Assessment of pulsatile insulin secretion derived from peripheral plasma C-peptide concentrations by nonparametric stochastic deconvolution

Abstract

The characteristics of pulsatile insulin secretion are important determinants of type 2 diabetes pathophysiology, but they are understudied due to the difficulties in measuring pulsatile insulin secretion noninvasively. Deconvolution of either peripheral C-peptide or insulin concentrations offers an appealing alternative to hepatic vein catheterization. However, to do so, there are a series of methodological challenges to overcome. C-peptide has a relatively long half-life and accumulates in the circulation. On the other hand, peripheral insulin concentrations reflect relatively fast clearance and hepatic extraction as it leaves the portal circulation to enter the systemic circulation. We propose a method based on nonparametric stochastic deconvolution of C-peptide concentrations, using individually determined C-peptide kinetics, to overcome these limitations. The use of C-peptide (instead of insulin) concentrations allows estimation of portal (and not post-hepatic) insulin pulses, whereas nonparametric stochastic deconvolution allows evaluation of pulsatile signals without any a priori assumptions of pulse shape and occurrence. The only assumption required is the degree of smoothness of the (unknown) secretion rate. We tested this method first on simulated data and then on 29 nondiabetic subjects studied during euglycemia and hyperglycemia and compared our estimates with the profiles obtained from hepatic vein insulin concentrations. This method produced satisfactory results both in the ability to fit the data and in providing reliable estimates of pulsatile secretion, in agreement with hepatic vein measurements. In conclusion, the proposed method enables reliable and noninvasive measurement of pulsatile insulin secretion. Future studies will be needed to validate this method in people with type 2 diabetes.

INTRODUCTION

Insulin is secreted by the β-cells into the portal vein in a pulsatile manner (11, 13). The amplitude and frequency of these pulses is decreased in people with type 2 diabetes (17), but similar abnormalities have been observed in association with obesity and with aging (9, 15). This has led to the suggestion that insulin pulse characteristics alter optimal insulin action (1, 2, 12). Indeed, in partially pancreatectomized dogs, impaired insulin action was associated with decreased insulin pulsatility (13). These observations raise the possibility that impaired insulin pulse characteristics may be important in the pathogenesis of type 2 diabetes.

However, there are significant obstacles to the optimal study of insulin pulsatility. After secretion into the portal vein (5), insulin is partially extracted by the liver so that sampling from the hepatic vein represents the net result of insulin secretion and hepatic extraction. This extraction is time variant and dependent on the characteristics of an insulin pulse (14). Portal vein sampling is an invasive procedure and rarely possible in humans. Hepatic vein sampling is currently the next best option to study (post-hepatic extraction) insulin pulses in humans (14). However, the expense and invasive nature of this procedure have limited its application to larger studies.

An alternative method, which overcomes the need for hepatic vein sampling, is provided by deconvolution of insulin secretion using peripheral venous concentrations, a commonly used method in the analysis of hormone secretion (26). However, the application of this method presents a series of challenges. First, if deconvolution is applied to peripheral insulin concentrations, the results obtained would ignore hepatic extraction and would represent only posthepatic insulin secretion. If deconvolution is applied to C-peptide concentrations [co-secreted with insulin in an equimolar ratio (10) and not extracted by the liver (16)], it is difficult to discern discrete pulses, since C-peptide has a much longer half-life and accumulates in the circulation compared with insulin (7).

Accordingly, we developed a new method that overcomes these problems by using nonparametric stochastic deconvolution applied to peripheral C-peptide concentrations after individualized determination of C-peptide clearance. We report that, when rates of C-peptide clearance are known (23), reconstruction of pulsatile insulin secretion over short and frequently sampled periods is feasible, and the pulse characteristics obtained are comparable with those obtained from hepatic vein insulin concentrations.

MATERIALS AND METHODS

Study subjects.

