Clamps and the indices built on them

Plasma glucose is held by a closed loop. Glucose stimulates the β-cell; insulin lowers glucose by suppressing hepatic glucose output and increasing uptake, mostly in muscle. At steady state, glucose sits wherever secretion and action balance.

That balance hides the cause. A fasting insulin of 20 µU/mL with normal glucose may be a resistant person whose β-cells are compensating well. A fasting insulin of 8 µU/mL with a glucose of 115 mg/dL may be a sensitive person whose β-cells are failing, or a resistant one whose β-cells already have. Illustrative

That leaves two unknowns and one observation, and every method in this course is a way of getting a second equation.

The homeostasis model assessment (HOMA) solves the loop with a computer model of it. Matthews and colleagues compared a patient's fasting glucose and insulin with the model's predictions to estimate two things at once, insulin resistance and β-cell deficit.

HOMA is often reduced to HOMA-IR. The founding paper returned two outputs, and it was candid about precision:

"The low precision of the estimates from the model (coefficients of variation: 31% for insulin resistance and 32% for β-cell deficit) limits its use."Matthews et al., Diabetologia 1985, Summary

HOMA's estimate of insulin resistance correlated with the euglycemic clamp (R_s = 0.88) in that paper. A good correlation across a group and a 31% coefficient of variation in one person are both true at once; the first supports population work, the second limits individual tracking.

Source: Matthews 1985

The clamp takes the other route and opens the loop. DeFronzo, Tobin and Andres explained the idea with the islet preparations it was meant to imitate in people:

"The excised pancreas or isolated islet preparation can be perfused at fixed hyperglycemic levels … It was with this type of control in mind that we had developed the glucose clamp technique. The technique places the plasma glucose concentration under the investigator's control and thus breaks the simple glucose-insulin feedback loop."DeFronzo, Tobin & Andres, Am J Physiol 1979;237:E214, p. E214

The name itself came from physiology: a footnote on the first page credits Joseph J. Blum of Duke, "who pointed out the analogy to the voltage clamp technique." As with a voltage clamp, you hold one variable fixed and read what it takes to hold it there.

Source: DeFronzo 1979

The 1979 paper describes two procedures, each answering one question:

The phrases in quotation marks are from the paper's abstract. Chapter 2 goes through the euglycemic clamp step by step, and Chapter 3 the hyperglycemic clamp.

Source: DeFronzo 1979

The 1979 subjects were 11 healthy volunteers aged 21 to 45, within 10% of desirable body weight, with a normal OGTT. They ate a weight-maintaining diet with at least 200 g of carbohydrate a day for 3 days, and were studied at 8 A.M. after a 12-hour fast.

Two catheters: one "into a brachial artery for blood sampling", one "into an antecubital vein for infusion of 20% dextrose in water", followed by a stabilization period of 45 to 60 minutes.

Practice note Most laboratories now sample arterialized venous blood from a hand vein kept in a heated box, usually with the infusion line in the opposite arm, rather than cannulating an artery. The principle is the same: sample blood whose glucose reflects what tissues receive.

Practice note The carbohydrate run-in is there because recent carbohydrate restriction can lower insulin-stimulated glucose uptake, so a subject who has been dieting can look more resistant than they are.

Source: DeFronzo 1979

Insulin is given as a 10-minute priming infusion that steps down every minute, then a constant 40 mU per m² body surface area per minute until 120 minutes. The prime was "calculated to raise the plasma insulin concentration 100 µU/ml".

Table 2 of the 1979 paper. The prime "can be adjusted upward or downward on a proportional basis to achieve any desired level of plasma insulin concentration." It produced an overshoot lasting about 20 minutes; the 40 to 120 minute plateau averaged 105 ± 5 µU/mL.

Without a prime, a constant infusion approaches its plateau exponentially, so the first half hour would be spent at a lower, changing insulin level. The prime fills the insulin space quickly. Interpretation

Source: DeFronzo 1979

As insulin rises, glucose begins to fall. The glucose infusion is started 4 minutes after insulin, empirically at 2.0 mg/kg/min, and raised to 2.5 mg/kg/min at 10 minutes. From the 10-minute sample on, a formula sets the rate every 5 minutes.

