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Original Studies |
Metabolic Modelling Group, Center for Measurement and Information in Medicine, City University (R.H., L.C.), London, United Kingdom EC1V OHB; the Diabetes Research Unit, University of Wales College of Medicine, Academic Center, Llandough Hospital and Community National Health Service Trust (S.D.L., R.P., D.R.O.), Penarth, South Glamorgan, United Kingdom CF64 2XX
Address all correspondence and requests for reprints to: Dr. Roman Hovorka, Metabolic Modelling Group, Center for Measurement and Information in Medicine, City University, Northampton Square, London, United Kingdom EC1V OHB. E-mail: r.hovorka{at}city.ac.uk
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Abstract |
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Introduction |
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A variety of oral glucose tolerance tests and meal tolerance tests (MTT) have been used extensively to diagnose NIDDM in a clinical setting. The oral load results in a typical postprandial exposure of the pancreas to glucose, and gut and vagal hormones. The measurement of pancreatic responsiveness, then, closely reflects the ability of the pancreas to produce insulin under normal physiological conditions.
Insulin and C peptide are cosecreted in an equimolar ratio by the pancreas, and this phenomenon has been successfully exploited to assess prehepatic insulin secretion in man (7, 8). Unlike insulin, C peptide is not cleared by the liver to any significant extent, and C peptide kinetics have been shown to be linear over a physiological to supraphysiological range of plasma C peptide concentrations (9). A population (standard) model of C peptide kinetics provides parameters of C peptide kinetics from a subject’s demographic data (10), avoiding the need to assess C peptide kinetics on an individual basis.
In the present study we aimed to assess pancreatic responsiveness during MTT. A model-based approach was adopted. A linear relationship between C peptide secretion and plasma glucose was postulated and combined with the population model of C peptide kinetics. Two indexes of pancreatic responsiveness were defined, one related to basal and the other to postprandial conditions. The approach was evaluated employing data collected in normal subjects and body mass index (BMI)-matched subjects with newly diagnosed NIDDM. This gave us the opportunity to assess the ability of the method to discriminate between healthy and disease states. The evaluation procedure included deconvolution and sensitivity analyses, validating the approach from the modelling point of view.
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Subjects and Methods |
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Two BMI-matched subject groups, 16 normal subjects (7 men and 9 women; age, 50 ± 10 yr; weight, 80 ± 14 kg; BMI, 29.2 ± 3.6 kg/m2) and 16 subjects with newly diagnosed NIDDM according to WHO criteria (5 men and 1 woman; age, 50 ± 9 yr; weight, 87 ± 13 kg; BMI, 29.3 ± 3.7 kg/m2) participated in the study. The subjects were admitted on the study day to the Diabetes Research Unit, Llandough Hospital (Penarth, UK). The study was approved by the South Glamorgan Local Research Ethics Committee.
Experimental protocol
After a 10-h overnight fast, the subjects were admitted to a metabolic unit, where they remained on bed rest throughout the study. Blood was taken via an indwelling iv cannula that was inserted into the antecubital fossa vein and connected via a three-way tap to a slow running infusion of saline. Blood samples were taken at -30, 0, 10, 20, 30, 40, 50, 60, 75, 90, 120, 150, and 180 min relative to meal ingestion. A mixed meal consisted of 15 g Weetabix, 100 g skimmed milk, 250 mL pineapple juice, 50 g white meat chicken, 60 g wholemeal bread, 10 g polyunsaturated margarine (75 g carbohydrates; total, 500 Cal; calorie contribution: 55% carbohydrate, 30% fat, and 15% protein). The subjects were required to consume the meal within 10 min.
C Peptide, insulin, and glucose assay
Blood was taken into fluoride oxalate for measurement of glucose (YSI 2300, YSI, Hants, UK) and into lithium-heparin for measurement of C peptide (11) and specific insulin (12). The within- and between-assay coefficients of variation were 5.4% and 8.8%, respectively, for the C peptide assay and 4.1% and 8.8%, respectively, for the insulin assay.
