Equivalence of the insulin sensitivity index in man derived by the minimal model method and the euglycemic glucose clamp

Equivalence of the insulin sensitivity index in

man derived by the minimal model method and

the euglycemic glucose clamp.

R N Bergman, … , A Volund, J M Olefsky

J Clin Invest.

1987;

79(3)

:790-800.

https://doi.org/10.1172/JCI112886

.

Studies were done to determine whether the minimal model approach and the glucose

clamp measure equivalent indices of insulin action. Euglycemic glucose clamps (glucose,

G: 85 mg/dl) were performed at two rates of insulin (I) infusion (15 and 40 mU/min per m2) in

10 subjects (body mass index, BMI, from 21 to 41 kg/m2). Insulin sensitivity index (SI) from

clamps varied from 0.15 to 3.15 (mean: 1.87 +/- 0.36 X 10(-2) dl/[min per m2] per microU/ml),

and declined linearly with increasing adiposity (versus BMI: r = -0.97; P less than 0.001). SI

from modeling the modified frequently sampled intravenous tolerance test varied from 0.66

to 7.34 X 10(-4) min-1 per microU/ml, and was strongly correlated with SIP(clamp) (r = 0.89;

P less than 0.001). SI and SIP(clamp) were similar (0.046 +/- 0.008 vs. 0.037 +/- 0.007

dl/min per microU/ml, P greater than 0.35); the relation had a slope not different from unity

(1.05 P greater than 0.70) and passed through the origin (P greater than 0.40). However, on

a period basis, SI exceeded SIP(clamp) slightly, due to inhibition of hepatic glucose output

during the FSIGT, not included in SIP(clamp). These methods are equivalent for

assessment of overall insulin sensitivity in normal and insulin-resistant nondiabetic

subjects.

Research Article

Equivalence of the Insulin Sensitivity Index in Man Derived

by the

Minimal

Model Method and the

Euglycemic

Glucose

Clamp

RichardN.Bergman,Rudy Prager, AageVolund, and JerroldM.Olefsky

Department ofPhysiology and Biophysics, University ofSouthernCalifornia School ofMedicine, Los Angeles, California 90033; Department ofMedicine, University ofCalifornia,SanDiego,and the Veterans Administration Medical Center, San Diego, California 92161

Abstract

Studiesweredone todetermine whetherthe minimal model

ap-proachand the glucose clamp measureequivalentindices of

in-sulin action. Euglycemic glucoseclamps(glucose,G: 85

mg/dl)

wereperformed at two ratesofinsulin (I)infusion(15 and 40 mU/min perin2)in 10 subjects (bodymass index, BMI, from 21to 41

kg/m2).

Insulin sensitivityindex

(SI)

from clampsvaried

from0.15 to 3.15(mean: 1.87±0.36 X 10-2 dl/Iminper

m2l

per

XU/ml),

anddeclined

linearly

with

increasing adiposity

(versus

BMI: r = -0.97; P <0.00t).

SI

frommodeling the modified frequently sampledintravenous tolerance test varied from 0.66 to7.34 X

10-4

min-'

per gU/ml, and wasstrongly correlated with

_SIp(cFOip)

(r=

0.89;

P<

0.001).

SI

and

SIP(clp)

weresimilar

(0.046±0.008 vs.0.037±0.007 dl/minper

tU/mt,

P >

035);

therelationhad aslope notdifferentfromunity (1.05P>0.70)

andpassedthrough the origin(P>0.40).However, on apaired basis,

SI

exceeded

SIP(cl,,amp)

slightly,due to inhibitionof hepatic

glucose outputduringtheFSIGT,notincludedin

_Smpowi).

These

methodsareequivalent for assessmentof overallinsulin sensi-tivityinnormalandinsulin-resistant nondiabetic subjects.

Introduction

Aconsensushasemergedthatinsulin resistance isanimportant component in the etiology of glucose intolerancein avarietyof metabolic conditions, including obesity (1), aging(2), and

non-insulin-dependent diabetes mellitus(3). Thus, itisanimportant goaltobeableto

quantify

thedegree of sensitivity ofthetissues

toinsulinasanindication oftheprevalenceand/orprogress

of

metabolic disease, and toevaluate theeffectiveness ofspecific therapies.Inrecent years, avariety of approacheshave been put

forthtoyield either

qualitative

(4)orquantitative indicesof in

vivo insulin sensitivity(5). Mostrecently,theeuglycemic clamp ofAndresandhis colleagueshasgained widespreaduse (6).

While theglucose clamp iswidely regarded as the "gold

standard" for sensitivity measurement, it remains primarilya laboratory procedure, because it requires sophisticated

equip-ment, highlytrained personnel,and it is costly andlabor

inten-Address reprint requests to Dr. Bergman. Dr. Prager is on leave from the SecondDepartment of Medicine, University of Vienna, Austria. Dr. Volund isavisiting scientist from the Novo Research Institute, Bagsvaerd, Denmark.

Receivedforpublication23 April 1986 and inrevisedform3 November 1986.

sive. There remainsaneed for

alternative

methods formeasuring

insulin sensitivity whichrequireless

experimental sophistication.

The minimal model methodologyhas been

proposed

as a simple alternativeto theglucose clamp. With this

method,

the computeris usedtocalculate insulin

sensitivity

from the

glucose

andinsulin dynamics observed during the

frequently sampled

intravenousglucosetolerancetest

(FSIGT1;

7-9).

The question hasarisen as to the accuracy ofthe insulin sensitivity index,

SI,

which is estimated from minimal model analysis oftheFSIGT.Donnerand hiscolleagues

(10),

and

Foley

et al.

(1

1) reporteda weak,

marginally significant

correlation

between insulin

sensitivity

determinedbythe minimal model

approach and the

euglycemic

clamp,

although

the reasonfor this lack of

correlation

was not

determined.

Beard and his

col-leaguesdemonstrated thatthecorrelation between these methods became muchstronger(r=

_0.83)

when

they

utilizedamodified FSIGT protocol, which entailedthe

sequential injection

of

glu-coseand

tolbutamide (12).

Theresults of Beardandhis colleaguessuggest that the min-imalmodel approach isan

alternative

tothe

euglycemic

clamp,

inthat acceptable estimates of insulin

sensitivity

may beobtained from either.However, theattractiveness ofthe

minimal

model approach would increase ifthe

sensitivity

index derived therein

were notjust related tothe

clamp-based index,

but

if,

in fact

these

independently

derivedmeasureswere

equivalent.

Inthepresent study,wemeasured the insulin

sensitivity

index inagroupof individuals of

varying body weight, using

boththe

euglycemic

clamp, andthe minimalmodel method. Our

goal

was todeterminewhether themodel-based sensitivity indexwas

simplyacorrelate of insulin sensitivity,orwhether

application

of the minimal model

yielded

the same measureof insulin sen-sitivityasthe

euglycemic

clamp method.

Methods

Subjects

10subjectswerestudied (TableI;9male, 1 female). Body mass indices varied from 21 to 41 kg/m2.Thus, 4 subjects were of normal weight, andtheremainderwereobese.

After

admission to the Special Diagnosis and Treatment UnitattheSan Diego VeteransAdministrationHospital, subjectswereputon aweight-maintainingdiet (32 kCal/kg per d) with the following composition: carbohydrate 45%, protein 15%, fat 40%, served in threeportions:

I/5

at8 a.m.,

%15

each at noon and 5 p.m. Each studywasperformedatleast 48hafter admission, beginning at7a.m., afteranovernight fast. All 10 patients were subjected to one euglycemic

clampstudy(insulininfusion rate 40 mU/min per

m2)

and an additional 1.Abbreviations used in this

paper:

BMI, body mass index; FSIGT, fre-quently sampled intravenous glucose tolerance test; GINF, glucose in-fusion;

HGO,

hepatic glucose output; Rd, glucose uptake; SA, surface area;

SI,

insulinsensitivity index;

SIP(CISIp),

clamp-derived

insulin

sensi-tivityindex; VD, distribution volume.

