MODELING IN PHYSIOLOGY
Population-based modeling to demonstrate extrapancreatic effects of
tolbutamide
A.
Rostami-Hodjegan1,
S. R.
Peacey2,
E.
George2,
S. R.
Heller3, and
G. T.
Tucker1
1 Department of Medicine and
Pharmacology, University of Sheffield, The Royal Hallamshire Hospital,
Sheffield S10 2JF; and
2 University Department of
Medicine, Clinical Sciences Centre, and
3 Diabetic Centre, Northern
General Hospital, Sheffield S5 7AU, United Kingdom
 |
ABSTRACT |
Tolbutamide is used
increasingly as an investigative tool in in vivo studies of the
physiology of glucose tolerance. Its hypoglycemic effect in nondiabetic
subjects is widely variable, reflecting possible variability in its
pharmacokinetics, an insulinergic response, an extrapancreatic effect
of the drug, or the hypoglycemic effect of insulin itself. Using
population-based modeling, we have investigated the kinetics and
dynamics of tolbutamide and assessed covariates in two groups of
healthy subjects. The results indicate a high variability in
insulinergic effect, measured by the area under of the curve of insulin
(0-60 min), in response to tolbutamide injection (coefficient of
variation = 29-96%). However, it appears that impaired insulin
sensitivity is compensated by higher insulin secretion in response to
tolbutamide. Thus the hypoglycemic effect of high insulin secretion is
minimal in insulin-resistant subjects. Application of the model
indicated that tolbutamide has appreciable extrapancreatic effects
mediated by prolongation of the residence time of insulin in a remote
effect and by enhancement of glucose effectiveness. An effect in
increasing the insulin sensitivity index is also possible but could not
be confirmed statistically for all groups of subjects studied. These
observations may explain inconsistencies between the results of
tolbutamide and insulin injection in the frequently sampled intravenous
glucose tolerance test and call for further study of insulin- vs.
tolbutamide-modified frequently sampled intravenous glucose tolerance
tests in the assessment of the insulin sensitivity and glucose
effectiveness indexes.
insulin secretion; insulin sensitivity; population
pharmacokinetics-pharmacodynamics; sulfonylureas; minimal model
 |
INTRODUCTION |
SEPARATION OF insulin-related and insulin-independent
hypoglycemic response requires the application of complex modeling
techniques (5). The introduction of the "minimal model" to
describe the interrelationship between insulin and glucose (5, 6)
during the frequently sampled intravenous glucose tolerance test
(FSIGT) can be considered a compromise in modeling, facilitating the
ability to separate insulin sensitivity from glucose effectiveness.
This approach, although more complex with respect to computation of parameters than classical clamp studies, is less laborious to implement
and, therefore, more suitable for population studies. The use of the
fasting levels of insulin and blood glucose in homeostatic models (23)
to assess insulin resistance is popular in epidemiologic studies (19),
but the accuracy of these models is questionable, and they do not
provide information on glucose effectiveness. As a result, the minimal
model is still considered the best choice for such studies.
Nevertheless, with use of the minimal model, epidemiologic studies are
costly and require large numbers of samples from each individual.
In contrast to conventional modeling techniques, which determine
individual parameter values, the population approach (21) is primarily
concerned with obtaining mean population parameter values and their
distributions. Bayesian, a posteriori, individual estimates of
parameter values may then be used to assess the effect of covariates on
each parameter (21). Such estimates can be obtained, despite the fact
that the number of data points obtained from each individual may be
less than the number of model parameters. The approach can minimize
sampling requirements from each individual dramatically while providing
valuable information on covariates affecting model parameters. Although
the population approach has been used successfully in many
kinetic/dynamic (K/D) studies (21), its use in the field of
physiology/endocrinology has not been considered widely and, to our
knowledge, has been reported only once (11).
We have applied the population approach to an adapted minimal model of
insulin action to investigate different responses to tolbutamide
infusion and their possible covariates. We obtained our data from a
series of euglycemic and, subsequently, hypoglycemic glucose clamp
studies that were repeated twice: once using insulin (insulin arm of
the study) and once using tolbutamide (tolbutamide arm of the study) as
the hypoglycemic agent (26, 27). The primary purposes of these studies
were to compare physiological and symptomatic responses to hypoglycemia
induced by insulin and tolbutamide (26) and to investigate the possible
role of paracrine mechanisms in glucose physiology (27). The data were
unique in the sense that, for the first time, they captured extensive K/D information on an old drug that is increasingly used as an experimental tool in clinical endocrinological investigations of
glucose metabolism.
The possible extrapancreatic actions of tolbutamide continue to be
controversial (31). Despite this controversy, the drug has been used in
an improved protocol for FSIGT to assess insulin sensitivity and
glucose effectiveness with greater precision (2, 38). Although not
commonly acknowledged, this use of tolbutamide depends on the
assumption that insulin secretion is the sole action of the drug or, at
least, that any extrapancreatic effect of tolbutamide is invariant
between different individuals or between different populations. This
may not be so. Therefore, in analyzing our experimental data (26, 27),
a particular attempt has been made to compare glucose effectiveness and
insulin sensitivity in the presence and absence of tolbutamide.
