Abstract
The authorsā perspective is described regarding modifications made in their clinic to glucose challenge protocols and mathematical models in order to estimate insulin secretion, insulin sensitivity and glucose effectiveness in patients living with Insulin-Requiring Diabetes and patients who received Pancreatic Islet Transplants to treat Type I diabetes (T1D) with Impaired Awareness of Hypoglycemia. The evolutions are described of protocols and models for use in T1D, and Insulin-Requiring Type 2 Diabetes (T2D) that were the basis for studies in the Islet Recipients. In each group, the need for modifications, and how the protocols and models were adapted is discussed. How the ongoing application of the adaptations is clarifying the Islet pathophysiology in the Islet Transplant Recipients is outlined.
Introduction
In this article we describe the evolution of the modifications we made in our clinic to glucose challenge protocols or mathematical models of insulin secretion, insulin sensitivity and glucose effectiveness, in order to study these parameters in patients with Insulin-Requiring Type2 Diabetes (T2D) and Type 1 diabetes (T1D), including T1D patients who have received Islet Transplants to treat their severe recurrent hypoglycemia and impaired awareness of hypoglycemia. This includes fitting of the Minimal Model of Bergman etĀ al. () to Intravenous Glucose Tolerance Tests (IVGTT), and of the ISEC model to Oral Glucose Tolerance Tests (OGTT). We revisit the adaptations that were made for use in T1D, and Insulin-Requiring Type 2 Diabetes (T2D) as it helps to build a cohesive account of the work in our clinic aimed at studying the pathophysiology of insulin secretion and insulin action in the Islet Transplant Recipients. In each group we consider what issues were encountered, how we overcame them, and why we chose to adapt the protocols or models.
Estimation of Insulin Sensitivity From Intravenous Glucose Tolerance Tests in T1D
Modification of Minimal Model to Apply to Stepped Insulin-Modified IVGTT in T1D
The Minimal Model of Bergman etĀ al. () consists of a Minimal Model of Glucose Disappearance (the āGlucose Minimal Modelā, gMM) [, Equations 1 & 2] and a Minimal Model of Insulin Kinetics (the āInsulin Minimal Modelā, iMM) [, Equation 3].
The gMM can be fitted to plasma glucose and insulin data from an IVGTT to simultaneously estimate Insulin Sensitivity (Si, increase in fractional glucose disappearance per unit increase in plasma insulin) and Glucose Effectiveness (Sg, ability of glucose per se to enhance its own disappearance independent of an increment in plasma insulin above basal).The iMM can be fitted to a IVGTT to estimate beta-cell responsiveness to glucose: first-phase responsivity (Phi1, amount of insulin (per unit volume) that can be accounted for by an assumed initial injection, per unit change in plasma glucose); and, second-phase responsivity (Phi2, the proportionality factor between glucose and the rate of rise of insulin secretion). Software to fit both models to IVGTT data includes Minmod (). An alternative method used in our laboratory utilizes the SAAM modeling program to fit the model equations 1 to 3 as described ().
Where: G(t) and I(t) are the time courses of glucose and insulin in plasma following a rapid intravenous injection of glucose; Gb and Ib are basal levels; X(t) is the insulin effect on net glucose disappearance; p1 is glucose-mediated glucose disposal; p2 is insulin degradation; p3 is insulin action; n is the insulin clearance; γ is the proportionality factor between glucose concentration and the rate of increase of second phase insulin secretion for plasma glucose levels G(t) that exceed h, the threshold glucose level.
Although this method successfully accommodated data from healthy subjects and a variety of pathological states in fitting the gMM, we found it could not fit data from many patients with Type 1 diabetes (T1D) because: there was insufficient insulin input into the model as commented by Pacini and Bergman (); and, insulin antibodies in many T1D interfered with the measurement of plasma insulin. In addition, Godsland and Walton showed that the success rate of minimal model analysis is reduced if the glucose does not return to baseline (). We subsequently applied a modification of the gMM, which included a model of the exogenous insulin infusions, to IVGTT data from T1D subjects who had undergone a modified exogenous insulin protocol (). This aimed to achieving sufficient insulin input to the model to regularize the glucose disappearance curves with sufficient features in the glucose curves to enable successful identification of the parameters (). We also addressed the frequent presence in T1D of insulin antibodies which interfere with the insulin radioimmunoassay, by measuring plasma free-insulin after precipitation of bound insulin according to the method of Nakagawa etĀ al. () using polyethylene glycol precipitation before freezing in order to avoid disturbing the equilibrium between free and antibody-bound insulin (). In a recent study using a dextran-coated charcoal insulin assay () in our clinic, insulin antibodies were detected in a very low percentage in non-diabetic subjects, but in 50% of T1D, and 74% of Islet Transplant Recipients (manuscript in preparation).