J.Clin.Invest.

©TheAmerican Society for Clinical Investigation, Inc.

TableI.Human Subjects

Age Sex Height Weight BMI Surfacearea

yr cm kg kg/rm2 m'

1 28 M 173 74 25 1.87

2 30 M 174 65 21 1.76

3 34 M 170 66 23 1.78

4 37 M 181 76 23 1.98

5 35 M 170 80 28 1.92

6 58 M 178 97 31 2.18

7 53 M 191 120 33 2.47

8 39 M 174 121 40 2.32

9 29 F 160 90 35 1.98

10 38 M 184 140 41 2.58

clamp study(15mU/minperm2)was also performed on eight of them. In addition, a singletolbutamide-modified FSIGT was performed on each subject. Studies were randomized, and performed on different days.

Allexperimental protocols were approved by the University of California at San Diego (UCSD) and Veterans Administration (VA) Human Subjects Research Review Committee of the UCSD and VA Medical Center. Informed consent was obtained from all subjects.

Glucose

clamp studies

Euglycemic glucose clamp studies were conducted as previously described (13). Intracatheters were placed in one antecubital vein and a dorsal hand vein cannulated in the retrograde direction. The hand was kept in a heating pad to provide arterialized venous blood. Labeled glucose

(3-[3H]glucose)

was injected (60 tCi) and infused (0.6

_,Ci/min)

thereafter for the entire experiment. 60 min after tracer infusion was begun, insulin was infused, continuing for 3 h. During the insulin infusion, glucose was maintained at 85 mg/dl by a variable infusion of 20% dextrose. The infusion was adjusted according to glucose determinations made every Smin on a glucose analyzer (Yellow Springs Instruments, Yellow Springs, OH). For calculation of insulin sensitivity, we defined glucose infusion rate as steady state by calculating the average rate over the final 40 min of insulin infusion. Additional blood samples for determination of insulin and glucose specific activity were collected every 20 min during the glucose clamp.

FSIGT

After placement of the two intracatheters, four basal samples were col-lected over 20 min,after which glucose (0.3 g/kg) was injected over 1 min,asdescribed (9). An additional injection of tolbutamide (Orinase i.v., Upjohn, Kalamazoo, MI) was given over 20 s, 20 min after glucose. Subjects with body mass index (BMI) < 30 kg/in2were given 300 mg tolbutamide; subjects with BMI > 30kg/M2were given 500 mg. These doses were equivalent to 4.19±0.40 mg/kg (SD) for the lower BMI sub-jects, and 4.52±0.80 mg/kg for the greater BMI subjects (P> 0.40). Blood samples (4 ml) were collected at the following times after glucose injection at t=0: 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 19, 22, 24, 25, 27, 30, 40, 50, 60, 70, 90, 100, 120, 140, 160, and 180 min. Addition of the tolbutamide injection to the glucose injection protocol decreases the coef-ficient of variation of the estimate of the insulin sensitivity index (SI) from 32 to 13% (reference 14, assuming a 2% coefficient of variationin

the glucose assay).

Analyticalmethods

Glucose kinetics. Specific activity and glucose data were smoothed using the optimal segments method(15), and glucose appearance and disap-pearance rates were calculated from the derivative form ofthe Steele

relationship(16).Hepatic glucose output was calculated as the difference between total glucose appearance rate and the rate of glucose infusion. Insulin was measured by double antibodyradioimmunoassay(17).

Data

analysis

and

statistics

Theinsulinsensitivityindexwascalculated from FSIGT resultsusing the program MINMOD (copyrightR. N. Bergman, 1986), whichwas

run onthe VAX-750attheUSCPhysiologyandBiophysics Department

(18).This program acceptsasinputthetemporalpattern ofplasmainsulin

duringtheFSIGT, andmustfitasimple (minimal)model of insulin-dependentglucoseutilizationtothe measuredglucosepattern. The model is the simplest mathematical representation that canaccount for the

dynamicsof glucoseduringtheFSIGT. Theequationsof the minimal modelare asfollows(7):dG(t)/dt=_-[pi +X(t)]G(t)+pGb, dX(t)/dt

=

_-p2X(t)

+

_p3I(t),

where

_G(t)

and

_I(t)

arethe

plasma glucose

andinsulin

concentrations,X(t) is insulin inacompartmentremotefromplasma,

andpi, P2, andp3 are model parameters. Gb and Ibare preinjection

glucose andinsulin concentrations. Parameter pi is the fractional dis-appearance rate ofglucose,atbasalinsulin, independentof the insulin response. ParametersP2and

p3

determine thekinetics of transport into

and outof the remote insulin compartment where insulin action is

ex-pressed.

Parameters of the model are estimated from least-squares fitting of theglucose data, and the insulin

SI

is calculated asthe ratio oftwoof the fitted model parameters (P3/P2, c.f. Appendix of reference 7). In

addition,thefittingprocedureyields the apparent volume of distribution ofglucose (VD)correspondingtothesinglecompartment of the minimal model, and

Sc(=

pi),fractionaldisappearancerateof glucoseindependent

of the insulin increment. The program MINMOD, adapted for the mi-crocomputer or the VAX computer may be purchased from Dr. R.

Bergman.

Standard statistical methods including paired and unpaired t tests, linear regression and correlation analysis were used to examine the re-lationship between measures of insulin sensitivity from the clamp versus the minimal model methods(19).

Results

Glucose clamps. The subjects ranged in BMI from 21 to41

kg/

m2

(TableI). Basal glucose production(equalsbasal uptake) was

relativelyconstantfor all individuals when normalized tobody

surface area (Table II, 79±13 (mean±SD) mg/min perM2; r

= 0.18 (NS) with BMI) as would be expected for nondiabetic

individuals (20). Unlike basal glucose production, therewas a wide rangeofbasal insulin levelsin these subjects (range, 7 to

46

_AU/ml),

andbasalinsulinwascorrelatedwithBMI (r =0.81, P<0.01).

Glucoseclampswere done at alow [15 mU/(min per

M2)]

ormoderate[40mU/(minperm2)] insulin infusionrate.Steady

stateinsulinlevelsattainedwere41±4 and114±6

_OU/ml

atthe

tworates, respectively (mean±SE,TableII).Glucose uptake(Rd) duringthe 140-180-min period variedamongsubjects from 68

to 156 mg/min perm2atthelower infusion rate; at thehigher

rate the range was 90 to 340 mg/min perM2. Glucose uptake

ateitherinfusionrate wasreducedasBMIincreased (correlation with BMI, r= -0.84 and-0.90atthe low and moderaterates

ofinsulin infusion).

Wehave previouslydefinedtheinsulinsensitivity index for

the euglycemic glucose clamp,

Sip(clamp),

asthesteadystateratio of the increment in glucose uptake (ARd) tothe increment in

plasma insulin concentration (Al), normalized tothe ambient

plasma glucose concentration (G) at which the clamp is

per-formed (5):

SIP(clamp)

= ARd/(AI X G).