Glossary
Ai |
A constant
|
AUC |
Area under the concentration (or rate)-time profile
|
BG |
Blood glucose
|
BG0 |
Fasting blood glucose
|
Bi |
A constant
|
BMI |
Body mass index
|
C |
Serum concentration
|
CE |
Concentration in a remote effect compartment
|
CTB |
Tolbutamide concentration
|
C50 |
Concentration of drug that produces half-maximum insulin secretion
|
CL |
Clearance
|
C/P |
Balance between consumption and production
|
CIns Lym |
Lymph insulin concentration in excess of fasting lymph insulin
|
CIns S |
Serum insulin concentration in excess of fasting serum insulin
|
d(C/P)/dt |
Rate of change of C/P (glucose disposal rate)
|
EH |
Hepatic extraction ratio
|
FBG |
Fasting blood glucose
|
FH |
Fraction of insulin in hepatic portal vein that avoids first-pass
hepatic metabolism
|
FLym |
Insulin lymph-to-serum ratio at steady state
|
FSI |
Fasting serum insulin
|
fu |
Unbound fraction of drug in serum
|
GEI |
Index of effectiveness of blood glucose in enhancing glucose
consumption
|
I |
Insulin mass in respective compartment
|
Ins |
Insulin central compartment
|
IR |
Insulin resistance
|
ISIS |
Index of sensitivity to effect of serum insulin in lowering blood
glucose
|
ISILym |
Index of sensitivity to effect of lymph insulin in lowering blood
glucose
|
k0 |
Zero-order infusion rate
|
ke 1 |
First-order rate constant defining the rate of insulin decline in the
central compartment
|
Kg |
A power function used to link blood glucose to insulinergic effect of
tolbutamide
|
kji |
First-order rate constant for transfer to compartment
j from compartment i
(when j = 0, this becomes an
elimination rate constant)
|
l |
Number corresponding to two disposition rate constants of tolbutamide
|
LBM |
Lean body mass
|
Lym |
Lymph compartment
|
ni |
Hill coefficient for insulinergic effect in
compartment i
[i = S (serum);
i = E (effect)]
|
Sec0 |
Baseline insulin secretion rate
|
Seci |
Insulin secretion rate [i = S
(serum); i = E (effect); when
i = 0 this becomes basal fasting level of insulin secretion
rate]
|
Secmax |
Maximum insulin secretion rate achieved by drug in corresponding
compartment
|
Sg |
Glucose effectiveness index as measured by minimal model
|
Si |
Insulin sensitivity index as measured by minimal model
|
ss |
Steady-state condition (or state of equilibrium between mass in 2 compartments)
|
T |
Infusion time
|
t |
Time of sampling
|
t |
Time between two consecutive samples
|
Tb |
Tolbutamide
|
TBF |
Total body fat
|
Thypo |
Start time of hypoglycemic phase in clamp studies
|
Tlag |
Lag time
|
Tload |
Infusion time of a loading dose of exogenous insulin
|
tmid |
Time midway between two consecutive samples
|
V |
Volume of distribution
|
VBG |
Central volume of distribution of glucose
|
VC |
Central volume of distribution of tolbutamide
|
 |
First-order disposition rate constant
|
 |
METHODS |
Data Base
The data base consisted of information on variable dextrose infusion,
blood glucose, and serum concentrations of tolbutamide, C-peptide, and
insulin (Table 1). Details of the subjects and protocols
have been published elsewhere (26, 27). All the subjects were healthy
nondiabetics (Table 2) with no family history of
diabetes. They were asked to avoid excessive exercise and alcohol on
the day before each study. The sequence of studies was randomized (unbalanced) for studies I-III
and studies IV and
V. Subjects fasted overnight before
each study.
The measurement of arterialized blood glucose and adjustments of
dextrose infusion were carried out as reported previously (26). Blood
glucose was maintained at a euglycemic level for a predefined period of
time (30-120 min, Table 1) and then allowed to fall gradually to a
controlled hypoglycemic level (except in study
I, where euglycemia was maintained throughout the
experiment). Recovery from the hypoglycemia was achieved by an increase
in the dextrose infusion and consumption of a high-calorie meal. Serum
was assayed for tolbutamide (7-13 time points), insulin (7-12
time points), and C-peptide (7-8 time points), as described previously (26).
Tolbutamide Kinetics
Serum concentrations of tolbutamide were fitted by a classical open
two-compartment model with sequential unequal intravenous infusion
inputs (Eq. 4 in
APPENDIX) (15) using the P-Pharm
population K/D program (version 1.3e, SIMED Biostatistics and Data
Processing, Créteil, France). The algorithm in P-Pharm is
described as being of the two-stage expectation-maximization type (24),
although some consider it to be more like the iterative two-stage
procedure proposed by Prévost (3).
Age, sex, weight, body surface area, serum tolbutamide binding, body
mass index, lean body mass (LBM), total body fat (TBF), and type of
study were investigated as covariates affecting the clearance and
volume of distribution of tolbutamide. Serum drug binding was measured
in the 5-min samples by ultrafiltration at 3,000 g, 37°C, for 30 min (Centrifree
micropartitioning device, Amicon). Body composition (TBF and LBM) was
estimated using bioelectrical impedance (model EZ 1500, Cranley Medical
Electronics, Birmingham, UK). Stepwise regression was used to identify
important parameters in the covariance model using P-Pharm.
C-Peptide Kinetics
Spline functions were used to fit serum C-peptide concentration data
and to calculate individual input function curves (i.e., concentration
change due to secretion per unit of time), as described by Eaton et al.
(12). Population values of elimination constants for deconvolution were
those reported by Polonsky et al. (29). The rate of C-peptide secretion
was then calculated using the reported population value of its volume
of distribution (65 ml/kg) (29). The partial area under the curve
(AUCp) up to 20 min (i.e., the
time that serum C-peptide achieved its maximum value) was used to
compare different subjects with respect to the production of C-peptide
in response to tolbutamide.
Insulin Kinetics
With the assumption of equimolar secretion of insulin and C-peptide,
the results of the analysis of C-peptide data were used as a measure of
insulin secretion. To estimate the hepatic extraction ratio of insulin,
individual values of insulin clearance were calculated from the insulin
arms of the studies (Eq. 16 in
APPENDIX). With the assumption that
tolbutamide does not alter insulin clearance (25), individual
extraction ratios were then calculated from integrated insulin
(C-peptide) secretion between 0 and 60 min, and the respective AUC of
serum insulin concentration was measured during respective tolbutamide
arms of the studies (Eq. 17 in
APPENDIX). Inasmuch as some of the
subjects received tolbutamide on two or three occasions, it was also
possible to estimate intrasubject variability in the hepatic extraction
of insulin.
Model-Independent Dynamics of Tolbutamide and Insulin
C-peptide secretion was considered a measure of the insulinergic
response to tolbutamide injection. Also, dextrose infusion rate was
used to construct an index for glucose disposal rate (Eq. 19 in
APPENDIX) and to evaluate the
hypoglycemic effect of insulin in the presence and absence of the drug.
Model-independent parameters (e.g., area under the curve up to 60 min)
were then used to determine whether the hypoglycemic effect estimated
at a given serum insulin level was comparable in the presence and
absence of tolbutamide.
K/D Modeling
Insulinergic effect of tolbutamide.
In the first part of the K/D analysis, insulin secretion was modeled
with respect to tolbutamide concentration and blood glucose (Eq. 1 in
APPENDIX). Insulin secretion was
defined at 5-min intervals from the simulations of C-peptide secretion,
as explained above.
The model consisted of two kinetic compartments and an additional
peripheral effect compartment that received a negligible mass of the
drug (15) (Fig. 1). The individual kinetic
parameters for tolbutamide, estimated as described above, were later
entered as covariates into a K/D link analysis (Eq. 1 in APPENDIX).

View larger version (21K):
[in this window]
[in a new window]
|
Fig. 1.
Pharmacokinetic-pharmacodynamic model used to describe biphasic
insulinergic effect of tolbutamide and synergistic influence of blood
glucose on this effect.
|
|
The transfer and elimination processes were considered to be first
order, as commonly assumed in classical kinetics (15). The output to
the effect compartment (defined by
kE 1) had
no significant effect on drug concentrations in the central compartment (15). The equation describing tolbutamide concentration in the effect
compartment was developed with only one unknown parameter, k0 E
(Eq. 5 in
APPENDIX).
