INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C REFERENCES

Glossary

New Model

EGP0	Endogenous glucose production extrapolated to zero insulin concentration (mmol/min)
EGPb	EGP at basal insulin concentration (mmol/min)
F01	Total non-insulin-dependent glucose flux (mmol/min)
g1(t), g3(t)	Concentrations of D-[U-13C]glucose and 3-O-methyl-D-glucose in the accessible compartment (mmol/l)
G(t)	Total glucose concentration in the accessible compartment (mmol/l)
I(t), Ib	Plasma insulin and basal (preexperimental) plasma insulin (mU/l)
k03	Transfer rate constant of 3-O-methyl-D-glucose excretion (min1)
k12	Transfer rate constant from nonaccessible to accessible compartment (min1)
ka1, ka2, ka3	Deactivation rate constants (min1)
kb1, kb2, kb3	Activation rate constants (min2 per mU/l)
q1(t), q2(t)	Masses of D-[U-13C]glucose in the two compartments (mmol)
q3(t), q4(t)	Masses of 3-O-methyl-D-glucose in the two compartments (mmol)
Q1(t), Q2(t)	Masses of native glucose in the two compartments (mmol)
Q10	Initial mass of native glucose in the accessible compartment (mmol)
SIT, SID, SIE	Insulin sensitivity of glucose distribution/transport, glucose intracellular disposal, and EGP (ml · min1 · kg1 per mU/l)
u1(t), u3(t)	Bolus doses of D-[U-13C]glucose and 3-O-methyl-D-glucose administered at 0 and 120 min (mmol/min)
U(t)	Bolus dose of the unlabeled glucose administered at 120 min (mmol/min)
V	Distribution volume of the accessible compartment (liters)
x1(t), x2(t), x3(t)	Remote effect of insulin on glucose distribution/transport, glucose disposal, and EGP, respectively (min1)

Two-Compartment Minimal Model

D	Administered dose of D-[U-13C]glucose at 120 min (mmol)
F01	Constant component of glucose uptake (fixed at 1 mg · kg1 · min1)
g(t)	plasma concentration of D-[U-13C]glucose (mmol/l)
Ib	Basal (postexperimental) insulin concentration (mU/l)
k21, k12, k02	fractional rate parameters (min1)
ka	Deactivation rate constant (min1)
kb	Activation rate constant (min2 per mU/l)
kp	Proportional term of glucose disposal (min1)
MCR	Basal metabolic clearance rate of glucose (ml · kg1 · min1)
q1(t), q2(t)	Masses of D-[U-13C]glucose in the two compartments (mmol)
S	Insulin sensitivity (ml · kg1 · min1 per mU/l)
V	Volume of the accessible compartment (liters)
x(t)	Remote insulin (min1)

One-Compartment Minimal Model

D	(Total) glucose dose (mmol)
G(t)	Plasma concentration of total (labeled and unlabeled) glucose (mmol/l)
Gb	Basal (postexperimental) glucose concentration (mmol/l)
Ib	Basal (postexperimental) insulin concentration (mU/l)
p1 = SG	Glucose effectiveness (min1)
p2	Deactivation rate constant (min1)
p3	Activation rate constant (min2 per mU/l)
SI	Insulin sensitivity (min1 per mU/l)
V	Distribution volume (liters)
x(t)	Remote insulin (min1)

INSULIN IS A POTENT ANABOLIC HORMONE, which activates metabolic pathways to regulate glucose metabolism and maintain homeostasis. Insulin stimulates glucose transmembrane transport and intracellular glucose disposal while also suppressing endogenous glucose production (EGP).

These pathways are measurable in particular tissues/organs by use of imaging methods such as nuclear magnetic resonance spectroscopy (18, 42) or multiple-tracer dilution techniques (11, 39). Techniques such as the glucose clamp or the minimal-model analysis of an intravenous glucose tolerance test (IVGTT) provide whole body aggregated measures of insulin action (5) without the ability to separate the three effects, with the exception of estimating EGP and peripheral glucose uptake during a labeled IVGTT (15, 27) or clamp (34, 35).

The sensitivity of glucose transport to insulin and the temporal pattern of its activation are currently unknown at the whole body level. Similarly, it is currently unknown to what extent the three pathways contribute to glucose lowering during dynamic conditions such as an IVGTT. Recent studies with mice indicate that a muscle-specific insulin receptor knockout does not alter glucose tolerance (12), raising questions about the relative importance of insulin-activated pathways.

