Diabetologia 9 Springer-Verlag 1991

Transcription

1 Diabetlgia (11) 34: X11478 Diabetlgia Springer-Verlag 11 Simple empirical assessment f Beta-cell functin by a cnstant infusin f glucse test in nrmal and Type 2 (nn-insulin-dependent) diabetic subjects J. C. Levy, A. Rudenski, M. Burnett, R. Knight, D. R. Matthews and R. C. Turner Diabetes Research Labratries, Radcliffe Infirmary, xfrd, UK Summary. The plasma insulin r C-peptide respnse t a -min cnstant glucse infusin 5 mg. kg ideal bdy weight-~, min-1 prvides Beta-cell assessment cmparable t mre intensive methds. In 14 diet-treated Type 2 (nn-insulin-dependent) diabetic subjects and 12 nn-diabetic subjects, plasma insulin and C-peptide cncentratins gave near linear plts against simultaneus glucse values. The 'glucse-insulin and glucse-c-peptide vectrs' (G-I and G-C vectrs), culd be extraplated t predict insulin and C-peptide levels during a 12 mml/1 hyperglycaemic clamp. Predicted cncentratins crrelated with clamp cncentratins, r =.4 and r =.8 respectively, p <.1, validating the vectrs as empirical glucse dse-respnse curves. The vectr slpes crrelated highly with %Beta, a mathematical mdel-derived measure f Beta-cell functin using cnstant infusin f glucse mdel assessment, Spearman r =.5 and.3 fr insulin and C-peptide, respectively. G-I vectr slpes in 21 diet-treated Type 2 diabetic subjects with fasting glucse (mean + 1 SD) mml/1, were lwer than in 28 nn-diabetic subjects, (gemetric mean, 1 SD range, 8.4 pml/mml ( ) and 25.1 pml/mml ( ), p <.1, respectively), indicating an impaired Beta-cell re- spnse. The G-I vectr slpes crrelated with besity in bth grups (r =.54 p <.2 and.72, p <.1 respectively), and, in 15 nn-diabetic subjects, crrelated inversely with insulin sensitivity as measured by a euglycaemic clamp (r = -.66,p <.1). Thus, Beta-cell functin needs t be interpreted in relatin t besity/insulin resistance and, taking besity int accunt, nly 4 f 21 diabetic patients had Betacell functin (G-I vectr slpe) in the nn-diabetic range. The fasting plasma glucse in the diabetic subjects crrelated inversely with the besity-crrected G-I and G-C vectr slpes (partial r = -.57, p <.1 and -.86, p <.1, respectively). The insulin r C-peptide respnse t the glucse infusin prvides a direct empirical measure f the Beta-cell functin, which can be interpreted in relatin t besity r t insulin resistance t assess underlying pancreatic respnsiveness. Key wrds: Type 2 (nn-insulin-dependent) diabetes mellitus, insulin secretin, Beta-cell functin, glucse tlerance test, insulin resistance, besity, hyperglycaemic clamp, euglycaemic clamp, plasma insulin, plasma C-peptide. A simple, easily applicable measure f Beta-cell functin is necessary fr epidemilgical studies f diabetes r fr mnitring the develpment f the disease. The hyperglycaemic clamp [1] prvides the mst reliable methd fr assessing pancreatic functin but requires t great an investment f resurces fr mst medium and large scale studies. Simpler tests, thugh cmmnly used, are less satisfactry. The ral glucse tlerance test cannt easily be used t assess Beta-cell functin, due t the cmplex interactin f increasing and then decreasing glucse and insulin cncentratins, large inter-individual variatin [2, 3], and the interference f gastr-intestinal factrs such as variable glucse absrbtin rates and 'incretin' effects [4]. The intravenus glucse tlerance test (IVGTT) prvides a supraphysilgical shrt-term stimulus t insulin secre- tin and a 'first phase' insulin respnse which can be precisely measured, but this is virtually cmpletely suppressed by nly mild levels f hyperglycaemia [5] and its relevance t everyday functin is uncertain. The 'secnd phase' insulin respnse f the IVGTT is difficult t interpret as it is a functin f varying glucse cncentratins which are themselves dependent n the first phase insulin secretin and insulin sensitivity. Beta-cell functin can be assessed frm the IVGTT using a minimal mdel [6], but 23 samples need t be taken ver 3 h, and interpretatin requires cmplex cmputer prgram manipulatin f the data [7]. Nn-glucse stimuli, such as amin-acids (e. g. arginine) r hrmnes such as glucagn r isprterenl may be used in the assessment f pancreatic functin, but pancreatic respnses t these are relatively preserved in diabetes

2 J. C. Levy et al.: Simple empirical assessment f Beta celi functin Table L Prtcl t: relatinship between vectr slpe and besity and fasting plasma insulin: characteristics f the nn-diabetic and diabetic subjects studied. Nn-diabetic Diabetic patients subjects Number f subjects Age (years: median and range) 46 (4453) 56 (42-7) BMI (kg. m 2: median and range) 23 (18-3) 25.4 ( ) Fasting glucse n diagnsis: _+ 3.2 (mml/1) BMI n diagnsis (kg. m-2 median and range) (22.66.) Duratin f diabetes (years, mean and range) 5 (1-1) Fasting plasma glucse (mml/1) 4.8 _ Fasting plasma insulin (pml/1) 2.3 ( ) 4.3 ( ) Fasting plasma C-peptide.45 (.245.7).57 ( ) (nmi/l) Glucse values are expressed as mean _+ 1 SD, insulin and C-peptide values as gemetric mean (1 SD range) due t glucse ptentiatin [8] and assessment f underlying Beta-cell respnsiveness requires clamping at different glucse levels []. These tests f Beta-cell functin are far remved frm the nrmal physilgical demands n the Beta-cell. In cntrast, a cnstant glucse infusin, prducing changes in glucse and insulin cncentratins in the physilgical pstprandial range, has prvided a basis fr bth Beta-cell functin and insulin sensitivity, interpreting the glucseinsulin feedback cycle with the aid f a structural mathematical mdel. The mdel incrprates Beta-cell functin (%B) and insulin sensitivity (% S) variables defined in relatin t a standard nn-bese nn-diabetic ppulatin, and predicts glucse, insulin and C-peptide cncentratins fr any cmbinatin f % B and %S in either steadystate, fasting cnditins ('hmestasis mdel assessment': HMA) [1] r after 6 min f a 5 mg.kg ideal bdy weight (IBW)-I. min- ~ intravenus glucse infusin, ('cntinuus infusin f glucse with mdel assessment': CIGMA) [11]. Thus, in any individual, plasma glucse and either insulin r C-peptide cncentratins measured either fasting r after the glucse infusin can be used t assess Beta-cell functin and insulin sensitivity by cmparisn with the mdel which indicates the values f % B and % S which wuld be expected t give the