After approval by the Mayo Clinic Institutional Review Board, 29 nondiabetic subjects recruited from among subjects who had previously participated in a series of published experiments (20, 24, 25) provided informed, written consent to participate in this study. All had originally been recruited on the basis of genotype at rs7903146, as outlined by Varghese et al. (25). The subjects (10 males and 19 females) had a mean age of 46 ± 2 yr, lean body mass of 48 ± 2 kg, total body mass of 79 ± 3 kg, and a body mass index (BMI) of 28 ± 1 kg/M² [see Supplemental Table S1 for a complete description of the studied cohort (https://doi.org/10.6084/m9.figshare.7764710); Supplemental Material can be found on the AJP-Endocrinology and Metabolism website]. They subsequently underwent a screening exam to ensure they were healthy and had no active illness and no prior history of diabetes mellitus and were not taking medications that might alter glucose metabolism. Body composition was measured by dual-energy X-ray absorptiometry (iDXA scanner; GE, Wauwatosa, WI). Participants met with a nutritionist and followed a weight maintenance diet (55% carbohydrate, 30% fat, and 15% protein) for ≥3 days before the study visit.

Experimental design.

Subjects were admitted to the clinical research unit at 1700 on the day before study. They then consumed a caffeine-free, standard 10 kcal/kg meal (55% carbohydrate, 30% fat, and 15% protein) and fasted overnight. The following morning (at ∼0630), an 18-g cannula was inserted retrogradely into a dorsal hand vein. This was then placed in a heated Plexiglas box maintained at 55°C to allow sampling of arterialized venous blood. Subjects were then moved to the radiology suite, where a hepatic vein catheter was placed via the femoral vein under fluoroscopic guidance (14, 19). Following their return, at 0800 (0 min) blood was sampled at 1-min intervals from the arterialized hand vein and from the hepatic vein (HV) at 2-min intervals over a 45-min period (euglycemic phase; Fig. 1A). At 0846 (46 min) a glucose infusion commenced, and the infusion rate was adjusted to rapidly achieve and maintain peripheral glucose concentrations of ∼150 mg/dl. Following the 30-min equilibration period (0915), blood was sampled as before during the hyperglycemic phase for an additional 45 min (Fig. 1A). At 1000 (120 min), all cannulas and the hepatic vein catheter were removed. Participants consumed a meal and left the Clinical Research Unit.

Fig. 1.

A: design of glucose clamp study. After the placement of the hepatic vein catheter, frequent blood sampling is performed to measure insulin (both in peripheral and hepatic vein) and C-peptide (in peripheral vein) concentrations. B–E: plasma glucose (B), insulin (C), and C-peptide (D) concentrations in the peripheral vein and insulin concentration in the hepatic vein (E) measured in an illustrative subject. Data in B, D, and E were collected every 2 min; data in C were collected every minute.

In addition, during a separate (and previously published) study (25), participating subjects received a bolus of C-peptide (60 pmol/kg) administered over 1 min during a somatostatin infusion (60 ng·kg⁻¹·min⁻¹) to enable individual calculation of C-peptide kinetics (24).

Analytic techniques.

Plasma samples were placed on ice, centrifuged at 4°C, separated, and stored at −20°C until they were assayed. Glucose concentrations were measured using a glucose oxidase method (Yellow Springs Instruments, Yellow Springs, OH). Plasma insulin was measured using a chemiluminescence assay (Access Assay; Beckman, Chaska, MN). Plasma glucagon was measured by radioimmunoassay (Linco Research, St. Louis, MO). C-peptide was measured using a two-site immunenzymatic sandwich assay (Roche Diagnostics, Indianapolis, IN) in accordance with the manufacturer’s instructions. This assay has reported intra-assay coefficients of variation (CV) of 0.9, 2.8, and 1.5% at 0.65, 1.61, and 3.33 nmol/l, respectively [see Supplemental Table S3 (https://doi.org/10.6084/m9.figshare.7764707)].

