Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT

Partitioning glucose distribution/transport, disposal,and endogenous production during IVGTT

ROMAN HOVORKA,1 FARIBA SHOJAEE-MORADIE,2 PAUL V. CARROLL,2

LUDOVIC J. CHASSIN,1 IAN J. GOWRIE,1 NICOLA C. JACKSON,2

ROMULUS S. TUDOR,1 A. MARGOT UMPLEBY,2 AND RICHARD H. JONES2

1Centre for Measurement and Information in Medicine, City University,London EC1V 0HB; and 2Department of Diabetes and Endocrinology,GKT School of Medicine, St. Thomas’ Hospital, London SE1 7EH, United KingdomReceived 10 July 2001; accepted in final form 17 December 2001

Hovorka, Roman, Fariba Shojaee-Moradie, Paul V.Carroll, Ludovic J. Chassin, Ian J. Gowrie, Nicola C.Jackson, Romulus S. Tudor, A. Margot Umpleby, andRichard H. Jones. Partitioning glucose distribution/trans-port, disposal, and endogenous production during IVGTT. Am JPhysiol Endocrinol Metab 282: E992–E1007, 2002. First pub-lished January 2, 2002; 10.1152/ajpendo.00304.2001.—We haveseparated the effect of insulin on glucose distribution/transport,glucose disposal, and endogenous production (EGP) during anintravenous glucose tolerance test (IVGTT) by use of a dual-tracer dilution methodology. Six healthy lean male subjects (age33 � 3 yr, body mass index 22.7 � 0.6 kg/m2) underwent a 4-hIVGTT (0.3 g/kg glucose enriched with 3–6% D-[U-13C]glucoseand 5–10% 3-O-methyl-D-glucose) preceded by a 2-h investiga-tion under basal conditions (5 mg/kg of D-[U-13C]glucose and 8mg/kg of 3-O-methyl-D-glucose). A new model described thekinetics of the two glucose tracers and native glucose with theuse of a two-compartment structure for glucose and a one-compartment structure for insulin effects. Insulin sensitivitiesof distribution/transport, disposal, and EGP were similar(11.5 � 3.8 vs. 10.4 � 3.9 vs. 11.1 � 2.7 � 10�2 ml�kg�1�min�1

per mU/l; P � nonsignificant, ANOVA). When expressed interms of ability to lower glucose concentration, stimulation ofdisposal and stimulation of distribution/transport accountedeach independently for 25 and 30%, respectively, of the overalleffect. Suppression of EGP was more effective (P � 0.01,ANOVA) and accounted for 50% of the overall effect. EGP wassuppressed by 70% (52–82%) (95% confidence interval relativeto basal) within 60 min of the IVGTT; glucose distribution/transport was least responsive to insulin and was maximallyactivated by 62% (34–96%) above basal at 80 min comparedwith maximum 279% (116–565%) activation of glucose disposalat 20 min. The deactivation of glucose distribution/transportwas slower than that of glucose disposal and EGP (P � 0.02)with half-times of 207 (84–510), 12 (7–22), and 29 (16–54) min,respectively. The minimal-model insulin sensitivity was tightlycorrelated with and linearly related to sensitivity of EGP (r �0.96, P � 0.005) and correlated positively but nonsignificantlywith distribution/transport sensitivity (r � 0.73, P � 0.10) anddisposal sensitivity (r � 0.55, P � 0.26). We conclude that,in healthy subjects during an IVGTT, the two peripheral insu-lin effects account jointly for approximately one-half of theoverall insulin-stimulated glucose lowering, each effect contrib-

uting equally. Suppression of EGP matches the effect in theperiphery.

glucose kinetics; compartment modeling; D-[U-13C]glucose;3-O-methyl-D-glucose; insulin action; glucose transport; glu-cose disposal; endogenous glucose production; intravenousglucose tolerance test

Glossary

New Model

EGP0 Endogenous glucose productionextrapolated to zero insulin con-centration (mmol/min)

EGPb EGP at basal insulin concentra-tion (mmol/min)

F01 Total non-insulin-dependent glu-cose flux (mmol/min)

g1(t), g3(t) Concentrations of D-[U-13C]glu-cose and 3-O-methyl-D-glucosein the accessible compartment(mmol/l)

G(t) Total glucose concentration in theaccessible compartment (mmol/l)

I(t), Ib Plasma insulin and basal (preexperi-mental) plasma insulin (mU/l)

k03 Transfer rate constant of 3-O-meth-yl-D-glucose excretion (min�1)

k12 Transfer rate constant from non-accessible to accessible compart-ment (min�1)

ka1, ka2, ka3 Deactivation rate constants (min�1)kb1, kb2, kb3 Activation rate constants (min�2

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)

Address for reprint requests and other correspondence: R. Ho-vorka, Metabolic Modelling Group, Centre for Measurement andInformation in Medicine, City University, Northampton Square,London EC1V 0HB, UK (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by thepayment of page charges. The article must therefore be herebymarked ‘‘advertisement’’ in accordance with 18 U.S.C. Section 1734solely to indicate this fact.

Am J Physiol Endocrinol Metab 282: E992–E1007, 2002.First published January 2, 2002; 10.1152/ajpendo.00304.2001.

0193-1849/02 $5.00 Copyright © 2002 the American Physiological Society http://www.ajpendo.orgE992

Q10 Initial mass of native glucose in theaccessible compartment (mmol)

SIT, SID, SIE Insulin sensitivity of glucose dis-tribution/transport, glucose in-tracellular disposal, and EGP(ml �min�1 �kg�1 per mU/l)

u1(t), u3(t) Bolus doses of D-[U-13C]glucoseand 3-O-methyl-D-glucose ad-ministered at 0 and 120 min(mmol/min)

U(t) Bolus dose of the unlabeled glu-cose administered at 120 min(mmol/min)

V Distribution volume of the accessi-ble compartment (liters)

x1(t), x2(t), x3(t) Remote effect of insulin on glucosedistribution/transport, glucose dis-posal, and EGP, respectively(min�1)

Two-Compartment Minimal Model

D Administered dose of D-[U-13C]glucoseat 120 min (mmol)

F01 Constant component of glucose up-take (fixed at 1 mg �kg�1 �min�1)

g(t) plasma concentration of D-[U-13C]glu-cose (mmol/l)

Ib Basal (postexperimental) insulin con-centration (mU/l)

k21, k12, k02 fractional rate parameters (min�1)ka Deactivation rate constant (min�1)kb Activation rate constant (min�2 per

mU/l)kp Proportional term of glucose disposal

(min�1)MCR Basal metabolic clearance rate of glu-

cose (ml �kg�1 �min�1)q1(t), q2(t) Masses of D-[U-13C]glucose in the two

compartments (mmol)SI

2* Insulin sensitivity (ml �kg�1 �min�1

per mU/l)V Volume of the accessible compart-

ment (liters)x(t) Remote insulin (min�1)

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 concen-

tration (mmol/l)Ib Basal (postexperimental) insulin concen-

tration (mU/l)p1 � SG Glucose effectiveness (min�1)

p2 Deactivation rate constant (min�1)p3 Activation rate constant (min�2 per mU/l)SI Insulin sensitivity (min�1 per mU/l)V Distribution volume (liters)

x(t) Remote insulin (min�1)

INSULIN IS A POTENT ANABOLIC HORMONE, which activatesmetabolic pathways to regulate glucose metabolismand maintain homeostasis. Insulin stimulates glucosetransmembrane transport and intracellular glucosedisposal while also suppressing endogenous glucoseproduction (EGP).