The target is each subject's own fasting glucose: the paper holds "each subject at his own basal arterial plasma glucose concentration," so that hypoglycemia "with its attendant counterregulatory neuroendocrine responses" never begins. Counterregulation would release glucagon, catecholamines and cortisol, raise hepatic glucose output and blunt uptake: the clamp would be measuring the stress response instead of insulin action. Interpretation

Source: DeFronzo 1979

Every 5 minutes the pump setting S_i is the sum of two parts:

The volume part, SV. (G_d − G_i) × 10 × (0.19 × body wt) is the glucose deficit or excess in mg across a glucose space of 0.19 L/kg. Dividing by the infusate concentration converts it to mL; dividing by 15 spreads the correction over 15 minutes "because the intravenously infused glucose required time for distribution." PF converts mL/min to a pump dial setting. The correction is never fully delivered, because a new sample replaces it 5 minutes later.

The metabolic part, SM. This tracks what tissues are taking up. It is the metabolic setting from two samples back, scaled by how far glucose is from goal now (FM_i) and five minutes ago (FM_i−1).

Why two samples back. The paper's example: the 50-minute sample is read out at 53 minutes, but the infusion that shaped it was the one set at 43 minutes from the 40-minute sample. So SM for the 50-minute sample builds on SM from the 40-minute sample.

Why FM_i−1 as well. Glucose requirements keep rising during a clamp. With only FM_i the formula "did not permit a rapid enough escalation"; the second factor carries the trend forward.

Start-up values. For the 10- and 15-minute samples SM_i−2 is assigned 4.0 mg/kg/min; FM_i−1 for the 10-minute sample is 1.00.

Source: DeFronzo 1979

The bench runs the formula above, unchanged, on a simulated subject. Plasma glucose is sampled every 5 minutes and each new rate starts 3 minutes later, as in the paper's 50/53-minute example. The formula is the paper's; the subject is a teaching model. Illustrative

Once glucose is steady, the glucose infused equals the glucose leaving the glucose space, "provided that endogenous glucose production is completely suppressed." Two corrections turn the infusion rate into glucose metabolized:

UC is urinary glucose loss, collected at the end and assumed spread evenly over the study; it matters in the hyperglycemic clamp (about 0.2 mg/kg/min there) and is small at euglycemia. SC, the space correction, accounts for glucose added to or removed from the glucose space when glucose drifts during a 20-minute period. M is computed for each 20-minute period and averaged over the five periods from 20 to 120 minutes.

Worked example from the paper. Glucose is 215 mg/dL at 20 minutes and 210 at 40 minutes. SC = (210 − 215) × 0.095 = −0.475 mg/kg/min, so M for that period is the mean infusion rate plus 0.475: glucose that left the space was metabolized without being replaced. A 10 mg/dL change gives a correction of 0.95 mg/kg/min.

The bench above computes M exactly this way once it reaches 120 minutes.

Source: DeFronzo 1979

The healthy reference. In the 1979 subjects, glucose was held at 90 ± 2 mg/dL (coefficient of variation 5.0%) and M averaged 7.00 ± 0.52 mg/kg/min. Four subjects restudied 3 to 4 weeks later gave 8.53 ± 0.77 against 8.43 ± 0.78 the first time.

The hidden assumption. M equals whole-body glucose disposal only if the liver has stopped producing glucose. If hepatic output is only partly suppressed, the infusion fills the gap between disposal and residual output, and M understates disposal by exactly the residual output. Interpretation Try the third preset on the bench: true disposal stays the same, but M falls.

The tracer fix. A primed-continuous infusion of labeled glucose ([3-³H]glucose in Matsuda 1999 and Abdul-Ghani 2007) measures the rate of glucose appearance, so endogenous production can be subtracted out: at steady state, disposal = infusion + residual endogenous production. (Matsuda 1999; Abdul-Ghani 2007, for the tracer used; the steady-state identity is mass balance) With basal endogenous production (EGP) and fasting insulin (FPI) in hand, Matsuda and DeFronzo computed hepatic insulin sensitivity from the clamp as 1,000 ÷ (EGP × FPI).