In contrast to most K/D models, which assume that the effect is exerted
only by drug located in the effect compartment (15), the insulinergic
effect of tolbutamide was considered to be mediated by drug in central
and effect compartments producing immediate and delayed effects,
respectively. The insulinergic effect in both compartments was
described by Hill functions (Eq. 1 in
APPENDIX).
To account for the proportional effect of hypoglycemia and
hyperglycemia on the insulinergic effect of tolbutamide (28), the
secretion was linked to blood glucose. Thus insulin secretion was lower
during hypoglycemia in proportion to the fall in blood glucose. The
time course of blood glucose was described by empirical equations that
varied depending on the study (Eqs.
6-8 in
APPENDIX).
Hypoglycemic effect of insulin.
In the second part of the K/D analysis, the hypoglycemic effect was
modeled with respect to insulin and glucose concentrations in the
presence and absence of tolbutamide. The hypoglycemic effect was
defined by the rate of glucose disposal [balance between
consumption and production (C/P), Eq. 19 in APPENDIX].
The frequency of sampling was the same as that used to monitor blood
glucose. The model used the assumptions of the minimal model (4, 6):
1) glucose inhibits its own
production and increases its utilization in proportion to its
concentration in plasma, 2) insulin
has a synergistic influence on these effects of glucose, and
3) the effect of insulin to promote the decline of glucose in plasma depends only on the concentration of
insulin in a remote compartment (e.g., lymph), or, as an alternative hypothesis, the effect of insulin to promote the decline of glucose in
plasma depends on the concentration of insulin in a remote compartment
as well as serum insulin (Fig. 2).

View larger version (23K):
[in this window]
[in a new window]
|
Fig. 2.
Model that describes synergistic effects of insulin and tolbutamide on
feedback control of glucose consumption-production by blood glucose
concentration.
|
|
The alternative hypothesis, although it investigated the importance of
serum insulin relative to that of lymph insulin, served as a validation
for the modeling. Thus the aim was to reaffirm the results of
experimental studies that have shown negligible effects from serum
insulin compared with lymph insulin. The improvement in model fitting
achieved by addition of the effect from serum insulin was assessed
using the Akaike information criterion (36).
Serum insulin concentrations were fitted by empirical functions that
varied for the insulin and tolbutamide arms of the studies (Eqs. 9-12 in
APPENDIX). In a two-stage K/D
analysis, individual values of the parameters of these empirical
equations were obtained (kinetics) and used as covariates in subsequent
K/D link analysis. Appropriate equations were developed (by
incorporating Eqs. 9-12 into
Eq. 14 in APPENDIX) to describe the time
course of insulin concentration in the remote (i.e., lymph;
Eq. 15 in
APPENDIX) compartment with two unknown parameters for the transfer rates between central and peripheral compartments (Fig. 2) that were obtained from simultaneous fitting of dynamic (glucose disposal rate) and kinetic data (blood glucose level and serum insulin concentration). Thus serum insulin concentration was linked to hypoglycemic effect via an effect compartment without the need to calculate actual concentrations in this
compartment. The K/D link model was described by equations similar to
those used in the minimal model (Eq. 3
or 4 in
APPENDIX). Data for the disposal
rate of glucose were used only when there was no significant difference
between the insulin and corresponding tolbutamide studies with respect
to the levels of counterregulatory hormones (27, 37).
By solving the K/D link model in the presence (studies
I, II, and IV) and
absence of tolbutamide (studies III
and V), insulin sensitivity index
(ISI), GEI, and
k0 Lym, a
constant describing the elimination of insulin from lymph, were
determined. The parameter k0 Lym
defined the onset and duration of effect mediated by insulin in
interstitial fluid.
Statistical Methods
Inter- and intraindividual variability of all parameters in the above
analyses was obtained by ANOVA. A paired
t-test was used to investigate
differences between protocols.
For population analysis, interindividual variability was obtained
directly from the computed fits. Differences between population measures in different protocols were tested using Student's
t-test for inference. Student's
paired t-test was used to investigate differences in a posteriori individual values obtained from different protocols.
 |
RESULTS |
Main Observations
Insulinergic effect of tolbutamide.
Despite similar serum tolbutamide concentrations in the study subjects
(Fig.
3A),
serum C-peptide concentrations (Fig.
3B) and serum insulin concentrations
(Fig. 3C) showed considerable interindividual variability during tolbutamide administration. The
insulinergic effect of tolbutamide (as measured by
AUCp of C-peptide) did not
correlate with tolbutamide AUC on the basis of total or free serum
concentrations of the drug.

View larger version (28K):
[in this window]
[in a new window]
|
Fig. 3.
Time course of serum tolbutamide
(A), serum C-peptide
(B), serum insulin
(C), and blood glucose
(D) and rate of dextrose infusion
required to produce euglycemia (E)
in subjects of study I (Table 1).
|
|
Blood glucose level was stable in all subjects (Fig.
3D). However, to maintain the target
level, frequent changes in dextrose infusion were required during all
studies (Fig. 3E).
Despite wide variation in serum insulin concentration after
tolbutamide, the hypoglycemic effect (as measured by AUC values for
C/P; Table 3) indicated low variation
between the subjects, suggesting a possible counterregulatory link
between insulin production in response to tolbutamide and the insulin
sensitivity of individuals. Thus the AUC of insulin during the
tolbutamide studies (studies I, II,
and IV) correlated significantly
with FSI (r = 0.83, P < 0.001 for regression analysis;
Fig. 4; also confirmed using a
nonparametric rank correlation test); the subjects with higher FSI
tended to produce higher insulin levels in response to comparable tolbutamide concentrations.

View larger version (21K):
[in this window]
[in a new window]
|
Fig. 4.
Relationship between insulinergic effect (solid line) of tolbutamide
and fasting serum insulin and between hypoglycemic effect of exogenous
insulin (dashed line) and fasting serum insulin.
|
|
Representative fits of the K/D model to the insulinergic effect of
tolbutamide and calculated blood glucose profiles are shown in Fig.
5. Table 4
summarizes the population values for the K/D parameters of tolbutamide
insulinergic effect and their variability. High values for Hill
constants were obtained for the immediate insulinergic response
mediated by serum tolbutamide and the delayed response mediated by the
drug in the peripheral effect compartment.

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 5.
Model fits to insulinergic effect data (C-peptide secretion) and blood
glucose levels in 2 representative subjects (subjects
2 and 3, study
II).
|
|
Hypoglycemic effect of insulin in the presence and absence of
tolbutamide.