These pathways are measurable in particular tis-sues/organs by use of imaging methods such as nuclearmagnetic resonance spectroscopy (18, 42) or multiple-tracer dilution techniques (11, 39). Techniques such asthe glucose clamp or the minimal-model analysis of anintravenous glucose tolerance test (IVGTT) providewhole body aggregated measures of insulin action (5)without the ability to separate the three effects, withthe exception of estimating EGP and peripheral glu-cose uptake during a labeled IVGTT (15, 27) or clamp(34, 35).

The sensitivity of glucose transport to insulin andthe temporal pattern of its activation are currentlyunknown at the whole body level. Similarly, it is cur-rently unknown to what extent the three pathwayscontribute to glucose lowering during dynamic condi-tions such as an IVGTT. Recent studies with miceindicate that a muscle-specific insulin receptor knock-out does not alter glucose tolerance (12), raising ques-tions about the relative importance of insulin-activatedpathways.

The present study was designed to estimate simul-taneously the effect of insulin on glucose distribu-tion/transport, glucose disposal, and EGP during anIVGTT. The aim was to compare the three pathwaysboth in terms of their sensitivities to insulin and intheir abilities to lower plasma glucose concentration.We employed a dual-tracer technique with the ad-ministration of D-[U-13C]glucose, a stable-label tracer in-distinguishable from native glucose, and 3-O-methyl-D-glucose, a marker of glucose transport. The data wereanalyzed using a novel model of glucose kinetics. Valida-tion of an EGP estimate was facilitated by administeringand reconstructing a variable infusion of another stable-label tracer, D-[6,6-2H2]glucose.

METHODS

Subjects and Experimental Protocol

Six healthy lean male subjects (age 33 � 3 yr, body massindex 22.7 � 0.6 kg/m2; means � SE) participated in thestudy, which was approved by the Ethics Committee, Guy’sand St. Thomas’ National Health Service Trust. Subjectsprovided written informed consent.

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

At �0830, a Venflon cannula was inserted into a vein ineach antecubital fossa. One cannula was used for samplingand the other for the administration of glucose infusates,which were given via a Harvard pump (Harvard Instru-ments, Millis, MA) and an IVAC 560 pump (IVAC, SanDiego, CA). The experiment commenced after a rest periodof �30 min. The subjects remained supine during the

E993PARTITIONING INSULIN ACTION

AJP-Endocrinol Metab • VOL 282 • MAY 2002 • www.ajpendo.org

studies and were allowed to sip water but otherwise had nooral intake.

At 0 min, an intravenous bolus was given of D-[U-13C]glu-cose (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 adminis-tered (0.3 g/kg, 50% aqueous dextrose solution over 1 min)enriched with D-[U-13C]glucose (subject 1: 20 mg/kg; subjects2–6: 10 mg/kg; the dose was reduced, because satisfactoryresolution of measurements was achieved with the lowerdose 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) intravenousinfusion of D-[6,6-2H2]glucose (range: 0–0.4, average: 0.2mg �kg�1 �min�1; MassTrace, Woburn, MA) with a time stepof 5–30 min started at 90 min and continued until the end ofthe study. The purpose of the infusion was to validate calcu-lations 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

All samples were immediately centrifuged, separated, andstored at �20°C until assayed.

Mass spectrometry analysis. Details of analysis have beenpublished previously (41). In brief, plasma samples werederivatized to obtain volatile esters of penta-O-trimethyl-silyl-D-glucose-O-methoxime by use of a modification of amethod described by Laine and Sweeley (33). Gas chroma-tography was performed on a Hewlett-Packard model 5890Series II with a Hewlett-Packard model 7673 autosampler(Hewlett-Packard, Woking, UK). Mass spectrometry analysiswas performed with a Hewlett-Packard model 5971A mass-selective detector. In the selected-ion monitoring mode, thefollowing ions were measured: mass-to-charge ratio (m/z) 261(M � 0) and 264 (M � 3) for 3-O-methyl-D-glucose and theinternal 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]glu-cose.

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

Data Analysis

Tracer-to-tracee ratio and tracer concentrations. Thetracer-to-tracee ratio (TTR) was calculated on the basis of thework by Cobelli et al. (21), with further elaboration by Rosen-blatt et al. (38). TTR represents a ratio of exogenously orig-inating glucose to endogenously originating glucose in thesample. In the case of 3-O-methyl-D-glucose, the endogenouscomponent is replaced by the internal standard.

The formulas to calculate TTR and concentrations ofD-[6,6-2H2]glucose, D-[U-13C]glucose, and recycled glucoseare given in APPENDIX A.

Modeling glucose kinetics. The new model describes thebasal period and the IVGTT. We used a two-compartmentstructure, which described adequately and simultaneouslythe kinetics of D-[U-13C]glucose, 3-O-methyl-D-glucose, andnative glucose and reflects current physiological knowledge(1, 16). The accessible glucose compartment (where measure-ments are made) represents plasma and tissues that equili-brate quickly with plasma. It contains plasma distributionspace and a portion of the interstitial distribution space (30).The nonaccessible compartment represents the slowly equil-ibrating pool and contains the remaining interstitial spaceand the intracellular distribution space.

It has been shown that insulin stimulates the transferfrom the accessible to the nonaccessible compartment (in-ward transfer) but fails to stimulate the reverse (outward)transfer at insulin concentrations comparable to those ob-served during an IVGTT (20). This observation of the selec-tive stimulation of inward transfer is consistent with thegreater stimulation of inward transport across the cell mem-brane in human skeletal muscle (11), reflecting recruitmentof glucose transporters. Insulin has also been shown to en-hance vasodilatation of skeletal muscle vasculature (3) andto increase muscle blood flow and its dispersion (45). Thestimulation of the inward transfer might therefore representinsulin action on glucose transport and glucose distribution,although studies with L-[14C]glucose in rat (47) and dog (43)have shown that glucose distribution is not affected by insu-lin. Farther on in the text, we refer to the effect on inwardintercompartmental transfer as the effect on distribution/transport. The inward intercompartmental transfer repre-sents the transport across the endothelium, transport intotissues, potential recruitment of distribution space, andtransport into cells by glucose transporters.

3-O-methyl-D-glucose is transported by the same specifictransporters as native glucose, i.e., it has identical inwardand outward transmembrane fractional rates but, crucially,does not undergo further metabolism intracellularly (10, 13).It is renally excreted (25).

The model includes non-insulin-dependent glucose uti-lization, described as a constant outflow (i.e., independentof glucose concentration) from the accessible glucose com-partment. Others have used a combination of a constantand proportional outflow (15), but our preliminary work onthe model excluded the proportional component, because ittended to converge to zero when estimated from the data.Normally, the ability of glucose to promote its own disposal(glucose effectiveness) is modeled via the non-insulin-de-pendent pathway. In the present model, it is included inthe insulin-dependent pathway (removal from the nonac-cessible compartment), being consistent with recent obser-vations (17) and the fact that the non-insulin-dependentutilization, which corresponds to the utilization by thecentral nervous system, red blood cells, kidneys, and liver,is saturated at euglycemia. The insulin-dependent utiliza-tion represents the insulin-stimulated intracellular glu-cose disposal (glucose phosphorylation) in muscle and ad-ipose tissues and is represented by an outflow from thenonaccessible compartment.

The model includes the effect of insulin on EGP suppres-sion in a formulation independent of glucose concentration.The model structure is shown in Fig. 1.