M/I. Dividing M by the steady-state plasma insulin gives glucose metabolized per unit insulin, "a reasonable index of tissue sensitivity to insulin"; the paper multiplies the ratio by 100 for convenience. Use it when insulin plateaus differ between subjects or studies.

Practice note In obesity, M per kg body weight mixes tissue sensitivity with body composition, because adipose tissue takes up little glucose. Many studies also report M per kg fat-free mass. Know which denominator a paper used before comparing its M-values with yours.

Sources: Matsuda 1999; Abdul-Ghani 2007; DeFronzo 1979

Glucose is "acutely raised to 125 mg/dl above basal levels by a priming infusion of glucose" and held there by a variable infusion using the same negative-feedback formula. No insulin is infused, so every change in plasma insulin comes from the subject's own secretion (net of hepatic and peripheral clearance).

Because the step is defined relative to each subject's basal glucose, every subject gets the same stimulus increment. Interpretation

Source: DeFronzo 1979

The prime was set by trial and error and is the same for everyone, computed per m²: 9,622 mg/m² over the first 14 minutes, "equivalent to approximately 240 mg/kg body wt in normal weight individuals or nearly 2 mg/kg for each mg/dl increase in plasma glucose."

In the 1979 subjects, glucose at 15 minutes averaged 220 ± 3 mg/dL, 1 ± 1% above goal.

Source: DeFronzo 1979

The same S_i = SV_i + SM_i formula runs every 5 minutes, now with G_d = G_b + 125. The paper's worked case: G_b = 90, G_d = 215, G_i = 205 gives FM_i = (215 − 90) ÷ (205 − 90) = 1.087, an 8.7% increase in the metabolic component.

Over 10 to 120 minutes, glucose averaged 213 ± 2 mg/dL (98 ± 1% of goal) with a within-study coefficient of variation of 3.7 ± 0.1%.

Source: DeFronzo 1979

Insulin was sampled "every 2 min for the first 10 min and every 10 min thereafter to determine both the early and late phases of insulin release." Sampling is dense early because first-phase release is over within minutes and sparse sampling misses it.

The response was biphasic, "an early burst of insulin release during the first 6 min followed by a gradually progressive increase." In the 11 healthy subjects, early (0 to 10 min) and late (10 to 120 min) insulin averaged 47 ± 6 and 64 ± 3 µU/mL.

Illustrative model The insulin curves are a teaching model; the dotted lines in the normal state are the 1979 healthy means.

Loss of the first phase is one of the earliest secretory defects described in people progressing toward diabetes; it is the part of the curve to look at first. Interpretation

Source: DeFronzo 1979

Glucose infused during a hyperglycemic clamp is disposed of under the subject's own insulin. The paper calls M here "essentially a measure of glucose tolerance": in an OGTT the dose is fixed and glucose is the measure; in the clamp glucose is fixed and the dose is the measure.

In the 1979 subjects M was 8.03 ± 0.68 mg/kg/min over 20 to 120 minutes; it rose only slightly from 20 to 60 minutes and then roughly doubled from 60 to 120. Urinary loss averaged 0.2 mg/kg/min. M divided by insulin, "a measure of tissue sensitivity to endogenously secreted insulin," was 13.08 ± 1.17 (mg/kg/min per µU/mL × 100).

The space correction is not reliable during the first 20 minutes, when glucose rises by 125 mg/dL, so M for that period was not reported.

Source: DeFronzo 1979

Later protocols add further stimuli to the same design. One example from DeFronzo's group (Merovci 2021): glucose "acutely raised and maintained at 100 mg/dL above baseline for 80 min", then raised to 400 mg/dL "for an additional 110 min", and at 160 minutes "an intravenous bolus of 5 g of arginine." Insulin secretion rates came from "deconvolution of the plasma C-peptide concentration curve."

The same study used these phases to compute a clamp-based disposition index; Chapter 6 covers it once the disposition index has been defined.

Practice note C-peptide is secreted with insulin in equal molar amounts but is not cleared by the liver on first pass, so it tracks secretion more closely than peripheral insulin does. Plasma insulin is secretion minus clearance.

Source: Merovci 2021

In the euglycemic and hyperglycemic clamps, the subject's islet keeps working: endogenous insulin and glucagon still change. The pancreatic (somatostatin) clamp removes those changes. Somatostatin is infused to suppress endogenous insulin and glucagon, and the investigator replaces each hormone at a chosen rate. Any change in glucose production can then be assigned to the hormone that was changed. Interpretation of the design.