Data analysis
Model of C peptide kinetics during MTT. It was assumed that
C peptide secretion is linearly related to the blood glucose
concentration. The linear relationship was imposed from the time of
meal ingestion until plasma glucose returned to its fasting
concentration. The model (Fig. 1
) of C
peptide kinetics is described by a set of differential equations:
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0, is the postprandial sensitivity index (per min),
M0, M0 0, is the basal sensitivity (per
min), and tmax is either 180 min or the time when plasma
glucose returns to its fasting value, whichever occurs
first.2
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M0 represents the ability of fasting glucose to stimulate ß-cell. M0 is numerically equal to the fasting C peptide divided by the fasting plasma glucose concentration. Both MI and M0 are normalized to the distribution volume of C peptide in the central compartment, i.e. the indexes represent secretion rates per unit volume of the central compartment.
The population model of C peptide kinetics was employed to obtain estimates of transfer rate constants k01, k21, and k12 from the subject’s age and classification (normal, obese, or NIDDM) using a regression model (10). The model parameters MI and M0 were estimated employing weighted nonlinear regression analysis (13). The plasma glucose concentration (the driving function) was taken as the model input, and the plasma C peptide concentration was taken as the model output. C peptide concentrations were zero weighted after the time when the plasma glucose measurement decreased below the fasting level to limit the estimation procedure to the period when (above fasting) glucose stimulus was present. Weights were defined as the reciprocals of the variance of the measurement errors. The measurement errors were assumed to be uncorrelated, with zero mean and a constant coefficient of variation (CV = 6%). The precision of parameter estimates was obtained from the inverse of the Fisher information matrix (13) and expressed as CV of the parameter estimate. The model is a priori uniquely identifiable when considering MI and M0 to be the model parameters, g(t) to be the model input, and c1(t) to be the model output (13).
Normalized residuals, i.e. differences between model-predicted and measured C peptide concentration divided by the SD of the measurement error, were calculated to assess the ability of the model to fit C peptide concentrations.
Sensitivity analysis.In the present study we adopted the
population model of C peptide kinetics to calculate transfer rate
constants k01, k21, and k12 (10).
To assess the effect of potential inaccuracies in k01,
k21, and k12 on estimates of MI and
M0, a sensitivity analysis was performed. The effects on
MI and M0 were evaluated by calculating the
percent change in MI and M0 estimates given a
10% change in kij (i.e. values
MI/kij x 0.1
kij/MI x 100% and
M0/kij x 0.1
kij/M0 x 100% were evaluated).
Deconvolution analysis. C Peptide secretion was also calculated employing a model-free calculation (deconvolution) without the use of plasma glucose data. These calculations were carried out to verify the assumption that C peptide secretion is linearly related to plasma glucose concentration during MTT.
The calculations were performed using the ISEC program (14), which implements a regularization method of deconvolution constrained to nonnegative values and also employs a population model of C peptide kinetics (10). The input consisted of plasma C peptide concentrations and the subject’s age, weight, height, gender, and classification (normal, obese, or NIDDM). ISEC calculated on the output C peptide secretion (picomoles per kg/min) in the form of a piecewise constant function. The regularization component of the deconvolution analysis was chosen according to the discrepancy principle (15) to obtain the CV of the residuals (differences between measured and estimated C peptide concentrations) identical to the measurement error (CV = 6%). C peptide secretion was calculated during the period when plasma glucose concentration was above the fasting level.
Statistical analysis
MI and M0 were compared between the two subject groups using t test. Statistical significance was declared at P < 0.05. Values are represented as the mean ± SD unless stated otherwise.
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Results |
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The two subject groups had different responses to the meal (see
Fig. 2). In normal subjects, plasma
glucose increased from a fasting level of 5.0 ± 0.5 mmol/L to a
maximum of 7.5 ± 1.3 mmol/L at 40 min, with a fall to the fasting
level by 90 min. In subjects with newly diagnosed NIDDM, the increase
in plasma glucose was from 12.6 ± 3.2 to 18.2 ± 4.4 mmol/L
at 75 min, and it failed to return to the fasting level by the end of
the study. In normal subjects, plasma insulin increased from a fasting
level of 51 ± 28 to 389 ± 219 pmol/L at 50 min and then
decreased to 88 ± 52 pmol/L at the end of the study. In subjects
with NIDDM, plasma insulin increased from a fasting level of 79 ±
46 to 279 ± 161 pmol/L at 120 min. In normal subjects, plasma C
peptide increased from 0.80 ± 0.36 to 2.63 ± 0.78 nmol/L at
60 min. In subjects with NIDDM, plasma C peptide increased from
0.99 ± 0.33 to 2.29 ± 0.79 nmol/L at 120 min.