E994 PARTITIONING INSULIN ACTION


Formally, the model consists of two compartments repre-senting the kinetics of D-[U-13C]glucose

dq1�tdt

� � � F01

VG�t� x1�t�q1�t � k12q2�t � u1�t q1�0 � 0

(1)

dq2�tdt

� x1�tq1�t � k12 � x2�t�q2�t q2�0 � 0 (2)

g1�t �q1�t

V(3)

two compartments representing the kinetics of 3-O-methyl-D-glucose

dq3�tdt

� � k03 � x1�t�q3�t � k12q4�t � u3�t q3�0 � 0

(4)

dq4�tdt

� x1�tq3�t � k12q4�t q4�0 � 0 (5)

g3�t �q3�t

V(6)

and two compartments representing kinetics of native glu-cose

dQ1�tdt

� � � F01

VG�t� x1�t�Q1�t � k12Q2�t

� EGP01 � x3�t� � U�t Q1�0 � Q10 (7)

dQ2�tdt

� x1�tQ1�t � k12 � x2�t�Q2�t

Q2�0 � Q1�0x1�0

x2�0 � k12

(8)

G�t �Q1�t � q1�t

V(9)

Insulin action is modeled by postulating three effect compart-ments (representing so-called remote insulin), affecting, inturn, glucose distribution/transport, disposal, and production

dx1�tdt

� � ka1x1�t � kb1I�t x1�0 �kb1

ka1Ib (10)

dx2�tdt

� � ka2x2�t � kb2I�t x2�0 �kb2

ka2Ib (11)

dx3�tdt

� � ka3x3�t � kb3I�t x3�0 �kb3

ka3Ib (12)

The meanings of the symbols are as follows: q1(t) and q2(t)represent the masses of D-[U-13C]glucose in the accessibleand the nonaccessible compartments, respectively (mmol);q3(t) and q4(t) represent the masses of 3-O-methyl-D-glucosein the two compartments, respectively (mmol); Q1(t) andQ2(t) represent the masses of native glucose in the twocompartments, respectively (mmol); Q10 represents the ini-tial mass of native glucose in the accessible compartment(mmol); x1(t), x2(t), and x3(t) represent the (remote) effect ofinsulin on glucose distribution/transport, glucose disposal,and EGP, respectively (min�1); k12 represents the transferrate constant from the nonaccessible to the accessible com-partment (min�1); F01 is the total non-insulin-dependentglucose flux (mmol/min); u1(t) and u3(t) represent bolus dosesof D-[U-13C]glucose and 3-O-methyl-D-glucose, respectively,administered at 0 and 120 min (mmol/min); U(t) representsthe bolus dose of the unlabeled glucose administered at 120min (mmol/min); k03 represents the transfer rate constant of3-O-methyl-D-glucose excretion (min�1); ka1, ka2, and ka3

represent deactivation rate constants (min�1); kb1, kb2, andkb3 represent activation rate constants (min�2 per mU/l); I(t)and Ib represent plasma insulin and basal (preexperimental)plasma insulin, respectively (mU/l); EGP0 represents endog-enous glucose production extrapolated to the zero insulinconcentration (mmol/min); V represents the distribution vol-ume of the accessible compartment (liters); g1(t) and g3(t)represent concentrations of D-[U-13C]glucose and 3-O-methyl-D-glucose, respectively (mmol/l); and G(t) is the totalglucose concentration (mmol/l).

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 tolerancetest (IVGTT). GV, total glucose concentration � volume.



Insulin sensitivity of glucose distribution/transport (SIT)and glucose disposal (SID) describe the effect of insulin on themetabolic clearance rate (MCR) of glucose. Insulin sensitivityof EGP (SIE) represents a reciprocal concept to the change inthe metabolic clearance (a change in EGP expressed as aglucose volume per unit time), and overall sensitivity[SI(T�D�E); all ml �min�1 �kg�1 per mU/l] describes the com-bined effect of insulin.

SIT represents the change in the glucose clearance rate dueto elevated glucose distribution/transport while annullingthe other two effects. Similarly, SID and SIE represent theindependent effect of insulin due to stimulated glucose dis-posal and suppressed EGP, respectively (see APPENDIX B for aformal definition of the sensitivities).

The model has twelve parameters: k12, k03, F01, ka1, kb1,ka2, kb2, ka3, kb3, EGP0, Q10, and V, with an alternativeparameterization: SIT

f � kb1/ka1, SIDf � kb2/ka2, and SIE

f �kb3/ka3. The model is theoretically identifiable (proof notshown). The glucose concentration of the two tracers and thetotal glucose was zero, weighted at 122 and 123 min duringthe parameter estimation process to allow glucose distribu-tion to be completed within the accessible compartment.

Stable-label two-compartment model of glucose kineticsduring IVGTT. For comparison, we estimated parametersof the stable-label two-compartment model of glucose kinet-ics during an IVGTT described by a set of differential equa-tions (46)

dq1�tdt

� � �kp �F01

VG�t� k21�q1�t � k12q2�t q1�0 � D

dq2�tdt

� � k02 � x�t � k12�q2�t � k21q1�t q2�0 � 0

dx�tdt

� � kax�t � kbI�t � Ib� x�0 � 0

g�t �q1�t

V

where q1(t) and q2(t) are masses of the tracer glucose in thetwo compartments (mmol); V is the volume of the accessiblecompartment (liters); kp is the proportional term of glucosedisposal (min�1); k21, k12, and k02 are fractional rate param-eters (all min�1); x(t) represents the remote insulin (min�1);kb (min�2 per mU/l) and ka (min�1) have similar meaning asp3 and p2 of the one-compartment minimal model; F01 is theconstant component of glucose uptake [fixed at 1 mg �kg�1 �min�1 (8)]; g(t) is plasma concentration of D-[U-13C]glucose(mmol/l); and D is the administered dose of D-[U-13C]glucoseat 120 min (mmol). The proportional term of glucose disposalkp is constrained to produce insulin-independent utilizationthree times higher than the insulin-dependent utilization atthe basal glucose concentration (Gb) and the basal insulinconcentration (Ib)

kp �3k21k02

k02 � k12�

F01

VGb

guaranteeing theoretical identifiability of the model. Themodel has six parameters k21, k12, k02, V, ka, and kb. Allmeasurements were included in parameter estimation.

The basal MCR of glucose (ml �kg�1 �min�1) and the insu-lin sensitivity index SI

2* (ml �kg�1 �min�1 per mU/l) are cal-culated as

MCR �F01

Gb� Vkp �

Vk21k02

k02 � k12

S12* �

Vk21k12kb

ka�k02 � k122

Minimal model of glucose kinetics during IVGTT. We alsoestimated parameters of the minimal model to enable com-parison with the newly developed model. The minimal modelof glucose kinetics after an IVGTT is described by two differ-ential equations (6)

dG�t � � p1 � x�t�G�t � p1Gb G�0 �DV

dx�t � � p2x�t � p3I�t � Ib� x�0 � 0

where G(t) is the plasma concentration of total (labeled andunlabeled) glucose (mmol/l); x(t) represents the remote insu-lin (min�1); Gb is the basal glucose concentration (mmol/l); Dis the (total) glucose dose (mmol); and p1 (min�1), p2 (min�1),p3 (min�2 per mU/l), and V (liters; the distribution volume)are model parameters. Insulin sensitivity (SI; min�1 permU/l) is defined as the ratio SI � p3/p2 and glucose effective-ness as SG � p1.

The glucose concentration was zero weighted from 2 to 5min after the administration of the unlabeled glucose bolus.