Representative fits of glucose disposal rate (with the assumptions of
Eq. 2 in
APPENDIX), together with
corresponding calculated blood glucose profiles, are shown in Fig.
6. Statistical analysis indicated that
addition of a hypoglycemic effect associated with serum insulin in the
second model (Eq. 3), although
reducing residuals, did not result in a significant improvement in the
fit. Thus population estimates of parameters are reported only for the
former model (Table 5).

View larger version (18K):
[in this window]
[in a new window]
|
Fig. 6.
Model fits to hypoglycemic effect data (glucose consumption-production
balance) and blood glucose levels in 2 representative subjects
receiving tolbutamide (subjects 2 and
3, study II).
|
|
An examination of individual parameter values indicated that insulin
elimination from lymph in the presence of tolbutamide decreased
significantly (7 cases) or was unchanged (6 cases) compared with the
corresponding study with insulin. Also, during the studies with
tolbutamide, GEI was increased in three cases and showed no change in
six. No subject had a decreased GEI in the presence of tolbutamide.
Similarly, ISI was increased (5 cases) or unchanged (8 cases) during
the tolbutamide arms, and no individual showed a significant
decrease.
Comparison of mean population values of
k0 Lym,
ISI, and GEI in the presence and absence of tolbutamide indicated that
the drug enhances GEI (P < 0.04 and
P < 0.0001 for
study II vs. study III and study IV vs.
study V, respectively). Also, when
data from study IV were compared with
those from study V, a significant (P < 0.0001) decrease in
the elimination of insulin from lymph was estimated. The decreased
insulin elimination during study II
was of borderline significance (P = 0.082). Despite a trend toward higher individual ISI values during the
studies with tolbutamide (studies II
and IV) than during the respective
insulin studies (studies III and
IV; Table 5), mean population values
of the ISI differed only between studies
IV and V
(P < 0.0001). Values were not
significantly different (P = 0.19) for
study II vs. study III. The model parameters of glucose disposal expressed
as their FSIGT equivalents are shown in Table
6.
Other Observations
Tolbutamide kinetics.
Intersubject variability in serum drug concentrations was less than
twofold and very similar in studies I,
II, and IV (Fig. 3A). Thus kinetic parameters showed
little inter- and intrasubject variability in comparison with the
high variability in the insulinergic and hypoglycemic effects of the
drug (Table 7).
C-peptide kinetics.
When tolbutamide was used as the hypoglycemic agent, serum
concentrations of C-peptide reached a maximum before 20 min (Fig. 3B), and the pattern of change in
its secretion, described by deconvoluted spline functions, was similar
(Fig. 7), indicating a common insulinergic
mechanism(s). After an initial peak of serum C-peptide secretion, there
was a second rise 40-60 min after the start of tolbutamide
infusion. Thus a constant serum concentration of tolbutamide (Fig.
3A) was not associated with a stable
C-peptide secretion (Fig. 7).

View larger version (26K):
[in this window]
[in a new window]
|
Fig. 7.
Derived C-peptide (insulin) secretion in all subjects.
Inset: estimated secretion in
subject 4, who consistently produced
much more C-peptide (insulin) than other subjects in response to
tolbutamide.
|
|
Serum C-peptide concentrations declined monotonically during
administration of exogenous insulin (studies
III and V; not shown). Monoexponential functions fitted to these concentrations
(r = 0.840-0.998, median 0.954)
indicated decay half-lives of 48 ± 5 and 27 ± 4 (SD) min in
studies III and
V, respectively (Table 8). The variability in decay rate was
small within each study [coefficient of variation (CV) = 10 and
14% for studies III and IV, respectively], whereas
AUCp values of C-peptide in
response to tolbutamide were widely variable (Table 8). AUC at 19 min has been used by other investigators to assess
-cell function using
insulin instead of C-peptide (18). Subject
4 had much higher serum concentrations of C-peptide in
response to tolbutamide than the other individuals (mean + 3.3 SD).
High intersubject variability was observed in the secretogenic effect
of tolbutamide (CV = 99%, n = 15),
whereas intrasubject variation (CV) in this effect was 15%
(n = 8).
Insulin Kinetics and Dynamics
As seen with C-peptide secretion, the serum insulin (Fig.
3C) and AUC values of serum insulin
during tolbutamide administration (Table 8) indicated high inter- and
low intrasubject variability. However, during insulin administration,
intersubject variability in serum insulin and AUC values was much lower
(Table 3). ANOVA showed no significant differences between calculated
clearances during the euglycemic or hypoglycemic parts of the study.
Clearance was similar in studies III
and V. Variability in the estimated hepatic extraction ratio of insulin was low (Table 8). The hypoglycemic response to exogenous insulin (studies
III and V) showed a
negative correlation with FSI [or insulin resistance index
(IRI)], with subjects having higher FSI (greater IRI) responding
with a lower hypoglycemic effect (Fig. 4). However, this correlation
was not significant (r = 0.25, P = 0.30). Multiple regression
analysis of the hypoglycemic response during studies
III and V showed that weight, age, and sex contributed independently to the effect. On
replacing weight with LBM and TBF, it was shown that the contribution of weight to hypoglycemic effect originates from LBM and is not dependent on the amount of TBF.
 |
DISCUSSION |
Sulfonylureas were first used to treat diabetes mellitus over one-half
century ago. However, despite extensive investigation, their exact site
and mode of action remain unclear (22). Although the acute insulinergic
effect of sulfonylureas is beyond doubt (22), contradictory results
have been reported with regard to their extrapancreatic and long-term
insulinergic effects (22). Despite these uncertainties, tolbutamide is
used as part of the implementation of the minimal model in FSIGT to
improve parameter estimation by generating an extra peak of endogenous
insulin (2, 38). This assumes that the drug itself does not change
insulin sensitivity or glucose efficiency. However, when the results of the tolbutamide- and insulin-injection FSIGT are compared with results
of clamp studies, it is clear that measures of ISI obtained by the two
FSIGT methods, despite showing a good correlation with clamp-derived
ISI values, are not concordant (7). Moreover, the values obtained from
the two FSIGT methods are different from each other (31, 32). In the
present study we have attempted to separate insulinergic and potential
extrapancreatic effects of tolbutamide by combining population K/D
modeling with an adapted minimal model of insulin and glucose
dynamics.