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The parameter estimation procedure estimated MI and M0 with precision in both subject groups. The precision of parameter estimates was high, with CVs of parameter estimates of 15% or less.
Strong significant differences in MI and M0
were found between the two subject groups (see Table 1). MI in subjects with newly
diagnosed NIDDM was reduced to about 20%, and M0 was
reduced to about 50% of the respective values in normal subjects.
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) clearly demonstrates the separation of
the two study groups. It also shows considerable intersubject
variability within each study group. MI and M0
were significantly correlated in subjects with NIDDM (Spearman
rs = 0.73; P < 0.005), but not in normal
subjects (rs = 0.01; P = NS).
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indicates that the model fit in
subjects with NIDDM was good, with a random distribution of normalized
residuals around the zero value. The mean residuals in normal subjects
during the first 75 min were within 1.8 of the C peptide measurement
error, with one exception at 30 min, when the mean residual was 2.2 of
the measurement error. At 90, 120, and 150 min, the mean residual was
between 2.6–3.7 of the measurement error. However, there is a lower
confidence in these values, as only six subjects contributed to the
calculation of the highest value (and four subjects to the second
highest value). Plasma glucose in the other subjects had already
returned to its fasting value. Runs test gave nonsignificant results,
indicating random distribution of positive and negative residuals.
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Estimates of MI and M0 were insensitive to 10% changes in k21 and k12 (<2% mean change in MI and M0). The transfer rate constant, k01, had the largest effect on estimates MI and M0. The percent effects on MI (mean, 6%) and M0 (mean, 10%) were approximately proportional to the percent change in the value of k01.
Deconvolution analysis
The deconvolution analysis enabled the C peptide secretion rate to
be calculated without employing glucose levels in the calculations. A
sample C peptide secretion rate is shown in the top panel of
Fig. 5 together with the plasma glucose
concentration to illustrate the relationship between the glucose
concentration and the C peptide secretion rate. The bottom
panel of Fig. 5 plots the C peptide secretion rate against the
plasma glucose concentration at the measurement points.
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, indicating major
differences in the patterns of C peptide secretion between the two
subject groups. The bottom panel shows the relationship
between the C peptide secretion rate and the plasma glucose
concentration. Visual assessment suggests that the relationship
between C peptide secretion and plasma glucose is linear during MTT and
is confirmed by a linear regression analysis (P <
0.001 for each group; mean data). The plots have the form of a
collapsed hysteresis loop, indicating that during MTT 1) the glucose
concentration controls C peptide secretion without any delay
(considering time resolution given by the sampling frequency); and 2)
there is no temporal effect on C peptide secretion during MTT,
i.e. increases and decreases in C peptide secretion are
fully explained by the increases and decreases in the plasma glucose
concentration without taking into consideration the effects of time or
other hormones.
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Discussion |
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TopAbstractIntroductionSubjects and MethodsResultsDiscussionReferences |
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The quantification of pancreatic responsiveness to nutrients under physiological conditions allows ß-cell function in the normal state to be more accurately assessed than with various methods of IVGTT. The absence of time-dependent potentiation of insulin release by glucose during MTT illustrates the importance of a physiological study design. The proposed method should prove useful, for instance, in exploring pancreatic responsiveness with a variety of genetically based ß-cell disorders or in longitudinal studies. MTT is a widely used test with a relatively simple experimental protocol. A considerable amount of historical data exists and can be reanalyzed, reducing financial and human costs.
Validity and limitations of the model
From the model development point of view (13), the validity of the method is assessed and supported by the precision of parameter estimates, the distribution of normalized residuals, the nonsignificance of the Runs test, the deconvolution analysis, and the sensitivity analysis.
Parameter estimates were calculated with high precision (CV of parameter estimates = <15%) in both normal subjects and subjects with NIDDM. This suggests that a standard MTT results in data that allow a model-based assessment over a wide spectrum of pancreatic ß-cell responsiveness. At lower parameter values, model-based methods occasionally fail to give precise estimates, and modifications of the experimental protocol are then required (17). This seems not be the case with the proposed method, and it therefore follows that no modification of the MTT protocol is needed even at the maximally reduced values of pancreatic responsiveness seen in the NIDDM group, facilitating a uniform protocol design.
When plasma glucose is about to return to its fasting value, the dominating role of postprandial glucose to control C peptide secretion is likely to be reduced, and the control is shared to a greater extent with other time-varying hormones and stimuli. This may explain the reduction of the model fit toward the end of the study in normal subjects and was the rationale behind zero weighting C peptide measurements after plasma glucose returned to its fasting value.