Unger and Cherrington, writing about what they call "insulinocentric skepticism" toward glucagon, credit the somatostatin clamp with demonstrating glucagon's action.

Practice note Doses of somatostatin and of basal insulin and glucagon replacement differ between laboratories and species. Take them from the protocol you are reproducing, not from a summary.

Source: Unger 2012

Insulin's first target is the liver. A glucose clamp without a tracer cannot separate a reduced need for infused glucose caused by less muscle uptake from one caused by continued hepatic output. A labeled glucose infusion measures total appearance; subtracting the infusion gives endogenous production. Interpretation

Both index papers in this course were validated against tracer clamps: Matsuda and DeFronzo (1999) and Abdul-Ghani and colleagues (2007) gave every subject a euglycemic insulin clamp with [3-³H]glucose. The hepatic insulin resistance index derived from the OGTT (Chapter 8) was validated against the tracer-measured product of endogenous glucose production and fasting insulin.

Sources: Matsuda 1999; Abdul-Ghani 2007

The simulator beside this step runs the three clamps on four people: normal tolerance, prediabetes, early and late type 2 diabetes. Choose a clamp and watch the same protocol separate them. Illustrative

It follows the rules this course has taken from the 1979 paper. The hyperglycemic clamp steps glucose 125 mg/dL above each person's own fasting level, so the person with diabetes starts higher and goes higher. The euglycemic clamp holds each person at their own fasting glucose, using the paper's feedback formula. Without a tracer, M misses whatever glucose the liver still releases, and the table shows by how much.

The values for each state are chosen to show the pattern, not taken from a cohort. Use the simulator to see the designs side by side, and the earlier chapters for the protocol details and the numbers you would cite.

Bergman, Phillips and Cobelli fitted two "minimal models" to a frequently sampled intravenous glucose tolerance test (glucose 300 mg/kg; 23 samples over 3 hours; glucose and insulin only) in 18 people. Each person got three parameters: insulin sensitivity S_I, and first- and second-phase β-cell responsivity φ₁ and φ₂.

"The three characteristic parameters (φ₁, φ₂, and S_I) represent an integrated metabolic portrait of a single individual."Bergman, Phillips & Cobelli, J Clin Invest 1981

They then proposed "the product of these two factors, φ₂·S_I, as a 'disposition index'." The hyperbola φ₂·S_I = 75 separated most good-tolerance from low-tolerance subjects; the product was 160 ± 26 versus 40 ± 7.

The same paper found that lean subjects with lower tolerance had low φ₂ with normal S_I, while obese subjects with lower tolerance had low S_I, so the same tolerance had different causes.

Source: Bergman 1981

In 93 apparently healthy people (fasting glucose under 6.4 mM, BMI 19.5 to 52.2), Kahn and colleagues found that the relation between S_I and four β-cell measures (fasting insulin, first-phase insulin response AIR_glucose, glucose potentiation slope, and secretory capacity AIR_max) "could not be distinguished from a hyperbola, i.e., S_I × β-cell function = constant," and fitted better than a line.

The shape has a practical consequence the abstract spells out: when sensitivity is high, large changes in sensitivity produce small changes in insulin; when sensitivity is low, small changes in sensitivity produce large changes in insulin.

Source: Kahn 1993

In his 2006 Banting Lecture Bergman defined DI = AIR_glucose × S_I, "the ability of the glucose regulating system to compensate for insulin resistance by increasing plasma insulin," and noted that the relation "has been referred to as the 'Hyperbolic Law of Glucose Tolerance'", citing Stumvoll, Tataranni and Bogardus (2005).

