Understanding

“Insulin Resistance”: Resistance Are Required

Both Glucose Resistance to Model Human Diabetes

AS. Ruder-ski, D.R. Matthews,

and Insulin

J.C. Levy, and RX. Turner

A mathematical model of normal glucose/insulin homoeostasis has been based on the known, experimentally determined responses of the liver and periphery to different glucose/insulin concentrations. Different defects of glucose resistance and insulin resistance have been applied to the model to investigate the degree to which these abnormalities could successfully predict the range of fasting glucose and insulin values found in normal, obese, and diabetic subjects. Modeling glucose resistance or insulin resistance at the liver or the periphery alone did not increase the plasma glucose to levels observed in diabetes, even when associated with marked deficiency of g-cell function. A defect of either glucose resistance or insulin resistance affecting both periphery and liver allowed a wider range of basal glucose and insulin concentration values, but resulted in unphysiologically low hepatic glucose output: with modeling insulin resistance, hyperglycemia suppressed glucose output, whereas with glucose resistance, raised insulin levels suppressed hepatic glucose output. A wide range of glucose and insulin values, with appropriate basal hepatic glucose output, could only be modeled by insulin resistance at both the liver and periphery with additional glucose resistance at the liver. The modeling results are in accord with investigative studies that suggest secondary hepatic and peripheral glucose resistance in response to hyperglycemia. Modeling provides a systematic means of examining the likely effect of different putative defects in a complex physiological system. Copyright 0 1991 bi W.B. Saunders Company

I

NSULIN DEFICIENCY is an unambiguous definition. There is no difficulty in appreciating its role in the pathophysiology of type 1 diabetes mellitus. The term “insulin resistance,” on the other hand, has come to denote a variety of metabolic abnormalities. These abnormalities have been considered to play an important role in the development of type 2 diabetes mellitus. Modeling of metabolism has been used to quantitate the degree of deficiency of insulin secretion and the degree of insulin resistance, in order to examine the interplay of these two factors in human patients.‘,’ This report studies the implications of modeling insulin resistance in different ways, and examines how well each model could account for the pattern of fasting glucose and insulin concentrations and basal glucose production rates found in type 2 diabetes mellitus. Models with few structural assumptions can be successful, as shown by the application of a minimal model to estimate sensitivity coefficients of control points. The minimal model of glucose and insulin metabolism of Bergman et al allows measurement of glucose and insulin sensitivity in normal and glucose-intolerant subjects.] Increasing knowledge of human physiology allows a slightly different approach in which a more detailed quantitative model of glucose turnover in a healthy human subject is constructed based on the known responses of individual organs. By including functions to describe peripheral tissue responses to glucose and insulin, hepatic responses to glucose and insulin, and pancreatic responses to glucose, it is possible to derive a series of simple, algebraic, and differential equations describing glucose turnover in man. Sensitivity analysis has been employed in this model,

altering the sensitivity coefficient of control points to assess the potential magnitude of their effects. The steady-state values of glucose concentration, insulin concentration. and hepatic glucose output obtained from the model have been compared with known values found in normal. obese, and diabetic man in a systematic examination of the possible types of deficits that might account for the impairment in glucose turnover commonly termed “insulin resistance.” The term “resistance” usually conveys a specific meaning. For example, in the subject of electric circuits, a component with a large resistance requires a larger electromotive force to drive electric current through it. A similar situation in the context of physiology would be the presence of a competitive antagonist inducing resistance to an agonist, so that higher concentrations were required to achieve the same effect. Although insulin antagonists have been postulated, their role is not substantiated in type 2 diabetes or obesity, which are commonly associated with insulin resistance. Insulin resistance may not bc analogous to the simple concept of resistance in the electrical circuit and could also occur as a result of a reduction in the number of hormone/ transmitter receptors in a system with spare receptors or as a result of an abnormal insulin receptor. Kahn draws the distinction between insulin resistance and insulin responsiveness, and resistance to glucose is also postulated.’ We examine here how different defects in the body’s response to glucose and insulin concentrations affect glucose turnover. The different defects include resistance or unresponsiveness to insulin and/or glucose in the liver and periphery, and their interaction with impaired B-cell function. BACKGROUND Peripheral

