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Original Studies |
San Raffaele Scientific Institute (A.C.), Milan, Italy; University of Southern California (R.N.B.), Los Angeles, California 90033; and Department of Electronics and Informatics, University of Padova (C.C.), I-35131 Padova, Italy
Address all correspondence and requests for reprints to: Prof. Claudio Cobelli, Department of Electronics and Informatics, Via Gradenigo 6/A, University of Padova, I-35131 Padova, Italy. E-mail: cobelli{at}dei.unipd.it
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Abstract |
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 Top Abstract IntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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Introduction |
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Nevertheless, due to the possible importance of an oral methodology, in this manuscript we examine the feasibility of measuring insulin sensitivity from an oral meal. To do this, we have coupled the classic minimal model of glucose kinetics (6) with a simple mathematical description of glucose absorption from the gastrointestinal tract. To examine the reliability of the meal-based index of insulin sensitivity, SI(oral), this parameter was compared with the insulin sensitivity index estimated from the insulin-modified frequently sampled iv glucose test (FSIGT) (7) measured in the same subjects.
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Subjects and Methods |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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The data used in the current study, provided by Dr. David Owens, are part of a published study (8) to which we refer for further details. Briefly, 10 healthy subjects (4 men and 6 women; age, 47.7 ± 2.6 yr; body mass index, 25.9 ± 1.2 kg/m2) with normal glucose tolerance received on different occasions an insulin-modified FSIGT or a meal tolerance test (MGTT). Both tests were performed in the morning after a 10-h overnight fast.
The insulin-modified FSIGT consisted of a 300 mg/kg glucose bolus at time zero, followed by an insulin injection of 0.03 U/kg at 20 min, as previously described (7). Blood was sampled at -30, -15, -1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, and 180 min.
The meal was mainly solid, with a small amount of juice and milk. It consisted of 15 g Weetabix, 10 g skimmed milk, 250 mL pineapple juice, 50 g white meat chicken, 60 g wholemeal bread, and 10 g polyunsaturated margarine. The total energy was 482 Cal; the total carbohydrate was approximately 75 g. The meal was eaten within 10 min. Blood samples were collected at -30, -1, 10, 20, 30, 40, 50, 60, 75, 90, 120, 150, 180, 210, and 240 min.
Analytical techniques
The plasma glucose concentration was measured by a glucose oxidase method. Immunoreactive insulin was measured in both tests by a conventional RIA method (antibody M8309 from Novo-Nordisk, Bagsvaerd, Denmark).
Data analysis
The analysis of both the FSIGT and the MGTT studies exploits the
classic minimal model (6). Whereas during the FSIGT
glucose enters the systemic circulation directly, during the MGTT food
is ingested, and nutrients, including glucose, encounter the systemic
circulation only after absorption from the gastrointestinal tract and
passage through the liver (see Fig. 1
).
Making explicit the appearance of exogenous glucose into the minimal
model yields:
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(t); during the MGTT/OGTT,
ra coincides with the rate of absorbed glucose,
i.e. ra(MGTT/OGTT) =
RaABS(t), where RaABS is
defined as the posthepatic appearance of newly absorbed glucose.
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Insulin sensitivity from the FSIGT
The minimal model parameters p1,
p2, p3, and V were
estimated by weighted nonlinear least squares from glucose and insulin
data collected during an insulin-modified FSIGT as previously described
(9). As is usual, measurements from the first 8 min after
iv glucose were ignored in model identification. The insulin
sensitivity index, SI(FSIGT) (milliliters per
kg/min·µU/mL), was calculated as:
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Insulin sensitivity from the MGTT
The challenge in using the minimal model to analyze oral
MGTT/OGTT data is to describe mathematically how exogenous glucose
reaches the systemic circulation. We made the assumption that the
profile of RaABS resembles an anticipated version
of glucose excursion above basal, 
g(t) = g(t) -
gb. Following the principle of parsimony, we used
a simple parsimonious parametric representation for describing the
relationship between RaABS and g:
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g with respect to RaABS, and b is a scale
factor. Initially we assumed g (
0) during the test; subsequently,
we generalized the analysis by allowing glucose to take on values below
its basal level late during the test.
Substituting the expression for RaABS given by Eq
III into the minimal model equations yields
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When the glucose concentration falls below the basal level during the
test, the equation for insulin sensitivity becomes
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g/g and g are separately calculated in the
intervals 0-t0 and t0-
, and the
negative AUC calculated in the interval t0- is
subtracted from the positive AUC calculated in the interval
0-t0. Calculation of SI(oral) with Eq VI and VII requires the investigator to insert values for GE and f. Generally, individual estimates of GE and f are not available. Therefore, mean values derived from the literature must be used. In the present study GE was fixed at 0.024 dL/kg·min, i.e. the mean value of glucose effectiveness in normal subjects reported in the review by Best et al. (13). Estimates of f, fraction of glucose taken orally to appear in the systemic circulation during an OGTT, vary between 70–100% (14) (see Discussion). In a previous study (15) we estimated that after a mixed meal the average absorption of oral glucose was 80% (n = 7; range, 67–95%). We thus set f = 0.8 in the formulas used to calculate SI(oral).