First, we show that variability in the population mean values of
kinetic parameters of tolbutamide is much less than the
variability in its hypoglycemic effect and therefore cannot explain the
wide variation in response. C-peptide concentration decreased during the administration of exogenous insulin (studies
III and V), as expected if exogenous insulin suppresses production of endogenous insulin. The rate of decline was invariant within each study. Thus
large differences in C-peptide level during tolbutamide arms (as
indicated by AUCp) were
attributed to a difference in C-peptide secretion rather than in its
disposition. Observation of similar individual C-peptide disposition is
consistent with claims that the use of population mean values of
kinetic parameters describing the elimination of C-peptide for the
purpose of deconvolution produces results similar to those obtained
when individual parameter values of C-peptide elimination are used
(34). Indeed, previous estimates of the kinetic parameters of C-peptide
are highly consistent (9, 29, 34).
The result of multiple regression analysis of glucose disposal rate
during the studies with exogenous insulin was consistent with knowledge
of factors influencing insulin sensitivity (e.g., weight, sex, and
age). This analysis also showed that subjects with a higher
muscle-to-fat ratio should have a greater hypoglycemic response.
A stable concentration of tolbutamide was not associated with stable
secretion of insulin. This is consistent with the findings of Lewis et
al. (20), who showed that only an increasing concentration of
tolbutamide, obtained by stepwise administration of multiple doses,
could produce a stable insulin secretion. Despite similar serum
tolbutamide concentrations in different individuals, the insulinergic response was highly variable between subjects,
one of whom (subject 4) clearly
showed a greater effect than the others. Surprisingly, the hypoglycemic
effect of the drug in this subject was no greater than that in the
others and was reproducibly in the middle of the range for dextrose
requirement (46-60th percentile). Further inspection of the data
indicated that the insulinergic response to tolbutamide was related to
the fasting level of insulin. The latter increases in
response to impaired insulin sensitivity (19, 23), such that blood
glucose is maintained in the normal range. This could explain
why individuals such as subject 4,
despite having higher insulin secretion in response to tolbutamide,
do not produce a greater hypoglycemic effect. The insulin
resistance of subject 4 was confirmed
during the clamp study with insulin, when, despite having
representative serum insulin levels, the subject required the lowest
infusion rate of dextrose to maintain the target blood
glucose concentration. A compensatory high insulinergic response to
glucose in insulin-resistant subjects is indicated when the product of
insulin secretion and ISI as measured by the minimal model remains
fixed (17). Therefore, a hyperbolic relationship exists between
-cell function and ISI as measured by the minimal model (17). This
confirms the in vitro observation that the drug mimics the insulinergic
effect of glucose action in releasing insulin from the pancreas (10).
Thus compensatory mechanisms of insulin resistance are common
to glucose and tolbutamide.
Two other important observations offered by the model with regard to
insulin secretion were the "allor-none" responses indicated by large Hill coefficients and an explanation for biphasic secretion of
insulin as well as the suppressive effect of hypoglycemia. These
observations confirm the findings of animal studies (13), explain the
difficulty encountered in establishing a dose-response curve for the
insulinergic effects of tolbutamide (22), and suggest a
homeostatic defense mechanism against severe hypoglycemia caused by
tolbutamide. The latter may account for the low incidence of
hypoglycemia in the clinical use of tolbutamide compared with other
sulfonylureas (16).
Perhaps the most important findings of this study were related to
extrapancreatic effects of tolbutamide. In a model-independent analysis, we showed that the effect of insulin may be prolonged by
tolbutamide, despite the fact that the elimination of insulin from
serum is unaffected (30). The present study confirms this by showing a
significant decrease in the elimination rate constant of insulin from a
remote effect compartment, which explains the prolongation of effects
of insulin. The half-life of insulin elimination from this compartment
increased from 14 to 21 min (study III
vs. study II) and from 3 to 19 min
(study V vs. study
IV). Our analysis reaffirms that serum insulin plays
an insignificant role in the overall economy of glucose, since a model
in which hypoglycemic effect was assumed to reflect serum and
peripheral (lymph) concentrations of insulin was no better than the
conventional representation of the effect mediated in a peripheral
compartment only. This observation also serves to validate the
reliability of our new model.
A significant increase in GEI was observed during the clamps with
tolbutamide. However, ISI values varied significantly in the presence
of the drug in only one of the study groups. Both effects were widely
variable (Table 5). Conversion of our GEI and ISI values to FSIGT
equivalents, assuming a mean population value for glucose volume of
distribution (for details see
APPENDIX), resulted in values within
the range previously obtained by application of the minimal
model to data from healthy subjects (4-7, 17, 32, 33).
The subjects of studies I-III
responded modestly to the proposed extrapancreatic effect of
tolbutamide relative to those who took part in studies
IV and V (only 3 subjects completed all studies). A notable difference between these two
groups was the higher insulin sensitivity (as indicated by the IRI;
Table 2) of the second group, many of whom were accustomed to regular exercise. It is also possible that the different response may have been
related to the time course of the effects, inasmuch as
studies IV and
V were shorter than
studies I-III (Table 1). This may
suggest that these effects of tolbutamide are of short duration and
cannot be measured easily over long periods of time.
In vivo evidence for a direct effect of tolbutamide remains
controversial. In a recent in vivo study by Lewis et al. (20), the
serum concentration of glucose during infusion of tolbutamide showed a
decline in patients with insulin-dependent diabetes mellitus (Fig. 4 in Ref. 20), which could imply a direct effect of
tolbutamide. However, the authors did not perform a trend analysis of
their data. Although the effects of tolbutamide on GEI and ISI as
measured by the minimal model (Si) shown in our study may be attributed to direct effects of tolbutamide, they may equally reflect large differences between peripheral and portal insulin
concentrations. Also, the presence of additional proinsulin and
C-peptide during tolbutamide administration may play a part.
Application of the minimal model to FSIGT with tolbutamide injection
results in Si values that are generally similar to those obtained by
clamp studies: only slightly higher in some cases (6) and slightly
lower in others (31). However, the original (14, 35) and more recent FSIGT studies using the insulin-injection protocol (31, 32) reported Si
values lower than those found in clamp studies. Thus values from FSIGT
with insulin injection are correlated with those from clamp studies but
are not concordant (31, 32). The possibility of a tolbutamide effect on
insulin sensitivity (but not glucose efficiency) has been suggested
earlier (4), but it was assumed that any systematic change would pose
no problem in comparative studies. The need for further studies to
assess the importance of the difference between tolbutamide- and
insulin-injection FSIGT protocols has been emphasized (4, 32). Almost
equivalent Si values from FSIGT with tolbutamide injection and clamp
studies but lower Si values from FSIGT with insulin injection (31, 32) suggest that tolbutamide injection may raise the true Si values. Studies in which the same individuals received tolbutamide- and insulin-injection FSIGT in a crossover design had not been reported before our analysis. However, Saad et al. (32) recently published the
results of such a study where Si and GEI as measured by the minimal
model (Sg) from tolbutamide-modified FSIGT were compared with results
from an insulin-modified FSIGT in the same group of subjects. The
findings of Saad et al. were essentially in agreement with the results
of our analysis, in that they observed substantial differences between
the two protocols. Although the Si value from the tolbutamide protocol
gave a quantitative measure of insulin action nearly equivalent (13%
lower) to that from the glucose clamp (the gold standard), the
estimates from the insulin protocol were 44% lower than those from the
glucose clamp. They also noted that the time course of insulin action
was more prolonged in the presence of tolbutamide, an effect that
was explained by changes in
k0 Lym in our
study.