Peripheral measurements of glucose and C-peptide, as well as insulin in the hepatic and peripheral vein, are reported in an illustrative subject in Fig. 1, B–E. Average concentrations are shown in Fig. 2.

Fig. 2.

Average plasma glucose (A), insulin (B), and C-peptide (C) concentrations measured in the peripheral vein; average insulin concentrations measured in the hepatic vein (D). Vertical bars represent standard error. Data in A, C, and D were collected every 2 min; data in B were collected every minute. ●, Measured data averaged across the population.

Assessment of pulsatile insulin secretion by stochastic nonparametric deconvolution.

In the mathematical characterization of the deconvolution problem (4), the sampled plasma hormone concentration (C-peptide in this case) can be viewed as a discrete signal (y_k) equal to the sum of the true sampled C-peptide concentration [CP(t_k)] and the measurement error (v_k), assumed to be independent, Gaussian with zero mean and known standard deviation. CP(t_k) is the C-peptide concentration CP(t) sampled every 2 minutes. CP(t) is the convolution between the unknown insulin secretion rate [ISR(t)] and the impulse response [g(t)], which is assumed to be a sum of exponentials since C-peptide kinetics have been shown to be linear (6). Deconvolution aims to determine the almost continuous ISR(t) from y_k, knowing g(t) and the characteristics of v_k. Given that an erroneous assumption on v_k may badly impact the results, we assessed the CV of our C-peptide assay at two concentration levels during fasting and three during hyperglycemia and did nine repeated measurements at each level. This analysis proved that C-peptide concentration is measured with an almost constant CV, with an average value of 1.045% and a standard deviation of 0.13%.

To reconstruct the ISR signal, we relied on nonparametric deconvolution (4), which does not require any assumption of the unknown input signal (see below). However, a critical aspect in the secretion estimation is the knowledge of hormone kinetics g(t), which can be derived from a population model, as proposed by Van Cauter et al. (23), or directly estimated from experimental data in each individual. To determine individual C-peptide kinetics in each subject, one needs to perform an additional experiment with somatostatin infusion and C-peptide bolus administration and measure C-peptide decay curve, as explained below.

Assessment of individualized C-peptide kinetics.

C-peptide kinetics can be described by a two-compartment linear model (6, 23), so that the impulse response of the system can be characterized by

$$\text{g}\left(\text{t}\right)={\displaystyle {\sum }_{i=1}^2{\text{A}}_{\text{i}}{\text{e}}^{-{\alpha }_i\text{t}}}.$$ (1)

We used the C-peptide decay data previously obtained for each subject (24) to estimate individual values for parameters A_i and α_i (together with their precision, CV%) by using the maximum a posteriori Bayesian estimator (22).

Stochastic nonparametric deconvolution from peripheral C-peptide concentration.

To assess the pulsatility of insulin secretion, we used nonparametric deconvolution (4) and peripheral C-peptide concentrations (21). A schematic representation of the convolution/deconvolution concept is shown in Fig. 3. Nonparametric regularized deconvolution has the advantage of not requiring any a priori assumption on the input of the system (insulin secretion in this case) apart from the degree of smoothness of the unknown signal. This information, together with the knowledge of the error variance associated with the output data, avoids the reconstruction of nonphysiological oscillation due to error(s) in the measured data. Briefly, ISR(t) can be obtained by minimizing an objective function (OF) that weights the fit of the data (the first term) and the regularity of the estimated ISR (the 2nd term):

$$OF={\left(y-Gu\right)}^T{\sum }_v^{-1}-\left(y-Gu\right)+\gamma u^T{F}^{T}Fu,$$ (2)

where y is the n-dimensional vector containing the measured C-peptide concentration, u is the n-dimensional vector whose components are samples of the secretion rate ISR(t), G is a n × n lower triangular matrix containing the information on the impulse response g(t), F is a n × n matrix summarizing the information on the regularity of the ISR signal, Σ_v is a n × n covariance matrix of measurement error, and γ is a parameter balancing the two requirements that can be estimated using the maximum likelihood criterion (4).