To simulate a more physiological insulin profile during the IVGTTs in T1D, stepped exogenous insulin was infused with the total dose modified to achieve near-normal glucose disappearance (Kg). The stepped protocol aimed at approximating the insulin profile seen during an IVGTT in healthy normal weight subjects, derived by simulation of insulin disappearance kinetics. The final pattern of insulin infusion (analogous to FigureĀ 2) was: 2-4Ā min = 14 mU of insulin per kg; 7-16min = 1 mU/min/kg; 17-50Ā min = 0.5 mU/min/kg; 51-180Ā min = rate estimated to maintain basal euglycemia based on the previous overnight insulin requirement. A model of the insulin infusion was added to the Minimal Model to estimate Si and Sg (FigureĀ 1) (), in 8 T1D subjects (age 21-38 y, BMI 20-26 kg/m2) versus 17 healthy control subjects(20-37 y, 19-25 kg/m2))ā.
FigureĀ 1
FigureĀ 2

Exogenous insulin protocol in T2D. This figure has been reproduced in a modified form from
The exogenous insulin protocol in T1D IVGTTs achieved near-normal plasma free-insulin levels: first-phase = 62 ± 9 SE mu/L; second-phase = 34 ± 9 mu/L, and Kg was normal at 1.3 ± 0.29 min-1 x 102 (
Alternatives to Stepped Insulin-Modified IVGTT in T1D
With regard to the stepped insulin infusions in the protocol, there can be alternative approaches that may not require as significant overhauls to the protocol. With the increasing use of continuous subcutaneous insulin pumps, a basal intravenous insulin infusion from 51 to 180 minutes may not be necessary during the IVGTT if the basal pump rate is continued, providing insulin assays are used with specificity for analogue insulin (
Stepped Insulin-Modified IVGTT Protocol With Epinephrine in T1D
A practical example and test of the robustness of the use of the Stepped IVGTT protocol (A.1) was our study to explore the relative roles of Sg and Si in the observed impairment of glucose disposal with epinephrine infusion in T1D (
Stepped Insulin-Modified IVGTT Protocol With Pulsatile Insulin Infusions in T1D
Another practical example of the robustness of protocol A.1 in T1D subjects, is our study of pulsatile insulin infusions in which, therapeutic levels of intravenous pulsatile insulin were compared with continuous intravenous insulin, at matching levels in T1D subjects (
The hypoglycemic effect of PI versus CI, estimated by glucose infusion rates, was approximately doubled in the 6 subjects with duration less than 10 years, (PI vs CI, 7.5 ± 2.7 vs 3.2 ± 0.6 µmol/kg/min p <0.05 Mann-Whitney) but did not differ in the 5 subjects with duration over 10 years (PI vs CI, 5.8 ± 2.4 vs 4.7 ± 2.2 µmol/kg/min). Insulin sensitivity from analysis of the IVGTT data was uniformly increased after PI versus CI with duration under 10 years (PI vs CI, 4.9 ± 1.4 vs 3.0 ± 1.0 min-1.mU-1. L x104). After 10 years diabetes duration insulin sensitivity was uniformly greater with CI than with PI (PI vs CI, 0.3 ± 0.1 vs 2.9 ± 1.6 min-1.mU-1. L x104, p <0.05 Mann-Whitney).
We concluded that, prolonged pulsatile versus continuous intravenous insulin resulted in a significant increase in hypoglycemic effects and insulin sensitivity in T1D with diabetes duration up to 10 years the differential effect of PI was dependent on duration of diabetes. This indicates that the use of a basal insulin infusion during the IVGTT in T1D patients who are not on insulin pumps, is effective in maintaining the constant pattern of glucose levels at the end of the IVGTT, despite pulsatile insulin infusions being used.
Estimation of Insulin Secretion and Insulin Sensitivity in T1D After Islet Transplantation
Pancreatic Islet Transplantation in T1D
Pancreatic islet transplantation (IT) is an established clinical treatment for people with T1D, who suffer with severe hypoglycemia unawareness. Islets are obtained from the pancreas of a deceased organ donor, purified and then transfused into the portal vein of the recipient. Restoring natural islet function improves glycemic control and can markedly reduce hypoglycemia. Transplant recipients need life-long immunosuppression to prevent rejection-mediated cell loss.