With respect to glucose effectiveness, and in contrast to our
observation, Saad et al. (32) found no significant difference between
GEI in the presence or absence of tolbutamide. However, they suggested
that this could be due to the fact that Sg is estimated mainly from
early glucose data, when no tolbutamide is present. Thus lack of a
difference in GEI determined from two protocols does not exclude the
possibility of a tolbutamide effect on GEI.
The results of our study and that of Saad et al. (32) provide
evidence for an extrapancreatic effect of tolbutamide after acute
administration. Our study also indicates that this effect is the most
variable component of tolbutamide K/D. Although glucose efficiency is
the main determinant (80%) of glucose uptake during FSIGT (18), the
dominant effect of tolbutamide on GEI, observed in our study, may not
change the estimates of Sg, since the information to calculate Sg is
mainly provided by samples taken before injection of tolbutamide (32).
Nevertheless, tolbutamide effects in prolonging the residence time of
the insulin in lymph and possible effects on insulin sensitivity are
potential sources of error when the tolbutamide FSIGT is used in
comparative studies of glucose physiology.
Conclusion
Application of a population approach to mathematical modeling
in endocrinology proved to be successful, inasmuch as many of the
findings with respect to insulin secretion, C-peptide kinetics, covariates for hypoglycemic effects of insulin, and the suppressive effect of hypoglycemia on insulinergic effects of tolbutamide were
consistent with previous reports based on classical data analysis.
Moreover, this approach afforded two new findings.
1) Variability in the insulinergic
effect of tolbutamide is related to the insulin sensitivity of
subjects. This is similar to the compensatory high insulinergic
response to glucose in insulin-resistant subjects and suggests
that compensatory mechanisms of insulin resistance are common to
glucose and tolbutamide insulinergic effects.
2)
Tolbutamide has extrapancreatic effects, inasmuch as it
prolongs the effect of insulin in a remote effect compartment (lymph) and may change ISI and GEI of glucose economy.
These effects may arise purely from direct effects of tolbutamide, or
they may reflect the portal-to-peripheral ratio of serum insulin.
The results of this study should encourage a wider use of the
population approach in mathematical modeling in endocrinology. They
also call for a reevaluation of the in vivo effects of tolbutamide and
reaffirm the view that measures of insulin sensitivity and glucose
efficiency from tolbutamide and insulin injection protocols are not
directly comparable.
 |
APPENDIX |
Main Model Fits
The two main model fits were 1)
insulin secretion (in response to tolbutamide infusion) vs.
time
|
(1)
|
|
|
and
2) glucose disposal vs.
time
|
(2)
|
or
|
(3)
|
Functions Describing Main Model Parameters
Some of the parameters of the above models were not constant with time.
These included the concentrations of tolbutamide and insulin in serum,
blood glucose level, and the concentrations of tolbutamide and insulin
in remote compartments (effect compartment and lymph compartment,
respectively). The time profiles of the first three of these parameters
were fitted by appropriate equations, and the individual values of
variables for each fit were subsequently entered as covariates for
individuals into the second stage (main fit). Variables determining the
two latter profiles were calculated during the main fit (K/D link
modeling). Thus simulation of the time profiles for these
concentrations was bypassed, since the variables were obtained from the
time profiles of dynamic effect.
Equations describing each of the parameters used within the main fits
are as follows.
Serum tolbutamide concentration vs. time (fitted in the 1st stage).
|
(4)
|
Tolbutamide concentration in a remote effect compartment
(incorporated into the K/D link model and fitted during the 2nd
stage).
|
(5)
|
|
|
Blood glucose level (fitted in the 1st stage).
For studies II-V (euglycemia and
subsequently hypoglycemia)
when
t < Thypo
|
(6)
|
when
t > Thypo
|
(7)
|
and for study I
(euglycemia)
|
(8)
|
Serum insulin concentration (fitted in the 1st stage).
For studies I, II, and
IV (tolbutamide arms of studies)
when
t < Tlag
|
(9)
|
when
t > Tlag
|
(10)
|
and for studies III and
V (insulin arms of studies)
when
t
Tload
|
(11)
|
when
t
Tload
|
(12)
|
Lymph insulin concentration (incorporated into the K/D link model).
The concentration of insulin in lymph was a function of its
concentration in serum, and the transfer rates between the central and
remote (lymph) compartment for insulin
With
the assumption of first-order transfer rates of insulin to and from the
peripheral compartment
(kLym 1 and
k0 Lym), the rate of change of insulin concentration in lymph (peripheral compartment) was described by
|
(13)
|
It
was also assumed that exit of insulin from the peripheral compartment
had no significant effect on its concentration in the central
compartment. Because, at steady state, input to and output from the
peripheral compartment should be equal, Eq. 13 was simplified to contain only one rate
constant
|
(14)
|
|
|
where the subscript ss indicates
steady-state condition (or state of equilibrium between mass in 2 compartments). FLym has been
reported to be 0.6-0.7 (1, 37). We used a fixed value of 0.67.
The concentration of insulin in lymph could then be described by
integrating Eq. 14, where
CIns S was replaced with
appropriate terms from Eqs. 9-12.
The unknown parameter in these equations,
k0 Lym, was estimated after incorporation of Eq. 15 into the general model of glucose disposal
(Eq. 2 or
3) and solving the K/D link model
|
(15)
|
Thus
it was possible to link the hypoglycemic effect to serum insulin
without obtaining the insulin concentration in the peripheral effect
compartment.
Other Calculations
Hepatic extraction and clearance of insulin.
Individual values of insulin clearance were calculated from the insulin
arms of the experimental studies as follows
|
(16)
|
The
hepatic extraction ratio of insulin during the tolbutamide arm(s) of
the studies was then calculated as follows
|
(17)
|
Glucose disposal rate.
In the absence of a change in blood glucose, the net balance of
consumption and production of glucose (C/P) after insulin or
tolbutamide injection was considered to be the amount of dextrose infusion required to maintain a constant level of blood glucose. By use
of manual adjustment of infusion, the added dextrose often over- or
underestimates the actual need for glucose, resulting in short-term
fluctuations in blood glucose. The following equation was used to
correct for such deviations
|
(18)
|
To
obtain d(C/P)/dt, the net balance was
then divided by the duration of sampling
(
t) and related to the
corresponding midtime [tmid = (t1 + t2)/2]
|
(19)
|
Conversion of GEI and ISI to their classical minimal model
equivalents.