Free-format reconstruction of EGP. EGP was also calcu-lated without imposing a relationship to insulin by using avariation of deconvolution methodology. Details are given inAPPENDIX C. In brief, D-[U-13C]glucose and 3-O-methyl-D-glu-cose (i.e., excluding native glucose) were employed to esti-mate the time-variant unit impulse response of the glucosesystem. An advanced numerical approach (regularized de-convolution with nonnegative constraint) calculated free-for-mat EGP.

These free-format calculations of EGP were validatedby reconstructing the infusion of the validation tracer (D-[6,6-2H2]glucose) (see APPENDIX C). The difference betweenthe reconstructed rates and the actual rates of the valida-tion tracer indicates the accuracy of the free-format estimateof EGP.

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

The measurement errors associated with D-[U-13C]glucose,D-[6,6-2H2]glucose, and 3-O-methyl-D-glucose were deter-mined experimentally from duplicate measurements. Belowa threshold concentration of 0.153 mmol/l, the standard de-viation (SD) of the measurement error associated with D-[U-13C]glucose was constant at 0.00133 mmol/l; above thethreshold, the coefficient of variation (CV) of the measure-ment error was constant at 0.87%. For D-[6,6-2H2]glucose, thethreshold concentration was 0.130 mmol/l, SD was 0.00593mmol/l, and the CV was 4.57%. For 3-O-methyl-D-glucose, thethreshold concentration was 0.07 mmol/l, SD was 0.00188mmol/l, and the CV was 2.68%.

The accuracy of parameter estimates was obtained fromthe inverse of the Fisher information matrix (14). The SAAMII v1.1.1 package (SAAM Institute, Seattle, WA) was em-ployed to carry out the calculations.

Statistical Analysis

Correlations were evaluated employing the Pearson corre-lation coefficient. Analysis of variance (ANOVA) with Tukey’s



post hoc analysis was employed to assess the relative contri-butions of the three insulin effects and their combinations onglucose lowering. ANOVA was also employed to compare thethree insulin sensitivities. Values are represented asmeans � SE or as mean (95% confidence interval) (log trans-formed to assure normality) unless stated otherwise.

RESULTS

Plasma Glucose, Insulin, and Glucose Tracers

The profiles of plasma glucose, plasma insulin, D-[U-13C]glucose, and 3-O-methyl-D-glucose during anIVGTT are shown in Fig. 2. Plasma glucose concentra-tion was raised from the basal level of 5.4 � 0.2 mmol/lto a maximum of 14.9 � 1.2 mmol/l at 122 min. Plasmainsulin and plasma C-peptide concentrations increasedfrom 8.0 � 0.2 mU/l and 0.43 � 0.07 nmol/l to amaximum of 96.5 � 56.9 mU/l and 1.67 � 0.75 nmol/lat 125 and 128 min, respectively. We observed a highinterindividual variability in the insulin response tothe unlabeled glucose bolus (Fig. 2).

The insulin profiles and the C-peptide profiles (notshown) demonstrated that the bolus of glucose tracersat 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 dou-ble-peak profile with the peaks well defined. The pro-files were smooth and confirmed the low level ofmeasurement error. The average concentration of re-cycled glucose was 0.007 mmol/l, with a maximumconcentration of 0.015 � 0.004 nmol/l at 125 min and adecrease to 0.006 � 0.003 mmol/l at the end of thestudy (profile not shown). These values were negligiblein comparison with D-[U-13C]glucose and D-[6,6-2H2]glucose concentrations.

Modeling Glucose Kinetics

The sample fit of the model to D-[U-13C]glucose, 3-O-methyl-D-glucose, and total glucose is shown in Fig. 3.Table 1 lists the parameters of the model and includesEGP at the basal insulin concentration. Before theinjection of unlabeled glucose, the fractional transferrate from the accessible to the nonaccessible compart-ment (inward rate) and insulin-mediated glucose dis-posal were 0.0266 � 0.0044 and 0.0042 � 0.0012min�1. After the bolus administration at 120 min, thesuppression of EGP followed the profile presented bythe activated glucose disposal more closely than that ofglucose distribution/transport (Fig. 4). EGP was sup-pressed by 70% (52–82%) (relative to basal) within 60min of the bolus administration. Glucose distribution/transport was maximally activated by 62% (34–96%)above basal at 80 min compared with maximum 279%(116–565%) activation of glucose disposal at 20 min.The deactivation of glucose distribution/transport wasslower than that of glucose disposal and EGP (P �0.02) with half-times of 207 (84–510), 12 (7–22), and 29(16–54) min, respectively.

Insulin sensitivities of distribution/transport, dis-posal, and EGP were similar [see Table 2; P � nonsig-

nificant (NS), ANOVA]. Insulin sensitivity of distribu-tion/transport was positively correlated with that ofdisposal (SIT vs. SID, r � 0.82, P � 0.05) but not withthat of EGP (SIT vs. SIE, r � 0.58, P � 0.23). EGP anddisposal sensitivities were not significantly correlated(SIE vs. SID, r � 0.50, P � 0.32).

The plot of weighted residuals is shown in Fig. 5. Theaverage SD of weighted residuals during the basal

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 adose of 10 and 16 mg/kg, respectively, at 120 min.



period tended to be smaller than that after the unla-beled 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 mea-surement error for all three substrates and a slightlybetter fit during the basal period than during theIVGTT.

Simulation runs with the model facilitated the sep-aration of the three effects of insulin on glucose lower-ing during IVGTT. The model was run in eight config-urations: 1) the three effects [i.e., the remote insulincompartments x1(t), x2(t), and x3(t)] following theirnominal (stimulated) levels during IVGTT; 2) the threeeffects fixed at their basal (i.e., 120-min) levels; 3–5)one effect following its nominal level and the other twoeffects fixed at their basal levels; and 6–8) two effectsfollowing their nominal levels and one effect fixed at itsbasal level.

Figure 6 shows the results of configurations 1 and3–5 relative to the baseline configuration (2) (the three

Fig. 3. Sample model fit to data measured in subject 5.

Table 1. Parameter estimates of the model of 3-O-methyl-D-glucose, D-[U-13C]glucose, and native glucoseduring a basal period and an IVGTT

Subject

k03 k12 kb1 kb2 kb3 SITf † SID

f † SIEf † F01 V EGP0 EGPb‡

(min�1) (10�4 � min�1

per mU/l)(10�4 �

per mU/l)(�mol �kg�1

�min�1)(l/kg) (�mol �kg�1

�min�1)

1 0.0075(2)*

0.0343(6)

0.0031(15)

0.0752(267)

0.0472(17)

29.4(4)

0.9(24)

401(2)

12.1(3)

0.18(1)

14.8(3)

12.1

2 0.0095(2)

0.0871(8)

0.0157(12)

0.0231(27)

0.0143(6)

18.7(11)

6.1(8)

379(2)

7.5(2)

0.13(1)

14.3(2)

8.9

3 0.0067(2)

0.0863(14)

0.0029(28)

0.0495(21)

0.0691(21)

81.2(12)

20.1(6)

578(4)

10.3(3)

0.22(2)

15.6(2)

12.0

4 0.0116(2)

0.0968(5)

0.0088(10)

0.0302(45)

0.0118(10)

86.1(7)

4.7(14)

720(4)

11.9(3)

0.14(2)

21.3(5)

13.4

5 0.0078(2)

0.0390(6)

0.0007(69)

0.1631(57)

0.0114(10)

72.4(11)

15.3(13)

961(3)

7.1(7)

0.14(1)

20.0(5)

10.7

6 0.0096(2)

0.0458(5)

0.0017(14)

0.0689(16)

0.0285(12)

19.1(4)

2.2(5)

81(5)

9.2(2)

0.13(1)

10.5(2)

9.5

Mean 0.0088 0.0649 0.0055 0.0683 0.0304 51.2 8.2 520 9.7 0.16 16.1 11.1�SE 0.0007 0.0115 0.0023 0.0207 0.0096 13.1 3.2 125 0.9 0.01 1.6 0.7

IVGTT, intravenous glucose tolerance test; parameters defined in GLOSSARY. *Accuracy of a parameter estimate expressed as a fractionalstandard deviation (%) . †SIT

f � kb1/ka1, SIDf � kb2/ka2, and SIE

f � kb3/ka3 used as an alternative parameterization. ‡Basal endogenous glucoseproduction (EGP) evaluated before the bolus given at 120 min.