The present study was designed to estimate simultaneously the effect of insulin on glucose distribution/transport, glucose disposal, and EGP during an IVGTT. The aim was to compare the three pathways both in terms of their sensitivities to insulin and in their abilities to lower plasma glucose concentration. We employed a dual-tracer technique with the administration of D-[U-¹³C]glucose, a stable-label tracer indistinguishable from native glucose, and 3-O-methyl-D-glucose, a marker of glucose transport. The data were analyzed using a novel model of glucose kinetics. Validation of an EGP estimate was facilitated by administering and reconstructing a variable infusion of another stable-label tracer, D-[6,6-²H₂]glucose.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C REFERENCES

Subjects and Experimental Protocol

The subjects underwent a 4-h IVGTT preceded by a 2-h investigation of glucose kinetics under basal conditions. The study was carried out after an overnight fast. No medication was given, and the subjects followed their standard diet regimen before the study.

At ~0830, a Venflon cannula was inserted into a vein in each antecubital fossa. One cannula was used for sampling and the other for the administration of glucose infusates, which were given via a Harvard pump (Harvard Instruments, Millis, MA) and an IVAC 560 pump (IVAC, San Diego, CA). The experiment commenced after a rest period of ~30 min. The subjects remained supine during the studies and were allowed to sip water but otherwise had no oral intake.

At 0 min, an intravenous bolus was given of D-[U-¹³C]glucose (5 mg/kg body wt; Cambridge Isotopes Laboratories, Promochem, Herts, UK) and 3-O-methyl-D-glucose (8 mg/kg; Sigma-Aldrich, Gillingham, Dorset, UK).

At 120 min, an intravenous glucose bolus was administered (0.3 g/kg, 50% aqueous dextrose solution over 1 min) enriched with D-[U-¹³C]glucose (subject 1: 20 mg/kg; subjects 2-6: 10 mg/kg; the dose was reduced, because satisfactory resolution of measurements was achieved with the lower dose and to limit costs) and 3-O-methyl-D-glucose (subject 1: 32 mg/kg, subjects 2-6: 16 mg/kg).

A variable, discontinuous (piecewise constant) intravenous infusion of D-[6,6-²H₂]glucose (range: 0-0.4, average: 0.2 mg · kg¹ · min¹; MassTrace, Woburn, MA) with a time step of 5-30 min started at 90 min and continued until the end of the study. The purpose of the infusion was to validate calculations of EGP.

Samples were taken at 10, 5, 0, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 30, 40, 50, 60, 80, 100, 105, 110, 115, 119, 122, 123, 124, 125, 128, 130, 132, 134, 136, 138, 140, 144, 148, 152, 160, 165, 170, 180, 190, 200, 210, 220, 230, 240, 260, 280, 300, 330, and 360 min. Samples were analyzed for insulin, C-peptide, glucose, D-[U-¹³C]glucose, 3-O-methyl-D-glucose, and D-[6,6-²H₂]glucose.

Assays

Mass spectrometry analysis. Details of analysis have been published previously (41). In brief, plasma samples were derivatized to obtain volatile esters of penta-O-trimethylsilyl-D-glucose-O-methoxime by use of a modification of a method described by Laine and Sweeley (33). Gas chromatography was performed on a Hewlett-Packard model 5890 Series II with a Hewlett-Packard model 7673 autosampler (Hewlett-Packard, Woking, UK). Mass spectrometry analysis was performed with a Hewlett-Packard model 5971A mass-selective detector. In the selected-ion monitoring mode, the following ions were measured: mass-to-charge ratio (m/z) 261 (M + 0) and 264 (M + 3) for 3-O-methyl-D-glucose and the internal standard 3-O-methyl-D-[²H₃]glucose (MassTrace); m/z 319 (M + 0), 321 (M + 2), 322 (M + 3) and 323 (M + 4) for the determination of D-[6,6-²H₂]glucose and D-[U-¹³C]glucose.