The values of GEI and ISI derived from our model are readily converted
to corresponding values of Sg and Si obtained in FSIGT experiments by
multiplying our values by the central volume of distribution of
glucose. For example, with the assumption of a value for the latter of
1.58 dl/kg (11), the average
Sg(FSIGT) in
study III (absence of tolbutamide) is
calculated as follows
ISI
in our model is converted to
Si(FSIGT) in the same way as GEI.
Thus Si(FSIGT) in
study III (absence of tolbutamide) is calculated as follows
Population Model Structure
In the population analysis the jth
measurement (e.g., CTB) for the
ith individual
(yij) is related
to the model parameters by the following expression (32)
|
(20)
|
where
f is a function (Eq. 4) describing the expected value of the response for
a given parameter vector
i
(e.g., k0 dose,
Vc,
1,
l,
k12,
T). The term
ij accounts for the (random)
error between the true value and the corresponding measurement and is
modeled as follows
|
(21)
|
where
ij is a normal distribution
with a mean of zero and a variance of
2 ×
. The power
is 0 (a homoscedastic model, used in fitting the blood glucose
profile) or 2 (a heteroscedastic model, used in all other fits), and
2 represents a scaler for error
variance. The population model for the parameters is
|
(22)
|
where
g is a known function describing the
expected value of
i as a
function of individual covariates
xi and the vector of true population parameters
and
i determines the
interindividual variability of the parameter and is assumed to have a
normal distribution with a mean of zero and a variance of
2
|
(23)
|
 |
ACKNOWLEDGEMENTS |
A. Rostami-Hodjegan was supported by research grants from the
Hallamshire Therapeutics Research Trust and the European Commission and
Overseas Research Award Scheme (ORS/9336009). E. George was supported
by a grant from the British Diabetic Association and the Research
Committee, Northern General Hospital Trust.
 |
FOOTNOTES |
Address for reprint requests: G. T. Tucker, University Dept. of
Medicine and Pharmacology, Section of Molecular Pharmacology and
Pharmacogenetics, The Royal Hallamshire Hospital, Sheffield
S10 2JF, UK.
Received 6 November 1996; accepted in final form 25 November 1997.
 |
REFERENCES |
1.
Ader, M.,
R. A. Poulin,
Y. J. Yang,
and
R. N. Bergman.
Dose-response relationship between lymph insulin and glucose uptake reveals enhanced insulin sensitivity of peripheral tissues.
Diabetes
41:
241-253,
1992[Abstract].
2.
Beard, J. C.,
R. N. Bergman,
W. K. Ward,
and
D. Porte, Jr.
The insulin sensitivity index in nondiabetic man: correlation between clamp-derived and IVGTT-derived values.
Diabetes
35:
362-369,
1986[Abstract].
3.
Bennet, J. E.,
and
J. C. Wakefield.
A comparison of Bayesian population method with two other methods as implemented in commercially available software.
J. Pharmacokinet. Biopharm.
24:
403-432,
1996[Medline].
4.
Bergman, R. N.
Towards physiological understanding of glucose tolerance: minimal-model approach.
Diabetes
38:
1512-1527,
1989[Abstract].
5.
Bergman, R. N.,
Y. Z. Ider,
C. R. Bowden,
and
C. Cobelli.
Quantitative estimation of insulin sensitivity.
Am. J. Physiol.
236 (Endocrinol. Metab. Gastrointest. Physiol. 5):
E667-E677,
1979[Abstract/Free Full Text].
6.
Bergman, R. N.,
L. S. Philips,
and
C. Cobelli.
Physiologic evaluation of factors controlling glucose tolerance in man.
J. Clin. Invest.
68:
1456-1467,
1981[Medline].
7.
Bergman, R. N.,
R. Prager,
A. Volund,
and
J. M. Olefsky.
Equivalence of the insulin sensitivity index in man derived by the minimal model method and the euglycaemic glucose clamp.
J. Clin. Invest.
79:
790-800,
1987[Medline].
8.
Caumo, A.,
A. Zerman,
R. Rizza,
and
C. Cobelli.
The dual tracer time-varying volume method for measuring hepatic glucose release in nonsteady state: theoretical and simulation results.
Comput. Methods Programs Biomed.
41:
243-267,
1994[Medline].
9.
Cobelli, C.,
and
G. Pacini.
Insulin secretion and hepatic extraction in humans by minimal model of C-peptide and insulin kinetics.
Diabetes
37:
223-231,
1988[Abstract].
10.
Cook, D. A.,
and
M. Ikeuchi.
Tolbutamide as mimic of glucose on
-cell electrical activity: ATP-sensitive K+ channels as a common pathway for both stimuli.
Diabetes
38:
416-421,
1989[Abstract].
11.
DeGaetano, A.,
G. Mingrone,
and
M. Castagneto.
NONMEM improves group parameter estimation for the minimal model of glucose kinetics.
Am. J. Physiol.
271 (Endocrinol. Metab. 34):
E932-E937,
1993.
12.
Eaton, R. P.,
R. C. Allen,
D. S. Schade,
K. M. Erickson,
and
J. Standefer.
Prehepatic insulin production in man: kinetic analysis using peripheral connecting peptide behavior.
J. Clin. Endocrinol. Metab.
51:
520-528,
1980[Abstract].
13.
Feldman, J. M.,
and
H. E. Lebovitz.
Biological activities of tolbutamide and its metabolites: a dissociation of insulin-releasing and hypoglycaemic activity.
Diabetes
18:
529-537,
1969[Medline].
14.
Finegood, D. T.,
I. M. Hramiak,
and
J. Dupre.
A modified protocol for estimation of insulin sensitivity with the minimal model of glucose kinetics in patients with insulin dependent diabetes.
J. Clin. Endocrinol. Metab.
70:
1538-1549,
1990[Abstract].
15.
Gibaldi, M.,
and
D. Perrier.
Pharmacokinetics. New York: Dekker, 1982, p. 239-245.
16.
Jackson, J. E.,
and
R. Bressler.
Clinical pharmacology of sulphonylurea hypoglycaemic agents.
Drugs
22:
295-320,
1981[Medline].
17.
Kahn, S. E.,
R. L. Prigeon,
D. K. McCulloch,
E. J. Boyko,
R. N. Bergman,
M. W. Schwartz,
J. L. Neifing,
W. K. Ward,
J. C. Beard,
J. P. Palmer,
and
D. Porte, Jr.
Quantification of the relationship between insulin sensitivity and
-cell function in human subjects: evidence for a hyperbolic function.