Table I. Euglycemic Clamp Results

Basal Low insulin Intermediateinsulin

Subject Insulin* Rd Insulin Rd Insulin Rd SMrtw)

X102 dl/(min.M2) 15mU/r2.min 40mU/min *m2 perAU/ml

1 16 76 51 150 102 277 2.75

2 9 90 45 149 112 340 2.86

3 8 65 35 132 108 328 3.09

4 8 55 31 129 76 237 3.15

5 7 95 38 156 102 284 2.34

6 10 90 33 87 118 235 1.58

7 4 79 27 83 141 265 1.72

8 43 78 133 90 0.15

9 12 81 109 135 0.66

10 46 77 64 68 138 106 0.36

Mean±SE 17±5 79±4 41±4 119±12 114±6 230±28 1.87±0.36

Correlation r= 0.81 0.18 -0.84 -0.90 -0.97

withBMI (P<0.01) (NS) (P< 0.01) (P<0.001) (P< 0.001) Insulinconcentration is expressed in uU/ml; Rd is expressed in mg/mi per

i2.

In2). As analternative,we could utilize theslopeof the best-fit linear regression of steady state Rd on steady stateplasmainsulin,

employing all threedata sets(basal, 15 and40

mU/min

perM2,

cf.reference 20).Table III lists the values of

Slpcl~,p)

calculated these fourpossible ways for the five lowest-BMI subjects. (We were not able to dothis forthe more obese subjects because

low-dose clampswere not performedon two ofthem, andin

the others there was no measurable effectonRdatthe 15

mU/

min perM2 _dose.) For the normal subjects, mean calculated

SIP(C,,mP) ranged

from 2.69to2.92 X 10-2

dl/(min

per M2) per

gU/ml,

and there were no significant differences between the

individualvaluesfor

Swp(clsmp),

forthefour methods ofcalculation (P> 0.50 for all paired comparisonsbetween groups in Ta-bleIII).

Inview ofthe similarities of

SIP(ctemP)

values calculated for

normalsubjects regardless ofthe insulin interval used,wechose

to utilize the0 to 40 mU/min per m2 data for calculation of Sxpclamp) since itcouldalso be used forthe obese subjects, and

TableIII. Calculationof

SIp(cfanp)*

inNormal

SubjectsUsingDifferentSetsofClampData

Values(X102 dl min-'perIAUImi)fordifferent insulin infusion rates(mU/min*p2)

Normal

subject 0-15 15-40 0-40 0-40regressiont 1 2.48 2.93 2.75 2.76

2 1.93 3.35 2.86 2.92 3 2.92 3.16 3.09 3.11

4 3.79 2.82 3.15 3.10 5 2.31 2.35 2.34 2.34

Mean±SEO 2.69±0.32 2.92±0.17 2.84±0.14 2.85±0.14

*_{Swpdi..p)is calculated as the change in}

Rddivided by the increment in insulin times the ambient glucose concentration[ARd/(Al-G)].

tSlopeof linearregressionfor data at 0, 15 and 40mU/ml2 min. Regression coefficient exceeded 0.99 for all regressions shown.

Nosignificantdifference was found between any pairs of values of_Smd.,p) cal-culatedby the four differenttechniques (P> 0.5, paired t test).

it was very similarto the value obtained using best-fit linear regression (TableIII).

Mean

SIP(CIamp)

for all subjectswas 1.87 X 10-2 dl/minper

In2) perMU/ml(Table II); however there was a wide range [0.15

to3.15 dl/(minpermi2) per

,MU/ml].

Apparentlythe rangewas

relatedtothevariability in adiposity. Fig. 1 shows thevery strong

correlation between BMI and S

_pdclamp)

(r = -0.97, Spclap)

- -0.156XBMI+

6.54).

This correlation could be influenced by age. However,amultiple correlation with age includedgave virtually the same relationship between BMI and

SIpeclap)

(SIp(ctemp)

=-0.159XBMI +0.008Xage+

6.33),

witha

partial

correlationcoefficient between

_Swpclmp)

and BMI of-0.97, while

SIp(clamp)x1 o2

4 r

di/(min.m2)

.jU/ml 31

x r=-0.97

P<0.001

x

0.0

. IP(clamp)--0.15Mo W .54* X\

20 30 40

Body Mass Index kg/m2

Figure 1.Relationship between insulinsensitivityindex from the

eu-glycemicglucoseclamps andadiposity.

_S(,,p)

is definedas(ARd/

AI *G), where ARd is the changeinRdbetween basal andatsteady

stateduring insulin infusionat40 mU/minperm2, Al is the

incre-mentin insulin, and Gistheglucose concentrationduringtheclamps (85 mg/dl).

2

F

1

thatwithagewasonly0.30 andwas not

signific

Thus, inthisgroupof subjects differencesin

_ag

theconclusion thatasmuchas95% ofthe vari

sensitivityofthisgroupcanbeaccountedforbyt

alone. Also, the data inFig. 1 suggest that the

sensitivityuponadiposityislinearandcontinua

decreasing abruptlyasadiposityexceedsa"thre:

Inadditiontothe strongcorrelation with

_bod3

wassomewhat more weakly (butsignificantly) relatedwith basal insulin concentration (r= -0

FSIGTresults. Allsubjects had asignificant sulinresponse (Fig. 2, integrated insulinoverbN

after glucose injection) which averaged 0.84±1 Xmin,andwhich was independentof adiposity ( IV, NS)Tolbutamide, injectedat 20

min,

induc

ondary peak in plasmainsulin(Fig. 2). The

_inteE

minabove basal responseafter tolbutamidewas4.

200

E

3

100

z

CO

z

0

400

- Go.

E

LL 2

C

C')

0

.. Gb..

to

-M-*N

0

I--0 30 60 90 120

Tolbutamide (300-500mg)

T

I

M

E(minut

Glucose

(0.3g/kg)

Figure2."Modified"frequently-sampled intravenousgl

ance test(9). Valuesontheordinate("basal")aretheav

fasting values.Dots representaveraged measuredvalues

jects; solidline in lowerpanelrepresentsminimal-model

data.Glucose(0.3g/kg)wasinjectedover1 minat t=C (300mg inlean, 500mg inobese)wasinjectedas abolt

later. Note thatfirstsevenglucosevaluesare notfitbyti

causetheyareelevatedbyincompletemixingin theextr

Intersection ofthe modelpredictionwiththeordinate_(p

at t=0ignoring mixing phase)isGo,theconcentration

have beenobtained if extracellularmixingwereinstantai

the averagebasal(preinjection) glucoseconcentration.

,ant

(P

>

0.05).

Pe

do notaffect ance ininsulin their

body

mass

dependence

of

us, rather than shold" value.

ml)

X min. In contrast tothe first

phase

insulinresponse,

tol-butamide-stimulated

plasma

insulin response increased with

adiposity

(r

= 0.88 with

BMI,

P<

0.001).

As

discussed,

this

adiposity-related

increment in insulin responsecouldnothave been caused

by

thedifferent dose oftolbutamide in themore

obese

patients,

sincethe dose per

body weight

was similarfor

leaner

(BMI

< 30

kg/M2)

versus moreobese

(BMI

>30

_kg/M2)

ymass,

Sncamp)

subjects

(see

Methods).

negatively

cor- Minimal model

analysis,

likethe

glucose

clamp,

revealeda

l.74,P<0.02). substantialrangeofinsulin

sensitivity (Table IV).

SI

varied from

first-phase

in- 0.66 X 10-4 to 7.34X 10-4 min-' per

MU/ml

(mean

SI

asal,

0-10 min = 3.59±0.79 X 10-4

min-'

per

,uU/ml).