From the Diabetes Research Laboratoties, Radcliffe Infirma?, Oxford, UK. Address reprint requests to A.S. Rudenski, MD, clo R.C. Turner, MD, Diabetes Research Laboratories, Radcliffe Injimary, Woodstock Rd, Oxford UK. Copyright 0 1991 by W.B. Saunders Company 00260495191/4009-0006$03.00/0 908

insulin Resistance

Insulin resistance has been thought to be a major feature of type 2 diabetes, particularly since the high basal plasma insulin concentrations found in obese type 2 diabetic patients by bioassay were confirmed by immunoassay.’ Peripheral insulin resistance was also indicated when diabetic patients had raised steady-state plasma glucose concentrations when infused with a standard glucose and Metabolism,

Vol40,

NoQ(September),1991:

~~90%917

MODELIING INSULIN RESISTANCE

insulin load while p-cell secretion was inhibited.’ Several studies have confirmed peripheral insulin resistance,6~” though direct measurement sometime has found no abnormality in glucose uptake by forearm muscle in patients with type 2 diabetes.’ The curve of glucose uptake versus insulin concentration was shifted to the right with an increased K, in diabetic subjects compared with nqndiabetic volunteers,‘” whereas the maximal response Vmax” was unaffected. Glucose transport in vitro into adipocytes at different msulin concentratipns, showed both a rightward shift of Is, and a reduction in Vmax.” Obesity appears to be a major factor inducing insulin resistance. Both obese nondiabetic and diabetic subjects have raised fasting insulin concentrations, whereas normal weight diabetic subjects have often been reported to have near-normal fasting insulin concentrations. When assessed by the steady-state glucose concentration during a standard glucose and insulin load in nondiabetic subjects, a 0.7 correlation was found with body mass index.” Insulin is less effective in obese than in non-obese subjects in stimulating glucose uptake,‘g-‘5 although antilipolytic action in obese subjects may be normal.” When studied with euglycemic clamps at different insulin concentrations, ni,ne of 11 obese subjects had a reduced maximal response Vmax, and the half-maximally effective insulin concentrations were also raised. Obese subjects had an impaired glucose transport into adipocytes” and a reduction in the number of insulin receptors on adipocytes.‘” This correlated with decreased sensitivity to insulin as assessed by the rate of decrease of plasma glucose after intravenously administered insulin.” The insulin resistance in diabetes may in part be due to deficient insulin receptor binding,” although no alteration has been observed by others. “J’ Reduced internalization of receptor-insulin complex and reduced insulin degradation by monocytes may occur in type 2 diabetes.‘” Beck-Nielson found impaired insulin binding to monocytes was more marked in obese subjects than in diabetic patientsz4 These data suggest that a postreceptor defect has a role in the insulin resistance of diabetes, whereas impaired insulin receptor binding is probably an important factor in obesity.

909

fact that in diabetes, impaired insulin responsiveness has been observed, as well as impaired insulin sensitivity. In summary, peripheral glucose uptake by tissues is reduced in patients with type 2 diabetes compared with nondiabetic subjects with similar prevailing glucose and insulin concentrations. Moreover, the balance of evidence suggests that there is a small but significant increase in basal glucose production by the liver, and that the liver does not suppress production in response to the effects of high glucose and insulin concentrations to the same extent as in the nondiabetic subject. The data concerning insulin receptor numbers and binding behaviour in type II are conflicting, but a postreceptor defect is probably the major feature.6 However, insulin insensitivity in obesity could be explained by a simple resistance problem at the level of the insulin receptor. THE MODEL DERIVATION

The model consists in its basic form of a set of equations that describe steady-state glucose production and uptake in various sites as functions of concentrations of glucose and insulin or of glucose alone, and the steady-state insulin secretion as a function of glucose concentration.‘,‘“,” In summary, Peripheral Glucose Uptake is a function f, of glucose concentration G and insulin concentration I: PGU = f&G, I) = 8.434 &,

iO.0838 + i&r]

Splanchnic Glucose Uptake is a function of glucose concentration: SGU=O&. Central Nervous System (CNS) Glucose Uptake is a function of glucose concentration: CGU = 0.4 tanh (0.45 G) Thus, near-maximal uptake is maintained until glucose levels fall below 3 mmolil or so. Hepatic Glucose Output is a function f, of glucose and insulin concentration:

Hepatic Insulin Resistance

The occurrence of a raised basal hepatic glucose production in type 2 diabetes in the presence of normal or raised plasma insulin levels and raised glucose levels suggests a failure of normal suppression of hepatic glucose production,‘s.‘6 and a similar shift of the response curve to the right is also found in obese subjects.” Hepatic Glucose Resistance

As basal glucose production is normal or slightly raised in the basal state despite hyperglycemia, which in normal subjects suppresses hepatic glucose output, there is probably an impaired response to glucose in type 2 diabetes.” Peripheral Glucose Resistance