Fig. 4. Mean insulin action (relative to basal; n � 6) (top) and meanglucose fluxes (bottom) associated with glucose distribution/trans-port [x1(t) and F21(t)], glucose disposal [x2(t) and F02(t)], and endog-enous glucose production (EGP) [x3(t) and EGP(t)]. Also in bottom:the reverse glucose flux from the nonaccessible compartment to theaccessible compartment [F12(t)] and the non-insulin-dependent dis-posal from the accessible compartment [F01(t)].



effects fixed at their basal levels). It is demonstratedthat suppression of EGP has the greatest and longestimpact on glucose lowering and accounts, at its maxi-mum, for �3 mmol/l out of the lowering magnitude of 6mmol/l. The effects of stimulated glucose distribution/transport and stimulated glucose disposal are smallerbut similar.

Glucose-lowering activities were quantified by areaunder the curve (AUC) of glucose differential profilesshown in Fig. 6 (see Fig. 7). Stimulation of disposal andstimulation of distribution/transport account each in-dependently 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 theoverall glucose-lowering AUC. The combination ofstimulated glucose disposal and stimulated glucosedistribution/transport is less potent than the two com-binations associated with EGP suppression (P � 0.05,ANOVA).

EGP

Individual profiles of EGP obtained by 1) free-formatcalculations and 2) model-based calculations are

shown in Fig. 8, documenting a similar pattern ob-tained by the two methods. When the two methodswere compared, AUCs associated with the EGP profileswere identical during the basal period (1,269 � 70 vs.1,265 � 71 �mol �kg�1 �min�1 for 120 min; P � NS,paired t-test), but during the IVGTT the free-formatmethod gave 16% lower AUC (1,455 � 180 vs. 1,737 �156 �mol �kg�1 �min�1 for 240 min; P � 0.005, pairedt-test), which was highly correlated with that obtainedby the model-based calculations (r � 0.95, P � 0.005).

The calculations are validated by the reconstructeddiscontinuous infusion of the validation tracer. Theactual infusion rates and the reconstructed infusionrates are shown in Fig. 9, documenting the ability of

Table 2. Insulin sensitivity associated with glucosedistribution/transport (SIT), glucose disposal (SID),glucose production (SIE); and overall sensitivity(SI(T�D�E))

Subject SIT SID SIE SI(T � D � E)

1 1.2 4.7 9.0 14.92 10.2 4.7 6.8 21.73 27.1 27.9 14.3 69.34 9.1 15.0 15.2 39.35 16.8 7.3 19.9 44.06 4.7 2.6 1.6 8.9

Mean 11.5 10.4 11.1 33.0�SE 3.8 3.9 2.7 9.2

Values are expressed as 10�2 � ml �min�1 �kg�1 per mU/l.

Fig. 5. Weighted residuals (means � SD; n � 6) associated withD-[U-13C]glucose, 3-OMG, and total glucose. Weighted residuals rep-resent differences between model fit and measurements normalizedby the measurement error.

Fig. 6. Glucose-lowering profiles during IVGTT with separate as-sessment of insulin effect on stimulating glucose distribution/trans-port, stimulating glucose disposal, and suppressing EGP. Profiles arerelative to baseline, which corresponds to “no incremental insulineffect” (the 3 effects fixed at their basal levels). The results wereobtained by model simulation with individual parameters (n � 6).

Fig. 7. Glucose lowering during IVGTT, with separate assessment ofthe insulin effect on stimulating glucose distribution/transport, stim-ulating glucose disposal, and suppressing EGP and combinations ofthe effects. Results are obtained by calculating areas under the curve(AUCs) of profiles such as those shown in Fig. 6.



the free-format method to calculate even discontinuousappearance rates throughout the experiment.

Quantitative analysis shows that 96 � 5% of thetotal validation infusion was recovered (statisticallynot different from 100%) with a mean square error of0.24 � 0.02 �mol �kg�1 �min�1, which suggests goodaccuracy of free-format EGP calculations.

Stable-Label Two-Compartment Model of GlucoseKinetics during IVGTT

The results of the stable-label two-compartmentmodel are given in Table 3. The two-compartmentmodel insulin sensitivity was tightly correlated withdistribution/transport sensitivity (SI

2* vs. SIT: r � 0.92,P � 0.01). It also correlated positively, but nonsignifi-cantly, with disposal sensitivity and sensitivity of EGP(SI

2* vs. SID: r � 0.73, P � 0.10; SI2* vs. SIE: r � 0.81, P �

0.05). SI2* was about one-half the sum of SIT and SID.

The mean deactivation rate of insulin action was sim-ilar to that of the deactivation of glucose disposal (kbvs. kb2, 0.0953 � 0.0143 vs. 0.0683 � 0.0207 min�1).

Minimal Model of Glucose Kinetics during IVGTT

The results of the minimal model of glucose kineticsare given in Table 4. The minimal model insulin sen-

sitivity index was tightly correlated with and linearlyrelated to sensitivity of EGP (SI vs. SIE: r � 0.96, P �0.005) (see Fig. 10). It also positively, but nonsignifi-cantly, correlated with disposal and distribution/trans-port sensitivities (SI vs. SID: r � 0.55, P � 0.26; SI vs.SIT: r � 0.73, P � 0.10). This indicates that the mini-mal model measures a mixture of the three indexes butprimarily reflects the insulin sensitivity of EGP.

It was of interest to investigate the relationshipbetween glucose effectiveness SG and parameters ofthe newly developed model. However, SG was not cor-related with the non-insulin-dependent utilization, theinward/outward fractional transfer rates at basal con-ditions, or the basal EGP. This is possibly due to anarrow range of SG values.

DISCUSSION

By combining a dual-tracer methodology with a newmodel of glucose kinetics, we have separated threeeffects of insulin during an IVGTT. Insulin sensitivi-ties of glucose distribution/transport, disposal, andproduction were quantified and their contributions toglucose lowering were assessed.

We were able to partition whole body insulin ac-tion into effects on glucose distribution/transport

Fig. 8. Individual profiles of EGP insubjects 1–6 calculated by 2 methods,model-based calculations and free-for-mat calculations, during basal condi-tions (0–120 min) and IVGTT (120–360 min).



and glucose disposal by simultaneously administer-ing 3-O-methyl-D-glucose and D-[U-13C]glucose, whereasglucose production was determined by additionallyconsidering the kinetics of native glucose. The newmodel describes the kinetics of the two glucose trac-

ers and native glucose by using a two-compartmentstructure for glucose and a one-compartment struc-ture for each insulin effect. The model describes bothsteady-state (pre-IVGTT) and dynamic (IVGTT) con-ditions.