Fig. 3.

Deconvolution methodology; the measured plasma C-peptide concentration (y_k, k∈Z) can be interpreted as the sum of the true sampled C-peptide concentration [CP(t_k)] and measurement error (v_k), assumed to be independent Gaussian with zero mean and known standard deviation. Every time one collects a sample CP(t_k) from a noise-free C-peptide pool CP(t) (t∈R), measurement error and other factors introduce error. The break is a graphical way to indicate that, every time the break closes, one is collecting a sample with noise from a noise-free C-peptide pool. CP(t_k) is the C-peptide concentration CP(t) (t∈R) sampled every 2 minutes, and CP(t) is the convolution between the unknown ISR(t) and g(t), which is assumed to be a sum of exponentials.

Once the pulsatile ISR(t) is reconstructed, it is possible to assess pulse frequency with standard techniques (18).

We analyzed the euglycemic and hyperglycemic portion of the signal separately; in each portion, we first calculated the average (basal) ISR (ISR_b^eu and ISR_b^hyper, respectively) and the above basal ISR (ISR_ab^eu and ISR_ab^hyper, respectively). We then obtained the ISR_ab power spectrum, using the FFT algorithm implemented in MATALB R2017b. Finally, we estimated the pulse period (defined here as the period of the fastest harmonic in the signal) as the inverse of the signal bandwidth. The pulse amplitude in each portion was assessed as the standard deviation (ISR_SD) of the above basal ISR.

In silico validation.

To overcome the lack of gold standard portal measurement of ISR, we validated the proposed method using simulated data, so that the “true” ISR is known and a quantitative comparison between “true” and reconstructed ISR can be made. To do so, we selected one pulsatile ISR profile from our results and used it as the noise-free input of the system. Assuming knowledge of the impulse response of the system [g(t) from Eq. 1], we first simulated the noise-free C-peptide concentrations as the convolution between ISR(t) and g(t) sampled every 2 min, with an added noise representing measurement error.

To evaluate the effect of measurement error on reconstructed ISR, we generated 100 realizations of Gaussian random noise with zero mean with a CV ranging from 1 to 3% (1% being the CV of our assay). We added the generated noise to the sampled concentration, thus creating 100 “noisy” concentration profiles for each CV value. We applied our algorithm to each of these simulated data sets and reconstructed 100 ISR profiles for each noise level. The simulated “true” pulse period and amplitude were compared with the reconstructed ones, and the percent differences were calculated as |true-reconstructed|/true%. Similarly, we investigated the sensitivity of the results to the error of estimated kinetics by applying our algorithm to noisy concentration data and 100 kinetic profiles randomly generated from kinetic parameter joint distribution.

Statistical analysis.

Data and results are presented as means ± SE for normally distributed variables and as median [IQR] otherwise. Comparison among parameters was performed using an unpaired, two-tailed Student t-test for normally distributed variables; conversely, when samples were not normally distributed, a two-tailed Wilcoxon test was used. A P value of <0.05 was considered statistically significant.

RESULTS

Assessment of individualized C-peptide kinetics.

The two-exponential model was able to describe C-peptide concentrations (Fig. 4), and the kinetic parameters were estimated with good precision (Table 1). As expected, the model using individualized C-peptide kinetics was able to better fit the data than the model using population-based C-peptide kinetics (23), with the latter significantly underestimating the data in the first 35–40 min and overestimating the data thereafter. This was in agreement with what we demonstrated previously in 56 subjects (24), of whom this cohort is a subset. The effect of this discrepancy on the estimation of pulse frequency and amplitude will be discussed below.

Fig. 4.

C-peptide kinetics; average prediction of the individualized (solid line) and the population (dashed line) 2-exponential models versus average data (○).

Table 1.