The present reportis 0.13

(mU/ml)

thefirst

using

the tolbutamide modifiedtest in obese

subjects,

r=_0.23,Table and the rangeof

SI

valuesis consistentwith

previous

reports in ,edalargesec- normaland obese

subjects

in whom the

previously

used

protocol

grated,22-180 (glucose alone)wasemployed (8, 12).

38±1.44

(mU/

The strong

dependence

of insulin

sensitivity

upon

adiposity

demonstratedwith

clamp

data

(Fig.

1)

wasconfirmed withthe minimal model method

(Fig. 3).

As with the

glucose clamp,

therewas amonotonicdecline in

sensitivity

with

increasing

BMI.

The correlation between model-based

SI

and BMIwas

-0.91,

(Table IV,P<

_0.001),

somewhat lower than the -0.97obtained withtheclamp.

Also,

the

relationship

between basalinsulinand

insulin

sensitivity

failedtoachieve

significance

whenthe model-based

SI

wasused

(r

=

_-0.54,

P=

_0.10).

Correlationbetween

glucose

clamp

and FSIGT results. We

foundastrongcorrelationbetween theinsulin

sensitivity

index

measured from the

glucose

clamps,

andthat fromminimalmodel

analysis

oftheFSIGT

(Fig.

4,

r=

_0.89;

P<

_0.001).

Ofadditional

-L--t~~-I

interest isthe

regression equation

between these

independently

measured parameters of insulin action:

_SI

= _1.94

_SIP(clamp)

- 0.03.

The

intercept (-0.03)

is notdifferent from 0.00

(P

>

_0.9).

In

_fact,

_analysis

ofthe dataindicatesthatanupper 95%

confi-dence limit forthis

intercept

isless than 20% ofthemaximum

SI

value obtained.

Thus,

from this

relatively

small

sample

of

patients

we were not able to

identify

any

factor,

unrelated to

insulin

sensitivity

itself which

significantly

biasedthe values of themeasuresobtained

using

the minimal modelorthe

glucose

clamp.

Equivalence

ofS1

and

SIP(clamp).

The fact that the

relationship

between

SI

and

SIP(camp)

passes

through

the

origin

provides

the

opportunity

todetermineif thesemeasures are

simply

correlated

with each other, or whether the clamp and minimal model methods are, in

fact,

measuring

thesame

_{physiological}

param-.,

eter.Todemonstrate

equivalence,

anadditional criterionmust 150 180 be met: notonly must theregressionline passthroughthe

origin,

but in

addition,

the

slope

of the

relationship

between

SI

and

es)

Slpclamp)must be indistinguishable from 1.00.

At first

glance

it mayseemthat the

relationship

shown in

Fig.

4failsto

satisfy

the secondcriteriontodemonstrate

equiv-lucosetoler- alence: the

slope

of the

regression

(1.94±0.35, slope±SE)

is

sig-ierageof3

nificantly

differentfrom 1.00

(P

<

_0.05).

_However,

thisapparent for 10sub- failuretosatisfythe secondcriteriondoesnotindicate

inequality

I fittothe between

SI

and

_SIFPcdamp)

because in Fig. 4 these parameters are

);

tolbutamide not expressed in the same units;

_SIP(cdamp)

is in units ofdl/(min

iS 20min per

m2)

per

,tU/ml;

_SI

is in units of min' per

usU/ml.

he model be- _{To examine whether the measures are equal (differences only}

racellular

flue

due to random error)

it

is necessary to convert the measures to

Iredicted value _{identical units. Both parameters can be expressed in terms of}

that would

neous. Gbis change in glucose clearance per change in plasma insulin con-centration.To maketheconversion for

SI,

itmustbe

multiplied

TableIV.ResultsfromtheFSIGTs

Glucose

Subject dose Integrated insulinoverbasal ((mU/ml)-min) SiX 104 g 0-10 min 22-180 min min'peryU/m1

1 15.3 0.647 0.490 6.32

2 19.5 1.215 0.981 6.79

3 19.8 0.794 1.765 4.88

4 22.8 0.439 1.247 7.34

5 24.0 1.005 3.884 2.46

6 29.1 0.178 2.697 1.98

7 36.0 1.310 3.461 2.71

8 36.3 1.331 10.883 0.87

9 27.0 0.434 4.159 1.94

10 42.0 1.008 14.227 0.66

Mean±SE 27.2±2.7 0.84±0.13 4.38±1.44 3.59±0.79

Correlationwith r= 0.23 0.88 -0.91

BMI (NS) (P<0.001) (P <0.001)

by thedistribution volumeof glucose

(SI

X VD, see Appendix). Theminimalmodel assumes asingleextracellular compartment ofglucose distribution, andthe volume of this compartment

(VD)

is

equal

totheratio ofthe

_glucose

dosetotheincrement inplasmaglucose. Thisincrementis thedifferencebetween the

post-injectionglucoseconcentrationandthe basal glucose: VD =Glucosedose/(Go-Gb).

Thepostinjectionglucoseconcentration

(Go)

is foundwhen the glucosedataisfittedtotheminimalmodel.Theglucosedata

fortheinitial 8minisnotfitted bythe modelbecauseduring this intervalglucoseis mixing inthe extracellularfluid (c.f., Fig.

2). When early mixing isignored,the intercept ofthe

model-predicted timecourseofplasmaglucose withtheordinateis the

predictedglucoseconcentrationthat would have been observed

ifglucose had mixed instantaneously in the 1-compartment

"glucose space."This value is

Go.

The values ofVDfor the 10subjectsarecalculated in Table V.The volumes ranged between 95.6 and 222 dl in the 10

sub-jects, averaging 16.1% ofbodywt.This fraction isconsiderably

lessthan the entire extracellular glucosespace, which has

pre-viously been estimatedtobe 26% of bodywt(21). In fact, the

apparentglucose distribution volumewasequalto0.62

multi-plied bythe estimated totalglucosedistribution volume.

SI_104

8

min-jU/ml

SI.1 04

min-1 pU/ml

6

4

x r =0.89

6 P<0.001

r =-0.9 1

P <0.00 1

4

2

0

2

_[

x

x

x

0

0

s 104=-O.32-BMI+13.1

20 30

Body Mass Index 40 kg/m2

Figure 3.Relation between insulin sensitivity index from the minimal model

(SI)

andadiposity.

SI

is obtained from fitting the minimal modeltotheglucose data obtained during the modified FSIGT.

1 2 4

SIP(C! am) di/(min-m2)

SIP(clamp)

_jJU/ml

Figure4.Linear relationship between sensitivity indices obtained from

fittingthe minimal modeltotheFSIGT(ordinate) or from the eugly-cemic glucose clamp data(abscissa).Note thatSIand

Sjp(Crp)

are ex-pressed indifferent units. Although slope is different from 1.00 (P

Table V CalculationofDistribution Volumefromthe Minimal ModelParameters

Subject Gb Go V(d) VD pool fraction" mg/dl mg/dl [Dose/(Go-Gb)] %body wt % bodyweight/26

1 88 289 110.0 14.9 0.57

2 101 301 97.5 15.0 0.58

3 95 302 95.6 14.5 0.56

4 96 282 121.9 16.0 0.62

5 92 250 151.9 19.0 0.73

6 100 253 190.2 19.6 0.75

7 96 275 201.1 16.8 0.65

8 91 284 188.1 15.5 0.60

9 104 322 123.9 13.8 0.53

10 108 297 222.0 15.9 0.61 Mean±SE 97±2 279±9 150.2±46.7 16.1±0.6% 0.62±0.02

To convert

SIpc1amp)

tochange in clearance per unit change ference in definition of sensitivity by the two methods: whereas in plasma insulin it is only necessary to multiply it by body

SIP(clamp)

measures theeffect of insulin to increase total glucose

surfacearea(seeAppendix). Thus, to demonstrate equivalence disposal,

SI

is a measureof theeffect of insulin to increase total

between

SI

andSIP(clamp) itis necessary to demonstrate that, on glucose economy, both by decreasing endogenous production average,

_SI

X VD=

_SIp(clamp)

Xsurface area. andby enhancementof uptake. Thus, the small difference be-Table VI lists both

_SI

and

Sip(clamp), respectively

corrected tween these two measures (S1-VD averaged 0.009 dl/min per with distribution volume, or surface area. The product

_SI

X VD uU/ml greater than Sipfciamp)*SA) might be explained by the

varied from 0.089 to 0.015 dl/min per

MU/ml

(mean inclusion of inhibition of hepatic glucose production in the

=0.046±0.008).