In diabetes, there is a peripheral deficit of glucose uptake that appears to be as important, if not more important, than that of obesity.’ Glucose resistance could account for the

HGO=f,(G,I)=2.33[1-=)(I--tanh[O.O755I]) Glucose concentrations are expressed in mmol/l, insulin concentration in mu/L, and glucose fluxes in mmoL/min per 70-kg human. In the steady state, hepatic glucose output matches uptake by peripheral tissues, CNS, and the splanchnic bed. It was decided to assign the same half-maximal effect of glucose to the liver, spanchnic bed, and periphery at a value of 8 mmol/L. Maximal glucose uptake would be greatest in the periphery. Insulin concentration is related to glucose concentration in the steady state, via an expression for insulin secretion rate, and a set of equations describing insulin kinetics in four pools: peripheral plasma (Ip) peripheral insulin receptors (IT)

910

RUDENSKI ET AL

portal plasma (1”) liver insulin receptors (IL) The details of this model have been published.2” Insulin Secretion Rate [ISR] is related to glucose concentration: for G I 2.5, ISR = 0 for 2.5 < G I 8.13, ISR = 0.0139 (G-2.5) + 0.0103 (G-2.5)’ for 8.13 < G, ISR = 0.405 + 0.348 (tanh 0.793 [G-9.3] t tanh 0.793 [9.3-8.131)

PGU = V,f,(S,G,S,I) Hepatic

in mmolimin

- k, (R - I,)& + k,I, IP

& I, = k,(R - I,&

iI”=

&I, = k,(R, IDR = FLOW = IDR = R = R, = V,, = V,, = k, = kZ = k, =

- (k: + k,)I,

ISR - IDR - k,(RL - IJI, V I”

glucose output (HGO),

is modified

HGO = f,(S,;,G,S,,

The units of insulin production are expressed per 70-kg human The insulin kinetics model is: & I, = p

f. absence of glucose and/or insulin feedback on basal hepatic glucose production. An absence of both insulin and glucose feedback fixes the glucose production rate to the normal steady-state value. All parameters had a value of 1 in the nondiabetic subject. Values are quoted as percentages of normal. Peripheral glucose uptake (PGU) was modulated as follows:

+ kJ,

W, - (kz + W,

FLOW (I, - Ip) transhepatic plasma flow 0.875 Umin post hepatic insulin delivery rate peripheral receptor concentration 12.90 nmol/L concentrations of liver insulin receptors 146 nmol/L peripheral plasma volume 2.75 L hepatic portal plasma volume 0.22 L 0.032 mini’ . nmol-’ L 0.019 min-’ 0.049 min-’

The model can be solved numerically to obtain the steadystate insulin concentration, I,, from the steady-state glucose concentration via the steady-state insulin secretion rate. The equations describing glucose turnover were solved for steady state to obtain the basal plasma glucose and insulin concentrations in the standard nondiabetic human. Parameters in the model were then modulated to account for altered function in the following ways: 1. Insulin secretion rate was modulated by a parameter B, p-cell function index, with secretion rate response decreasing as B fell below 100%. 2. A peripheral defect in glucose metabolism was modeled either by a. reduced sensitivity to insulin (S,) b. reduced sensitivity to glucose (S,), or by c. reduced responsiveness of glucose uptake (V,) (ie, reduced Vmax) 3. The deficits modeled at the liver were d. reduced liver sensitivity to insulin (S,,), e. reduced liver sensitivity to glucose (S,,), or

as follows:

I)

Glucose is taken up by insulin-dependent and insulinindependent tissues, peripherally and portally. Glucose uptake by tissues considered to be insulin-independent users of glucose, such as the brain and splanchnic bed, were assumed to be unaffected in their responses. The steady-state values for insulin and glucose conccntrations for the different combinations of p-cell factor and glucose and insulin “resistance” were calculated from the set of nonlinear equations by a computer program using a regula falsi”’ method to find values at which net glucose flux (glucose output minus glucose uptake) was zero. These values were plotted out on graphs with glucose (mmol/L) on the horizontal axis and insulin (mu/L) on the vertical axis as the points of intersection of contour lines of constant p-cell function and constant glucose turnover response parameters. The models were examined to determine the extent to which they could explain the range of fasting glucose and insulin concentrations and hepatic glucose output found in normal and diabetic man (Fig 1). The sequence of unitary defects and combinatorial defects modeled are in Table 1. RESULTS