Insulin, C-peptide, and glucose assay. Sample tubes for glucose contained fluoride oxalate and those for C-peptide K-EDTA and Trasylol. Plasma glucose was measured using an enzymatic method on a Clandon glucose analyzer (Yellow Springs Instrument, Yellow Springs, OH) with a 1.5% within-assay coefficient of variation (CV). Plasma immunoreactive insulin and plasma C-peptide were measured by double-antibody radioimmunoassay techniques. The within-assay CVs were 6 and 5%, respectively.

Data Analysis

Tracer-to-tracee ratio and tracer concentrations. The tracer-to-tracee ratio (TTR) was calculated on the basis of the work by Cobelli et al. (21), with further elaboration by Rosenblatt et al. (38). TTR represents a ratio of exogenously originating glucose to endogenously originating glucose in the sample. In the case of 3-O-methyl-D-glucose, the endogenous component is replaced by the internal standard.

Modeling glucose kinetics. The new model describes the basal period and the IVGTT. We used a two-compartment structure, which described adequately and simultaneously the kinetics of D-[U-¹³C]glucose, 3-O-methyl-D-glucose, and native glucose and reflects current physiological knowledge (1, 16). The accessible glucose compartment (where measurements are made) represents plasma and tissues that equilibrate quickly with plasma. It contains plasma distribution space and a portion of the interstitial distribution space (30). The nonaccessible compartment represents the slowly equilibrating pool and contains the remaining interstitial space and the intracellular distribution space.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   A: model of the 3-O-methyl-D-glucose kinetics; B: the D-[U-13C]glucose kinetics; C: the kinetics of unlabeled (native) glucose; and D: the 3 insulin effects during an intravenous glucose tolerance test (IVGTT). GV, total glucose concentration × volume.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

1

1

1

1

2

1

1

Stable-label two-compartment model of glucose kinetics during IVGTT. For comparison, we estimated parameters of the stable-label two-compartment model of glucose kinetics during an IVGTT described by a set of differential equations (46)



where q₁(t) and q₂(t) are masses of the tracer glucose in the two compartments (mmol); V is the volume of the accessible compartment (liters); k_p is the proportional term of glucose disposal (min¹); k₂₁, k₁₂, and k₀₂ are fractional rate parameters (all min¹); x(t) represents the remote insulin (min¹); k_b (min² per mU/l) and k_a (min¹) have similar meaning as p₃ and p₂ of the one-compartment minimal model; F₀₁ is the constant component of glucose uptake [fixed at 1 mg · kg¹ · min¹ (8)]; g(t) is plasma concentration of D-[U-¹³C]glucose (mmol/l); and D is the administered dose of D-[U-¹³C]glucose at 120 min (mmol). The proportional term of glucose disposal k_p is constrained to produce insulin-independent utilization three times higher than the insulin-dependent utilization at the basal glucose concentration (G_b) and the basal insulin concentration (I_b)
guaranteeing theoretical identifiability of the model. The model has six parameters k₂₁, k₁₂, k₀₂, V, k_a, and k_b. All measurements were included in parameter estimation.

1

1

1

1

Minimal model of glucose kinetics during IVGTT. We also estimated parameters of the minimal model to enable comparison with the newly developed model. The minimal model of glucose kinetics after an IVGTT is described by two differential equations (6)

where G(t) is the plasma concentration of total (labeled and unlabeled) glucose (mmol/l); x(t) represents the remote insulin (min¹); G_b is the basal glucose concentration (mmol/l); D is the (total) glucose dose (mmol); and p₁ (min¹), p₂ (min¹), p₃ (min² per mU/l), and V (liters; the distribution volume) are model parameters. Insulin sensitivity (S_I; min¹ per mU/l) is defined as the ratio S_I = p₃/p₂ and glucose effectiveness as S_G = p₁.

Free-format reconstruction of EGP. EGP was also calculated without imposing a relationship to insulin by using a variation of deconvolution methodology. Details are given in APPENDIX C. In brief, D-[U-¹³C]glucose and 3-O-methyl-D-glucose (i.e., excluding native glucose) were employed to estimate the time-variant unit impulse response of the glucose system. An advanced numerical approach (regularized deconvolution with nonnegative constraint) calculated free-format EGP.

Parameter estimation. Model parameters were estimated by employing a nonlinear, weighted, least squares algorithm. The weight was defined as the reciprocal of the square of the measurement error.