_SIPmclamp)

X surfaceareavaried from 0.062 to model-based measure.

0.003 (mean0.037±0.007). During theeuglycemicclamp,the exogenous glucoseinfusion

Therelationshipbetween

_SI

and

Sip(clamp)

expressed iniden- mustcompensate for both the decrease in endogenous glucose

tical units isshown inFig.5.Again,theintercept isnotdifferent production and theincrease in glucose uptake. Therefore, the

from 0.00 (P> 0.40). The slope of the relationship between rateof glucoseinfusion is an indication of the total effect of the

these indices ofinsulin sensitivitywas1.05±0.19(SE).Thisslope infused insulinonglucose economy. Thus, we recalculated

in-isindistinguishable from 1.00 (P>0.7). Thus,for the group as sulin sensitivity from clamp data using glucose infusion (GINF)

awhole,these two measuresof insulin sensitivity,

SI

and

_SmPfc]p)

in placeof

Rd

for the basal to 40

mU/M2

perminclampstudies. apparentlysatisfiedthecriterion forequivalence discussedabove. The sensitivity index parameter based on infusion is SI(clamp), Careful examination ofTable VIreveals, however,thaton defined as(AGINF/(AI*G)). Thislatter parameter (XSA) av-a subject by subject basisthere was a modest but significant eraged

0.052±0.007

dl/min per uU/ml for the 10subjects,slightly tendency for

SIX

VD to exceed

_SmPfcIamp)

surface area (SA) (P exceedingthemodel-based valueof0.046±0.008(Fig. 6). Thus,

<0.05 pairedttest). Onepossible causeof this tendency fora the subtle decrement in theinsulin sensitivitymeasure seenwhen greatersensitivityparameterwith the model approach is a dif- Rdwasused was morethan compensatedforwhen totalglucose

TableVI. CalculationofSimilar Indices ofInsulin SensitivityfromFSIGTandGlucoseClampResults

Subject SI* VD [SI- VD] SIPdp) SA [SIP(mp) SAJ

X10o xbo2

1 6.32 110.0 0.070 2.75 1.87 0.051

2 6.79 97.5 0.066 2.86 1.76 0.050

3 4.88 95.6 0.047 3.09 1.78 0.055

4 7.34 121.9 0.089 3.15 1.98 0.062

5 2.46 151.9 0.037 2.34 1.92 0.045

6 1.98 190.2 0.038 1.58 2.18 0.034

7 2.71 201.1 0.054 1.72 2.47 0.043

8 0.87 188.1 0.016 0.15 2.32 0.003

9 1.94 123.9 0.024 0.66 1.98 0.013

10 0.66 222.0 0.015 0.36 2.58 0.009

Mean±SE 0.046±0.008 0.037±0.007

*Unitsaredefinedas

follows: SI,

min'

per

uU/ml;

VD,

dl;

SIP(C,~,P),

dl/(min-

m2)

pertU/ml;SA

(surface

area),

m2;

SIy VD,and

(SIP(clmpP)

SA)

_are

r = 0.89 P<0.001

(SI.VD)=

1.05

K

K

(SIP(clamp),S

A )+ 0.007

0.02 0.04 0.06 0.08

(SIP(cIamp):

S A ) dl/min

jUU/mI

FigureS.Relationship between sensitivity index measured from the FSIGT (ordinate) and the clamps (abscissa) transformed so that both parameters are expressed in identical units.

SI

is multiplied by glucose distribution volume;

Snd.P)

is multiplied by body surface area (see text andAppendix).Theslopeoftherelationshipis notdifferent from unity (P>0.7) and the intercept is indistinguishable from 0.00 (P

>0.40). Dashed line is line of unity slope, zero intercept.

infusionrate wassubstitutedin the

clamp-based

index ofinsulin sensitivity. Thisresultis consistent withthenotionthat the small

decrease in

SIP(cIamp)

SA compared to

SI

* VD was due to thelack of inclusionof liverglucose productioninherent in the R4-based,

clamp-derived sensitivityindex

S1p(clamp).

Thesubstitutionof GINF for Rd did not change the

equiv-alentrelationship between the clamp based and model-based

sensitivity

indices.

Slope

of the

relationship

between

Sl(ckmp)

and

SI

was0.93(notdifferentfrom 1.00, P > 0.5); theinterceptwas -0.003(notdifferentfrom 0.00, P > 0.5, data notshown). Discussion

Insulin resistanceis animportantfactorunderlyingtheglucose intolerance observedin a variety ofmetabolic disorders. Among theseconditionsare some of majorepidemiologic importance,

suchasaging, obesity,andNIDDM,as well asseveralless prev-alentdiseases (22-24). Given the benefits that accrue from a betterunderstandingof theseconditions,itfollowsthat it is

im-portanttodevelop approachestoassess insulin sensitivitywhich entailminimumrisk anddifficulty,but whichprovide maximum quantitative information. The availability of such approaches

has thepotentialforimproved classificationofmetabolic illness, better prognosis,andearlier detectionandintervention.

The euglycemic clamptechnique, conceived by Andres et al.(6) and widelyexploitedby others (c.f.reference 5)remains

themostdirect approach toassessment ofwhole-body insulin sensitivity. Using theclampone maydeterminea direct dose-responserelationship betweenthe steady stateconcentrationof

insulininplasmaand the effect ofinsulintosuppress endogenous glucose production andenhance glucose uptake. However, as we and others havediscussed elsewhere,even these data can be

difficultto interpret if comparisons are made amongglucose

clampresults obtainedatdifferentplasmaglucose and/or insulin

levels (25).

Theabove

considerations

haveencouraged us to examine alternative approachestomeasuring insulin

sensitivity.

In

par-ticular,we have beensearching foramethodwhichcircumvents

someof theaspectsofthe

clamp

whichhave

prevented

itsuse outside the clinical research laboratory. The criteria we have

attemptedtofulfill includethefollowing: (a)nospecial

equip-mentrequirements forthe performance of thetest, (b) a test

that may be

performed

in an office rather than a laboratory setting (suchatestcouldbeused for field

studies),

(c) reduced

laborrequirements,and(d) minimization of risk. Inaddition,

andpossiblymoreimportant, we havedesiredamethodology for which (e) the attainment of steadystateisnota

necessity.

Finally, itwas hoped that thetestwould

provide

an accurate assessmentof insulin sensitivity which was

(within

limits) in-dependent of

glycemia

and

insulinemia.

To strive to satisfy these

aforementioned

criteria we have made use ofthedigital computerto analyze the dynamics of plasma insulinandglucose observed following glucose

injection.