The fasting plasma glucose and insulin concentrations in normal subjects and newly presenting type 2 diabetic patients are shown in Fig 1. Figures 2 through 5 illustrate the range of glucose/insulin concentrations obtained from the model by adjusting individual parameters that are candidates for inducing “insulin resistance.” Tables 2 through 4 indicate the rate of hepatic glucose output and fasting values for representative cases for 25%’ glucose or insulin sensitivity combined with 100% p-cell function (Table 2) 100% glucose insulin sensitivity combined with 25% p-cell function (Table 3) and 25% function of both insulin secretion and of glucose or insulin sensitivity (Table 4). UNITARY

DEFECTS OF GLUCOSE OR INSULIN RESISTANCE

Glucose and Insulin Resistance

at the Liver

When a combination of hepatic insensitivity to glucose was modeled with different insulin secretory defects (Fig 2a), a wide range of glucose values was obtained but peripheral and hepatic responsiveness to insulin was such that steady-state insulin levels did not exceed 10 mu/L.

911

MODELING INSULIN RESISTANCE

Glucose and Insulin Resistance at the Periphery A

When peripheral glucose resistance was modeled (Fig 2c), a wide range of glucose values was obtained, but basal insulin concentration did not exceed 15 mu/L, as this suppressed hepatic glucose output below normal. When impairment in peripheral glucose uptake responsiveness (V,) was modeled, basal hyperinsulinemia was not obtained, as the normal hepatic response to insulin resulted in low glucose production rates. This gave a similar picture to that resulting from peripheral glucose resistance. When peripheral insensitivity to insulin was modeled (Fig 2d), a narrow range of basal glucose and insulin concentrations was obtained, due to the hepatic sensitivity to insulin and glucose. This was compounded by the ability of hyperglycemia to overcome the inhibitory effect of insulin resistance on peripheral glucose uptake.

A

A A AA A AA A A tAAA

B A

kA

AA AA

Glucose and Insulin Resistance at the Liver and Peripheg

10

5

15

20

Basal Glucose Concentration (mmol/l) Fig 1. Basal plasma glucose and insulin concentrations in 132 newly presenting type 2 diabetic patients (A) and 98 nondiabetic subjects (+), indicating the range of values that need to be encompassed by a model of the pathophysiology of diabetes.

When a combination of insensitivity to insulin at the liver, was modeled with different insulin secretory defects (Fig 2b), basal glucose concentrations greater than 12 mmol/L were not achieved, for hyperglycemia was still able to exert an inhibitory effect upon hepatic glucose output, and peripheral glucose uptake increased sufficiently to match the increased hepatic glucose output.

When glucose sensitivity at the liver and periphery were equally reduced (Fig 2e), the glucose values covered a wide range, but the insulin concentrations were less than 20 mu/L, as a consequence of insulin’s ability to suppress glucose production at the liver. When insulin sensitivity at the liver and periphery were equally reduced (Fig 2f), a wide range of basal insulin and glucose values could be simulated, but the glucose concentration did not exceed 12 mmol/L. since the raised glucose alone would drive its own uptake and suppress its own production. COMBINATORIAL RESISTANCE

DEFECTS OF GLUCOSE AND/OR

INSULIN

AT THE PERIPHERY WITH SECONDARY

GLUCOSE OR INSULIN RESISTANCE

AT THE LIVER

Peripheral Glucose or Insulin Resistance With Secondary Hepatic Glucose Downregulation and Normal Insulin Feedback on the Liver When impairment of peripheral glucose sensitivity was modeled, with glucose feedback to the liver fixed to normal by adjusting hepatic glucose sensitivity appropriately (Fig 3a), the insulin values did not rise above 15 mu/L, since

Table 1. Different Combination of Defects That Could Constitute “Insulin Resistance” 1. Ulnitary defects of glucose resistance or insulin resistance by Erimary glucose resistance

Primary insulin resistance

(a) at liver

(a) at liver

(II) at periphery

(b) at periphery

(I:) at liver and periphery

(c) at liver and periphery

2. Combinatorial defects with primary glucose or insulin resistance at periphery and different secondary defects at the liver Erimary glucose resistance

Primary insulin resistance

(a) with secondary glucose resistance at liver

(a) with secondary glucose resistance at liver

(b) with secondary insulin resistance at liver

(b) with secondary insulin resistance at liver

(I:) with both secondary glucose and insulin resistance, ie, fixed

(c) with both secondary glucose and insulin resistance, ie, fixed

basal hepatic glucose output

basal hepatic glucose output

3. Combinatorial defect of glucose or insulin resistance at both liver and periphery with different secondary defects Primary insulin resistance at liver and periphery _Primaryglucose resistance at liver and periphery With secondary downregulation at liver of insulin sensitivity