He reported that Weyer and colleagues, following Pima Indians, identified DI as "the strongest predictor of conversion from normal glucose tolerance to type 2 diabetes" over 5 years. (Bergman 2007, as stated in the lecture)

Source: Bergman 2007

Move the person. Each curve is a line of constant disposition index: everyone on one curve has the same capacity to hold glucose, whatever mix of secretion and sensitivity gets them there. Illustrative units

The compensation path slides along a curve: sensitivity falls, secretion rises, DI holds and so does glucose. The failure path drops through the curves: sensitivity falls and secretion does not rise enough. A person can still have more insulin than a lean control and be failing, because adequacy is judged against the curve. Interpretation

Is it really a hyperbola? The test is a log–log slope of −1 between secretion and sensitivity. Utzschneider and colleagues found that with HOMA-S as the sensitivity measure, the confidence limits included −1 for normal and impaired tolerance "but not diabetes."

Shared inputs. When secretion and sensitivity are both computed from the same OGTT glucose and insulin values, part of any inverse relation can be arithmetic. Chapter 8 shows how Retnakaran tested this.

Precision. A product carries the error of both factors. Chapter 8 gives the measured test–retest numbers.

Source: Utzschneider 2009

The index divides an insulin secretion term by insulin resistance:

ΔI/ΔG is the rise in plasma insulin relative to the rise in plasma glucose during the OGTT: the β-cell's output per unit of glucose stimulus. Dividing by insulin resistance (equivalently, multiplying by insulin sensitivity) asks the disposition-index question: is that output enough for this person's resistance? Interpretation

The term and symbol are DeFronzo's: Figure 3 of his Banting Lecture is captioned "Insulin secretion/insulin resistance (disposition) index (ΔI/ΔG ÷ IR)." DeFronzo writes that "all subjects" in the cohorts behind that figure had an OGTT with glucose and insulin "every 15 min" and "a euglycemic insulin clamp to measure insulin sensitivity"; the VAGES report itself states that 58 of its 319 subjects had a clamp.

Read the methods of each paper. The time window for ΔI/ΔG (0 to 30 min or 0 to 120 min), whether Δ means a concentration difference or an incremental area, and whether IR comes from the clamp or from the Matsuda index all vary between papers from the same group. The workbench in Chapter 9 lets you choose each of these.

Sources: DeFronzo 2009; Abdul-Ghani 2006

Pooling the San Antonio Metabolism study and the Veterans Administration Genetic Epidemiology Study (NGT 318, IGT 259, type 2 diabetes 201; n = 778), DeFronzo plotted the index against the 2-hour plasma glucose of the OGTT:

"If a 2-h plasma glucose <140 mg/dl is considered to represent 'normal' glucose tolerance, subjects in the upper tertile (2-h PG = 120–139 mg/dl) have lost two-thirds of their β-cell function … subjects in the upper tertile of IGT (2-h PG = 180–199 mg/dl) have lost 80–85% of their β-cell function."DeFronzo, Banting Lecture, Diabetes 2009;58:773–795, p. 774

Gastaldelli and colleagues reported the same pattern in the San Antonio cohort: NGT subjects with 2-hour glucose of 6.1 to 7.8 mmol/L (110 to 140 mg/dL) "already have a greater than 50% decline in the plasma insulin response to a glucose challenge."

Sources: DeFronzo 2009; Gastaldelli 2004

It is a cross-sectional gradient. Each figure compares groups of different people binned by 2-hour glucose. No one in these data was followed while losing two-thirds of their β-cell function. "Lost" is a comparison with the lowest 2-hour-glucose bin. Interpretation

The decline is in insulin relative to the stimulus. Despite the wording "plasma insulin response", Gastaldelli's decline is in insulin relative to the glucose stimulus (ΔI/ΔG, and ΔI/ΔG ÷ IR). Absolute plasma insulin follows an inverted U across these groups and may be normal or high. (Gastaldelli 2004, Results, Figs 2–3)

"β-cell function" is β-cell function relative to resistance. It is not β-cell mass. Function can fall from glucotoxicity, lipotoxicity or loss of incretin effect with mass intact, and some of that is reversible. Interpretation

Reading values off a figure. The percentages are DeFronzo's stated reading of his Figure 3; the figure's axis is not labeled finely enough to re-derive them independently. Cite them as his statement. (DeFronzo 2009; the page image was checked)

Sources: Gastaldelli 2004; DeFronzo 2009

When both a hyperglycemic clamp and a measure of sensitivity are available, the same logic applies with clamp terms. Merovci and colleagues (2021) took insulin sensitivity as "the mean glucose infusion rate during last 20 min … of each hyperglycemic clamp step divided by mean plasma insulin concentration during the corresponding period (M/I)," and computed "the insulin secretion/insulin resistance (IS/IR) (disposition) index" as "M/I × CP0–10, M/I × CP10–80, M/I × CP90–160, and M/I × CPArg 0–10, where CP = C-peptide." In DeFronzo's group the clamp form of IR is the inverse of M/I, so the clamp disposition index is a secretion term multiplied by M/I.

