) were estimated.
|
|
In this in vivo cortisol disposition model, parameters for in vivo
binding to CBG were Bmax (Eq. 7) and
KdCBG-free (Eq. 8)
|
(7)
|
|
(8)
|
Considering that the concentration of cortisol not bound to CBG
is the driving force for the interaction with CBG, the concentration of
the cortisol-CBG complex at equilibrium (BCBG) is given by the following equation
|
(9)
|
where CBGfree is the cortisol concentration not
bound to CBG in the central compartment (CBGfree = QCBG-free/Vc). Remenbering that
CBGfree represents free plus albumin-bound cortisol,
CBGfree can be described by the following equation
|
(10)
|
Then, substituting from Eq. 10 into Eq. 9
and rearranging gives
|
(11)
|
When Eqs. 1 and 11 are considered, the
following relation can be established
|
(12)
|
where Kd CBG-free and
Kd refer to CBGfree and F as driving
concentrations for cortisol-CBG interaction, respectively.
The plasma clearance of CBG-free cortisol (ClCBG-free;
ml · kg
1 · min
1) was
calculated from the estimated parameters using Eq. 13
|
(13)
|
Experiment 2.
The kinetic parameters for [3H]cortisol were calculated
from the plasma cortisol activity concentration
[disintegrations · min
1
(dpm) · ml
1] time profile using a statistical
moment approach. The area under the curve (AUC*) was calculated from
time 0 to tlast using the arithmetic
trapezoidal rule.
The total plasma cortisol clearance (Cl*T,
ml · kg
1 · min
1) was
calculated using Eq. 14
|
(14)
|
where AUC* (dpm · min · ml
1) is
the area under the plasma cortisol activity concentration-time curve,
and dose (dpm/kg) is the dose of [3H]cortisol
administered. The corresponding plasma CBG-free cortisol clearance
(Cl*CBG-free;
ml · kg
1 · min
1) was
then computed taking into account the relationships defined by
Eqs. 15 and 16. By definition of clearance
|
(15)
|
and
|
(16)
|
where dX*/dt is the overall elimination
rate of [3H]cortisol, TOT* is the total labeled plasma
cortisol concentration, and CBG*free is the plasma
CBG-free labeled cortisol concentration.
By combining Eqs. 15 and 16
|
(17)
|
Because dexamethasone was injected 3 h before radiolabeled
cortisol, in this experiment there was no endogenous (cold) cortisol, and TOT* is given by the general relationship (Eq. 18)
|
(18)
|
where F* is the free labeled cortisol. Taking into account that
in our experimental conditions Kd >> F* and
after rearranging Eq. 18, we then obtained Eq. 19
|
(19)
|
Equation 19 can be rewritten as Eq. 20
|
(20)
|
By definition, F*(NS + 1) is the plasma
CBG*free cortisol concentration. Thus Eq. 20 can be written as Eq. 21
|
(21)
|
Inspection of Eq. 21 indicates that the
TOT*-to-CBG*free ratio is a constant; thus,
Eq. 17 can be expressed by Eq. 22
|
(22)
|
where Cl*T is obtained from Eq. 14, and Bmax, Kd, and
NS are determined by in vitro binding experiments.
Cl*CBG-free calculated from Eq. 22,
i.e., by a noncompartmental analysis, can be compared with that
obtained by modeling total plasma cortisol concentrations (see
Eq. 13).
Experiment 3.
The entry rate of cortisol (ER, mg/h) was calculated for each ewe by
use of Eq. 23
|
(23)
|
in which ClCBG-free values were obtained for the
three cortisol doses determined using the modeling approach
(experiment 1), and AUCCBG-free is the area
under the steady-state plasma CBG-free concentration-time curve
calculated using the arithmetic trapezoidal rule from t = 100 to t = 260 min for the first period and from
t = 40 to t = 220 min after the
beginning of each perfusion for the second period. CBGfree
were calculated from Eq. 24, adapted from Tait and Burstein
(21)
|
(24)
|
where TOT is the measured total plasma cortisol concentration,
and Bmax and Kd CBG-free are the
individual means of CBG-binding parameter values obtained for the three
cortisol doses with the modeling approach (experiment 1).
Statistical analysis.