With secondary downregulation at liver of glucose sensitivitiy With secondary downregulation at liver and periphery of glucose sensitivity

RUDENSKI ET AL

912

Insulin resistance

Glucose resistance

a

50

at liver

I 40

d

I

at periphery

p= 200

at liver and periphery

10

4

8

12

16

0

20

Basal Glucose concentration

4

8

(mmolil)

insulin feedback to the liver resulted in lower hepatic glucose output when insulin was elevated. Varying peripheral glucose turnover responsiveness, V,, yielded a similar picture. Peripheral Glucose or Insulin Resistance With Secondary Hepatic Insulin Downregulation and Normal Glucose Feedback on the Liver When impairment of peripheral glucose sensitivity was modeled, with hepatic insulin sensitivity adjusted to give a normal feedback onto glucose production (Fig 3c), a wide range of insulin values was obtained. However, steady-state glucose values in the absence of insulin were low because of the lack of effect of low insulin in increasing glucose output. In addition, a decreasing glucose production rate was found at high basal glucose values. When reduction in peripheral glucose uptake responsiveness, V,, was modeled, the range of glucose concentrations was again limited because the effect of low insulin concentrations leading to an increase in hepatic glucose output

12

Fig 2. Unitary defects of glucose resistance or insulin resistance affecting liver, periphery, or both. Model prediction of basal glucose and insulin concentrations resulting from the interaction of insulin or glucose sensitivity at specific sites with different degrees of S-cell function (B = 200%. 100%. 50%, 25%. 10% normal) shown as the series of continuous lines with positive slope. The different degrees of insulin/glucose sensitivity (S = 200%. 100%. 50%, 25%. 10% normal) are indicated by the series of broken lines of negative slope.

was lost, while that of high glucose levels in suppressing glucose production was maintained. A similar picture to that in Fig 3c was obtained. When peripheral insulin resistance was modeled with insulin resistance at the liver determined by the basal insulin concentration (Fig 3d), a very narrow range of values was obtained. Raised glucose levels suppressed glucose production, and as a low insulin concentration did not lead to an increase in hepatic glucose output, glucose concentrations did not increase realistically in response to insulin deficiency. Peripheral Glucose or Insulin Resistance With Fixed Basal Hepatic Output Independent of Glucose and/or Insulin Concentration When the peripheral glucose sensitivity was varied, with maintenance of normal basal glucose output by adjusting sensitivity of the liver to glucose and insulin according to basal glucose, G, and basal insulin, I, such that G

x

S,, = 4.8 mmol/L (the normal basal glucose value).

913

MODELING INSULIN RESISTANCE

Glucoaa raalstanwat periphery

b

50-a

Insulinmistam al peripherv

Secondary glucose resistance

40

al her

30 .

20.

p 2 %#9Cdlfunchon

'O. 0

$5$jyQQ~v&Q dp ,:-. )........_. ...............__.......--.. d

Secondary insulin resistance at liver

I f

5ore

!'"200

glucose and msulin rewtance 30

20.

10.

Fig 3. Glucose or insulin resistance at periphery with different secondary defects at liver. Model predictions of basal glucose and insulin concentrations (see Fig 2 legend).

0 4

16

12

20

Basal Glucose concentration

Glucoseresistanceat liverand periphery

12

8

16

20

(mmolil)

Insulinresistanceat liverand periphery

4

8

12

16

20

24

BasalGlucoseconcentration(mmol/I) Fig4.

Glucose or insulin resistance at both liver and periphery with secondary resistance at the liver. Model predictions of basal glucose and

insulin concentrations

(see Fig 2 legend).

914

RUDENSKI

Insulin resistanceat liver and periphery

.,_.

. . ..__.... ,.__,,,,,,,

COMBINATORIAL RESISTANCE

16

20

AL

wide range of values, but when insulin output approached zero, the liver sensitivity to insulin became infinite. The pattern was very similar to that produced by altering peripheral glucose sensitivity (Fig 3e). When peripheral insulin sensitivity was reduced, with normal glucose output being maintained by the liver (Fig 3f), the range of possible glucose values was limited. This was a consequence of glucose driving its own peripheral uptake.