Clamp versions remove the gut, incretins and variable gastric emptying from the measurement; OGTT versions keep them. They answer slightly different questions, and a person can look different on each. Interpretation

Sources: Merovci 2021; Gastaldelli 2004; Abdul-Ghani 2006

By 1999 the clamp was the reference method, but it is invasive and slow. The OGTT was routine, and yet, in Matsuda and DeFronzo's words, "it has been difficult to derive meaningful information about whole-body, peripheral tissue, or hepatic sensitivity to insulin from the results of the OGTT."

They studied 153 people (62 normal, 31 IGT, 60 diabetic; age 18 to 71; BMI 20 to 65). Each had a 75 g OGTT after a 10- to 12-hour fast, with glucose and insulin at −30, −15, 0, 30, 60, 90 and 120 minutes, and a euglycemic insulin clamp with [3-³H]glucose.

Source: Matsuda 1999

In the paper's words: "10,000/square root of [fasting glucose × fasting insulin] × [mean glucose × mean insulin during OGTT]."

Units are part of the formula. The constant 10,000 assumes mg/dL and µU/mL. Entering mmol/L and pmol/L changes the value by a fixed factor and makes it incomparable with published values. Convert first.

Source: Matsuda 1999

G₀ × I₀, the fasting product. High fasting glucose despite high fasting insulin means insulin is not restraining glucose in the fasting state, when glucose comes mostly from the liver. This is the same product that HOMA-IR scales. Interpretation

Ḡ × Ī, the post-load product. High mean glucose despite high mean insulin after a glucose load means insulin is not clearing the load, where muscle does most of the work. Interpretation

The square root. The product of two G × I terms has squared units; the square root returns it to G × I units. It is the geometric mean of the fasting and post-load products, so each state carries equal weight. Interpretation (arithmetic)

10,000 ÷ …. Inverting turns resistance into sensitivity (higher is more sensitive); 10,000 scales the result into single or low double digits.

The authors' own summary of what it captures: "This index represents a composite of both hepatic and peripheral tissue sensitivity to insulin."

How it responds. Because ISI ∝ 1/√(I₀ × Ī), doubling every insulin value halves the index, while doubling only the fasting insulin lowers it by a factor of √2, about 29%. The same holds for glucose. Interpretation (arithmetic)

Source: Matsuda 1999

An OGTT with samples at 0, 30, 60, 90 and 120 minutes. Illustrative

Change the values in the workbench (Chapter 9) and the same breakdown appears for your numbers.

Against whole-body glucose disposal during the tracer clamp, the index correlated at r = 0.73 (P < 0.0001) in the 153 subjects.

r = 0.73 means r² ≈ 0.53: about half of the between-person variance in clamp disposal is shared with the index. That is strong for a test that needs only a 2-hour OGTT, and it leaves room for an individual to be misclassified. Interpretation (arithmetic)

The same paper computed hepatic insulin sensitivity from the clamp as 1,000 ÷ (EGP × FPI). The Matsuda index does not separate liver from muscle; Abdul-Ghani's indices (Chapter 8) were designed to.

Sources: Matsuda 1999; Abdul-Ghani 2007

Units. See the warning under the formula.

Insulin conversion. Papers convert pmol/L to µU/mL with different factors (6.0 and 6.945 are both in use). Converting with 6.0 instead of 6.945 makes every insulin value about 16% higher and the Matsuda index about 14% lower, so the factor must be stated. Interpretation (arithmetic) The workbench offers both.