It is worth noting that evaluation of SI(oral) requires that the AUCs are calculated from the beginning of the test (time zero) until the glucose system returns to the pretest steady state. In the present study, insulin sensitivity values were calculated over the interval 0–240 min (see Discussion), and AUCs were computed using the trapezoidal rule.
Sensitivity analysis
Because values of glucose effectiveness, GE, and fractional splanchnic absorption of oral glucose, f, are assumed in this method, we examined the dependence of calculated SI(oral) upon the assumed values of GE and f. A sensitivity analysis was performed in which we evaluated how the estimate of SI(oral) changes in relation to a ±50% change in glucose effectiveness (assuming GE between 0.036 and 0.012 dL/kg·min) and in relation to a ±20% change in the absorption of oral glucose (assuming f between 0.96–0.64).
The impact of a shorter duration of the MGTT (180 instead of 240 min) and of a reduction of the sampling frequency (one sample every 30 min) on the estimation of SI(oral) was also evaluated by calculating SI(oral) from the glucose and insulin data measured at -30, -1, 30, 60, 90, 120, 150, and 180 min.
Statistical analysis
Results are given as the mean ± SEM. Due to the presence of a subject who was very sensitive to insulin, the distributions of SI(FSIGT) and SI(oral) were not normal. We thus used the Wilcoxon signed rank test to evaluate differences between SI(FSIGT) and SI(oral), and Spearman’s rank correlation coefficient (rs) to examine the strength of the association between them.
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Results |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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. Of note is that by the end of the MGTT
at 240 min, glucose and insulin had both virtually returned to their
respective pretest levels. Of course, this does not prove that all oral
glucose had been absorbed or that the metabolism of oral glucose was
complete (see Discussion).
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for the 10 subjects.
SI(oral) was strongly correlated with
SI(FSIGT) (rs = 0.89;
P < 0.01; see Fig. 3).
Despite the strong correlative relationship between the tests, the
absolute values of SI(oral) and
SI(FSIGT) were significantly different from each
other, with the value from the oral test being about twice that from
the iv test (13.6 ± 3.9 vs. 6.2 ± 1.3 x
10-4
dL/kg·min/µU·mL; P < 0.01). When calculation of
SI(oral) was performed relying on a reduced
sampling schedule of only eight glucose and insulin samples collected
between 0–180 min, results were virtually the same;
SI(oral) was 12.9 ± 3.5 x
10-4 dL/kg·min/µU·mL
and remained very well correlated with SI(FSIGT)
(rs = 0.90; P < 0.01). Of note
is that accuracy was maintained in individual subjects, as demonstrated
by the strong correlation between the two
SI(oral) estimates obtained from the full and the
reduced sampling schedule (rs = 0.99;
P < 0.01).
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Discussion |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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It would be beneficial if the simpler oral route of glucose administration could be the basis upon which SI were calculated. In the present work we have developed the theoretical framework for such a methodology. This approach was originally rejected because of the need to estimate the rate of entry of orally taken glucose into the systemic circulation. However, at that time we were most concerned with studies using small numbers of subjects in which iv administration was feasible and not prohibitively costly. However, the accelerating rate of appearance of large studies encouraged us to reexamine this methodology.
In the present study we introduce a new approach that exploits the minimal model, but adds a parsimonious parametric representation of splanchnic glucose absorption that allows the measurement of insulin sensitivity in each individual from an AUC type of calculation. Obviously such a calculation is simpler to perform than the nonlinear estimation procedure required for the iv method (6, 18).
We have examined this new approach to derive estimates of insulin sensitivity from meal glucose tolerance data in 10 subjects with normal glucose tolerance. Comparing the SI index obtained with this approach with the insulin-modified iv test by correlation analysis revealed a strong and highly significant correlation between the SI index measured in the two experiments (rs = 0.89; P < 0.01). This result suggests that both methods are measuring similar physiological phenomena, most likely the sum effects of insulin to enhance glucose uptake by peripheral tissues (mostly muscle) and concomitantly suppress liver glucose output. The present results are reminiscent of the linear relationship between results from the minimal model and the euglycemic glucose clamp method (10). Thus, it can be argued that the meal tolerance test (and presumably the oral glucose tolerance test) can be used, along with Eq VI and VII above, to yield an acceptable index of insulin sensitivity in normal individuals.