Deconvolution analysis strongly supported the assumption that C peptide secretion is linearly related to plasma glucose concentration during MTT. A linear relationship has also been observed during a gradual infusion of exogenous glucose in normal subjects (18). Others have already employed the slope of the regression line between insulin secretion rates and blood glucose both during a meal and after oral glucose as a measure of ß-cell responsiveness or secretory capacity (19, 20). Compared to those approaches, the novelty of the present method is due to the use of a composite coherent model to describe both the secretion and elimination processes of C peptide.
The sensitivity analysis suggested that estimates of MI and M0 are insensitive to potential errors in transfer rate constants, k12 and k21. A proportional relationship between a change in k01 and a change in MI and M0 was observed. The model employs a regression model of C peptide kinetics approximating parameters from the subject’s age and category. The individual estimation of k01 (7) has the potential to improve the accuracy of MI and M0 estimates. The extent of improvement, however, is limited, as the error due to the population estimates has been shown to be, on the average, about 10% (10). An intraindividual variation in k01, k21, and k12 of similar magnitude was found by measuring these values in the same subjects on two or more occasions (10), suggesting that biological variability and/or experimental error are similar to the error due to the use of the regression model.
Gastric inhibitory polypeptide and glucagon-like peptide-1-(7–36 amide) are glucose- and fat-dependent gut hormones that may explain the greater insulin secretory response with oral compared to iv glucose (incretin effect) (21). The insulin response to oral glucose is augmented by the incretin effect in a dose-response fashion in normal subjects (22, 23).
MI is a composite index, and its strength is that it provides an overall measure of pancreatic responsiveness after meal ingestion and is directly related to day to day physiological conditions. This strength is also its weakness, as it does not allow defects in the net glucose effect and the incretin effect to be separated. It is currently unclear whether the size of the meal or the meal composition affects the calculated values of MI and M0. Further studies are required to assess whether MI and M0 can be compared across experimental designs that include different meal sizes and compositions and thus potentially different incretin effects.
Normal subjects vs. subjects with NIDDM
In subjects with newly diagnosed NIDDM, pancreatic responsiveness was reduced in the fasting state by approximately 50% and during meal stimulation by approximately 80%. We further investigated the relationship between higher concentrations of plasma glucose and pancreatic responsiveness (24).
A linear regression analysis of the relationship between fasting plasma
glucose and M0 and MI was carried out in
diabetic subjects (Fig. 7). Strongly
significant negative relationships indicated that progressively reduced
pancreatic responsiveness is associated with chronic exposure to an
elevated glucose concentration. Extrapolation to normoglycemia showed
that M0 would attain 95% and MI 40% of the
corresponding values observed in normal subjects.
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) is explained by a linear association of the two
indexes with fasting plasma glucose. The association is very strong and
seems to dominate over other possible relationships. In normal
subjects, however, this association is weakened, as for an identical
(normal) fasting glucose level there is a high intersubject variability
in both M0 and MI. Other factors seems to step
in and act, in totality, differently on the two indexes, as documented
by the lack of correlation between the two indexes. Several other simple tests measuring pancreatic ß-cell responsiveness are available. These employ an infusion of glucose with (4) or without a simultaneous insulin (6) or glucagon infusion (25). The Homeostasis Model Assessment (HOMA) approach is one of the simplest methods and calculates an index of ß-cell function from fasting plasma glucose and insulin levels (5). All of these methods allow insulin sensitivity to be estimated simultaneously with pancreatic responsiveness. Hyperglycemic clamp, a more experimentally complicated method, allows simultaneous assessment of insulin sensitivity and secretion (26). No method is currently available that would provide an index of insulin action during MTT (or oral glucose tolerance test), and the present method to estimate pancreatic responsiveness therefore has to be combined with an additional experiment if insulin sensitivity is to be estimated.
In summary, a new methodology to measure pancreatic responsiveness during MTT has been developed. By enhancing the standard population model of C peptide kinetics with a model of C peptide secretion, the postprandial pancreatic ß-call responsiveness can be quantified from plasma glucose and C peptide levels.
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Footnotes |
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2 A Windows-based program that calculates indices
M0 and MI can be obtained from the
author.
Received May 15, 1997.
Revised October 20, 1997.
Accepted November 12, 1997.
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