patient's values. Althugh mathematical mdelling is a pwerful technique used rutinely in the physical sciences, its applicatin t clinical situatins has ften been regarded with suspicin. The mdel assumes that glucse stimulated Beta-cell functin may be described by a functin applicable t bth basal and glucse stimulated cnditins. In diabetes, a Beta-cell Vm~x deficit is mdelled as affecting bth first and secnd phase respnses, fr which there is experimental supprt [12]. In rder t validate these cncepts and t prvide a direct means f assessing Beta- 48 cell functin withut the use f a mdel, we shw that glucse, insulin and C-peptide changes during the 5 mg. kg IBW- 1. min- 1 glucse infusin generate empirical linear pancreatic dse respnse relatinship (here termed the glucse-insulin (G-I) and gtucse-c-peptide (G-C) 'vectrs'), which may be used t predict an individual's respnse t a 12 mml/1 hyperglycaemic clamp. In additin, we shw that the vectrs can be described by a single variable, the vectr slpes, which crrelate clsely with the estimate f Beta-cell functin, %B, derived frm the mathematical mdel with either CIGMA r HMA assessment. The relatinship between the vectr assessmerit f Beta-cell functin in nn-diabetic and Type 2 (nn-insulin-dependent) diabetic subjects and their besity has been studied. Althugh Type 2 diabetic patients have impaired pancreatic functin, a relatinship between Beta-cell functin, besity and insulin sensitivity is preserved, s that the G-I r G-C vectr slpes need t be interpreted in relatin t besity r t a measure f insulin sensitivity t assess the underlying pancreatic respnsiveness in a patient. Subjects and methds Subjects Prtcl 1 - glucse infusin. The characteristics f the glucse-insulin and glucse-c-peptide vectrs were studied in 87 cntinuus -rain 5 rag- kg IBW- ~- min - ~ glucse infusins in 28 nn-diabetic and 21 Type 2 diabetic subjects (38 subjects had tw glucse infusins). All diabetic subjects, including thse in prtcls 2, 3 and 4, belw, had presented with fasting plasma glucse values greater than 7.8 mml/1 n diagnsis. The relatinship between the vectr slpes and besity and fasting plasma insulin and C-peptide were studied in the first f the tw glucse infusins in each subject. Nne f the diabetic subjects was n any hypglycaemic medicatin befre these tests and had been n a weight-maintaining diet fr at least ne mnth befre being studied. ClinicaI details f the subjects are presented in Table 1. Prtcl2 - glucse infusin fllwed by hyperglycaemic clamp. Twelve nn-diabetic subjects and 14 Type 2 diabetic subjects (median fasting plasma glucse 7.6, range mml/1) were given a cntinuus -rain glucse infusin 5 mg. kg IBW- 1. rain- a fllwed by a -rain 12 mml/l hyperglycaemic glucse clamp. Nne f the nn-diabetic subjects had a family histry f diabetes. Their details are presented in Table 2. Prtcl3 - glucse infusin fllwed by euglycaemic clamp. In 15 nn-diabetic subjects, the cnstant glucse infusin was fllwed by a -min euglycaemic clamp t assess the relatinship between the vectr slpe and insulin sensitivity. Their details are presented in Table 3. Prtcl 4 - reprducibility f vectr slpes. Twenty-eight subjects (five Type 2 diabetic subjects, five first-degree relatives f Type 2 diabetic subjects and 18 nn-diabetic subjects) had repeat tests within 3 mnths f their first glucse infusin (median 4 weeks, range.5 t 13 weeks) t assess reprducibility f their respnse. Their details are presented in Table 4. Physilgical tests a. Glucse infusin. Fllwing a 14-h vernight fast, subjects were given a cnstant 5 mg-kgibw-~.min -I glucse infusin by an IMD pump (Abingdn, UK) int an antecubital vein fr min.

3 4 Table 2. Prtcl 2: glucse infusin - hyperglycaemic clamp study. Plasma glucse, insulin and C-peptide fasting, at the end f the cnstant glucse infusin and at the end f the hyperglycaemic clamp Nn-diabetic subjects Diabetic patients Number f subjects Age (years: median and range) 53 (4-63) 56 (42-7) BMI (kg. m -2) 24 (18-3) 26 (21-33) Fasting glucse n diagnsis (mml/i) BMI n diagnsis (kg. m -2 median and range) 26.3 ( ) Duratin f diabetes (years, mean and range) 6 (4-1) Fasting levels Glucse (mml/1) Insulin (pml/1) 25.5 ( ) 36.8 ( ) C-peptide (nml/i).43 ( ).56 (.344).4) Glucse infusin ( mins) Glucse (mml/1) Insulin (pml/1) 125 (71-222) 83.6 ( ) C-peptide(nml/1) 1.51 ( ).8 ( ) Hyperglycaemic clamp Glucse (mml/1) 11.7 (.8) 12.5 (1.3) Insulin (pml/1) 3 ( ) 12 ( ) C-peptide (nml/1) 2.45 ( ) 1.23 ( ) Glucse values are expressed as mean _+ 1 SD, insulin and C-peptide values as gemetric mean (1 SD range) Table 3. Prtcl 3: glucse infusin - euglycaemic clamp study. Plasma glucse, insulin and C-peptide fasting, at the end f the cnstant glucse infusin and at the end f the euglycaemic clamp Number f subjects 15 Age (years: median and range) 4 (4-63) BMI (kg. m- 2) 23.5 ( ) Fasting levels Glucse (retl/l) Insulin (pml/1) 32 (16-65) C-peptide (nml/1).47 (.324).6) Glucse infusin ( mins) Glucse (retl/l).5.8 Insulin (pml/i) 211 ( ) C-peptide (nml/1) 1.84 ( ) uglycaemic clamp Glucse (mml/1) Insulin (pml/1) 265 (18-353) C-peptide (nml/1).65 (.444).5) Glucse values are expressed as mean 1 SD, insulin and C-peptide values as gemetric mean (1 SD range) Table 4. Prtcl 4: details f subjects wh had repeated tests within 3 mnths Subject grup Nn-diabetic First degree Type 2 diasubject relative betic patient Number f subjects Sex (M/F) / 4/1 3/2 Age (years: median and range) 45 (2-63) 51 (2-5) 56 (43-63) BMI (kg.m 2) 23 (2-36) 28 (23-2) 3 (2442) Fasting glucse (mml/1) _+ 2.3 Arterialised bld samples were taken frm a distal vein in a heated arm. Fur 5-min plasma samples were taken initially and samples were taken at 1-min intervals thrughut the infusin, and als at 55 min and 85 min. Samples were assayed fr glucse, insulin and C- peptide J. C. Levy et al.: Simple empirical assessment f Beta-cell functin b. Hyperglycaemic clamp. Fllwing the cnstant glucse infusin, plasma glucse levels were stabilised at 12 mml/1 fr rain by means f a variable glucse infusin, the rate f which was determined by 2-rain bld samples assayed fr whle bld glucse by YSI glucse analyser (Yellw Springs Instrument C. Cleveland, hi, USA) and an unbiased iterative cmputer prgram [13]. During the last 15 min f the hyperglycaemic clamp, fur 5-rain bld samples were taken t determine plasma