Secondary glucose resistance at liver

12

ET

24

Basal Glucose concentration(mmol/l) Fig 5. Insulin resistance at liver and periphery with secondary glucose resistance at liver and periphery. Model predictions of basal glucose and insulin concentrations (see Fig 2 legend).

and I x S,, = 5.3 mU/L (the normal basal insulin value), a wide range of values was obtained (Fig 3e). However, when insulin output approached zero, the liver sensitivity to insulin became infinite, and steady-state glucose concentrations were limited from rising too high by glucose production remaining normal, instead of increasing as it does in type 2 diabetes. Impairment of peripheral glucose uptake responsiveness, V,, with hepatic glucose and insulin sensitivities adjusted to fix glucose output to normal. yielded a

DEFECTS OF GLUCOSE AND/OR

INSULIN

AT BOTH THE LIVER AND PERIPHERY

When glucose resistance was modeled at both the liver and the periphery (Fig 4a), with hepatic insulin sensitivity in inverse proportion to the insulin concentration, a wide range of glucose and insulin values was obtained (Fig 4a). Hepatic glucose output was increased in states where basal glucose or basal insulin was high. However, low insulin values did not result in increased hepatic glucose output. When insulin resistance was modeled at the periphery and the liver, with hepatic glucose sensitivity inversely in proportion to the increase in fasting glucose concentration (Fig 4b), a wide range of glucose-insulin values was obtained. Low insulin values resulted in an increase in hepatic glucose production, which drove basal glucose concentration to high values. Glucose production was elevated in states where glucose was high, whether insulin was high or near normal. The same model with peripheral and hepatic insulin insensitivity was assessed with both hepatic and peripheral glucose sensitivity adjusted by the basal glucose conccntration (Fig 5). Again, as increased basal glucose concentration resulted in secondary glucose resistance at both the

Table 2. Effect of Varying Different Forms of Resistance With p-Cell Function 100% on Fasting Plasma Glucose (fpG), Insulin (fpl), and Hepatic GlucoseOutput(HG0)

SGL

SIL

SG

(%I

WI

W)

fpG

S,

(mmol/L1

WI

fP' (mUILl

HGO (mmolimin~

Figs

100

100

100

100

100

4.8

5.3

0.96

25

100

100

100

100

5.2

7.0

1.06

2a

100

25

100

100

100

5.7

9.4

1.21

2b

100

100

25

100

100

5.3

7.2

0.76

2c

100

100

100

25

100

5.0

6.2

0.87

2d

100

100

100

100

25

5.4

7.7

0.72

25

100

25

100

100

5.6

9.1

0.82

100

25

100

25

100

6.6

14.8

1.02

2f

91*

100

25

100

100

5.3

7.4

0.77

3a

951

100

100

25

100

5.1

6.3

0.87

3b

89'

100

100

100

25

5.4

7.9

0.73

2e

100

45t

25

100

100

6.1

11.7

0.89

3c

100

61t

100

25

100

5.6

8.8

0.92

3d

100

35t

100

100

25

6.6

15.2

0.86

73s

37t

25

100

100

6.5

14.3

0.96

3e

80'

47t

100

25

100

6.0

11.3

0.96

3f

66*

25t

100

100

25

7.3

21.0

0.96

25

23t

25

100

100

7.6

23.0

1.20

4a

701

25

100

25

100

6.9

17.4

1.06

4b

67'

25

25

100

7.2

19.6

1.01

5

67*

NOTE.Normalvalues arelisted onthetopline.

lS,,secondarilyadjusted suchthat(l/lOO)x

S,, x G = 4.8mmol/L.

tS,,secondarilyadjusted suchthat(l/lOO)x S,,x I= 5.3mu/L.

915

MODELING INSULIN RESISTANCE

Table 3. Effect of Reducing p-Cell Function to 25% With Different Forms of Resistance That Maintain Hepatic Glucose Output

SGL

(%:’

SK

Wb

SG

W)

S,

VR

WI

I%)

fpG

fPl mu/L

HGO (mmol/mml

ImmollL)

Figs

100

100

100

100

100

4.8

5.3

0.96

100

100

100

100

100

7.7

2.8

1.04

2a

100

100

100

100

100

7.7

2.8

1.04

2b

-

100

100

100

100

100

7.7

2.8

1.04

2c

100

100

100

100

100

7.7

2.8

1.04

2d

100

100

100

100

100

7.7

2.8

1.04

100

100

100

100

100

7.7

2.8

1.04

100

100

100

100

100

7.7

2.8

1.04

2f

56”

100

100

100

100

8.6

3.8

1.12

3a

56,’

100

100

100

100

8.6

3.8

1.12

3b

5E’*

100

100

100

100

8.6

3.8

1.12

100

535t

100

100

100

5.8

1.0

0.91

3c

100

535t

100

100

100

5.8

1.0

0.91

3d

100

535t

100

100

100

5.8

1.0

0.91

73*

321t

100

100

100

6.6

1.7

0.96

3e

73’