Fig. 9. Individual profiles of the vali-dation tracer (D-[6,6-2H2]glucose) cal-culated by the free-format method (i.e.,the same method used to calculate afree-format estimate of EGP) are com-pared with the actual piecewise con-stant infusion.

Table 3. Parameter estimates of the stable-label two-compartment model of glucose kinetics during an IVGTT

Subjectk02,

min�1k12,

min�1k21,

min�1kb,

min�1SI

f†,10�4 � min�1 per mU/l

V,l/kg

MCR,ml �min�1 �kg�1

SI2*,

10�2 � ml �min�1 �kg�1 per mU/l

1 0.0042(14)*

0.0295(14)

0.0253(5)

0.0519(93)

3.7(20)

0.16(1)

2.08(3)

4.0(30)

2 0.0047(5)

0.2283(14)

0.2063(16)

0.1418(55)

4.6(7)

0.14(5)

2.38(4)

5.8(7)

3 0.0105(48)

0.0604(128)

0.0161(83)

0.0582(82)

59.6(50)

0.22(6)

2.12(6)

25.6(39)

4 0.0045(6)

0.1234(9)

0.0979(8)

0.1211(53)

9.4(6)

0.15(2)

2.10(3)

10.7(8)

5 0.0069(7)

0.2166(23)

0.0915(26)

0.0978(13)

33.3(7)

0.18(4)

1.99(3)

23.3(4)

6 0.0064(8)

0.0669(23)

0.0375(15)

0.1009(19)

4.6(9)

0.14(2)

1.89(3)

3.1(4)

Mean 0.0062 0.1209 0.0791 0.0953 19.2 0.17 2.09 12.1�SE 0.0010 0.0345 0.0290 0.0143 9.3 0.01 0.07 4.1

*Accuracy of a parameter estimate expressed as a fractional standard deviation(%). †SIf � kb/ka used as an alternative parameterization.



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

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

The conventional assessment of the insulin effectduring IVGTT employs the (one-compartment) mini-mal model (6) with the administration and analysis ofnative glucose. As a result, the minimal model SI is amixture of the three insulin effects. Our analysis showsthat, unexpectedly, the suppression of EGP dominatesthe mixed measure of SI, as indicated by its highestcorrelation with SIE (r � 0.96, P � 0.005). The othertwo effects are also represented (0.55 � r � 0.73). SI isoften associated with the insulin effect in the periph-ery, but our study shows that SI reflects primarily liversensitivity in healthy subjects.

Inward and outward transmembrane glucose trans-ports have been estimated by Bonadonna and col-leagues (9, 11) in skeletal muscle by use of a dual-tracer methodology. The rates were calculated byanalyzing washout curves of L-glucose and labeled 3-O-methyl-D-glucose at the steady state. During fastingconditions in healthy subjects, values of inward trans-port were higher (0.066 � 0.004 vs. 0.027 � 0.004min�1) and values of outward transport smaller(0.038 � 0.003 vs. 0.065 � 0.011 min�1), but stillcompatible with the present study.

Another estimate on the whole body level was ob-tained from a two-compartment model of glucose kinet-ics during basal and insulin-stimulated (hyperinsu-linemic glucose clamp) conditions (20, 24). Duringbasal conditions, similar values of the outward trans-port were obtained. The inward transport rate wasslightly higher (0.043 � 0.005 vs. 0.027 � 0.004min�1), but it should be noted that glucose disposalwas partitioned in a 3:1 ratio between the accessible

and nonaccessible compartments to overcome an iden-tifiability problem. During the insulin-stimulated con-ditions (�100 mU/l), the inward transport increasedapproximately twofold (which compares with valuesobtained in the present study), whereas the outwardtransport was slightly reduced.

At basal state, insulin exerts a relatively small con-trol over glucose disposal. Data shown in Table 1 indi-cate that a model-based estimate of insulin-dependentglucose uptake is �1.4 �mol �kg�1 �min�1 (EGPb � F01)or �13% of the total glucose turnover. At basal condi-tions, non-insulin-dependent glucose uptake domi-nates. This is in agreement with observations made byothers (8) and is also compatible with studies showingthat acute suppression of basal insulin levels has onlya limited effect on whole body glucose utilization[�20% (22, 23)].

The relative “unimportance” of insulin-dependentdisposal at basal insulin also explains that insulin is“less” effective in promoting glucose uptake than atphysiological hyperinsulinemia. Raising basal insulinby 50% results, in our model, in a 50% increment ininsulin-dependent glucose uptake, but this increaseswhole body glucose disposal by only �7%. However,when insulin-dependent disposal dominates, such asduring hyperinsulinemic clamps (e.g., insulin infusionat 0.5 mU �kg�1 �min�1), insulin has a nearly propor-tional effect on glucose disposal (subject to reachingsaturation of its action).

The model gives temporal patterns of insulin actions.Glucose disposal is rapidly activated fourfold abovebasal and quickly deactivated, with a half-time of 12min. Glucose distribution/transport is activated muchmore slowly, 1.6-fold above basal [compared with 1.6-to 2.0-fold increase in GLUT4 content in skeletal mus-cle plasma membranes in healthy subjects at physio-logical levels of insulin (48)]; it is deactivated againvery slowly, with a half-time of 200 min, and remainselevated at the end of the study. EGP is suppressed ina similar temporal pattern as glucose disposal is acti-

Fig. 10. Insulin sensitivity measured by the minimal model (SI) isclosely related linearly to sensitivity of EGP (SIE) measured by thenew model.

Table 4. Parameter estimates of the minimal modelduring an IVGTT

Subject p2, min�1 SG, min�1SI†, 10�4 � min�1

per mU/l V, l/kg

1 0.0243(0)* 0.0092(0) 4.2(0) 0.18(0)2 0.0245(6) 0.0078(9) 3.5(2) 0.12(0)3 0.0315(10) 0.0099(13) 8.3(4) 0.25(1)4 0.0441(24) 0.0057(58) 5.8(18) 0.19(3)5 0.0275(56) 0.0122(67) 10.3(18) 0.17(6)6 0.0291(51) 0.0245(42) 0.7(74) 0.13(9)

Mean 0.0302 0.0116 5.5 0.17�SE 0.0030 0.0027 1.4 0.02

*Accuracy of a parameter estimate expressed as a fractional stan-dard deviation (%). †SI � p3/p2 used as an alternative parameteriza-tion.



vated. The half-time of deactivation of EGP suppres-sion (30 min) compares with that of glucose disposal.

Together, these data show that insulin activates anddeactivates intracellular disposal and EGP quickly,whereas glucose distribution/transport is activated/de-activated slowly, explaining the “memory” effect ofinsulin, i.e., the observation that glucose clearance iselevated well beyond the time when insulin returns toits basal level.

The effect of insulin and its partitioning can beexpressed at steady-state conditions or during dynamicconditions. Insulin sensitivities and clearance ratessuch as the minimal model SI or the newly defined SIT(and the end-stage glucose infusion rate during glucoseclamps) are measures of insulin action at an incremen-tal insulin concentration extrapolated to steady-stateconditions. On the other hand, AUCs of glucose-lower-ing profiles, such as those evaluated in the presentstudy, are measures of insulin effects during specificdynamic conditions. The benefit of the former is thatthey are, in principle, independent of the test andcharacterize the metabolic system. However, they mayprovide an inaccurate impression about the amount ofglucose removed via the insulin-dependent pathway.This is due to the nonlinearity of the glucose systemand the delayed onset of insulin actions. The presentstudy therefore evaluates both modalities (i.e., insulinsensitivities and glucose-lowering AUCs), because theyprovide complementary information.