glucse, insulin and C-peptide. c. uglycaemic clamps. Fllwing the glucse infusin, subjects had a -min 4 pml- kg IBW- :. rain : insulin infusin, primed by an initial 1 rain at duble this rate, and plasma glucse was allwed t fall t 4.5 mmt/1 and was clamped at this level by means f 2-min samples and the glucse clamp prgram. The mean rate f glucse infusin during the last 2 min f the clamp was divided by the subjects' ideal bdy weight t give the 'M' value. This was then divided by the mean f fur 5-min determinatins f plasma insulin at the end f the clamp t give 'M/I', which was used as an index f whle bdy insulin sensitivity. Bichemistry Plasma glucse was determined by a hexkinase methd n the Cbas Bi centrifugal autanalyser (Rche, Welwyn Garden City, UK). Insulin and C-peptide were determined by a charcal separatin immunassay technique [14]. Calculatins Glucse-insulin and glucse-c-peptide vectrs. Insulin and glucse and C-peptide and glucse values befre and during the glucse infusin were pltted against each ther (Fig. 1) and assumed t represent segments f glucse-insulin and glucse-c-peptide dse respnse curves. Linear and quadratic mdels with insulin as the dependent variable were fitted by the least squares methd and tested by stepwise regressin. The linear mdel was chsen t represent adequately the glucse-insulin relatinship (see results). The G-I and G-C 'vectrs' were defined as the segment f the regressin line (determined by all the glucse-insulin r glucse-c-peptide pairs) lying between the mean fasting and the mean 8, 85 and -rain glucse values. The regressin line may be described by means f tw cefficients: the vectr slpe and the cnstant term i. e., Insulin = vectr slpe glucse + cnstant. _ Ca. =.,,s--~ ~ ~.~-~176 f,, j.j" /%..-'j" L,~,~,.,..," Glucse 8 (mml/i) ?, F...! s y I... ~3[ ~ ~:Z " ,~.~ W ~D-I4 [ '~'~'~'" i';>'~?~176 ""... ~,..., _ ) Glucse (mml/i) Time (min) Fig. l. Left panel: glucse, insulin and C-peptide plts vs time in ne individualduringthe5 mg.kgidealbdyweight 1.min :glucse fusin and at end f hyperglycaemic clamp. Right panel, upper: insulin, lwer: C-peptide, pltted against glucse with regressin lines (G-I and G-C Vectrs) thrugh glucse infusin pints nly extended t the end-clamp ache glucse cncentratin

4 J. C. Levy et al.: Simple empirical assessment f Beta-cell functin The tw cefficients f the resulting linear equatins in 54 different individuals were als examined by linear regressin analysis. Because f the linearity f the glucse-insulin and glucse-cpeptide plts, the slpes f the G-I and G-C vectrs may be mre simply estimated frm their extremities, taken as the mean - 1, - 5 and -rain fasting values and either the mean 5, 55 and 6-min value r the mean 8, 85 and -min value with the vectr slpes calculated by dividing the 6 r -min increments frm fasting f insulin r C- peptide by the crrespnding increments in glucse, i.e. 816/8G6, and ~C6/~G6, r 81/~G and ~C/8G. HMA and CIGMA %B. Fasting glucse, insulin and C-peptide values were calculated as the mean f three 5-min values and evaluated by reference t the HMA mdel. This is a physilgically structured cmputer mdel f the glucse-insulin feedback system which predicts fasting glucse, insulin and C-peptide levels based n different cmbinatins f B eta-cell functin (% B) and insulin sensitivity (% S). Actual fasting data (glucse and insulin r glucse and C-peptide pairs) can be 'read back' frm cmputer predictins t give %B (HMA %Bi r %Be respectively). %S values are als generated by this prcedure. The ~reading back' prcess was dne by linear interplatin between 18 HMA mdel generated lines representing plasma glucse and insulin values fr values % B between 5% and 2%. 'ne hur' achieved glucse, insulin and C-peptide levels were calculated as the mean f the 5, 55 and 6-min samples after the start f the 5 mg-kg IBW-~. min- 1 glucse infusin and evaluated by reference t the CIGMA mdel. This is a cmputer simulatin f the glucse infusin which predicts ne hur achieved glucse, insulin and C-peptide cncentratins given differing cmbinatins f %B and %S. As in the HMA mdel, actual achieved glucse-insulin and glucse-c-peptide pairs are read back frm cmputer predictins t give % B (CIGMA % Bi and % Be) r % S values. stimatins f %B, which are derived frm pint data (either fasting r ne hur achieved values) are mathematically independent frm the vectr slpes which are derived frm incremental data during the glucse infusin. Reprducibility. The standard frmula fr the standard deviatin f duplicate samples was used fr repeated determinatins f the G-I and G-C vectr slpes, ~J(Y.difference2/2N) [2], was expressed as a percentage f the mean value f the slpes t give the cefficient f variatin. Statistical analysis Grup results are presented as means ( + 1 SD), r in the case f insulin r C-peptide levels and vectr slpes, as gemetric means (1 SD range), except when therwise indicated. xcept in the cntext f regressin equatins, simple crrelatin was assessed by nnparametric measures (Spearman rank cefficients) t avid verestimatin f cefficients by high r lw extreme values. Parametric methds were used fr partial crrelatin. Crrectin f vectr slpes by cvariates in nn-diabetic and diabetic grups was dne using the regressin methd t btain the cmmn cefficient. Statistical calculatins were perfrmed using the SPSS-X statistical package (Chicag, Ill., USA). Results Prtcl 1: glucse infusin-hyperglycaemic clamp study Glucse infusin and hyperglycaemic clamp data. Glucse insulin and C-peptide values in the fasting state, at the end f the cnstant glucse infusin and at the end f the hyperglycaemic clamp are shwn in Table 2. During the glucse clamps, the intra-individual standard deviatin f 41 the ten 2-min samples cmprising the last 2-rain perid had a median value f.2mml/1 (range.8 t.82 mml/1), the intra-individual standard deviatin f bld glucse during the penultimate 2-rain perid was median.1mml/1 (range mml/1) and the percent difference in plasma glucse between the mean f the ten samples frm the last 2-min perid and the mean f the ten samples cmprising the previus 2-min perid had a median f -.2% (range - 4. t 6.4%). Linearity f G-I plts and assessment f vectr slpe by linear regressin r rati f increments. Time-matched glucse and insulin values in 87 glucse infusins were highly crrelated using a linear mdel, with