Assays. Insulin immunoassays differ in calibration and in cross-reactivity with proinsulin. Values from different assays are not directly comparable, and published reference ranges carry their assay with them. Practice note

Which samples go into the mean. The mean of 0, 30, 60, 90 and 120 minutes is not the mean of 0, 30 and 120. Abbreviated versions exist and give different numbers; state which you used. Practice note

Insulin clearance. The index reads plasma insulin. A person who clears insulin slowly has higher plasma insulin for the same secretion and the same tissue sensitivity, and a lower Matsuda index. Interpretation

Exogenous insulin. The index assumes the insulin measured is the subject's own response to the glucose load. Insulin therapy breaks that assumption. Interpretation

Measurement error. Retnakaran's laboratory used a coefficient of variation of 21.9% for the Matsuda index in its error modeling. No cut-off is given in this course: published thresholds depend on the cohort and the insulin assay.

Source: Retnakaran 2008

The four formulas below are written as in Retnakaran 2008, which tested them side by side:

The insulinogenic index divides by a small number. When glucose barely rises by 30 minutes, the index becomes unstable or negative; flag any result where G₃₀ − G₀ is small. Interpretation

Practice note These equations are taken from Stumvoll 2001, as cited by Retnakaran. The workbench applies them with insulin in pmol/L and glucose in mmol/L, the only units that give values in the expected range; the original was not opened to confirm this.

Source: Retnakaran 2008

The ÷ 22.5 form is the one Retnakaran used, citing Matthews 1985. Utzschneider used the Oxford web calculator for HOMA-S.

Sources: Retnakaran 2008; Utzschneider 2009

Utzschneider's oral DI. In 613 Japanese-American subjects followed for 10 years:

"Among nondiabetic subjects at baseline, baseline DIo predicted cumulative diabetes at 10 years (P < 0.001) independent of age, sex, BMI, family history of diabetes, and baseline fasting and 2-h glucose concentrations."Utzschneider et al., Diabetes Care 2009

Retnakaran's product (ISSI-2). Of ten secretion × sensitivity pairings tested, total AUC_ins/AUC_gluc × Matsuda was the one that met the hyperbola criterion (β = −0.99, 95% CI −1.66 to −0.33, in 277 women with normal tolerance). "The product of these two indices emerges as a potential OGTT-based measure of β-cell function." By 2009 the product was called ISSI-2, "the insulin secretion-sensitivity index-2" (Retnakaran 2009).

Sources: Utzschneider 2009; Retnakaran 2008; Retnakaran 2009

Abdul-Ghani, Matsuda, Balas and DeFronzo (2007) derived two organ-specific indices from the same OGTT in 155 Mexican-American subjects (100 NGT, 55 IGT), each validated against a tracer clamp:

The muscle index correlated with clamp insulin sensitivity (glucose disposal per unit steady-state insulin) at r = 0.78; the hepatic index with the tracer-measured EGP × fasting insulin at r = 0.64.

The authors' own limit on the muscle index: "In subjects with type 2 diabetes, the plasma glucose concentration often rises continuously during the last hour (60–120 min) of the OGTT. Therefore, determination of muscle insulin sensitivity using the current approach is not feasible." The workbench refuses to compute it when glucose has no fall after its peak.

Source: Abdul-Ghani 2007

OGTT secretion and sensitivity indices share their inputs: the same fasting and post-load values sit in both. An inverse relation between them can come partly from that sharing. Retnakaran's group tested it directly:

"… with insulin secretion and insulin sensitivity measures taken from different OGTTs in the same individual. Because these indices do not share the same insulin and glucose measurements, any observed hyperbolic relationship on this analysis could not be on the basis of statistical auto-correlation."Retnakaran et al., Obesity 2008

In that cross-day test only AUC_ins/AUC_gluc × Matsuda held (β = −1.12). The insulinogenic index (β = −2.28), both Stumvoll indices and the incremental AUC ratio did not.

Source: Retnakaran 2008

Hudak and colleagues gave 89 people two OGTTs a median of 86 days apart and computed a panel of commonly used indices from each. In the same people over the same interval, the revised QUICKI had a coefficient of variation of 2.8% and the oral disposition index 28.8%.

A tenfold difference in repeatability between indices computed from the same OGTTs reflects the formulas: log transforms compress variation, and differences and ratios of early timepoints amplify it. Interpretation For one patient followed over time, prefer an index with a known, low test–retest error; for group comparisons, the noisier indices are often still adequate.

Source: Hudak 2021