Diabetes
42:
1663-1672,
1993[Abstract].
18.
Kahn, S. E.,
R. L. Prigeon,
D. K. McCulloch,
E. J. Boyko,
R. N. Bergman,
M. W. Schwartz,
J. L. Neifing,
W. K. Ward,
J. C. Beard,
J. P. Palmer,
and
D. Porte, Jr.
The contribution of insulin-dependent glucose uptake to intravenous glucose tolerance in healthy human subjects.
Diabetes
43:
587-592,
1994[Abstract].
19.
Laasko, M.
How good a marker is insulin level for insulin resistance.
Am. J. Epidemiol.
137:
959-965,
1993[Abstract].
20.
Lewis, G. F.,
G. Steiner,
K. S. Polonsky,
B. Weller,
and
B. Zinman.
A new method for comparing portal and peripheral venous insulin delivery in humans: tolbutamide versus insulin infusion.
J. Clin. Endocrinol. Metab.
78:
66-70,
1994.
21.
Mandema, J. W.
Population pharmacokinetics and pharmacodynamics.
In: Pharmacokinetics: Regulatory, Industrial, Academic Perspectives, edited by P. G. Welling,
and F. L. C. Tse. New York: Dekker, 1995, p. 411-450.
22.
Marchetti, P.,
and
R. Navalesi.
Pharmacokinetic-pharmacodynamic relationships of oral hypoglycaemic agents: an update.
Clin. Pharmacokinet.
16:
100-128,
1989[Medline].
23.
Matthews, D. R.,
J. P. Hosker,
A. S. Rudenski,
B. A. Naylor,
D. F. Treacher,
and
R. C. Turner.
Homeostasis model assessment: insulin resistance and
-cell function from fasting plasma glucose and insulin concentrations in man.
Diabetologia
28:
412-419,
1985[Medline].
24.
Mentré, F.,
and
G. Gomeni.
A two step iterative algorithm for estimation in nonlinear mixed effect models with an evaluation in population pharmacokinetics.
J. Biopharm. Stat.
5:
141-158,
1995[Medline].
25.
Navalesi, R.,
A. Pilo,
and
E. Ferrannini.
Kinetic analysis of plasma insulin disappearance in non-ketotic diabetic patients and in normal subjects. A tracer study with 125I-insulin.
J. Clin. Invest.
61:
197-208,
1978[Medline].
26.
Peacey, S. R.,
E. George,
A. Rostami-Hodjegan,
C. Bedford,
N. Harris,
C. A. Hardisty,
G. T. Tucker,
I. A. Macdonald,
and
S. R. Heller.
Similar physiological and symptomatic responses to sulphonylurea and insulin induced hypoglycemia in normal subjects.
Diabet. Med.
13:
634-641,
1996[Medline].
27.
Peacey, S. R.,
A. Rostami-Hodjegan,
E. George,
G. T. Tucker,
and
S. R. Heller.
The use of tolbutamide-induced hypoglycaemia to examine the intraislet role of insulin in mediating glucagon release in normal humans.
J. Clin. Endocrinol. Metab.
82:
1458-1461,
1997[Abstract/Free Full Text].
28.
Pfeifer, M. A.,
J. B. Halter,
R. Graf,
and
D. Porte, Jr.
Potentiation of insulin secretion to nonglucose stimuli in man by tolbutamide.
Diabetes
29:
335-340,
1980[Abstract].
29.
Polonsky, K. S.,
J. Licinio-Paixao,
B. O. Given,
W. Pugh,
P. Rue,
J. Galloway,
T. Karrison,
and
B. Frank.
Use of biosynthetic human C-peptide in the measurement of insulin secretion rates in normal volunteers and type I diabetic patients.
J. Clin. Invest.
77:
98-105,
1986[Medline].
30.
Rostami-Hodjegan, A.,
S. R. Peacey,
E. George,
S. R. Heller,
and
G. T. Tucker.
The insulinergic effect of tolbutamide during euglycaemic clamp in non-diabetic subjects
pharmacokinetic-pharmacodynamic modelling (Abstract).
Br. J. Clin. Pharmacol.
41:
464P,
1996.
31.
Saad, M. F.,
R. L. Anderson,
A. Laws,
R. M. Watanabe,
W. W. Kades,
Y.-D. I. Chen,
R. E. Sands,
P. J. Savage,
and
R. N. Bergman.
A comparison between the minimal model and the glucose clamp in the assessment of insulin sensitivity across the spectrum of glucose tolerance.
Diabetes
43:
1114-1121,
1994[Abstract].
32.
Saad, M. F.,
G. M. Steil,
W. W. Kades,
M. F. Ayad,
W. E. Elswafy,
R. Boyadjian,
S. D. Jinagouda,
and
R. N. Bergman.
Differences between the tolbutamide-boosted and the insulin-modified minimal model protocols.
Diabetes
46:
1167-1171,
1997[Abstract].
33.
Steil, G. M.,
A. Volnud,
S. E. Kahn,
and
R. N. Bergman.
Reduced sample number for calculation of insulin sensitivity and glucose effectiveness from the minimal model. Suitability for use in population studies.
Diabetes
42:
250-256,
1993[Abstract].
34.
Van Cauter, E.,
F. Mestrez,
J. Sturis,
and
K. S. Polonsky.
Estimation of insulin secretion rates from C-peptide levels: comparison of individual and standard kinetic parameters for C-peptide clearance.
Diabetes
41:
368-377,
1992[Abstract].
35.
Welch, S.,
S. S. P. Gebhart,
R. N. Bergman,
and
L. S. Philips.
Minimal model analysis of intravenous glucose tolerance test-derived insulin sensitivity in diabetic subjects.
J. Clin. Endocrinol. Metab.
71:
1508-1518,
1990[Abstract].
36.
Yamaoka, K.,
T. Nakagawa,
and
T. Uno.
Application of Akaike's information criteria (AIC) in the evaluation of linear pharmacokinetic equations.
J. Pharmacokinet. Biopharm.
6:
165-175,
1978[Medline].
37.
Yang, Y. J.,
I. D. Hope,
M. Ader,
and
R. N. Bergman.
Insulin transport across capillaries is rate limiting for insulin action in dogs.
J. Clin. Invest.
84:
1620-1628,
1989[Medline].
38.
Yang, Y. J.,
J. H. Youn,
and
R. N. Bergman.
Modified protocols improve insulin sensitivity estimation using the minimal model.
Am. J. Physiol.
233 (Endocrinol. Metab. Gastrointest. Physiol. 2):
E595-E602,
1987.
AJP Endocrinol Metab 274(4):E758-E771
0193-1849/98 $5.00
Copyright © 1998 the American Physiological Society