a median crrelatin cefficient f.2 ( interquartile range). A quadratic mdel was als tested, but in nly 5 f 81 tests did the quadratic mdel accunt fr mre than an extra 1% f the variance (r squared) f the G-I plt when cmpared t the linear mdel. Because f the success as well as the shnplicity f the linear mdel it was adpted t describe the glucse - insulin/c-peptide relatinship during the glucse infusin. The regressin methd f deriving the vectr slpe was cmpared t a simpler incremental methd: that f dividing the increment in insulin between mean fasting and mean 8, 85 and -min values by the crrespnding increment in glucse (~I/~G). The regressin derived vectr slpe crrelated clsely with the incremental derivatin, r =.7, p <.1 in 57 individuals (Table 5). The mean estimate by the incremental methd was 12% (1 SD range, % ) f the crrespnding slpe calculated by regressin. Furthermre, because f the linearity f the vectr, its slpe may als be derived frm any ther tw pints alng its length, e. g. the fasting and mean 5, 55 and 6-min pints (~I6/~G6), which crrelated with the regressin derived vectr slpe, Spearman r;.4, p <.1, 816USGs being 85% (75-113%) f the regressin derived slpe. Thus, a clsely crrelating estimate f the regressin-derived vectr slpe may be btained frm a shrter, 6-rain infusin. Linearity f G-C plts and assessment f vectr slpe by linear regressin r rati f increments. Linear regressin equatins (G-Cvectrs) were derived frm glucse-cpeptide plts in 87 glucse infusin tests in 56 individuals. The median linear crrelatin cefficient was.5 (interquartile range.1-.7). A quadratic mdel increased the value f r 2 by mre than 1% in nly 14 cases, and hence a linear mdel f the G-C plts was used as an adequate representatin f the G-C relatinship during the -rain glucse infusin. The vectr slpe derived by regressin crrelated clsely with the slpes calculated as ~C/~G as 8C6/8G~ (Spearman r =. and.5, p <.1 respectively). The G-C vectr slpes calculated by ~C/~G and 5C6/~G6 were 13% (4-114%) and 7% (58-18%) f the crrespnding regressin derived values. G-I and G-C vectr slpe - cnstant-term crrelatin. In any individual, the regressin line thrugh the G-I plt may be described by tw cefficients,

5 42 Table 5. Spearman crrelatin cefficients between G-I and G- C vectr slpes, ascertained by regressin (Reg ") and rati f increments, hmestasis mdel assessment (HMA) and cntinuus infusin f glucse with mdel assessment (CIGMA) mdel Beta-cell estimates (% B) in 21 Type 2 (nn-insulin-dependent) diabetic and 28 nn-diabetic subjects and eight first-degree relatives f Type 2 diabetic subjects G-I vectr slpe Reg: G-I vectr slpe HMA %B CIGMA % B Regressin 1 81/8G /8G HMA %B 81/ 816/ In- C-pep In- C-pep- 8G 8G6 sulin sulin tide Insulin C-peptide CIGMA %B Insulin C-peptide Hyperglycaemic Clamp a Insulin Reg n G-C vectr slpe HMA %B CIGMA %B G-C vectr slpe Regressin 1 8C/8G 8C6/8G HMA %B Cl 8C6/ In- C-pep In- C-pep- 8G 8G6 sulin sulin tide Insulin C-peptide CIGMA %B Insulin C-peptide Hyperglycaemic Clamp a C-peptide a Crrelatins n glucse-infusin - hypergtycaemic clamp studies nly in 14 diabetic and 12 nn-diabetic subjects. All significance levels are greater thanp <.1 It = vectr slpe x Gt + cnstant term (1) where It and Gt represent plasma insulin and glucse at any time t during the cnstant infusin. An analgus equatin with different cefficients represents the G-C vectr. In 57 individuals (21 Type 2 diabetic and 28 nn-diabetic subjects and eight first-degree relatives f Type 2 diabetic subjects), there was a clse linear crrelatin between the G-I vectr slpe and the cnstant term (r =., p <.1) (Fig.2a), the relatinship between the tw cefficients being described by the equatin, G-I cnstant = pi G-I vectr slpe + q~ (2) where pi = _+. mml and q~ = pml. (The nrmal and diabetic grups may be cmbined because there was n significant difference between the grups fr pi and qi: diabetic p~ = mml, qi pml; nn-diabetic p~ = mml, q~ = > "7 (_ a e-. b "5 ~D > i J. C. Levy et al.: Simple empirical assessment f Beta-cell functin [] "-, ""-. -4 [] "-. [] "-, "-.. ""-.., -6, i i I G-I vectr slpe (pml/mml) ""-.,.. ",,. [] "-.. ",... -.l I= -4 I i [ i b G-C vectr slpe (nml/mml) Fig.2. (a) Glucse-insulin (G-I) and (b) glucse C-peptide (G-C) vectr slpes pltted against vertical psitins f vectr with respect t glucse axis (vectr cnstant term). pen squares: nn-diabetic subjects, clsed circles: diabetic subjects pml; first-degree relatives f diabetic patients p~ mml, q~ = pml). Similarly, the crrelatin between the slpes and cnstant terms f the G-C vectrs was als high (Fig. 2b): r =.4, p <.1, the equatin being: G-C cnstant = pc x G-C vectr slpe + qc (3) where pc = mml and qc = nml. (There was n significant difference between the grups fr p~ and q~: diabetic p~ = mml, qi= pml; nn-diabetic pi = mml, q~ = pml; relatives pj = mml, q~ = pml). While the vectr slpes and the cnstant term in equatin 1 are cefficients f individual vectrs, p~ and qi fr G-I vectrs (equatin 2) and pc and qc fr G-C slpes (equatin 3) are essentially ppulatin parameters defining the relatinship between the tw cefficients in any individual. Within the limits f the accuracy f this bservatin, these ppulatin parameters may be used in an individual t calculate the cnstant term in equatin 1given the slpe f that individual's vectr. Thus, the vectr slpes alne are sufficent t describe the empiricalpancreatic glucse respnse relatinship during the glucse infusin. Since, in any individual, insulin levels bth in the fasting state and during the glucse infusin are related t glucse