Statistical Analysis

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C REFERENCES

Plasma Glucose, Insulin, and Glucose Tracers

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Plasma concentrations of glucose, insulin, D-[U-13C]glucose, and 3-O-methyl-D-glucose (3-OMG) during IVGTT (means ± SE; n = 6). D-[U-13C]glucose and 3-OMG concentrations were normalized to a dose of 10 and 16 mg/kg, respectively, at 120 min.

The insulin profiles and the C-peptide profiles (not shown) demonstrated that the bolus of glucose tracers at 0 min did not stimulate insulin secretion.

After the two boluses at 0 and 120 min, both D-[U-¹³C]glucose and 3-O-methyl-D-glucose presented a double-peak profile with the peaks well defined. The profiles were smooth and confirmed the low level of measurement error. The average concentration of recycled glucose was 0.007 mmol/l, with a maximum concentration of 0.015 ± 0.004 nmol/l at 125 min and a decrease to 0.006 ± 0.003 mmol/l at the end of the study (profile not shown). These values were negligible in comparison with D-[U-¹³C]glucose and D-[6,6-²H₂]glucose concentrations.

Modeling Glucose Kinetics

1

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Sample model fit to data measured in subject 5.

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Mean insulin action (relative to basal; n = 6) (top) and mean glucose fluxes (bottom) associated with glucose distribution/transport [x1(t) and F21(t)], glucose disposal [x2(t) and F02(t)], and endogenous glucose production (EGP) [x3(t) and EGP(t)]. Also in bottom: the reverse glucose flux from the nonaccessible compartment to the accessible compartment [F12(t)] and the non-insulin-dependent disposal from the accessible compartment [F01(t)].

Insulin sensitivities of distribution/transport, disposal, and EGP were similar [see Table 2; P = nonsignificant (NS), ANOVA]. Insulin sensitivity of distribution/transport was positively correlated with that of disposal (S_IT vs. S_ID, r = 0.82, P < 0.05) but not with that of EGP (S_IT vs. S_IE, r = 0.58, P = 0.23). EGP and disposal sensitivities were not significantly correlated (S_IE vs. S_ID, r = 0.50, P = 0.32).

The plot of weighted residuals is shown in Fig. 5. The average SD of weighted residuals during the basal period tended to be smaller than that after the unlabeled glucose bolus (D-[U-¹³C]glucose: 1.6 vs. 2.4; 3-O-methyl-D-glucose: 1.4 vs. 1.6; total glucose: 1.5 vs. 2.0), indicating an average misfit slightly above the measurement error for all three substrates and a slightly better fit during the basal period than during the IVGTT.

View larger version (31K): [in this window] [in a new window]   Fig. 5.   Weighted residuals (means ± SD; n = 6) associated with D-[U-13C]glucose, 3-OMG, and total glucose. Weighted residuals represent differences between model fit and measurements normalized by the measurement error.

Simulation runs with the model facilitated the separation of the three effects of insulin on glucose lowering during IVGTT. The model was run in eight configurations: 1) the three effects [i.e., the remote insulin compartments x₁(t), x₂(t), and x₃(t)] following their nominal (stimulated) levels during IVGTT; 2) the three effects fixed at their basal (i.e., 120-min) levels; 3-5) one effect following its nominal level and the other two effects fixed at their basal levels; and 6-8) two effects following their nominal levels and one effect fixed at its basal level.

Figure 6 shows the results of configurations 1 and 3-5 relative to the baseline configuration (2) (the three effects fixed at their basal levels). It is demonstrated that suppression of EGP has the greatest and longest impact on glucose lowering and accounts, at its maximum, for ~3 mmol/l out of the lowering magnitude of 6 mmol/l. The effects of stimulated glucose distribution/transport and stimulated glucose disposal are smaller but similar.

View larger version (23K): [in this window] [in a new window]   Fig. 6.   Glucose-lowering profiles during IVGTT with separate assessment of insulin effect on stimulating glucose distribution/transport, stimulating glucose disposal, and suppressing EGP. Profiles are relative to baseline, which corresponds to "no incremental insulin effect" (the 3 effects fixed at their basal levels). The results were obtained by model simulation with individual parameters (n = 6).