C-peptide kinetic parameter of the individualized and population 2-exponential models

	A1, liters–1	A2, liters–1	α1, Min–1	α2, Min–1
Individualized	0.197 ± 0.0047	0.041 ± 0.0026	0.089 ± 0.0027	0.0199 ± 0.0002
Population	0.183 ± 0.0026	0.055 ± 0.0010	0.146 ± 0.0012	0.0200 ± 0.0002

Results are reported as means ± SE.

Pulse reconstruction: model fit and pulsatile secretion estimation.

Nonparametric deconvolution provided a good fit of the peripheral C-peptide data and a reliable reconstruction of pulsatile insulin secretion. Individual pulses are clearly discernable, allowing measurement of pulse frequency and amplitude. Figure 5 shows the results obtained for one illustrative subject during euglycemia (Fig. 5, left) and hyperglycemia (Fig. 5, right).

Fig. 5.

Performance of nonparametric stochastic deconvolution in 1 illustrative subject in euglycemia (left) and hyperglycemia (right). Top: peripheral C-peptide concentration data (○) versus model prediction (solid lines). Bottom: reconstructed insulin secretion rate.

Pulse reconstruction: in silico validation.

Figure 6 shows the true (dashed) versus reconstructed ISR (mean: solid line; 5th to 95th percentile range: gray area) in euglycemia and hyperglycemia at different noise levels (CVs of 1, 2, and 3%). With CV = 1%, the reconstructed signals resembles the true ISR. However, as the noise level increases, the uncertainty of the estimated ISR increases and the agreement between true and reconstructed signals degrades. In particular, during euglycemia the percent difference (median [IQR]) between true and estimated pulse period was 3 (33%), 34 (31%), and 43% (47%), whereas the median percent difference between true and estimated pulse amplitude was 10 (13%), 17 (16%), and 18% (18%), with CV = 1, 2, and 3%, respectively. In hyperglycemia, the pulse periods error was 2 (25%), 35 (48%), and 63% (78%) and the pulse amplitude error 9 (10%), 13 (16%), and 16% (21%). The results of the sensitivity analysis to kinetic parameter error are reported in Supplemental Fig. S1 (https://doi.org/10.6084/m9.figshare.7764743) and Supplemental Table S2 (https://doi.org/10.6084/m9.figshare.7764704).

Fig. 6.

In silico validation. True (dashed lines) versus reconstructed insulin secretion rate (ISR) (mean: solid line; 5th to 95th percentile range: gray area) in euglycemia (top) and hyperglycemia (bottom) for 3 levels of the superimposed measurement error [coefficient of variation (CV) = 1 (left), 2 (middle), and = 3% (right)].

These results show that it is possible to reconstruct pulsatile insulin secretion using our methodology when precise C-peptide measurement (CV ∼1%) is available.

Pulse reconstruction: nonparametric deconvolution versus HV insulin.

ISR reconstructed with the proposed method was compared with HV insulin measurements. Figure 7 shows the results in two illustrative subjects, with subject no. 1 being the same subject illustrated in Fig. 5. Reconstructed ISR profiles resemble insulin pulses measured in the HV in most of the subjects, one of whom is subject no. 1 in Fig. 7. The differences in the scale are explained by the fact that the HV signal is a concentration and not a secretion rate, and the HV signal has been subject to hepatic insulin extraction, so that graphical comparison can only be qualitative. On the other hand, in 17% of the HV profiles, one of whom is subject no. 2 in Fig. 7, the agreement is weaker.

Fig. 7.

Comparison of insulin concentration in the hepatic vein (top) and insulin secretion rate reconstructed by deconvolution (bottom) in 2 illustrative subjects. Subject no. 1 is the same as represented in Fig. 5. ●, Measured data, individual values measured in subject nos. 1 and 2.

However, the percent difference between pulse periods derived from HV insulin versus ISR was on average 23 ± 3 and 24 ± 2% in euglycemia and hyperglycemia, respectively. Moreover, only 7% (in euglycemia) and 4% in (hyperglycemia) of the subjects showed a percentage difference between estimated periods >50%.