Insulin temporal action can be represented in threeways. First, there are the effect (remote) compart-ments, which represent the direct stimulation of phys-iological phenomena such as the recruitment of glucosetransporters or the stimulation of glucose phosphory-lation (see Fig. 4, top). Second, glucose fluxes quantifythe flow rates between/to/out of compartments andprovide information about the absolute movement ofthe glucose mass (see Fig. 4, bottom). Finally, glucose-lowering profiles reflect changes in plasma glucose dueto a negative net balance of glucose fluxes (see Fig. 6 foran example).

The three temporal profiles differ due to structuralproperties of the glucose system. For example, glucosedisposal (i.e., the insulin-dependent uptake) is acti-vated fast, but due to its structural distance from theaccessible (plasma) compartment, glucose loweringwill first be initiated in the nonaccessible (intracellu-lar) compartment, where it will depend on glucoseavailability, and then glucose removal will be propa-gated into the accessible compartment via an increasedconcentration gradient, creating a lag between thetemporal patterns.

Glucose distribution/transport is activated mostslowly and reaches a smaller fraction of its asymptotic(i.e., achievable at the steady state) value during anIVGTT compared with, say, the suppression of EGP.Together with the structural effect on the temporalpatterns as discussed above, this means that, althoughthe three pathways have identical effects on glucoseclearance at steady-state conditions as exemplified byidentical sensitivities, during dynamic conditions the

glucose-lowering potency differs. It therefore followsthat the study of the glucose system under dynamicconditions provides important and complementary in-formation about the actual contribution of metabolicpathways to glucose lowering compared with the pro-jected contributions obtained from studies at steady-state conditions such as glucose clamps.

The model includes a specification of EGP and itssuppression that is independent of glucose concentra-tion. In a separate analysis, we examined this asser-tion and postulated that EGP(t) � EGP0[1 � x3(t) �kLG(t)], where kL represents the effect of glucose onEGP suppression (1). However, such a formulation wasnot appropriate, as we observed no improvement in themodel fit, poor parameter accuracy, and no improve-ment in the Akaike information criterion (data notshown).

It is generally perceived that both glucose and insu-lin contribute to EGP suppression during an IVGTT(4). However, a study in subjects with type 1 diabetesclearly demonstrated that glucose on its own does notsuppress EGP during an IVGTT (37). The study in-volved two IVGTTs in each subject, one with “normal”insulin response and the second with basal insulin.Endogenous glucose concentration was calculated; thisconcentration corresponds to glucose originating fromendogenous sources, and the calculations are modelindependent. During the IVGTT with basal insulin,endogenous glucose concentration remained un-changed for �90 min after a glucose bolus, with atendency of endogenous glucose to increase toward theend of the IVGTT. This shows that EGP is not sup-pressed by glucose during an IVGTT when insulin ismaintained at basal level.

When insulin is elevated during an IVGTT, as in thepresent case, there is no direct evidence of an exacer-bated effect of glucose on EGP suppression. On thecontrary, with the use of data obtained from glucoseclamp studies, an increase in glucose has little or nofurther effect when glucose production is alreadymarkedly suppressed by elevated insulin concentra-tions (2, 36).

It therefore follows that, during glucose clamps, glu-cose substantially suppresses its production at basalinsulin, but this effect is negligible at elevated insulin.During shorter exposure, such as during an IVGTT,the glucose effect is not present even at basal insulin,supporting our formulation of EGP suppression.

We further assessed the correctness of the specifica-tion of EGP. We estimated a subset of model parame-ters related to D-[U-13C]glucose and 3-O-methyl-D-glu-cose but omitting native glucose (i.e., using Eqs. 1–6,10, and 11) from D-[U-13C]glucose and 3-O-methyl-D-glucose measurements (results not shown). The pa-rameter estimates were virtually identical to thosecalculated from the complete model (with the exceptionof parameters kb1 and SIT

f in subject 5, which were,respectively, six times higher and two times smaller),demonstrating model consistency and coherence.

The validity of model-derived EGP is supported by agood comparison with free-format estimation of EGP



(see Fig. 8). The free-format estimation is, in turn,validated by the infusion and accurate recovery of thevalidation tracer (see Fig. 9).

The two-compartment minimal model by Vicini et al.(46) can be seen as the immediate precursor of our newmodel. The insulin sensitivities SIT and SID dissect thetwo-compartment minimal model index SI

2*. It appearsthat SI

2* reflects primarily the sensitivity of the distri-bution/transport pathway, but its deactivation reflectsthat of the disposal pathway. Thus SI

2* mixes proper-ties of both pathways. However, the minimal modelunderestimates the sensitivity of the periphery (SI

2* isabout one-half of the sum of SIT and SID).

In our study, we used nonarterialized venous bloodcompared with the traditional use of arterialized ve-nous blood. It is known that, during an IVGTT, asignificant arteriovenous difference exists during 1–7min in the case of glucose and 1–2 min in the case ofinsulin concentration (26). This difference has littleeffect on estimates of insulin sensitivity using theminimal model (26). In our model, only two glucosemeasurements at 4 and 6 min are expected to beunderestimated, potentially affecting parameters esti-mated from the early stage of IVGTT, i.e., the volumeof distribution, non-insulin-dependent glucose disposal( 80% of total disposal), and the inward transport(modulated by SIT). However, the effect on SIT is likelyto be small, as above-basal, insulin-stimulated distri-bution/kinetics are elevated in later stages of IVGTT,providing information for their accurate estimation.

The new model does not have insulin actions xi(t)centered on the basal insulin (i.e., insulin action is notzero at basal insulin) as do the two minimal models.The new model represents insulin action above zeroinsulin concentration.

The traditional specification of xi(t) to representabove-basal action has theoretically attractive proper-ties: it is not assumed that at zero insulin the action iszero (as our model does). However, its practical usesuffers from several drawbacks. First, basal insulin ismeasured with error, and it is well recognized that thismeasurement error propagates into error in the esti-mate of insulin sensitivity. Furthermore, postexperi-mental values are used for basal insulin, because theseare normally lower than preexperimental values andthere is need to avoid negative insulin action at the endof IVGTT. Such a choice is difficult to justify on purelyphysiological grounds. Second, we wanted a model thatcould be used under other experimental scenarios suchas glucose clamp (40) to make direct comparison withIVGTT-derived indexes without the need to “correct”for different basal insulin values.

The partitioning of the peripheral effect into thedistribution/transport effect and the disposal effectrests on using an adequate model structure and obtain-ing a good fit to 3-O-methyl-D-glucose and D-[U-13C]glu-cose profiles. Physiological considerations guided theconstruction of the model (see DATA ANALYSIS). The eval-uation of the residuals demonstrates the ability of themodel to fit the data throughout the experiment (seeFig. 5).

Normalized residuals were at times outside the �2to �2 range. This applies mainly to 3-O-methyl-D-glucose and D-[U-13C]glucose after administration ofboluses and to unlabeled glucose toward the end of theIVGTT. The accuracy of analytical techniques associ-ated with 3-O-methyl-D-glucose and D-[U-13C]glucosemeasurements is very high, resulting in very largeweights when calculating weighted residuals. Sam-pling time error during frequent sampling stages (afteradministration of boluses) therefore exerts an exacer-bated effect on the lack of fit and explains part of theobservations. EGP is known to decrease during pro-longed fasting, and this may explain the lack of fittoward the end of the experiment in relation to theunlabeled glucose.