The results are reported as means ± SD. The Systat 8.0 Statistics
program (SPSS, Chicago, IL) was used for statistical analysis. A
P value <0.05 was considered significant. Plasma cortisol
concentrations below the limit of quantification of the assay were
arbitrarily fixed at 1 ng/ml. CBG-binding parameters and total and
CBG-free cortisol kinetic parameters obtained 1) after
different cortisol doses given at 1-wk intervals according to a
crossover design using a modeling approach (experiment 1)
and 2) by the reference radioisotopic method or equilibrium
dialysis (experiment 2) were compared using an ANOVA for
repeated measurement design including one factor (dose) followed by a
Dunnett's two-sided test. The nonparametric Wilcoxon test was used to
compare the cortisol entry rates calculated from plasma CBG-free
cortisol clearance and CBG-binding parameters obtained with the
modeling approach with corresponding real cortisol perfusion rates.
 |
RESULTS |
In all experiments, the plasma cortisol concentrations obtained
3 h after a 0.1 mg/kg intravenous dexamethasone administration were below the level of quantification of the assay in all ewes, i.e.,
2 ng/ml.
In Vivo Radiolabeled Cortisol Disposition and In Vitro Binding
Experiments
Figure 2 shows the time course of
[3H]cortisol activity concentration in six ewes after an
intravenous administration of 5 µCi/kg [3H]cortisol.
Figure 3 shows the observed and fitted
concentrations of cortisol bound to plasma proteins as a function of
free cortisol concentrations, obtained by equilibrium dialysis, for a
representative ewe. Mean total and CBG-free cortisol kinetics and
CBG-binding parameters obtained from the plasma activity and
equilibrium dialysis are given in Table
1.

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Fig. 2.
Semilogarithmic plot of [3H]cortisol
activity concentration vs. time in 6 ewes after administration of 5 µCi/kg [3H]cortisol.
|
|

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Fig. 3.
Plasma protein-bound (B) concentrations as a function of
free cortisol concentrations obtained by equilibrium dialysis for a
representative ewe ( ) and fitting of protein-bound (B,
thick line), CBG-bound (BCBG, thin line), and albumin-bound
(BAlb, thin line) cortisol obtained from Eq. 1
by a computerized nonlinear least squares regression program.
Inset: the shape of fitted curves for low free cortisol
concentrations.
|
|
The mean plasma total cortisol clearance, obtained by using the
trapezoidal rule, was 11 ± 1 ml · kg
1 · min
1. The mean
values of Bmax, Kd, and
NS evaluated by in vitro equilibrium dialysis were 69 ± 13 nM (25 ± 5 ng/ml), 9.6 ± 1.9 nM (3.5 ± 0.7 ng/ml), and 1.1 ± 0.3, respectively. From the individual in vitro CBG-binding parameters (Eq. 1) and in vivo plasma activity
(Eq. 14), the individual values of what we considered to be
the reference values of plasma CBG-free cortisol clearance were
computed using Eq. 22 (53.9 ± 15.7 ml · kg
1 · min
1).
In Vivo Total Plasma Cortisol Modeling
The semilogarithmic plot for observed total plasma cortisol
concentrations and fitted total and CBG-free plasma cortisol
concentrations vs. time after intravenous administration of cortisol at
three level doses (0.05, 0.2, and 1 mg/kg) is shown in Fig.
4 for a representative ewe. The data were
well fitted to the equation corresponding to a bicompartmental model
and including the nonlinear binding to CBG. The estimations of the
parameters, i.e., A, K, Vc,
k10, k12, and
k21, and their precisions are given in Table 2.

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Fig. 4.
Semilogarithmic plot for observed total plasma cortisol
concentrations ( ) and fitted (thick line) total and
simulated CBG-free (thin line) plasma cortisol concentrations vs. time
after iv administration of cortisol at 3 dose levels [1
(A), 0.2 (B), and 0.05 mg/kg (C)] in
a representative ewe. Simulated CBG-free plasma cortisol concentrations
were obtained using Eq. 24.
|
|
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Table 2.
Estimated parameters of the pharmacokinetic model describing the in
vivo disposition of CBG-free cortisol, after the intravenous
administration of cortisol at the dose of 1 mg/kg
|
|
Figure 5 shows the interindividual
variations of total, CBG-free plasma cortisol clearance, and
CBG-binding parameters obtained after the 0.05, 0.2, and 1 mg/kg
intravenous cortisol administrations (experiment 1) and
corresponding reference values evaluated by a radioisotopic method and
equilibrium dialysis, respectively (experiment 2). The mean
total and CBG-free cortisol kinetic parameters and mean CBG-binding
parameters obtained after administration of these three doses are given
in Table 1.