Theinjection of glucose is simpletoperform,andvirtually risk free. By

implementation

ofthe"minimal model" of insulin-dependentnetglucose disappearanceon thecomputer(5, 7-9),

we have beenabletodescribe the effect ofchangesinplasma insulin on the postinjection decline of plasma glucose. From

the model parameters whichemergefrom thefitting

procedure,

wecancalculatethe

SI.

Thissensitivity parameter isameasure

oftheeffect ofanincrement in plasma insulintoenhance the fractionalnetdisappearance of glucose fromanassumed single compartment of extracellular glucose

distribution.

Thereis

ev-idence that within the

physiological

rangethis parameter is rel-atively independent ofthelevels of

glycemia

and

insulinemia

at whichit is determined(12, 26).

The

potential

oftheminimal model

approach

seemed to us to

satisfy

mostofthe

requirements

wehadsetdown.However, Donner et al. recently reported a very weak

correlation

(r

= _0.44) between insulin

sensitivity

from the minimal model analysis, and that observed on a group of subjects using the

euglycemic

clamp (10, 11). Given the demonstrated utility of the clamp, theDonner etal.reportsseemedtodemonstrate that

theminimalmodel approach violatedthe accuracycriterion.If

SI

wereindeedaninaccurate

index,

sucharesult would

severely

limit the usefulness of the minimalmodelapproach.

Recentresults reported by Beard and his colleagues, in

col-laborationwith someofus (12), have led to apotential expla-nation forthesomewhat disappointing resultsofDonneret al. We showed that thecorrelation between the minimal model method and the

euglycemic

clamp could be considerably strengthened(r=0.83)if the dataused as abasisforcalculating

SI

wereobtainednot from a glucose injection alone, but from a

"modified"

FSIGT protocol in which tolbutamide wasalso injected20 min afterglucose.Thismodified protocol produced

asignificantly greater plasma insulin responsethan glucosealone,

and asubstantial portion oftheinsulinresponseoccurredafter the0-8 minpostglucose injection mixing period(27). Because

themodel requiresasubstantial effect ofinsulin after the initial

glucose

mixing periodtocalculateaprecise measureofinsulin

sensitivity, addition of the tolbutamide to the injection protocol (SI-VD)

0.08 di/min

JJU/ml

0.06

0.04

0.02

caused asubstantial increase inthecorrelation between

model-based and clamp-model-based sensitivity (12). However, ourearlier studiesfailedtoaddress theissue ofthe accuracyofthe

SI

esti-mate: is

SI

from the FSIGT simply proportional to

clamp-de-termined insulin sensitivity, or is it infact equivalent to the

sensitivityparameterobtained fromtheclamp?Demonstrating equivalencerepresentsavalidationnotonlyoftheFSIGT-based

SI,

butavalidation oftheminimalmodelaswell.

The present resultsconfirm astrongand highlysignificant correlation between the insulin sensitivityindex measured by thetwomethods.Infact,in the presentstudiesthere was a

ten-dency forthecorrelationtobehigherthan waspreviouslyfound

(r=0.89 comparedwith0.83); presumablythis may be explained

bythefactthat in the presentstudiesweusedsubjects ofwidely

varying body mass index, and are thus able to compare

_SI

and

SIp(clamp)

in

obesity,

while Beard usedonly normal-weight subjects.

Theincreased variability of adiposityresulted in awider range

of

_SI

in the presentstudies (0.66to7.34 X 10-4

min'

per

_gU/

ml, an11-folddifference).Assuming that a wider range in insulin

sensitivitywould beobtained with a greater variability of

adi-posity, a stronger correlation would be expected, based upon

statistical principles (19).

Of particular interestwasthenegativerelationship between

insulinsensitivity and obesity in these studies as BMI increased above the normal range(Figs. 1 and 3). While we haveinsufficient

datatodeterminewhetheradipositywillleadtorelativeinsulin

resistance within the normal limits of body mass index, appar-ently evenmildobesitycanhave a measurableeffectandpossibly lead to thenegativeriskfactorsassociated with diminished

sen-sitivity

tothe hormone. Further, evenafter moderate obesity

occurs,progressiontomoresevereobesityleadsto anadditional,

measurabledecline ininsulinaction.

Moresignificantthan the strong correlation between

SIp(cialnp)

and

_SI

inthe presentstudiesarethe following facts: first, that the correlation passed through the origin (0, 0); second, that when properly correctedfordifferencesinunits, the slope of the

relationship wasclose to unity. Inaddition, when glucose

in-fusionrate wasusedas abasisfor calculating clamp-based sen-sitivity, meanvaluesofsensitivitywerevery similarwith both methods(0.046 versus0.052dl/minper uU/ml). These results

providestrong evidence that theminimal model method and theeuglycemic clamparemeasuringthesamephysiological pa-rameter, rather thanreflecting differentprocesseswhichhappen

tobe relatedtoeach other. In

addition,

these results

imply

that

there is no important

factor,

unrelated to insulin

sensitivity,

which systematically biases the measurement ofeither

SI

or Si(clamp). Statedin moregeneral terms, these results demonstrated that (exceptforrandomerrordueto measurementand

biological

variationbetweensuccessive measurements)

_SI

=

_SllmcLwp),

pro-vidingthat both parametersareexpressedinidentical units.

Itshould beemphasizedthatforacorrelation

analysis

tobe valid, the parameters correlatedwitheach othermustbe assessed completelyindependently, i.e.,theremust notbe anycommon

measuredvariable thatcontributestothe valueof both

param-etersbeingcorrelated.This criterion appliestothevariables

cor-related inFig.4 aswellasinFig. 5.Thus,

SI

and

SIP(cdamp)

were

determinedonthesameindividual,butondifferentdays

using

entirely

independentmethods. Theindependencecriterion also

appliestotheunit-correctedvariablescorrelated inFig.3

(SI

VD versus

_SMLpcp)

-SA); nofactor iscommon tobothmeasurements.

Parameters

SI

and VDareboth calculatedfrom the FSIGTalone;

SIPFclamp)

isdetermined from theclampalone,while surfacearea

isestimatedfromheightandweight (28).Ifthisimportant

con-sideration of the independence of correlated parameters isnot

obeyed,the correlation coefficient between the different measures of insulin sensitivity could notbetaken perse asevidence of equivalence of the twomeasures.

In the previous study of Beard et al. the regression line did not pass through the origin. A possible reason for the non-zero positive intercept in the earlier study was that sequential eugly-cemic clamps were performed on a single day, at two levels of insulin infusion. In contrast, in the present experiments the clamps were done at different rates of insulin infusion, on dif-ferent days. Because the effect of insulinonglucose disposal is long lasting (29), in sequential infusion studies there may be a "memory effect," such that aprevious insulin infusion could augment the glucose uptakeduring afollowing infusion. Insulin infusion at a low rate followed by a higherone could act to increase ARd and therefore the value of SI(clamp) relative toSI,

andthis effectwould beprogressivelymoresignificantathigher insulininfusion rates.Thisputativememoryeffect might explain

the apparentinsulin-dependent bias ofSJ(clamp) in the previous study.