Effect of individualized versus population kinetics in pulse reconstruction.

Measuring individual C-peptide kinetics requires an additional experiment using somatostatin to inhibit endogenous insulin secretion and injection of a C-peptide bolus. Therefore, we investigated the effect of using a population (23) instead of an individualized model of C-peptide kinetics on pulse reconstruction.

Average reconstructed ISR profiles are shown in Fig. 8. In this cohort, the use of population kinetics resulted in significantly higher reconstructed ISR (especially in the hyperglycemic phase), in agreement with the finding that the impulse response is significantly underestimated (Fig. 4) in the first 35–40 min after administration of a C-peptide bolus. In particular, ISR_b and pulse amplitude are significantly overestimated with the population model during both the euglycemic and hyperglycemic phase, whereas pulse period seems to be unaffected by the use of population kinetics (Table 2).

Fig. 8.

Average insulin secretion rate estimated with nonparametric stochastic deconvolution, using an individualized (black lines) and population (gray lines) 2-exponential kinetic model.

Table 2.

ISR_b, pulse amplitude, and period calculated from ISR reconstructed by stochastic deconvolution with an individualized vs population two exponential model in euglycemia and hyperglycemia

	Individualized	Population	P Value Individualized Vs. Population
Euglycemia
ISRb, pmol/min	136.60 ± 8.88	148.97 ± 5.28	0.009
Pulse amplitude, pmol/min	60.33 ± 5.00	63.70 ± 5.28	0.003
Pulse period, min	5.46 ± 0.33	5.75 ± 0.38	0.079
Hyperglycemia
ISRb, pmol/min	400.88 ± 25.03	446.44 ± 30.27	0.001
Pulse amplitude, pmol/min	173.85 ± 14.46	180.20 ± 14.69	0.005
Pulse period, min	5.14 ± 0.21	4.98 ± 0.20	0.085
P value (euglycemia vs. hyperglycemia)
ISRb	<10−13	<10−12
Pulse amplitude	<10−9	<10−10
Pulse period	0.432	0.100

Results are reported as means ± SE. ISR_b, basal insulin secretion rate; ISR, insulin secretion rate.

Assessment of pulse period and amplitude: euglycemia versus hyperglycemia.

In this cohort of nondiabetic subjects, our analysis shows that ISR_b and pulse amplitude are significantly higher during the hypercemic than during the euglycemic period. Conversely, pulse period are similar in the two cases, regardless of whether they are estimated using population or individualized C-peptide kinetics (Table 2).

DISCUSSION

The ability to reliably and noninvasively assess pulsatile insulin secretion in humans is important since impaired insulin pulsatility is associated with insulin resistance and type 2 diabetes (17). In this study, we have developed a noninvasive method based on stochastic nonparametric deconvolution and peripheral C-peptide measurement to reconstruct the pulse characteristics of insulin secretion in a given individual. This was achieved without a priori assumptions as to the underlying patterns of insulin secretion.

The method has been validated by resorting to simulated data where the true ISR profile is known and a quantitative assessment of reconstructed profiles can be made. Results show that it is possible to accurately reconstruct the pulsatile insulin secretion from peripheral C-peptide measurement, but to properly assess the pulse period, very precise C-peptide measurements (CV around 1%) are needed. This can be a limitation for the usability of the method; however, this was the case with our assay. It is worth noting that, in addition to assay error, other sources of error may affect the measured concentration (e.g., a delay in sample collection or mistakes in sample handling and processing), which are difficult to quantify. Therefore, the reported CV is a lower estimate of the true global measurement error.

On the other hand, pulse amplitude seems to be less affected by the magnitude of the measurement error. Another limitation of the proposed method is the high sampling frequency required to accurately reconstruct ISR. Simulations showed that the minimum sampling frequency needed is one sample every 2 min, as performed in this study. Performance degraded already with one sample every 3 min (data not shown).