6 J. C. Levy et al.: Simple empirical assessment f Beta-cell functin 43 c 3 c.q 13. ' _ a 1 I 2 2 V 13."" 1 1 clamp insulin (pml/i).i c3 levels in a simple linear fashin by the G-I vectr (equatin 1), and, in a wide range f individuals, the G-I vectr slpes were fund t be linearly related t the vectr psitins (equatin 2), these tw relatinships may, in thery be cmbined t give an expressin fr deriving the vectr slpe frm any time pint, within the cnfines f the accuracy f the ppulatin parameters pi and % vectr slpe = (It - qi)/(gt + Pi) (4) i. e. in thery the vectr slpe may be determined by any pint alng the dse - respnse segment, fr example fasting values (thugh this wuld be increasingly inaccurate as the pint apprached an insulin level f qi and a glucse level f p~) r values at 6 min r min. A similar argument may be applied t the G-C vectr slpes. The existence f 'ppulatin parameters' Pi and qi, r Pc and q gives rise t certain theretical predictins which are testable empirically (see appendix). v "13 ~." "--.D" - u "(3 b I I I Clamp C-peptide (nml/i) Fig.3. Predicted 12 ml/l clamp levels f (a) insulin and (b) C-peptide derived by extensin f vectrs as in Figure 1, pltted against actual mean end clamp insulin r C-peptide values. Slid line: line f unity, dtted line: regressin line thrugh predicted pints (D C (D ca 3 d) "13 C :"," Mean f tests / / 4 8 First test 1 12 d) c- d) Mean f tests /.8 c.4 d) (,.4./.8,.8 First test Fig.4. Reprducibility f vectr slpes. Left panel: glucse-insulin vectr slpe (pml/mml): upper: inter-duplicate differences pltted against mean values, lwer: secnd estimatin pltted against first estimatin, right panel: glucse-c-peptide vectr slpe (nml/mml): upper: inter-duplicate differences pltted against mean values, lwer: secnd estimatin pltted against first estimatin. G-I plts and predictin f clamp insulin levels. In 48 separate glucse infusin-hyperglycaemic clamp tests in 28 individuals the G-I vectrs were used t predict the actual plasma insulin acheived at the end f the -min hyperglycaemic clamp. In mst cases this was dne by extraplating the vectr t the clamp glucse cncentratin (12.2 +_ 1. mml/1). In sme diabetic subjects, hwever, plasma glucse during the cnstant glucse infusin rse higher than this and the predicted respnse was btained by interplatin f the vectr at the clamp glucse level. The crrelatin between actual and predicted insulins was high (Spearman r =.4, p <.1) (Fig. 3a) (in 2 clamps in nn-diabetic subjects r =.84 p <.1, in 27 clamps in diabetic subjects r =.7 p <.1). Since the difference between predicted and actual clamp insulin cncentratin increased with the insulin level, lgarithmic transfrmatin was used t examine their relatinship. Mean predicted levels represented 7.3% + 4.3% SM f actual levels, (ne SD residual range 54-%, p <.1). G-C plts and predictin f clamp C-peptide levels. In 46 clamps in 28 individuals, the G-C vectrs predicted C-peptide levels at the end f the hyperglycaemic clamp with a crrelatin cefficent f.8, p <.1 (Fig. 3 b). (In 1 clamps in nn-diabetic subjects r =.1, p <.1, in 27 clamps in diabetic subjects r =.8 p <.1). In cntrast with predictins frm G-I vectrs t clamp insulin levels, errrs f predictin frm G-C vectrs did nt increase with clamp C-peptide levels, and predicted levels were cnsistently.31 ( _+.8) nml/1 lwer than actual clamp C-peptide levels (residual SD =.2 nml/1). Cmparisn between G-I and G-C vectrs and % Beta calculated frm the CIGMA mdel. The G-I and G-C vectr slpes crrelated with the mdel-derived %B values derived frm glucse, insulin and C-peptide values after 55 rain f the glucse infusin (CIGMA) (Spearman r =.2 and.4 respectively, p <.1, Table 5). Cmparisn between G-I and G-C vectrs and % Beta calculated frm HMA mdel The G-I and G-C vectr slpes crrelated with the mdel-derived %B values derived frm fasting glucse, insulin and C-peptide values

7 44 5 s 6 > (5 8 "5 c- _ 6 > i 1 1 C,2 i i r "'".,--'" ~ ~ e [].,-~--,~P a... ~ 8... dt... e []..... [~... G---- ~... -.~ ~ " e e.. Bdy mass index (kg/m 2) Fig.& (a) Glucse-insulin (G-I) and (b) glucse-c-peptide (G-C) vectr slpes pltted against BMI in 23 nn-diabetic (pen squares) and 21 diabetic subjects (clsed circles) (HMA) (Spearman r=.86 and.67, p <.1) (Table 5). Reprducibility f G-I and G-C slpes. The mean f the differences between first and secnd estimatins f G-I slpes were nt significantly different frm zer ( SM pml/mml). G-I slpes frm secnd tests are pltted against first test results in Figure 4, the insert shwing the differences pltted against the mean f the tw estimatins (mean 25.4 pml/mml, range pml/mml). The cefficient f variatin f G-I slpes was 21%. This wuld be due t variatin frm true physilgical variability n the ne hand, and t variability arising frm assay techniques, sampling and strage etc, n the ther. The derivatin f the vectr slpe by the least squares methd allws an estimatin f the standard errr fr each G-I slpe. The median percent standard errr f the G-I slpes n all 28 tests was 11.2%. Mean differences between first and secnd estimatins f G-C slpes were nt significantly different frm zer ( SM nml/mml). G-C slpes frm secnd tests are pltted against the first test and differences pltted against the mean f the tw estimatins (mean.16 pml/mml, range nml/mml) in Figure 4. The cefficient f variatin f G-I slpes was 16%. The median percentage standard errr f the G-I slpes n all 28 tests was 8.3%. G-I and G-C vectrs in nn-diabetic and Type 2 diabetic subjects. G-I and G-C vectr slpes were calculated in the 28 nn-diabetic and 21 Type 2 diabetic subjects. In bth grups the distributins f insulin, glucse and vectr J. C. Levy et al.: Simple empirical assessment f Beta-cell functin slpes were psitively skewed, and statistics were perfrmed n lgarithmically transfrmed data. The gemetric mean G-Islpes (+ISD range) were 28.4pml/mml ( ) and 7.7 pml/mml (3.2-1.), respectively, (p <.1), and G-Cslpes were.254 nml/mml ( ) and.6 nml/mml ( ) p <.1, in the nn-diabetic and diabetic subjects. Hwever, althugh there was a significant difference between the gemetric means f the tw grups, there was a cnsiderable verlap between individual values, with 11 f 21 G-Ivectr slpes and 6 f 21 G-C vectr slpes in diabetic subjects falling within the nrmal range, defined as mean SD f the nrmal grup. Relatin f G-I and G-C vectrs t besity. In 28 nndiabetic subjects with n family histry f diabetes, there was a significant linear relatinship between Beta-cell functin expressed as lg G-I vectr slpe and besity (BMI) (Fig. 5 a), thus Lg1 (G-I Vectr slpe) =.7 ( _+.17) x BMI -.21 ( +.4), r =.63, p <.1 (figures in brackets represent standard errrs f the cefficents). This did nt appear t be medi- t-" v Q} if} " m.5 3 a 1 c- c3) _ -~.1 i ~ "13.1 m~.5 3 ~~ ~ dp %. u i i i l b Fasting plasma glucse (mml/i) Fig.& (a) Glucse-insulin (G-I) vectr slpes and (b) glucse-cpeptide (G-C) vectr slpes in 23 nn-diabetic (pen squares) and 21 diabetic subjects (clsed circles) crrected fr BMI, using the cmbined vectr slpe-% ideal bdy weight regressin f the tw grups, pltted against fasting plasma glucse.