Oneofthe primarysimplifications implementedin the model is that during the FSIGT, glucose distribution can be described by a single compartment representation, despite evidence for three-compartment distribution of labeled glucose moieties when sufficient time is allotted (30, 31). Apparently, sinceglucose is rapidly normalized during the FSIGT (as compared, for

ex-ample, totheglucoseclamp) little filling of the slow compart-mentstakes place. Thatequivalent one-compartment represen-tationis adequate to account for FSIGTdynamicsis supported by ourpreviousdemonstrationofsingle-exponentialrestitution of the blood glucose, following glucose injection, when the in-crease ininsulin was prevented by somatostatin(32). Thus, dur-ing the FSIGT, the glucose distribution system can be repre-sentedby anequivalent one-compartment model, withasingle distribution volume, VD. Whereas it remains unknown what tissues in the body account for thisequivalentsingle compart-ment,it remains, asSteelepointedout many years ago(33), a useful conceptual framework for describing glucose dynamics

when arelatively shorttimeframe is available for glucose

dis-tribution.

Particularlyinteresting in thisregardarethecalculated values

for VD(Table V)whichwere estimated by fittingthe minimal model. This apparent volumeofdistribution, calculated from the increment in plasma glucose (corrected for extracellular mixing), averaged 16.1% ofthe body wt.This value represents 0.62 timesthe total glucose distribution space, prevously esti-mated to equal 26% of the body wt (21). What is interesting

about the 0.62 factoris that it is almost equaltothe so-called "pool fraction" Steele andhis colleagues proposed many years ago (16, 21, 32). Those

investigators proposed

that one could calculate the rate of glucose

production

during

the

non-steady

state by assuming a single-compartment distribution volume equal to 65% of the total distribution

volume,

when insufficient

timewasavailable forglucose

equilibration

into the entire three-compartment extracellular volume. Their conclusionwas vali-dated in the dog under limited conditions

by

Radziuk and Vranic(34).

Thestrikingequivalence oftheapparent distribution volume

oftheminimal model tothe

previously

validated

pool

fraction suggests that for the short time

periods

andlimited

glucose loads,

sim-plification

is adequate to represent glucose kinetics. In addition, predictionofthepreviously validatedone-compartment volume can beconsidered an independent validation ofthe minimal

model.

The ability ofthemodelingprocess toyield ameasure of the single compartment equivalent glucose VD in individual subjects(Table V)raisesthepossibility thatVDitself, estimated fromtheminimalmodelfit, couldbeused in theSteele relation,

rather than the"population" valueof 0.65 X 26% body

wt,

as is usually done (34). Independentstudies willhave tobedone todetermine ifusing individualized estimates ofthe pool fraction fromtheminimalmodelprovidesa moreaccurate assessment

ofglucoseturnover ratesfromtheSteelerelationship thanusing theassumedpool fraction, 0.65.

Ofcourse, weobservedsomevariation in the relationbetween

SI

and

_SIP(cwmp)

_(i.e.,

individual

points

didnotlie

exactly

onthe

line of equality).What cannotbedetermined fromthe present study arethe factors that contributetothisvariability:howmuch isdue to day-to-day variation in insulin sensitivity itself, how

much toimprecision inthe clamp measurement, and how much toimprecision in the minimal model analysis.Thefactthatthe

correlationwas notimproved markedly by substituting glucose infusion for

R&

inthecalculation of clamp-based sensitivity in-dicatesthatthe variancewas notduetofailuretoinclude liver inhibition in

_SIP(camp).

Actualreproducibility determinations will require future studies of repetitivemeasuresof sensitivity inthe sameindividuals,

using

thetwomethods.

Despite the overall equivalencebetweensensitivity from the clampand themodel,wedidfind,on apaired basis,a

marginally

significant

tendency for the

sensitivity

to be

higher

with the

FSIGTthanwiththeclamps, whenthe values werenormalized

toidentical units(Table VI,

Fig.

6).A

possible explanation

for this isthatthereisadifferencebetween thedefinitions of insulin

1.00

E

I-0 ._

C

.E

I-V

0 co

0.08

0.06

0.04

0.02

0.00

sensitivity using the clamps, versus minimal

model-analyzed

FSIGT data.Withclamps, wedefinedsensitivity intermsofthe

action of insulin to augmentglucose utilization (Rd). In the FSIGT,however, model-derived sensitivity is defined interms oftheability of insulintobothaugmentglucose utilization and

toinhibithepatic glucoseoutput.Thus, it is the total effect

of

insulinon the net glucose economy ofthebody which is rep-resented in

Si.

Therefore, it would notbe

surprising if,

ona

subject-by-subject basis,

the

higher sensitivity

found fromthe FSIGTcompared to the glucoseclampsmay havebeendue to theinclusion ofthelivereffectin thedefinition of insulin sen-sitivity.

Thehypothetical role of

inhibition

ofhepatic glucoseoutput

(HGO)tothehigher sensitivity measured by FSIGT

compared

to

SIp~clamp)

is diagramed in Fig. 7. The average increment in sensitivityof FSIGTmeasurement over theRd based measure-ment was 0.009dl/minperuU perml(Table VI),and

this

in-crement wasapproximatelythe samefor normal and obese

sub-jects (Fig.7).

Thehypothesisthatthe increment inthemodel-based

com-paredto theRd-based sensitivity is due toinclusion of HGO inhibition intheformer, leads to two

predictions.

First,the increment of the FSIGT-basedoverthe Rd-based sensitivity can beaccounted forbysome

fraction

of the basal

rateofHGO, becauseinsulincandono more thancompletely inhibit HGO regardless of the concentration achieved

during

the FSIGT.Theincrement in themodel-based

compared

tothe

Rd-based

sensitivity

canbe

expressed

interms

comparable

with glucose turnover bymultiplying by the clamp glucose

concen-tration (85 mg/dl) andtheincrementininsulin duetothe 40

mU/m2

per mininsulin infusion (average, 98

AU/ml),

and di-vidingby thesurfacearea.Sotransformed,the0.009dl/minper

,uU/ml

difference is

equivalent

to36

mg/min

perM2. The latter

BMI

<

3 0

(n=

5)

0

I

E

Zco 0 z

I-z w co)

SIP(clamp)-S A _SI-Vd

_SI(cIlmp)-

A

Figure 6. Comparison of three expressions of the insulin sensitivity index in the 10 subjects. All parameters are in units ofdl/minper MU/ml.

_Smd(.p)

iscalculatedfrom euglycemic clamps using Rd only

[SIpz,,dp)

=

_ARd/(AI

G)].SIis from the minimal model

(p3/

P2,seeMethods), whileSl(Cp)is calculated from clamp data using glucoseinfusiondata only

[SI(dp)

= AGINF/(AI-G)].GINF is the

incrementin glucose infusion at steady-state, and it is equal to

(ARd-_AHGO).

6-

4-

2-

4-

2-I

coL

_{_L}

n

BMI

>

30

(n=5)

iiia~T1

HGO

GLUCOSE UPTAKE

HGO

GLUCOSE UPTAKE

SIP(CLAMP) SI SI(CLAMP)

Figure7.Mean values of three expressions of the insulin sensitivity in-dex (see legendtoFig. 6) for subjects withBMI <30 orBMI >30

kg/

m'.

It is

hypothesized (see Discussion)

that theincrement in

SI

or

valueis less than the basal glucoseproduction (Table II). There-fore, the extent to which insulinsensitivity measured with the FSIGT exceeds that based upon Rd isconsistentwith half the basalhepatic glucose output being inhibited during the FSIGT protocol.

Second, the concept that the increment in sensitivity of the FSIGT-based value over the Rd-based value is due to partial

suppression ofHGOduring the FSIGT isconsistent with the

factthat when total glucose infusion (Rd increase + HGO de-crease) was used as abasis forexpressing sensitivity, the value

obtainedexceeded theFSIGT-based value by 0.006 dl/min per

,gU/ml

(24mg/min perM2).We expectsensitivitytobehigher wheninfusion rate was the basis for the calculation because the liver was 70-100% suppressed during the 40 mU/min perM2

glucose clamps.