321t

100

100

100

6.6

1.7

0.96

3f

73*

321t

100

100

100

6.6

1.7

0.96

100

2e

535t

100

100

100

5.8

1.0

0.91

4a

56X

100

100

100

100

8.6

3.8

1.12

4b

53f

100

100

100

9.2

4.7

1.03

5

53’

NOTE. Normalvalues (B = 100%) areontopline,otherlines are for B = 25%. *S,,secondarilyadjusted suchthat(l/lOO)x S,, x G = 4.8 mmol/L. tS,,secondarilyadjustedsuchthat(l/lOO)x S,,x

I = 5.3mu/L.

liver and the periphery in non-CNS tissue, a wide range of glucose and insulin values was obtained. DISCUSSION

The inclusion of different defects in the model indicates that no unitary defect of insulin or glucose sensitivity, with or without deficient p-cell function, could produce the range of fasting plasma glucose and insulin results observed

in practice. A review of the literature indicates that various abnormalities have been observed, and these have been applied to the model to assess their potential effect. When impairment at the liver alone was modeled, the normal responses at the periphery prevented the wide range of basal glucose and insulin concentrations observed in clinical practice. In models where impairment at the periphery alone was allowed, high insulin or glucose levels

Table 4. Effects of a Combination of Different Forms of Resistance With B_Cell Function Reduced to 25%

SC,

(%I)

St

WI

SG

1%)

S,

VR

W)

i”h)

fpG

(mmol/L)

fPl (mu/L)

HGO (mmollmin)

Figs

1011

100

100

100

100

4.8

5.3

0.96

2!j

100

100

100

100

9.3

4.9

1.20

2a

100

25

100

100

100

8.8

4.2

1.25

2b

100

100

25

100

100

8.8

4.2

0.86

2c

1011

100

100

25

100

8.0

3.1

1.00

2d

100

100

100

100

25

9.2

4.8

0.80

2lj

100

25

100

100

10.4

6.7

0.97

100

25

100

25

100

9.7

5.5

1.08

2f

49’

100

25

100

100

9.8

4.7

0.93

3a

53”

100

100

25

100

9.0

4.5

1.05

3b

4Jx

100

100

100

25

10.3

6.6

0.84

2e

100

180t

25

100

100

7.9

3.0

0.81

3c

100

515t

100

25

100

5.8

1.0

0.90

3d

100

133t

100

100

25

8.7

4.0

0.78

46”

81t

25

100

100

10.3

6.6

0.96

3e

69* 39*

265t 46t

100 100

25 100

100 25

7.0 12.4

2.0 11.6

0.96 0.96

3f -

25

100

100

11.8

9.6

1.10

4a

100

25

100

12.5

12.0

1.21

4b

25

100

13.6

17.3

1.07

5

25

55t

39*

25

36*

25

36*

NOTE. Normal values (B = lOO%)are listed onthetop line. *S,,secondarilyadjusted suchthat(l/lOO)x S,, x G = 4.8mmol/L. tS,,secondarilyadjusted suchthat(11100)x S,,x I= 5.3mu/L.

916

suppressed hepatic glucose output, a prediction that is at odds with experimental results. This was still a problem in models where insensitivity to either glucose or insulin alone was modeled equally at the liver and in the periphery. Physiological considerations would demand that glucose output be kept above some minimal value irrespective of ambient steady-state glucose-insulin values. This requires that a liver “homeostat” be able to reset itself to respond to basal glucose and insulin appropriately. Models were therefore formulated where sensitivity of the liver to basal glucose and insulin concentrations was adjusted so that each would appear to exert an effect equivalent to the normal concentrations of 4.8 mmol/L glucose and 5.3 mu/L insulin, these being the basal steady-state concentrations achieved in the model when all parameters were 100% normal. In other words, basal hepatic glucose output would be kept at a normal value. While such models had the advantage of glucose output not being suppressed by high glucose or insulin concentrations, they had the obvious drawback of not allowing any variation in basal glucose output at all, so that low insulin concentrations would not result in increased glucose output by the liver. It was therefore decided to examine models where only one of the feedback inputs into the liver, glucose or insulin, was modulated by a sensitivity parameter so as to exert an apparently normal effect. Models in which liver sensitivity to insulin was determined by the basal insulin concentration so that feedback would be equivalent to 5.3 mu/L, and in which no such secondary adjustment was incorporated for hepatic glucose sensitivity, manifested the drawback of low insulin concentrations not causing glucose output from the liver to increase, thereby allowing reasonably high steady-state glucose concentrations. Models where glucose sensitivity at the liver was adjusted according to the basal glucose concentration, so that the liver would respond as if the basal glucose concentration were normal (4.8 mmol/L here) behaved variably. In models where no impairment of response to insulin was modeled at the liver, high levels of insulin could not be achieved in the steady state because of suppression of hepatic glucose output. The model with peripheral and hepatic insulin resistance with secondary hepatic glucose resistance fitted well with physiological observations. A wide range of glucose and insulin values was allowed in the steady state. as might be found in patients in real life. Varying insulin sensitivity at the liver allowed for the shifts in K, observed when constructing stimulus-response curves of suppression of hepatic glucose output versus insulin concentration in the cases of obesity and diabetes mellitus. The secondary hepatic glucose resistance obviated the problem of high glucose suppressing hepatic glucose production. On reflection, it would seem obvious that the hyperglycemic state of diabetes must be accompanied by glucose insensitivity at the liver. When this is modeled, the liver loses its sensitivity to changes in glucose concentration in diabetic states. The supposition of a secondary glucose resistance to hyperglycemia has not been directly experimen-