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Fig. 5.
Interindividual variations of total, CBG-free plasma cortisol
clearance, and CBG-binding parameters [maximal binding capacity
(Bmax) and dissociation constant
(Kd)] estimated by modeling the kinetics of
total plasma cortisol concentrations obtained after the intravenous
administration of cortisol at 3 dose levels (0.05, 0.2, and 1 mg/kg)
and corresponding reference values evaluated by a radioisotopic method
and equilibrium dialysis, respectively. ClT, total
clearance; ClCBG-free, clearance of CBG-free cortisol.
|
|
The mean plasma CBG-free cortisol clearance evaluated by modeling
the disposition of exogenous cortisol concentrations obtained after
cortisol administration at different doses (48 ± 9, 58 ± 12, and 39 ± 12 ml · kg
1 · min
1 for 0.05, 0.2, and 1 mg/kg doses, respectively) did not differ significantly from
the control value obtained by the radioisotopic method (54 ± 16 ml · kg
1 · min
1, Dunnett's
test, P > 0.05). Similarly, the mean Bmax
values obtained by the modeling approach for the three cortisol levels
(54 ± 9, 92 ± 44, and 95 ± 43 nM for 0.05, 0.2, and 1 mg/kg doses, respectively) did not differ significantly from the mean
values obtained by equilibrium dialysis (69 ± 13 nM, Dunnett's
test, P > 0.05).
Kd values equivalent to those evaluated by the
modeling approach (i.e., Kd CBG-free) can be
estimated by multiplying the individual in vitro
Kd values [9.6 ± 1.9 nM, mean in vitro Kd (Kd in
vitro) value, experiment 2] by the
corresponding calculated NS + 1 values [2.1 ± 0.3, mean (NS + 1) value]. The mean
Kd CBG-free obtained by the modeling approach
(23.8 ± 5.3 and 13.6 ± 6.2 nM for 0.05 and 0.2 mg/kg doses)
were not different from the mean apparent Kd
values evaluated by equilibrium dialysis (20.1 ± 5.3 nM,
experiment 2, Dunnett's test, P > 0.05), whereas the mean Kd CBG-free obtained by the
modeling approach for the 1 mg/kg dose (9.8 ± 5.9 nM) was
significantly lower than the mean apparent Kd
value evaluated by equilibrium dialysis (Dunnett's test,
P = 0.005)
The individual mean values for plasma CBG-free cortisol clearance and
CBG-binding parameters obtained after administration of cortisol at
three dose levels were used in the following experiments to calculate
and compare cortisol entry rates with known corticoid perfusion rates
(experiment 3).
Validation of the Method of Estimation of Cortisol Production Rate
Figure 6 shows the individual plasma
total and CBG-free cortisol concentration profile in six ewes and
predictive values obtained during the perfusion of corticoid at
different rates (0.27, 1.6, 2.7, 12, and 18 mg/h). For each perfusion
level, an individual cortisol entry rate was calculated from the
kinetic and CBG-binding parameters estimated by the modeling approach
(experiment 1). Figure 7 shows
the mean cortisol entry rates calculated using our modeling approach
and the corresponding mean actual corticoid perfusion rates. The
calculated entry rates of cortisol were not different from the actual
perfusion rates (Wilcoxon test, P > 0.05).

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Fig. 6.
Total and CBG-free plasma cortisol concentration (ng/ml) obtained
in 6 ewes (thin line) and predictive values (thick line) during the
perfusion of cortisol at different rates (0.27, 1.6, 2.7, 12, and 18 mg/h). The predictive total and CBG-free plasma cortisol concentrations
were calculated from the mean cortisol kinetic and CBG-binding
parameters estimated by using our modeling approach.
|
|

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Fig. 7.