Assuming that the inhibition of HGO is responsible for the larger estimate of insulin sensitivity when the FSIGT is used, compared toRd-based glucose clamps, we can reach certain

con-clusions regardingthecontribution oftheinsulin-mediated

in-hibition of HGO, compared to insulin stimulation of glucose uptake.First, in normalindividualsonlyabout 17%of

SI

is due

toinsulin inhibition ofHGO; the remainder is due to insulin

increasingRd(Fig. 7). Therefore, in such individuals it will matter little whether the liver effect is included in the overall sensitivity

determination. Second, thecontribution ofHGOinhibitionto

sensitivity wassimilarin obeseindividualsand normals(0.008 versus0.009dl/min

_perguU/ml).

Therefore, it would make little

difference for comparing insulin sensitivitybetween normal and obese individuals whether the FSIGT ortheRd-based glucose clampwasused.Infact, the absolutedifferenceinsensitivities

would bevirtually the same (FSIGT: 0.062-0.029 = 0.033

dl/

min per uU/ml; Rd-based clamp values: 0.053-0.021 = 0.032

dl/min per

MU/ml).

Therefore, itappears tobejustifiedto use the parameter

_SI

forassessing insulin action inindividuals of

differing sensitivity to the hormone, even though

SI

includes

within it the effects ofinsulin to inhibit endogenous glucose

production and to augmentglucoseutilization.

While the present datais consistentwith the idea that the

slightly

higher indexcalculated fromtheFSIGT is duetoliver suppression,it isstill possiblethat thereisanalternativereason. Onepossibility isthat steadystate glucose utilization was not achievedinourclampexperiments, despite 180 minofinsulin

infusion. This artifact could result in an underestimate of

SIP(clamp)

. Other

possibilities

include unaccounted for loss of

glu-coseviarenalexcretion whichwould leadtooverestimation of

VD. Thelatterpossibilityseemsunlikely since<3%ofinjected

glucoseisclearedduringan intravenous glucosetolerance test (35, 36),and renal clearance wouldcontributenot to

SI,

but the

term independent ofthe insulin response, SG

(32).

However,

whether oursuppositioniscorrectthat thesmalldifferential is

due toinclusion ofliver

suppression

in

SI,

butnot

SIP(clamp),

or

whether thedifferential is dueto some othercause remainsto

be testedexperimentally.

Inconclusion, the present data demonstrate that minimal model analysis ofthe frequently sampledintravenous glucose

tolerance test yields a measure of insulin

sensitivity

which is

equivalenttothesameparameter measured

by

the

euglycemic

glucoseclamp.The results

imply

that themeasureis dominated

byextrahepaticeffects ofthehormone.Previous poor correlation betweenthese methodswas

apparently

dueto

suboptimal

dy-namic testing protocols,rather than

inadequacy

of the minimal modelitself. In addition, the FSIGT is less labor intensive and

requires less specialized equipment than the glucose clamp, and the FSIGT yields some information about B-cell function (8). Therefore, the present results indicate that the minimal model method ispotentially useful for measuring insulin sensitivity in longitudinal or cross-sectional epidemiologic studies of insulin resistance in nondiabetic individuals, when use of the glucose clamp is not feasible for economic or practical reasons. Ofcourse, it will be necessary to extendvalidationstudies to a wider variety ofconditions and to larger populations if general use of the

methodology

istoberecommended.

Appendix

Whilethey both reflect insulin sensitivity,

SI

andSIPclamp)arenot directly comparable because they are expressed in different units(SI in min-' per

AU/ml

andSIPfclamp) in dl/(min per M2) per

_AU/ml).

Toconvert them to acommon unit it is necessaryto useconversion factors which emerge from the method used to estimate them:

_SI

should be converted using parameters estimated for theminimal model approach; SIP(clamp) con-versionmust usefactorsassociated with the euglycemic glucose clamp. Thefundamentaldifference between

_SI

andSIpn(camp)asused in the presentworkis that theformer expresses the effect of insulin to increase netfractional disappearance of glucose from the extracellular "glucose space" (i.e.,rate ofnet glucose disappearance divided byamount of glucose in thepool).2 The latter representstheeffect of insulin to enhance glucose clearance (rate of glucose uptake divided by plasma glucose con-centration) per unit body surfacearea.Thus, thesetwoparametersare

normalized todifferent measures of body "size"; the former tothevolume of distribution of glucose of the minimal modelitself,the lattertobody surface area. However, both parameterscan be easily converted toa common index of insulinsensitivity: the effect ofaunitarychange in insulin to cause a given increment in glucose clearance.3 For purposes of discussion, letusdefine the parameter Sc, which represents the insulin sensitivity index in units of increment in glucose clearance per unit

in-crementin plasmainsulin,expressed in units of deciliters per minute permicrounit per milliliter.

Glucoseclamp. Toreiterate,

SIpFc.amp)

is definedas(ARd/(AI X G)), where Rd is expressed in mg/min per unit surface area of the body, I is inMU/ml,andG is in mg/dl. Theunits ofSIP(clamp)aredl/(min perM2)

perAU/ml, orclearance per unit surfaceareadivided by insulin

con-centration.To convertSIP(clamp)toSc,wesimplymultiplyby the surface

areaof the individual expressed in M2. Then, fortheeuglycemicclamp, S,will beexpressedindl/minperAU/ml:

Sc=

Sip(clamp)

xsurfacearea. (Al)

Minimal model. Thefractional disappearance rate asused in

SI

is thenetglucosedisappearanceratedividedbytheglucose"pool"size, where thepool size is the massofglucosein the single glucose

com-partmentof the minimal model itself. Thus,ifwedefine VDasthe

as-sumedsinglecompartmentdistributionspacewithglucoseconcentration

G,thenet_{disappearance}rateisgivenasthefractional ratemultiplied

by VD-G.However, to convertthenet rate to_glucoseclearance it has

tobedividedbyG.Thus,Gdropsout, andto convert_SIto_Scwe_simply

2. "Net" glucose disappearance refers to thesum ofany decrease in glucoseproduction plusincrease inglucoseuptake,eitherofwhich will

act tolower theplasmaglucoseconcentration.

3. Actually, for SI this isgiven in termsofnet_glucose clearance; for

SIFPclamp)this definition is made in terms of absolute glucose clearance

(theinsulin-induceddecrementin HGO isnotincluded).This distinction

resultsinasmall butsignificantdifferencebetweenSIand

Spfciamp)

ina

given individual (see

Discussion).

Also,it is

important

to notethat

al-though glucose clearance itselfdecreases significantly at physiological

multiply

SI

by VDexpressed in dl. ThenScwill beexpressed indl/min perMU/ml:

SC= SI

X

VD.

(A2)

Summary.Thus, byexpressingparameters

_Smd..p)

andS, according

toequationsAl andA2, respectively,theyareconvertedtothecommon

parameter Sc, expressedin dl/minper

gU/ml.

We may demonstrate

equality, then,if

SIXVD=SIp(clamp)X surfacearea. (A3)

Note thatthequantities of theleft hand side ofequation A3 are

measuredindependently of thoseontherighthandside. This excludes bias in thestatisticalcomparisonof thetwomethods formeasuringS,. Acknowledaments

We aregratefultoMarilynAderfor her aid inproducingthemanuscript. This workwassupportedbygrants from the National Institutes of Health to Drs.Olefsky (AM-33649)andBergman(AM-29867),andby

theMedical Research Service of the Veterans Administration Medical Center, SanDiego,CA.

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