8 J. C. Levy et al.: Simple empirical assessment f Beta-cell functin 5 C- v C (D > i ( a [] -"" [] ---'"" 3 -~"" [3 ~...6--~[] "~ 1 1 Fasting insulin (pml/i) [3... -~ b ~... ~..er"-'rh ~ [3 n _ 14 -~.1 C).y"'" ~1 > y I ( b Fasting C-peptide (nml/i) Fig. 7, (a) Glucse-insulin (G-I) vectr slpes pltted against fasting plasma insulin and (b) glucse-c-peptide (G-C) vectr slpes pltted against fasting plasma C-peptide in 23 nn-diabetic (pen squares) and 21 diabetic subjects (clsed circles). 5 CZ. v (. ~D > ( 1 1 ""',43.. l',. "'"-. [3 "'-.. D """'-. I.5 ], i ""',,.. uglycaemic clamp M/I (pmukglbw/min) i 1.5 Fig.& -I vectr sipes in 15 nn-diabetic subjects pltted against insulin sensitivity (ttal bdy glucse uptake in euglycaemic clamp (g mean insulin = 223 pml/1)/plasma insulin. ated by fasting glucse levels since there was n independent crrelatin between fasting glucse and either the G-I r G-C vectrs r BMI in the nn-diabetic subjects. In 21 Type 2 diabetic subjects, there were significant and ppsing partial crrelatins between lg G-I vectr slpe and BMI (partial r =.5,p <.5) and fasting plasma glucse (FPG) (partial r = -.57,p <.1), thus, Lgt (G-I Vectr slpe) --.6 ( +.2) x BMI -. ( +.28) x FPG -.3 ( +.56), multiple r =.7, p <.1. Multiple regressin against bth %IBW and FPG was pssible because there was n significant crrelatin between these tw independent 45 variables (r =.7, NS). The cefficients f % IBW in the diabetic subjects did nt differ significantly frm the equivalent cefficient in the nn-diabetic grup. Crrecting fr besity as cvariate, nly 4 f 21 G-I vectr slpes fell within 2 residual standard deviatins f the mean value fr nn-diabetic subjects (Fig. 5 a). G-I vectr slpes crrected fr besity are pltted against fasting plasma glucse in Figure 6 a. In the nn-diabetic subjects there was n significant relatinship between Lg G-C vectr slpe and %IBW, but in the diabetic subjects, ppsing partial crrelatin cefficents between lg G-C vectr slpe and BMI and FPG were significant (partial r =.63, p <.1 and partial r = -.86, p <.1) with a multiple regressin equatin f Lg1 (G-C Vectr slpe) =.45 ( +.13) x BMI -.14 ( +.2) x FPG ( +.36), multiple r =.88, p <.1. G-C vectr slpes crrected fr besity are pltted against fasting plasma glucse in Figure 6b. Relatin f G-I and G-C vectrs t fasting insulin and C-peptide cncentratins. In the nn-diabetic subjects, a significant linear relatinship was fund between the G-I vectr slpe and lg fasting plasma insulin (FPI), LG~ (G-I vectr slpe) =.7 ( _+.13) x Lg1 (FPI) +.3 ( +.2), r =.76,p <.1, and a weaker relatinship was seen between the G-C vectr slpes and fasting plasma C-peptide (FPC), Lg1 (G-C Vectr -.45 ( +.6), slpe) =.41 ( +.16) x Lg, (FPC) r =.45,p <.5. In 21 Type 2 diabetic subjects, there were significant and ppsing partial crrelatins between lg G-I vectr slpe and lg FPI (partial r =.58, p <.1) and FPG, (partial r = -.66, p <.1), the multiple regressin equatin expressing these relatinships being, Lg1 (G-I vectr slpe) =.78 ( +.25) x lg1 (FPI) -.11 ( +.3) x FPG -.45 ( _+.41), multiple r =.71, p <.1. A similar relatinship existed fr lg G-C vectr slpe, lg fasting plasma C-peptide (FPC) and FPG (partial r =.66, p <.1 and partial r = -.87, p <.1), with multiple regressin equatin Lg1 (G-C Vectr slpe) =.74 ( +.2) x lg1 (FPC) -.13 ( +.2) x FPG +.3 ( +.15), multiple r =.8,p <.1. When the crrelatin between the vectr slpes and FPI and FPC were taken int accunt, the verlap between nrmal and diabetic grups was much reduced, with nly 4 f 21 G-I slpes and 3 f 21 G-C slpes in diabetic subjects falling within 2 residual standard deviatins f the respective nrmal ranges (Fig. 7). Vectr slpe and insulin sensitivity. In 15 nn-diabetic subjects wh underwent a euglycaemic clamp fllwing the

9 46 5 / 4 ~_ 3._c 2 c l ::ii Glucse (mml/i) Fig.. The regressin lines thrugh the data f each nrmal individual (cntinuus) and diabetic individual (discntinuus) shwing the radiatin frm a seemingly cmmn 'null pint' cnstant glucse infusin, the median CV (standard deviatin/me an in each individual) f infusin rates in the last 1 2-min samples (last 2m in) was 1.5% (range % ), the median CV f the previus ten 2-min samples (penultimate 2 min) was 1.1% (range % ) and the median percent difference in mean infusin rates in these tw perids was 2.3% (range -3 t 3%). The median CV (standard deviatin/mean in each individual) f bld glucse in the last ten 2-min samples (last 2 min) was. mml/1 (range.4-.17), the median CV f the previus ten 2-min samples (penultimate 2min) was. mml/1 (range.5-.23) and the median percent difference in mean infusin rates in these tw perids was 2.6% (range-.2 t 6.4%). Insulin levels were 223 ( ) pml/1. G-I vectr slpes were significantly negatively crrelated t insulin sensitivity as measured by ttal bdy glucse requirement divided by insulin cncentratin (M/I), r =.66,p <.1 (Fig.8). Discussin During the min f the glucse infusin in nrmal subjects, plasma glucse traverses the physilgical pstprandial range, with an increment f apprximately 4 mml/1, and therefre insulin and C-peptide changes reflect a clinically relevant pancreatic respnse t glucse. The linearity f the glucse-insulin and glucse-c-peptide plts is an empirical finding. It arises in part because the rapid "firstphase" insulin respnse at the beginning f the glucse infusin, succeeded by a slwer rise, is matched by a similar pattern in glucse levels, due t the cmbined effects f slw equilibratin in a multi-cmpartmental system and the prgressive fall in the rate f glucse appearance in the system as hepatic glucse utput is suppressed [15]. Hwever, after the first 1 min f the infusin, the rise in plasma glucse is gradual and unidirectinal and is matched by the rise in plasma insulin r C-peptide. The plts derived by linear regressin between fasting and 6 r -min values have been termed glucse-insulin and glucse C-peptide 'vectrs' and the slpes have been shwn t represent the Beta-cell dse-respnse curve. J. C. Levy et al.: Simple empirical assessment f Beta-cell functin G-I and G-C vectrs can be extraplated t predict insulin and C-peptide levels that wuld be achieved at a glucse cncentratin f 12 mml/1. When cmpared with actual plasma insulin r C-peptide respnse t a subsequent -min hyperglycaemic clamp, the predicted values shwed a high degree f crrelatin with G-I plts, which predicted a cnsistent 7% f clamp insulin values, and G-C plts which predicted clamp C-peptide levels with a small cnstant abslute amunt ver a wide range f pancreatic functin. Sme underestimatin f actual clamp values wuld be expected, due t the prgressive rise seen in insulin and C-peptide levels during the maintained hyperglycaemia f a clamp [1], and this underestimatin wuld be expected t increase with the length f the clamp. Hwever, the relatinship between the predicted and actual respnses is simple, as demnstrated in Figure 3. The greater difference between