It is important to stress that the validity of our modelis limited to the conditions observed in the presentstudy; i.e., the model describes kinetic events related toglucose disposal and glucose production during basalconditions and during an IVGTT. Extrapolations toother conditions, such as sustained hyperinsulinemiaobserved during glucose clamps, need model modifica-tions such as the inclusion of saturable inward trans-port (40).

There are considerable interindividual variations inthe partitioning of insulin sensitivities and the relativeand absolute contribution of the three pathways toglucose lowering. Further studies investigating the ef-fect of various pathological conditions and diseases,particularly type 2 and type 1 diabetes, are warrantedto link molecular, cellular, and whole body defects (9,12, 18, 48).

In conclusion, we have partitioned the effect of insu-lin on glucose kinetics during an IVGTT into threecomponents, which represent stimulated glucose dis-tribution/transport, stimulated glucose disposal, andsuppressed endogenous glucose production. In healthysubjects, the two peripheral effects account jointly forapproximately one-half of the overall insulin-stimu-lated glucose lowering, each effect contributing equally.Suppression of endogenous glucose production matchesthe effect in the periphery.

APPENDIX A: CALCULATING TRACER-TO-TRACEERATIO

The formulas to calculate TTR of D-[6,6-2H2]glucose (zD),D-[U-13C]glucose (zU), and recycled glucose (zR) in the mix-ture of tracee and tracers (sample) are

zD �1Dc

1.0151� � rD � rDN � rR � rRN � 0.0401�rU � rUN�

zU �1Dc

� � 0.1436 � 0.0004rU�rR � rRN � rD � rDN

� �0.0004�rR � rDN � 0.6745�rU � rUN�

zR �1

0.7461Dbc� � rR � rRN�0.0004�0.0006rU � 1.0151rD

� 0.987260 � �rD � rDN�0.0004�1.0151rR � 0.0407rU

� 0.2968 � �rU � rUN�0.0004�0.0407rD � 0.0006rR

� 0.0394�



where rD, rU, and rR are the raw isotope (area) ratios M �2/M � 0, M � 4/M � 0, and M � 3/M � 0, respectively, in thesample; rDN, rUN, and rRN are the raw isotope ratios M �2/M � 0, M � 4/M � 0, and M � 3/M � 0, respectively, in thepreexperiment sample (tracee only); and the common denom-inator Dc is calculated as

Dc � 0.0004�rD � rR � 0.00002rU � 0.6905

The calculations assume that D-[U-13C]glucose molecules canbe recycled into glucose molecules with m/z of M � 2 and M �3, but not M � 4, and that the same amount of D-[U-13C]glucose molecules is recycled in molecules with m/z ofM � 2 and M � 3 (31, 32).

The formula to calculate the TTR of 3-O-methyl-D-glucose(zO) in the mixture of the tracer and the internal standard is

zO �rO � rON

1.0230 � 0.0151rO

where rO is the raw isotope ratio M � 0/M � 3 in the mixture,and rON is the raw isotope ratio M � 0/M � 3 in the internalstandard.

The concentrations of D-[U-13C]glucose (gU), D-[6,6-2H2]glucose (gD), and recycled glucose (gR) are obtained as

gU � zU

C1 � zU � zD � zR

gD � zD


gR � zR


where C is the (total) glucose concentration in the sample.The concentration of 3-O-methyl-D-glucose (gO) is obtained as

gO � zOgS

where gS is the concentration of the internal standard 3-O-methyl-D-[2H3]glucose.

The derivation of the formulas follows principles describedelsewhere (29).

APPENDIX B: DEFINING INSULIN SENSITIVITIES

Insulin sensitivity of glucose distribution/transport (SIT),glucose disposal (SID), EGP (SIE), and overall sensitivity[SI(T�D�E); all ml �min�1 �kg�1 per mU/l] are defined as

SIT � ��Q̇1�t/G�t

�I�t �x2�t � x2bx3�t � x3b

� Vx2b

x2b � k12

kb1

ka1

SID � ��Q̇1�t/G�t

�I�t �x1�t � x1bx3�t � x3b

� Vx1bk12

�x2�t � k122

kb2

ka2

SIE � ��Q̇1�t/G�t

�I�t �x1�t � x1bx2�t � x2b

�EGP0

G�tkb3

ka3

SI(T�D�E) � ��Q̇1�t/G�t

�I�t� SIT � SID � SIE

The basal values x1b, x2b, and x3b correspond to pre-IVGTTquantities (i.e., values at 120 min). Similarly, G(t) and x2(t)represent pre-IVGTT values for the purpose of evaluatinginsulin sensitivities.

APPENDIX C: FREE-FORMAT CALCULATIONS OF EGPAND RECONSTRUCTION OF VALIDATION TRACERINFUSION

The endogenous glucose concentration GE(t) due to EGPafter an IVGTT was calculated using a model-independentapproach (19). Only the assumption of the isotopic indistin-guishability was made.

The total glucose concentration G(t) includes the endoge-nous component GE(t), the unlabeled exogenous glucose com-ponent GX(t), and the tracer component gU(t)

G�t � GE�t � GX�t � gU�t (13)

The components gU(t) and GX(t) are fixed at a ratio E, E �gU(t) � GX(t), which is given by the (D-[U-13C]glucose) enrich-ment of the glucose bolus administered at 120 min. SolvingEq. 13 for GE(t), we obtain

GE�t � G�t � gU�t1 � E

E(14)

The general form of the relationship between glucose appear-ance a(t) and the resulting glucose concentration c(t) is de-scribed by an integral equation

c�t � ��

t

h�t, �a��d� (15)

where h(t,�) is the (time-variant) unit impulse response of theglucose system. The impulse response h(t,�) was defined as asum of two exponentials (a function of �) for t between twosampling points

h�t, � � A1,ie� �i,1� � A2,ie

� �i,2� for ti � t � ti � 1

where values A1,i, A2,i, �i,1, and �i,2 were determined from thetwo-compartment model of D-[U-13C]glucose defined by Eqs.1, 2, 3, 10, and 11.

A separate parameter estimation was carried out to calcu-late the time-variant unit impulse response. The concentra-tions of D-[U-13C]glucose and 3-O-methyl-D-glucose excludingthe concentration of native glucose were employed to esti-mate a subset of model parameters (omitting EGP-relatedparameters, i.e., 8 parameters: k12, k03, F01, SIT

f , kb1, SIDf , kb2,

and V) for the purposes of free-format reconstruction of EGP.The submodel is defined by Eqs. 1–6, 10, and 11. The integralequation Eq. 15 is ill conditioned and was therefore solvedusing a regularization method (28, 44). The regularizationcomponent consisted of the norm of second differences toprovide a piecewise constant appearance rate a(t). The regu-larization coefficient, which defines the extent of smoothing,was chosen individually by assessing the fit to the data andthe distribution of residuals.

EGP(t) was calculated by substituting the endogenousglucose concentration GE(t) (see Eq. 14) for c(t) in Eq. 15. Theinfusion of D-[6,6-2H2]glucose (the validation tracer) was re-constructed by substituting D-[6,6-2H2]glucose concentrationfor c(t) in Eq. 15.

This work was in part supported by the Special Trustees of St.Thomas’, Diabetes UK, and the European Community InformationSociety Technologies Programme (the Adicol Project IST-1999–14027). Susan C. Wood provided secretarial support.

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Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT

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