Glucose-lowering activities were quantified by area under the curve (AUC) of glucose differential profiles shown in Fig. 6 (see Fig. 7). Stimulation of disposal and stimulation of distribution/transport account each independently for ~25 and 30% of the overall glucose-lowering AUC. Suppression of EGP is more influential (P < 0.01, ANOVA) and accounts for ~50% of the overall glucose-lowering AUC. The combination of stimulated glucose disposal and stimulated glucose distribution/transport is less potent than the two combinations associated with EGP suppression (P < 0.05, ANOVA).

View larger version (17K): [in this window] [in a new window]   Fig. 7.   Glucose lowering during IVGTT, with separate assessment of the insulin effect on stimulating glucose distribution/transport, stimulating glucose disposal, and suppressing EGP and combinations of the effects. Results are obtained by calculating areas under the curve (AUCs) of profiles such as those shown in Fig. 6.

EGP

1

1

1

1

View larger version (26K): [in this window] [in a new window]   Fig. 8.   Individual profiles of EGP in subjects 1-6 calculated by 2 methods, model-based calculations and free-format calculations, during basal conditions (0-120 min) and IVGTT (120-360 min).

The calculations are validated by the reconstructed discontinuous infusion of the validation tracer. The actual infusion rates and the reconstructed infusion rates are shown in Fig. 9, documenting the ability of the free-format method to calculate even discontinuous appearance rates throughout the experiment.

View larger version (34K): [in this window] [in a new window]   Fig. 9.   Individual profiles of the validation tracer (D-[6,6-2H2]glucose) calculated by the free-format method (i.e., the same method used to calculate a free-format estimate of EGP) are compared with the actual piecewise constant infusion.

Quantitative analysis shows that 96 ± 5% of the total validation infusion was recovered (statistically not different from 100%) with a mean square error of 0.24 ± 0.02 µmol · kg¹ · min¹, which suggests good accuracy of free-format EGP calculations.

Stable-Label Two-Compartment Model of Glucose Kinetics during IVGTT

1

Minimal Model of Glucose Kinetics during IVGTT

View larger version (8K): [in this window] [in a new window]   Fig. 10.   Insulin sensitivity measured by the minimal model (SI) is closely related linearly to sensitivity of EGP (SIE) measured by the new model.

It was of interest to investigate the relationship between glucose effectiveness S_G and parameters of the newly developed model. However, S_G was not correlated with the non-insulin-dependent utilization, the inward/outward fractional transfer rates at basal conditions, or the basal EGP. This is possibly due to a narrow range of S_G values.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B APPENDIX C REFERENCES

By combining a dual-tracer methodology with a new model of glucose kinetics, we have separated three effects of insulin during an IVGTT. Insulin sensitivities of glucose distribution/transport, disposal, and production were quantified and their contributions to glucose lowering were assessed.

We were able to partition whole body insulin action into effects on glucose distribution/transport and glucose disposal by simultaneously administering 3-O-methyl-D-glucose and D-[U-¹³C]glucose, whereas glucose production was determined by additionally considering the kinetics of native glucose. The new model describes the kinetics of the two glucose tracers and native glucose by using a two-compartment structure for glucose and a one-compartment structure for each insulin effect. The model describes both steady-state (pre-IVGTT) and dynamic (IVGTT) conditions.

The results show that the liver plays an important role in the restoration of glucose homeostasis after an IVGTT. Suppression of EGP accounts for approximately one-half of the overall glucose-lowering effect. The peripheral effect accounts for the other half and is divided into two approximately similar components, which are attributed to the stimulation of distribution/transport and disposal.

EGP suppression results from both direct insulin effect (e.g., at the site of the liver) and indirect effect [e.g., FFA mediated (7)]. Thus our measure of insulin sensitivity of EGP suppression is a combined index of direct and indirect effects.

The conventional assessment of the insulin effect during IVGTT employs the (one-compartment) minimal model (6) with the administration and analysis of native glucose. As a result, the minimal model S_I is a mixture of the three insulin effects. Our analysis shows that, unexpectedly, the suppression of EGP dominates the mixed measure of S_I, as indicated by its highest correlation with S_IE (r = 0.96, P < 0.005). The other two effects are also represented (0.55  r  0.73). S_I is often associated with the insulin effect in the periphery, but our study shows that S_I reflects primarily liver sensitivity in healthy subjects.