actual and predicted clamp levels fr insulin than C-peptide may reflect the nn-linearity f insulin remval [16-18]. Hwever, the cnsistency f the predictins validates the G-I and G-C plts as representatins f the glucse respnsiveness f the Beta-cell in the physilgical range. The plts may be regarded as empirical linear dse-respnse plts. As the Beta-cell secretin-stimulus curve is sigmidal in shape [1-24] it is nt clear at first sight why a linear dse - respnse relatinship was btained. Hwever, studies f the glucse-insulin dse respnse curves generated frm repeated glucse infusins are apprximately linear between 5-12 mml/1 [1], and the nrmal basal glucse value prbably lies near the pint f infiexin f the sigmidal curve [25]. The straight-line relatinship may be represented by tw cefficients, the slpe f the line and a cnstant term representing its psitin with respect t the glucse axis. Hwever, in a large grup f individuals with widely differing pancreatic respnsiveness, the cefficients were highly crrelated and either may be derived frm the ther, within the bunds f experimental errr. In ther wrds, nly ne cefficient is necessary t describe Betacell functin, and we have used the vectr slpe rather than the cnstant term as it is mre intuitively representative f Beta-cell functin. The linearity f the plts als means that their slpes may be derived simply frm the rati f incremental insulin r C-peptide and incremental glucse btained frm samples taken frm fasting and frm the end f a 6 r -min glucse infusin, and this simple methd f calculatin crrelated clsely with the regressin based methd. The insulin and C-peptide vectr slpes are simple, empirically derived measures f Beta-cell functin, as expressed in the respnse f peripheral plasma insulin r C- peptide t glucse. Several mre cmplex measures f Beta-cell functin exist, including the hyperglycaemic clamp [1], the minimal mdel interpreted IVGTT [7], and the glucse ptentiatin slpe [8]. Cmparisn f the vectr slpes with the latter tw is utside the scpe f this study. Hwever, the vectr slpes crrelate clsely with the results f hyperglycaemic clamping, which, althugh reflecting the resultant f insulin and C-peptide secretin and clearance rates rather than pure glucse respnsiveness at the cellular level, prvides the 'gld standard' measure f effective pancreatic respnse t glucse. The

10 J. C. Levy et al.: Simple empirical assessment f Beta-cell functin glucse clamp is an intensive prcedure limited t experienced research departments and small-scale studies. n the ther hand estimatin f the vectr slpe frm a simple cntinuus glucse infusin is a much easier and cheaper prcedure, and thus mre suited t assessing Beta-cell functin in medium and large-scale studies. The reprducibilities f the G-I and G-C vectrs, as assessed by cefficients f variatin, cmpare favurably with that f either glucse [2] r insulin [3] cncentratins during the GTT, and particularly with the insulin/glucse rati measured 1 h after ral glucse [3], even thugh the latter was repeated after nly a 48 h interval. The ttal intra-individnal variatin assessed by the cefficient f variatin f the G-I and G-C vectr slpes in duplicate tests was 21% and 16% respectively. This will derive frm bth true physilgical variatin n the ne hand, and the versimplificatin f the linear assumptin and technical errrs such as assay imprecisin and sampling and strage variability, n the ther. This may be assessed by the median percent standard errrs f vectr slpes as 12.2 and 1.2% respectively. Thugh these tw estimates f variability are nt strictly cmparable, they give a qualitative impressin f a relatively large cntributin frm technical errrs. It is likely that the reprducibility f the G-I vectr slpes will imprve with technical imprvements in the insulin assay. The success f a single variable in describing the pancreatic respnse in the physilgical glucse range is pssibly surprising, as insulin secretin in vitr and in viv cnsists f tw 'phases', the first phase being said t be particularly impaired in Type 2 diabetes [5]. Hwever, this cnclusin was based n studies using an IVGTT, in which an impaired first phase leads t later hyperglycaemia which prvides a greater stimulus t the secnd phase. In studies which attempt t standardise the secnd phase glucse stimulus such as the blus-infusin studies f Cerasi et al. the dse respnse caracteristics f the tw phases f insulin secretin tended t vary in parallel [1]. This can be achieved mre successfully using glucse clamping technlgy, and during stepped hyperglycaemic clamps at different glucse levels, bth phases were similarly impaired in mild Type 2 diabetic subjects [12]. Thus, a reduced G-I r G-C vectr slpe represents a glbal decrease in the Beta-cell respnse. The slpe f the glucse-insulin vectr is linearly related t its psitin ver a wide range f nn-diabetic and diabetic individuals implying that the vectr slpe may be calculated frm the insulin and glucse values at any pint, frm equatin 4. This is an empirical cnfirmatin f the assumptins used in the HMA-CIGMA structural mathematical mdel which generates Beta-cell and insulin sensitivity measurements frm plasma glucse and insulin r C-peptide cncentratins at single time pints. These measures, derived frm plasma glucse, insulin and C-peptide cncentratins either in the fasting steadystate (HMA) [1] r after an ideal bdy weight standardised glucse infusin (CIGMA) [11], are mathematically independent frm the vectr slpes, and experimentally independent frm the results f the hyperglycaemic clamp. Hwever, there is a high degree f crrelatin between the HMA and the CIGMA derived %B, 47 the vectr slpes and the hyperglycaemic clamp insulin and C-peptide cncentratins. This supprts the HMA- CIGMA mdel assumptin that the plasma glucse is the main Beta-cell regulatr in bth fasting and glucsestimulated states [26, 27]. The Beta-cell respnse t the glucse infusin can be expressed either as the empirical vectr slpe r as the mdel (CIGMA) derived % B. The vectr slpes have the advantage f ease f calculatin and mdel free evaluatin, whereas the direct expressin f %B in terms f a nrmal reference ppulatin may assist interpretatin f the result. Mdel assessment f the glucse, insulin and C- peptide changes during the glucse infusin als prvides a measure f insulin sensitivity as well as Beta-cell functin. The G-I and G-C vectr slpes in nn-diabetic and Type 2 diabetic subjects cnfirm marked impairment in Beta-cell respnsiveness in the diabetic grup taken as a whle. The tw grups shw sme verlap, which at first sight suggests that apprximately half f these mild Type 2 diabetic subjects have Beta-cell respnsiveness in the nrmal range, albeit in the cntext f a higher ambient glucse cncentratin. Hwever, bth nn-diabetic and diabetic subjects shw a significant assciatin between G-I vectr slpe and besity expressed as %ideal bdy weight. Taking this int accunt, nly 4 f 21 