In order to apply both iMM and gMM to analyze IVGTTs in Islet Transplant Recipients (ITR), we found there was a need to further modify the protocol and model compared to the T1D analyses, building on the investigations done on T2D IVGTTs discussed below.
Extension of Modifications of Protocol and Model to T2D
The Minimal Model of Bergman etĀ al. could only be used in early studies of T2D subjects if they had sufficient endogenous insulin secretion. An adequate increase during the IVGTT in the AUC of insulin levels was necessary to be able to fit the Minimal Model. To overcome this limitation, exogenous insulin protocols have been used in IVGTTs in T2D to enable the Minimal Model to estimate Si and Sg (
FigureĀ 3

Modification of Minimal Model to accommodate T2D data with the physiological exogenous insulin protocol. This figure has been reproduced in a modified form from
Adaptation by adding the delay element improved identification of Si and Sg from 37.5% (BMM) to 100% (MMD) in this largely insulin-requiring T2D group. Si in these T2D subjects was lower than normal(1.86 ± 0.60 v 8.65 ± 2.27 min-1.mU-1.L x 104,p <.01 Mann-Whitney). The reduced Si values were confirmed in this T2D group with 2-stage euglycemic clamps (Si CLAMP = 2.02 ± 0.42 min-1.mU-1.L x 104, p > 0.4 vs IVGTT Mann-Whitney). Sg was not significantly reduced (2.00 ± 0.25 T2D v 1.55 ± 0.26 normal, min-1 x 102). Use of the delay in normal subjects did not improve the fit.
These results suggest that insulin action at physiological insulin levels in insulin-requiring T2D may not be a single phase, possibly due to impaired trans-capillary endothelial transfer.
In the process of protocol selection, we found that, since our protocol could accommodate insulin requiring T2D, some needed free insulin assay, and some may need basal insulin infusions during the IVGTT. These studies indicate that, in T2D with minimal insulin secretion such as insulin-requiring T2D, we would recommend using an IVGTT protocol with basal insulin infusion during the IVGTT.
Delay in Insulin Secretion During IVGTT and OGTT After Islet Transplantation in T1D
Selection of the exogenous insulin protocol for IVGTT for Islet Transplant Recipients (ITR) in our clinic was informed by our previous adaptations in T1D and T2D. Free insulin assays were used if insulin antibodies were detected in individual subjects, and this was necessary in about 75% of cases. Although ITRs have features similar to T2D, their insulin sensitivity was more similar to T1D so that a more standard exogenous insulin protocol could be used, and without the need for a delay element in the modeling. Approximately 50% of ITRs became insulin independent and had better homeostasis of the basal glucose and insulin. In these subjects we were able to model IVGTTs without exogenous insulin supplementation as described (
In the ITRs we chose also to model plasma C-peptide responses during the glucose challenges to estimate Insulin Secretion Rates by the ISEC methodology (
FigureĀ 4

The post-transplant first-phase insulin secretion (Phi1) during an IVGTT, when calculated by ISEC analysis of plasma C-peptide levels, was reduced in insulin independent Islet Transplant recipients - compared with matched healthy controls.
We extended our studies of the delays of early secretion of insulin to include Oral Glucose Tolerance Tests (OGTT) because this test included the incretin effects (
Our studies using OGTTs in Islet Transplant recipients (
Our ITR subjects were 7 T1D patients (Group A, gender 7F, age 56 ± 4 SE yr, BMI 19.8 ± 1.0 kg/m2, T1D duration 46 ± 10 yr.) who had achieved insulin-free status following IT as described in our Multicenter Trial (
Plasma glucose, insulin and C-peptide were measured at 30 minute intervals during the OGTTs, and as previously described (
Insulin secretion rates were calculated by using ISEC to fit a model of C-peptide kinetics to the plasma C-peptide concentrations during both IVGTTs and OGTTs (
Although the transplant recipientsā mean OGTT 2-hour glucose was elevated (13.8 ± 1.7 mmol/L), 2 recipients were classified as non-diabetic (<11.1), and all recipientsā glucoses returned to baseline (5.8 ± 1.2) by 4-hours. (FigureĀ 5).
FigureĀ 5

Mean ± SE plasma glucose concentrations during 75g OGTTs in the 7 Insulin-independent Islet Transplant Recipients, and in the 9 Nondiabetic Controls.