Mean cortisol entry rates calculated in 6 ewes using the
cortisol kinetic and CBG-binding parameters estimated by using our
modeling approach and corresponding mean actual cortisol entry rates
during the perfusion of cortisol at different rates (0.27, 1.6, 2.7, 12, and 18 mg/h).
|
|
 |
DISCUSSION |
Our modeling approach to total plasma cortisol kinetics after the
suppression of endogenous cortisol secretion by dexamethasone, which
takes into account the specific binding of cortisol to CBG, enabled us
to estimate the plasma CBG-free cortisol clearance and CBG-binding
parameters (Bmax, Kd CBG-free)
simultaneously. We have demonstrated that these parameters were
reasonably well estimated by comparing them with those obtained by
conventional methods, i.e., in vitro equilibrium dialysis for
Bmax and Kd in vitro × (NS + 1) and tracer cortisol kinetics for CBG-free
cortisol clearance. We have also shown that the same parameters
estimated in vivo could be used to determine a cortisol entry rate by
mimicking adrenal cortisol secretion with different rates of
intravenous cortisol perfusion.
Plasma cortisol kinetics have already been investigated in ewes by
means of a constant infusion of [3H]cortisol (9,
16-18, 20); the reported range of clearance values extended
from 13.5 to 25 ml · kg
1 · min
1. Such high
variability is to be expected, since the clearance calculated from a
tracer kinetic study is a total plasma cortisol clearance (i.e., a
variable and not a parameter) that fluctuates permanently with the
pulsatility of cortisol secretion. Indeed, it is generally admitted
that steroid hormones enter cells exclusively via the pool of free
hormone (15). Consequently, only the free plasma cortisol
can be cleared from the plasma. In physiological conditions, the free
plasma cortisol concentrations are of the same order of magnitude as
the Kd of cortisol to CBG (10 nM), and the
binding of cortisol to CBG is a nonlinear (saturable) process. This
means that the relationship between total plasma cortisol and CBG-free
cortisol is nonlinear within the physiological range of cortisol
concentrations; hence, the total cortisol clearance is nonlinear with
respect to the physiological plasma cortisol concentrations. This is no
longer the case when the plasma cortisol becomes very low (as in our
tracer experiment) or very high (as just after our intravenous cortisol administration).
Determination of a cortisol production rate using a plasma clearance
approach requires determination of the plasma cortisol clearance, which
is a parameter and not a variable. The plasma CBG-free clearance
corresponds to this putative clearance, and the ultimate goal of the
present experiment was to show that the CBG-free clearance can easily
be estimated using an in vivo modeling approach and is not subjected to
any dose dependency (i.e., nonlinearity of an origin other than
cortisol binding to CBG).
To estimate the CBG-free clearance, we used the modeling approach used
for inhibitors of angiotensin-converting enzyme (22), with
these drugs binding specifically and saturably to circulating converting enzymes in the same way that cortisol binds to CBG.
For a newly developed model, the first question faced is its
identifiability. A model is identifiable when it is able to give a
unique value of the parameters when an infinite number of observations is available. We performed several fittings of the individual concentration-time curves with different initial values of the parameters, and we obtained in all cases the same individual parameter estimations. Moreover, the model was fitted to error-free data simulated with several sets of parameter values and provided unique solutions corresponding to these parameter values. This ability of a
model to give a unique solution with a finite number of observations is
generally considered an indication that the model is identifiable. The
formal proof of identifiability is a complicated mathematical undertaking, especially for nonlinear models, which was in our opinion
beyond the scope of this paper.
On the basis of this physiologically based model, the interpretation of
the triphasic cortisol disposition after cortisol intravenous
administration differs from that involving a classical open
tricompartmental model. Indeed, if the initial phase of cortisol disposition also describes a distributional process to a peripheral compartment, the second phase reflects the clearance of CBG-free cortisol, and the terminal phase is related to the release of cortisol
from CBG-binding sites. Another particularity of this model is that the
steady-state volume of distribution and plasma half-life of CBG-free
cortisol are not parameters but variables, and that is why they were
not reported here. In other words, the binding-dependent nonlinearity
of the model influences the value of the volume of distribution of
CBG-free cortisol.
On the other hand, the plasma CBG-free cortisol clearance is
structurally independent of CBG binding, but there was no guarantee that the actual CBG-free clearance was a concentration-independent parameter. Indeed, mechanisms other than binding to CBG can be the
cause of nonlinearity. The present study showed the independence of
plasma CBG-free cortisol concentrations, thus suggesting that clearance
of the cortisol not specifically bound to CBG is a parameter able to
characterize cortisol disposition, whatever the total plasma cortisol
concentration. In other words, within the range of doses tested
(0.05-1 mg/kg), there was no evidence of saturability of plasma
CBG-free cortisol clearance (i.e., of cortisol metabolism), thus
indicating the very high intrinsic capacity of the clearing process for cortisol.