relatively mild diabetic subjects had vectr slpe values in the nrmal range. Bagdade et al. [28] reprted an assciatin in nrmal subjects between the fasting plasma insulin level and the insulin respnse t an ral glucse tlerance test, and the inverse relatinship between Beta-cell functin and insulin sensitivity has been nted in several experimental situatins [2, 2, 3]. This relatinship is reflected in the psitive assciatin between vectr slpe and fasting plasma insulin, and this is supprted directly by the negative crrelatin between vectr slpe and insulin sensitivity as assessed by the euglycaemic clamp. These results cnfirm the imprtance f taking the prevailing degree f insulin sensitivity int accunt in the assessment f Beta-cell functin in bth nn-diabetic and diabetic subjects [3] and this can be dne either with a measure such as the fasting plasma insulin r frm the degree f besit), as that is a majr determinant f insulin resistance. n theretical grunds ne might expect a direct measure f insulin resistance, the fasting plasma insulin, wuld be the better index, but the assay imprecisin at lw fasting levels and the pulsatility f basal insulin secretin [31] prbably make current measurements sub-ptimal, s that measurement f besity becmes a better indirect assessment f insulin resistance in the general ppulatin. The negative assciatin between the besity-crrected vectr slpes and fasting plasma glucse in the diabetic subjects underlines the fact that the severity f diabetes is linked t the severity f Beta-cell functin. Nevertheless, the besity-crrected vectr slpe remained subnrmal in the majrity f the diabetic subjects wh, n dietary management, had managed t reduce their fasting glucse levels t the nrmal range. In summary, insulin and C-peptide cncentratins during a lw dse glucse infusin, when related t simultaneus glucse cncentratins, generate an empirically li-

11 48 near relatinship which may be taken as a measure f the Beta-cell glucse dse respnse, as it predicts the insulin levels achieved by the hyperglycaemic clamp, the 'gld standard' clinical test f Beta-cell functin. The characteristics f this 'vectr' may be summarised in a single variable, the 'vectr slpe' which may be used t describe Beta-cell functin in the physilgical range. The vectr slpe agrees clsely with the Beta-cell cefficient generated by the CIGMA mdel. The glucse infusin test is suited t the assessment f Beta-cell functin in large ppulatins r prspective studies. The measured Betacell functin is affected by the degree f besity and the prevailing insulin resistance. The underlying characteristic Beta-cell functin f a patient can be discerned by its evaluatin with respect t the prevailing insulin resistance. Acknwledgements. We thank Ms. B. Barrw fr excellent nursing assistance and Karl Thmae GmbH and Beechams Pharmaceutical C. fr financial supprt. Appendix The existence f ppulatin parameters relating the slpes and the cnstant terms f the vectr equatins has extensins which give rise t testable predictins. quatin 4 fr the equatin f the regressin line thrugh the insulin - glucse plt in any individual in terms f the ppulatin parameters Pi and q~ and the slpe f that line, the 'vectr slpe', may be rearranged t give It - q~ = vectr slpe x (at + pi), (5) where It and Gt are the insulin and glucse cncentratins at any pint alng the extended insulin - glucse plt. A predictin f this equatin is that fr any individual, the pint n this line where plasma glucse equals - p~ will have an insulin value f % This has three cnsequences. Firstly, all G-I vectrs shuld cnverge n a single pint, ( - pi, qi), the 'null pint'. The vectrs f the 28 nn-diabetic and 21 Type 2 diabetic subjects are superimpsed in Figure, and within the bunds f experimental errr, this predictin wuld appear largely t be supprted (thugh this figure cnstitues an illustratin rather than a verificatin f the predictin, since it shws the data upn which the predictin was based). Secndly, it wuld be expected that fr a particular individual, a change in Beta-cell functin, e.g. assciated with prgressin f diabetes, r a marked change in insulin sensitivity (see results sectin), such as a significant lss f weight, wuld be assciated with the rtatin f the vectr arund this 'null pint', rather than, fr instance, a parallel translatin f the vectr n the glucse - insulin plane. The third testable cnsequence is that nly a limited cmbinatin f vectr slpe and psitin n the glucse - insulin plane was pssible. It wuld nt appear t be pssible, fr instance, t have bth a lw fasting plasma glucse and a high fasting insulin with a lw vectr slpe, r, cnversely, a high fasting glucse and lw fasting insulin with a high vectr slpe. References 1. DeFrnz RA, Tbin JD, Andres R (17) Glucse clamp technique: a methd fr quanti~ing insulin secretin and resistance. Am J Physi1237: McDnald GW, Fisher GF, Burnham C (165) Reprducibility f the ral glucse tlerance test. Diabetes 14: J. C. Levy et al.: Simple empirical assessment f Beta-cell functin 3. lefsky JM, Reaven GM (174) Insulin and glucse respnses t identical ral glucse tlerance tests perfrmed frty-eight hurs apart. Diabetes 23: McIntyre N, Hldswrth CD, Turner DS (164) New interpretatin f ral glucse tlerance. Lancet II: Brunzell JD, Rbertsn R Lerner RL, Hazzard WB, nsinck JW, Bierman L, Prte Jr D (176) Relatinships between fasting plasma glucse levels and insulin secretin during intravenus glucse tlerance tests. 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12 J. C. Levy et al.: Simple empirical assessment f Beta-cell functin tin in besity: measure f Beta cell sensitivity and capacity. Diabetes 23: Ashcrft S J, Hammnds R Harrisn D (186) Insulin secretry respnses f a clnal cell line f simian virus 4-transfrmed B cells. Diabetlgia 2:72% Pelknen, Taskinen M, Nikkila A (174) arly respnse f plasma insulin t small dses f intravenus glucse: effect f besity. J Clin ndcrin13:418m McCarthy ST, Harris, Turner RC (177) Glucse cntrl f basal insulin secretin in diabetes. Diabetlgia 13: Hlman RR, Turner RC (17) Maintenance f basal plasma glucse and insulin cncentratins in maturity-nset diabetes. Diabetes 28: Bagdade JD, Bierman L, Prte Jr D (167) The significance f basal insulin levels in the evaluatin f the insulin respnse t glucse in diabetic and nndiabetic subjects. J Clin Invest 46: Threll JI (173) ffect f transient elevatin f plasma insulin within physilgic levels (simulated early insulin respnse) n bld glucse. J Clin ndcrinl Metab 37: Beard JC, Ward WK, Halter JB, Wallum B J, Prte Jr D (187) Relatinship f islet functin t insulin actin in human besity. J Clin ndcrinl Metab 65:5% Lang DA, Burnett M, Ward GM, Matthews DR, Turner RC (182) Pulsatile, synchrnus plasma insulin and glucagn secretin in man. Diabetes 31:22-26 Received: 2 April 1 and in revised frm: 26 February 11 Dr. J. C. Levy Diabetes Research Labratries Radcliffe Infirmary Wdstck Rad xfrd X2 6H UK