One striking result from the present study is that although one might predict a one to one concordance between the FSIGT and MGTT estimates of SI because they both rely on the minimal model and have the same units, we found that SI(oral) was numerically twice as great as SI(FSIGT) (13.6 vs. 6.2 x 10-4 dL/kg·min/µU·mL). Several explanations for this unexpected result may be suggested. One possibility is that the way RaABS is depicted in the model is not sufficiently accurate. To allow derivation of SI from MGTT/OGTT data, we resorted to a simple parametric description based on the idea that RaABS is an anticipated version of glucose excursion above basal. The question of whether this description is too simplistic needs to be addressed by future studies in which the time course of RaABS will be accurately assessed with the appropriate modeling and experimental techniques (such as the specific activity clamp). However, we speculate that the high degree of association between SI(FSIGT) and SI(oral) makes it unlikely that the description of RaABS is affected by gross errors. Another possibility is related to the fact that with this method one is forced to estimate the fraction of glucose taken by mouth that appears in the vena cava, emanating from the liver. There are several reasons why f, which was assigned a value of 0.8, may have been overestimated in this study. First, we assumed that gastrointestinal absorption of glucose is finished by 240 min. This was done for convenience, because the database used herein included a 240-min meal tolerance test. However, in a mixed meal tolerance test, absorption of nutrients is much slower than with a carbohydrate meal. Certain peptide hormones, such as glucagon-like peptide-1 (GLP-1), act as brakes on motility and may well slow the movement of ingested carbohydrate down the gastrointestinal tract. We can expect that this phenomenon would be less of a problem with an OGTT, because the so-called brake peptides are released with intake of fat. However, the value of 0.8 for f is not without foundation. In a previous MGTT study (15) in which f was estimated, particular care was employed in terms of frequency of blood sampling, duration of the experiment, and modeling analysis. Of course, we cannot exclude that in the present MGTT study f was lower than 0.8 (in the literature there are studies reporting values of f as low as 0.7 for the OGTT). Thus, further careful examination of fractional absorption of orally administered glucose is justified to determine the external value of f that should be used with the present new methodology. An additional caveat is that there may well be differences in f for different states, particularly in patients with diabetes, in whom neuropathy may alter gastrointestinal function.
Despite these considerations, it is possible that the outcome of SI(oral) > SI(FSIGT) is not due solely to an overestimation of f. In fact, as shown by the sensitivity analysis, even with f reduced to 0.64, SI(oral) is reduced only to 10.7 x 10-4 dL/kg·min/µU·mL, still higher than SI(FSIGT). In this regard it is important to remember that the minimal model is based upon a single compartment simplification of glucose distribution. It has been shown that this simplification causes difficulties in accounting for the rapid changes in glucose concentration experienced after an iv glucose injection (11, 12, 19). In contrast, it is likely that when glucose and insulin change more slowly, such as during a MGTT or an OGTT, a single compartment representation is sufficiently adequate (20). Whether the single compartment simplification may differently affect the calculation of SI from the iv vs. the oral test requires further examination.
Another possible explanation for the finding of SI(oral) > SI(FSIGT) is related to the different routes of glucose and insulin appearance during the meal and the FSIGT. During the meal, both glucose and insulin reach the peripheral circulation after passing through the portal vein. In contrast, during the insulin-modified FSIGT, glucose is injected iv, and the insulin concentration is the result of a mix of endogenously secreted insulin and exogenously administered insulin, the latter component being predominant after insulin injection at 20 min. The possibility that SI(FSIGT) is influenced by the use of peripheral, rather than portal, insulin delivery appears unlikely in view of the recent evidence from Steil et al. (21). These investigators demonstrated directly, by portal vs. peripheral infusion, that during the FSIGT portal insulin delivery per se does not significantly affect insulin’s ability to inhibit hepatic glucose release after an iv glucose challenge. Thus, it does not seem likely that in the present study SI(FSIGT) was underestimated with respect to SI(oral) due to the use of peripherally administered exogenous insulin during the FSIGT. A far as the different route of glucose administration is concerned, Cherrington and co-workers (22) have reported evidence suggesting that when glucose enters the systemic circulation through the portal vein, a neurally mediated portal signal is triggered that enhances glucose uptake by the liver. However, as this portal signal appears to inhibit nonhepatic glucose uptake by an amount identical to the amount it increases hepatic glucose uptake, the insulin sensitivity of glucose-consuming tissues should not be affected. Whether such a portal signal is also able to enhance the inhibitory effect of insulin on hepatic glucose production (which would augment the overall insulin sensitivity) is still unknown.
Another factor that could contribute to augment SI(oral) with respect to SI(FSIGT) is GLP-1. Specifically, while GLP-1 is a known insulin secretagogue, there is some evidence that this peptide may stimulate insulin-independent glucose disposal in peripheral tissues (23). Alternatively, there may be other gastrointestinal factors enhancing insulin sensitivity at the liver or muscle that remain to be identified.