ISEC analysis of the plasma C-peptide allowed estimation of Insulin Secretion Rates (FigureĀ 6), showing a delay in early insulin secretion with clear improvement in the latter half of the OGTT. The relationship of this improvement to incretin effects requires further investigation.
FigureĀ 6

Mean ± SE Pre-hepatic insulin secretion rates estimated from the plasma C-peptide concentrations by deconvolution using the program ISEC, during 75g OGTTs in the 7 Insulin-independent Islet Transplant Recipients, and in the 9 Nondiabetic Controls.
Only measuring early insulin release during OGTTs could underestimate later secretion by ~30% in islet transplantation, correlating with our previous report using IVGTTs (
However, our findings support a role for also testing the early secretion using IVGTT. When C-peptide-derived Insulin Secretion Rates during the IVGTTs were estimated using ISEC, the initial post-transplant first-phase insulin secretion was reduced in recipients compared with healthy non-diabetic subjects. This confirms our previous conclusion based on plasma insulin concentrations (
Reduced IVGTT Phi1 after islet transplantation could reflect the same factors as the delayed insulin secretion during OGTT. For example it has been suggested that increased beta-cell overdrive could cause depletion of readily-releasable insulin stores. This marker of beta cell dysfunction provides a parameter that could be monitored in addition to indices of beta cell mass. Alternatively, these reduced insulin responses could represent recurrence of autoimmune beta cell damage similarly to that observed with reduced first phase insulin responses in pre-type 1 diabetes patients (
Future Directions in IVGTT and OGTT After Islet Transplantation in T1D
Future evaluation of beta cell function in islet transplant recipients would be improved by better understanding of the interaction of insulin sensitivity, glucose effectiveness and the parameters of beta cell secretion of insulin. It is well accepted that insulin secretion and sensitivity are best interpreted together, because of the hyperbolic relationship between these two parameters (
Overall Summary
We have presented our perspective of the application of the Mathematical Models to the analysis of intravenous and oral glucose challenges in Type I diabetes. The modifications of the protocols necessary to apply these models also to Type I diabetes patients who have received Islet Transplants were elaborated. Islet Transplant Recipients represent a pathophysiological state that is similar to T2D, but has some distinct differences. These differences are exposed by application of the modified protocols and models of insulin secretion and action. In our preliminary studies, IVGTT versus OGTT parameters provided additional insights into the pathophysiology of transplanted islets, reflecting beta cell dysfunction rather than only monitoring beta cell mass (
Funding
The work discussed in this manuscript was supported by grants from Diabetes Australia Research Foundation, St Vincentās Hospital Research Foundation, National Health and Medical Research Council of Australia, and the Juvenile Diabetes Research Foundation.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Ethics statement
The studies involving human participants were reviewed and approved by St Vincentās Hospital Human Research Ethics Committee. The patients/participants provided their written informed consent to participate in this study.
Author contributions
GW, JG, JW, and RB collaborated on the investigations that form the basis of this perspective. GW wrote the initial draft based on previous discussions with the coauthors, and JG, JW, and RB made substantial contributions to revisions of it. All authors contributed to the article and approved the submitted version.
Acknowledgments
We acknowledge the support of St Vincentās Hospital Melbourne, St Vincentās Pathology, University of Melbourne, and Directors of the Department of Endocrinology and Diabetes, Prof. F. Alford, Prof. K. W. Ng, and Prof. R. MacIsaac.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Summary
Keywords
mathematical modeling, type 1 diabetes mellitus, islet transplantation, insulin secretion, insulin sensitivity, minimal model, C-peptide model
Citation
Ward GM, Walters JM, Gooley JL and Boston RC (2021) Adapting Protocols or Models for Use in Insulin-Requiring Diabetes and Islet Transplant Recipients. Front. Endocrinol. 12:611512. doi: 10.3389/fendo.2021.611512
Received
29 September 2020
Accepted
28 June 2021
Published
16 July 2021
Volume
12 - 2021
Edited by
Susanna Rƶblitz, University of Bergen, Norway
Reviewed by
Kyle C. A. Wedgwood, University of Exeter, United Kingdom; Thomas Linn, University of Giessen, Germany
Updates

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Copyright
Ā© 2021 Ward, Walters, Gooley and Boston.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Glenn M. Ward, gmward@unimelb.edu.au
This article was submitted to Systems Endocrinology, a section of the journal Frontiers in Endocrinology
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