The pulses reconstructed using nonparametric deconvolution are also compared with the pattern of changing insulin concentrations measured in the HV during both experimental conditions (euglycemia and hyperglycemia). The qualitative comparison of the two signals is generally good, as shown, for example, in Fig. 7, left, despite a few cases that show weaker agreement between the two profiles (Fig. 7, right). In particular, ∼17% of the insulin profiles in the hepatic vein show limited or absent pulsatility. We believe that those HV insulin profiles are not reflective of the underlying pulsatile secretion (11) and hypothesize that the reason for which pulses are not evident in HV measurement could in part be due to the dampening effect of hepatic extraction or insufficient sampling frequency. On the other hand, the percent difference between pulse periods calculated with our method and from HV insulin is relatively small (between 23 and 24% on average). As regards comparison of pulse amplitude, this can only be qualitative, since HV insulin concentrations are the result of insulin secretion into the portal vein and subsequent hepatic extraction. Of note is that pulsatile secretion reconstructed from C-peptide concentrations represents the prehepatic or portal insulin secretion rate. Unfortunately, C-peptide was not measured in HV in this study due to the limited blood volume that could be drawn.

Analysis of the reconstructed pulsatile secretion reveals that pulse frequency during hyperglycemia is unchanged from that observed during euglycemic conditions. However, both basal (non-pulsatile) and pulsatile (amplitude) secretion are significantly increased by hyperglycemia. This suggests that pancreatic β-cells are highly synchronized and that the frequency of oscillation is subject specific and glucose independent. It remains to be proven whether this methodology can ascertain differences in pulse amplitude and frequency as glucose tolerance worsens and type 2 diabetes develops.

The main limitation of our method is that it requires a separate experiment to measure C-peptide kinetic parameters in a given individual, as described previously (25). Therefore, we also examined the possibility of using population-based C-peptide kinetics, as described by Van Cauter et al. (23) and used by several groups (8), including ours (3, 24), to measure insulin secretion in response to an oral or intravenous challenge using C-peptide concentrations. Our results show that the use of population-based kinetics does not affect measurement of pulse frequency. On the other hand, in our cohort of 29 nondiabetic subjects, pulse amplitude and basal secretion rate are significantly overestimated when the population model is employed (Fig. 7 and Table 2). It remains to be ascertained whether this difference is constant across disease states, e.g., when comparing people with normal glucose tolerance versus people with type 2 diabetes. If that were the case, then perhaps population-based C-peptide kinetics could be utilized in these situations. This is deserving of further study.

In summary, we have proposed and tested a noninvasive method to assess prehepatic pulsatile insulin secretion from frequently sampled peripheral C-peptide concentrations based on nonparametric stochastic deconvolution. The reconstructed secretory bursts can then be analyzed with standard techniques to calculate pulse frequency and amplitude. Further studies are needed to validate the method in impaired glucose tolerant and type 2 diabetic subjects.

GRANTS

This study was supported by the National Institute of Diabetes and Digestive and Kidney Diseases (DK-78646), University of Padova Research Grant CPDA145405, and the Mayo Clinic General Clinical Research Center (UL1-TR000135).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

M.C.L. and C.D.M. analyzed data; M.C.L., A.V., R.A.R., A.M., G.D.N., C.C., and C.D.M. interpreted results of experiments; M.C.L. prepared figures; M.C.L. and C.D.M. drafted manuscript; M.C.L., A.V., R.T.V., A.S., R.A.R., A.M., G.D.N., and C.C. edited and revised manuscript; M.C.L., A.V., R.T.V., J.C.A., A.S., N.E.K., R.A.R., A.M., G.D.N., C.C., and C.D.M. approved final version of manuscript; A.V. conceived and designed research; A.V., R.T.V., J.C.A., A.S., and N.E.K. performed experiments.