RUDENSKI ET AL

tally substantiated, although it is known that reducing glycemia improves “insulin resistance.” One could hypothesize that hyperglycemia might downregulate glucose transporters, possibly by causing intracellular relocation so that they are no longer available for further glucose uptake. A model primarily including peripheral insulin resistance as a raised %, does not encompass the reductions in maximal responsiveness to insulin found in diabetic patients by the majority of investigators. This prompted formulation of another model, as illustrated in Fig 4, which was best able to account for the different findings in subjects with type 2 diabetes mellitus. Glucose resistance was introduced secondary to basal hyperglycemia into the periphery, as well as the liver. The simple way to do this was to adjust the responses to glucose at the periphery in the insulin-sensitive tissues according to basal glucose concentration in the same way as in the liver so that secondary to hyperglycemia both the liver and periphery become glucoseresistant. This means that an innate insensitivity to insulin, as might occur with obesity, therefore, results in a greater defect in glucose uptake and hence in much higher glucose and insulin levels. Another consequence of any insulin resistance being accompanied by additional insensitivity to glucose is that hepatic insulin resistance is not so marked in the diabetic state and so glucose production is not that much greater than normal values. However, Baron et al, have reported similar rates of non-insulin-mediated glucose uptake in type 2 diabetic patients and control subjects at comparable levels of hyperglycemia.‘” Capaldo et al have even reported increased responsiveness of forearm non-insulin-mediated glucose uptake in diabetic subjects in response to hyperglycemia.” However, the diabetic patients did receive a continuous subcutaneous insulin infusion until 4 hours before the experiment, to attain euglycemia, a factor that may have altered the actual diabetic response of muscle to glucose. The model with glucose insensitivity does simulate the decreased maximal response of glucose uptake to insulin found in diabetic states, and implies that the glucose resistance of diabetes might be secondary, rather than primary. In summary, the availability of a structural model of glucose-insulin homoeostasis has enabled a study of the possible elements that might contribute to impaired glucose turnover responsiveness in man. Only certain permutations of type and site of deficit of insulin or glucose resistance were able to result in the wide range of steady-state variable values actually observed in diabetic and obese patients. More specifically, it was found that the resistance had to affect both the liver and the periphery. The liver had to remain sensitive to low insulin levels to allow for increased hepatic glucose output in insulin deficiency. It had to incorporate an element of insulin resistance, so as not to suppress glucose production rates in basal hyperinsulinemic states, such as obesity, but it also had to incorporate an element of resistance to glucose, so as not to decrease glucose output rate in the states of basal hyperglycemia. such as type 2 diabetes.

MODELING

INSULIN RESISTANCE

917

This mathematical model does not attempt to describe the whole of the physiology of the insulin-glucose relationship. The basis of this report is the introduction of different defects in glucose handling in to the normal model, in order to dete:rmine which ones can mimic the range of plasma glucose and insulin concentrations and glucose production rates observed in type 2 diabetes. This demonstrates that unitary hypotheses of insulin or

glucose resistance are unlikely to be true and that only combinatorial defect at both the liver and periphery can explain the wide range of insulin and glucose concentrations found in practice. Many different defects probably occur in different patients, and further investigation of pathological mechanisms in individual patients is required. This will determine the degree to which the model is appropriate or needs further development.

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feature

4. Yalow YS. Berson SA: Immunoassay of endogenous plasma in man. J Clin Invest 39:1157-1175,196O

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