Another factor that may play some role is glucagon. It is worth emphasizing that the effects of glucagon on glucose metabolism are not explicitly described by the minimal model. In fact, the model interprets glucose and insulin data, during both the meal and the FSIGT, as the result of the effects of only two factors: glucose effectiveness and insulin sensitivity. Thus, it is possible that the different patterns of glucagon secretion during the FSIGT and the meal may alter the calculation of SI. The glucagon concentration is inhibited in either the FSIGT or meal protocol. There are, however, contrasts in the patterns by which glucagon returns to its basal level. During a meal, glucagon begins a slow resumption to the basal level after approximately 90 min (24). In contrast, during the insulin-modified FSIGT, glucagon shows a rapid and marked increase after 30 min that counteracts the glucose-lowering effect achieved by means of the exogenous insulin injection (21). An increasing glucagon has two concomitant and opposite effects on hepatic glucose production: it stimulates hepatic glucose production and potentiates insulin inhibitory effect on hepatic glucose production. The net effect observed by Steil et al. was a quick resumption of hepatic glucose production from nearly complete suppression back to basal [in humans, as shown by Vicini et al. (25), hepatic glucose production also exhibits a marked overshoot over the baseline]. It can be speculated that this behavior of hepatic glucose production, occurring in concomitance with a still elevated insulin profile, is likely to be interpreted by the minimal model as the inability of insulin to maintain the inhibition of hepatic glucose production. This might lead to an underestimation of insulin sensitivity during the insulin-modified FSIGT, and thus contribute to reduce SI(FSIGT) with respect to SI(oral).
Glucose uptake is dependent upon insulin-independent as well as insulin-dependent mechanisms. In the present oral-based method the insulin-independent component, glucose effectiveness, was assumed. Fortunately, however, the resulting insulin sensitivity value was virtually independent of the estimate of glucose effectiveness. A ±50% change in glucose effectiveness produces only a ±2.3% change in the estimate of SI(oral). Thus, at least in normal subjects, the MGTT/OGTT estimate of SI does not seem to depend on the assumed value for glucose effectiveness. However, the relative importance of glucose effectiveness to overall glucose tolerance increases substantially in subjects with impaired glucose tolerance as well as those with type 2 diabetes. Thus, the relative unimportance of the estimate of effectiveness to the insulin sensitivity value requires additional examination in different groups of volunteers.
Clearly, calculating insulin sensitivity from an oral test is appealing. Insulin sensitivity derived from MGTT/OGTT data appears to require only eight glucose/insulin samples between 0 and 180 min. In fact, the mean value of SI(oral) and its degree of correlation with SI(FSIGT) did not change when only eight samples (two basal samples and one sample every 30 min until 180 min) were used in AUC calculations.
In conclusion, a new approach for the estimation of insulin sensitivity from a meal tolerance test has been presented that exploits the minimal model approach. The SI index obtained with this approach in normal subjects appears to be closely associated to the one estimated from insulin-modified FSIGT data. Therefore, our results indicate that the minimal model applied to the analysis of MGTT/OGTT data is potentially useful to measure insulin sensitivity when use of the insulin-modified FSIGT is not feasible for economic or practical reasons. The present study in normal humans is the first attempt and an obvious prerequisite. Further work is needed to define the domain of validity of this method throughout the whole range of insulin sensitivity and assess its applicability to patients with diabetes mellitus. If validated in disease states, the new test may be preferable to the FSIGT in large studies because of its simplicity.
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Appendix |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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The purpose here is to show how insulin
sensitivity can be calculated from MGTT/OGTT data. Making reference to
Fig. 1
, we denote with RaABS(t)
(mgkg-1min-1) the rate of appearance of the
ingested glucose into the systemic circulation during a MGTT/OGTT. To
give RaABS(t) a parsimonious representation, we make the
assumption that its profile resembles an anticipated version of the
glucose excursion above basal, g(t)=g(t)-gb. The
simplest functional relationship between RaABS and g
accounting for this idea is the following:
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g with respect to RaABS and b is a
scale factor. RaABS can thus be written as follows:
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g is
always nonnegative during the test. We will deal after with the more
general case in which glucose concentration displays an undershoot
below its basal level in the final part of the test.
Substituting the expression for RaABS(t) given
by Eq AII into the minimal model equations yield:
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g) until the end of
the experiment. To cope with such inadequacy of Eq AII (but retaining
at the same time the simplicity and usefulness of its description of
RaABS) we split the description of RaABS by
distinguishing the intervals that precede and follow t0:
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g
are separately calculated in the intervals 0-t0 and to- and
the negative AUC calculated in the interval t0- is
subtracted from the positive AUC calculated in the interval
0-t0.
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Acknowledgments |
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Received December 8, 1999.
Revised July 25, 2000.
Accepted July 28, 2000.
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References |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionAppendixReferences |
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