The plasma clearance of CBG-free cortisol was ~45
ml · kg
1 · min
1, i.e.,
rather high. Considering the hepatic (32 ml · kg
1 · min
1) and kidney
(12-17 ml · kg
1 · min
1)
blood flow rates in the ewe (16), it can be suggested that cortisol is an efficiently cleared analyte and that CBG-free cortisol elimination is rate limited by the liver and kidney blood perfusion rates. This was probably the cause of the relatively high interoccasion variability observed between the means of the plasma free cortisol clearance. In contrast to the plasma clearance of CBG-free cortisol, that of total cortisol depends on cortisol binding to CBG, thus supporting the view that CBG binding protects cortisol from a liver (or
kidney) first-pass effect.
Our physiologically based model for total cortisol disposition also
enabled the CBG-binding capacity and CBG affinity for cortisol to be
determined in vivo. The Kd CBG-free was 16 nM.
In our model, the nonspecific binding of cortisol to albumin was
ignored; if the NS parameter was included, we were faced
with a problem of structural identifiability for three of the estimated parameters, i.e., k10,
Kd, and NS. This nonidentifiability
was indicated by the fact that a model including a nonspecific binding parameter (i.e., NS) did not have any effect on the fitting
of data simulated without NS. This could be because cortisol
displays a gradient of affinity, ranging from low affinity for albumin, intermediate affinity for the enzymatic or clearing transport system,
and high affinity for CBG, which could explain why, when the clearance
process is under investigation, the free and albumin-bound cortisol
behave identically and are both subject to hepatic (and kidney) elimination.
The accuracy of the plasma CBG-free cortisol clearance determined by
our modeling approach was supported by two lines of evidence resulting
from our tracer experiment and from the computation of plasma total
cortisol clearance after administration of a large intravenous cortisol
dose. When the plasma cortisol concentrations became very high (with
respect to Kd CBG-free), the cortisol disposition became linear because of the total saturation of CBG. Thus,
during most of the cortisol disposition after a large cortisol dose,
the total plasma cortisol clearance can be considered equal to the
plasma CBG-free cortisol clearance. This was the case in our experiment
in which the total plasma cortisol clearance (31 ml · kg
1 · min
1) after a
dose of 1 mg/kg was not significantly different from the plasma
CBG-free cortisol clearance. Because of the linearity of the plasma
CBG-free cortisol clearance, it can easily be approximated to the
plasma total cortisol clearance using a statistical moment (i.e.,
noncompartmental) approach. It should be kept in mind that a very
simple data analysis of this kind cannot be used to determine Bmax and Kd, the two other
parameters required to estimate a cortisol production rate based on the
plasma CBG-free cortisol clearance. However, if Bmax,
Kd, and NS have been independently
determined in vitro, the cortisol production rate can be very simply
determined by combining the plasma total cortisol clearance and the
CBG-free cortisol concentration profile, which can be computed using in vitro Bmax, Kd, and NS
(see Eq. 24).
On the other hand, when the cortisol secretion was totally suppressed
by dexamethasone, the kinetic disposition of the radiolabeled cortisol
also became linear, because the actual radiolabeled maximal plasma
cortisol concentrations were low with respect to
Kd CBG-free (~1.6 nM). The analysis of the
radiolabeled cortisol disposition using a statistical moment approach
(i.e., without any specified structural cortisol model disposition)
could be used to measure a plasma total cortisol clearance, this being
the minimal possible value of plasma total cortisol clearance compared
with the total clearance obtained after a high cortisol dose, which is
its maximal limit. Thus, in the present experiment, the range of plasma
clearance of total cortisol varied by a factor of three.
The theoretical relationship between this minimal value of plasma total
cortisol clearance and that of plasma CBG-free cortisol clearance was
determined (see Eq. 22). The measured total plasma clearance
was used conjointly with Bmax, Kd in
vitro, and NS obtained by in vitro dialysis to
confirm that the plasma CBG-free clearance obtained from in vivo
modeling was comparable to that obtained with tracer kinetics and in
vitro dialysis parameters.