Inward and outward transmembrane glucose transports have been estimated by Bonadonna and colleagues (9, 11) in skeletal muscle by use of a dual-tracer methodology. The rates were calculated by analyzing washout curves of L-glucose and labeled 3-O-methyl-D-glucose at the steady state. During fasting conditions in healthy subjects, values of inward transport were higher (0.066 ± 0.004 vs. 0.027 ± 0.004 min¹) and values of outward transport smaller (0.038 ± 0.003 vs. 0.065 ± 0.011 min¹), but still compatible with the present study.

Another estimate on the whole body level was obtained from a two-compartment model of glucose kinetics during basal and insulin-stimulated (hyperinsulinemic glucose clamp) conditions (20, 24). During basal conditions, similar values of the outward transport were obtained. The inward transport rate was slightly higher (0.043 ± 0.005 vs. 0.027 ± 0.004 min¹), but it should be noted that glucose disposal was partitioned in a 3:1 ratio between the accessible and nonaccessible compartments to overcome an identifiability problem. During the insulin-stimulated conditions (~100 mU/l), the inward transport increased approximately twofold (which compares with values obtained in the present study), whereas the outward transport was slightly reduced.

At basal state, insulin exerts a relatively small control over glucose disposal. Data shown in Table 1 indicate that a model-based estimate of insulin-dependent glucose uptake is ~1.4 µmol · kg¹ · min¹ (EGP_b  F₀₁) or ~13% of the total glucose turnover. At basal conditions, non-insulin-dependent glucose uptake dominates. This is in agreement with observations made by others (8) and is also compatible with studies showing that acute suppression of basal insulin levels has only a limited effect on whole body glucose utilization [<20% (22, 23)].

The relative "unimportance" of insulin-dependent disposal at basal insulin also explains that insulin is "less" effective in promoting glucose uptake than at physiological hyperinsulinemia. Raising basal insulin by 50% results, in our model, in a 50% increment in insulin-dependent glucose uptake, but this increases whole body glucose disposal by only ~7%. However, when insulin-dependent disposal dominates, such as during hyperinsulinemic clamps (e.g., insulin infusion at 0.5 mU · kg¹ · min¹), insulin has a nearly proportional effect on glucose disposal (subject to reaching saturation of its action).

The model gives temporal patterns of insulin actions. Glucose disposal is rapidly activated fourfold above basal and quickly deactivated, with a half-time of 12 min. Glucose distribution/transport is activated much more slowly, 1.6-fold above basal [compared with 1.6- to 2.0-fold increase in GLUT4 content in skeletal muscle plasma membranes in healthy subjects at physiological levels of insulin (48)]; it is deactivated again very slowly, with a half-time of 200 min, and remains elevated at the end of the study. EGP is suppressed in a similar temporal pattern as glucose disposal is activated. The half-time of deactivation of EGP suppression (30 min) compares with that of glucose disposal.

Together, these data show that insulin activates and deactivates intracellular disposal and EGP quickly, whereas glucose distribution/transport is activated/deactivated slowly, explaining the "memory" effect of insulin, i.e., the observation that glucose clearance is elevated well beyond the time when insulin returns to its basal level.

The effect of insulin and its partitioning can be expressed at steady-state conditions or during dynamic conditions. Insulin sensitivities and clearance rates such as the minimal model S_I or the newly defined S_IT (and the end-stage glucose infusion rate during glucose clamps) are measures of insulin action at an incremental insulin concentration extrapolated to steady-state conditions. On the other hand, AUCs of glucose-lowering profiles, such as those evaluated in the present study, are measures of insulin effects during specific dynamic conditions. The benefit of the former is that they are, in principle, independent of the test and characterize the metabolic system. However, they may provide an inaccurate impression about the amount of glucose removed via the insulin-dependent pathway. This is due to the nonlinearity of the glucose system and the delayed onset of insulin actions. The present study therefore evaluates both modalities (i.e., insulin sensitivities and glucose-lowering AUCs), because they provide complementary information.

Insulin temporal action can be represented in three ways. First, there are the effect (remote) compartments, which represent the direct stimulation of physiological phenomena such as the recruitment of glucose transporters or the stimulation of glucose phosphorylation (see Fig. 4, top). Second, glucose fluxes quantify the flow rates between/to/out of compartments and provide information about the absolute movement of the glucose mass (see Fig. 4, bottom). Finally, glucose-lowering profiles reflect changes in plasma glucose due to a negative