It can be seen from Eq. 22 that the relationship
between plasma CBG-free cortisol clearance (a parameter) and the plasma
clearance of total radiolabeled cortisol (also a parameter here) is
only determined by Bmax, Kd, and
NS, which control the free cortisol fraction (fu), with
fu = Kd(NS + 1)/[Bmax + Kd(NS + 1)]
or fu = Kd CBG-free/(Bmax + Kd CBG-free);
thus, Cl*T = Cl*CBG-free × fu.
In the present experiment, fu = 0.20, indicating that the minimal
possible plasma clearance of total cortisol was ~20% of that of
CBG-free cortisol.
The validity and usefulness of our modeling method for the evaluation
of cortisol production rate was tested by determining the cortisol
entry rate simulated by constant cortisol infusion in
dexamethasone-suppressed ewes from plasma CBG-free cortisol kinetics
and from the CBG-binding parameters determined by the in vivo modeling
approach. We were thus able to show that these parameters could be used
to determine cortisol production rate for a wide range of perfusion
levels extending from physiological levels to levels 10 times greater
than the CBG maximal binding capacity.
The production rate of cortisol has been investigated extensively in
humans (3, 10, 12, 13) and in different species, including
horses (14) and ewes (7, 17, 18), but the
results have varied according to the methodological approach used.
Stable isotope infusion combined with chromatographic mass
spectrometric detection has permitted an accurate determination of
cortisol production rate in humans (5). These methods
require the application of cumbersome and expensive analytical methods
(HPLC/mas spectrometry) that are not always readily available to
research laboratories.
The cortisol metabolic clearance method is based on the use of
radioisotopic tracers that do not interfere with endogenous cortisol
secretion. The production rate is obtained by measuring a series of
snapshot-specific cortisol activities that enables accurate evaluation
of the cortisol production rate but not computation of a cortisol
clearance term, which is a parameter. This clearance term, which can be
derived from a tracer trial, is only a local variable that depends on
the actual plasma cortisol concentration and cannot be reused for
another experiment. In contrast to all of the aforementioned methods,
our method of cortisol production rate measurement is simple, easy to
perform, accurate, and inexpensive, and it only requires in vivo
modeling. Such a method should encourage the use of cortisol production
rate rather than total cortisol plasma concentrations to assess the
influence of different factors, such as stress, exercise, and disease
on adrenal gland function. Indeed, the nonlinear relationship between
cortisol production and plasma cortisol concentrations has often led to
inadequate conclusions on adrenal secretion when only the plasma total
cortisol concentrations are used as end points. Alexander and Irvine
(1) showed that social stress altered CBG levels in
horses, resulting in an increase of free cortisol concentrations,
whereas no effect was detected when only the total cortisol was
measured. Exercise in that species was shown to trigger a sixfold
increase in the adrenal secretion rate, which was not accurately
reflected by the more limited increase (2-3×) of plasma cortisol
concentrations (14). Our modeling approach recently
enabled us to show that the hypercortisolism of scrapie-affected ewes
(19) resulted from a large increase in cortisol production
rate (5×), whereas the plasma total cortisol concentrations were only
doubled (7).
In conclusion, we have developed a method of evaluating the cortisol
production rate based on modeling of cortisol kinetics after cortisol
administration in dexamethasone-suppressed ewes. This method enabled us
to simultaneously 1) characterize the capacity of cortisol
elimination in this species by a parameter, the CBG-free cortisol
clearance, and 2) evaluate the plasma CBG-binding
parameters. In most mammal species, the saturable binding of cortisol
to CBG greatly contributes to the nonlinear cortisol disposition and accounts for the discrepancy between the cortisol production rate and
cortisol plasma concentrations. Hence, our model of cortisol disposition can be extended to these species after an initial validation step to ensure that the binding of cortisol to CBG is the
only mechanism that contributes to the nonlinear cortisol disposition.
Such a methodological approach could also be developed to study the
disposition of molecules for which the nonlinear disposition is
attributable to their saturable binding to plasma proteins.
We are grateful to S. Baurès, N. Gautier, and J.F.
Sutra for assistance and F. Lyazrhi for critical analysis of the statistics.
Address for reprint requests and other correspondence: P. L. Toutain, Laboratoire de Physiologie & Thérapeutique, Ecole
Nationale Vétérinaire de Toulouse, 23 chemin des Capelles,
31076 Toulouse (E-mail: pl.toutain{at}envt.fr).
The costs of publication of this
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