Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm

BACKGROUND: Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available. METHODS: A formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data. RESULTS: The degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5–5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation. CONCLUSION: Dimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms

Investigating the Role of Islet Cytoarchitecture in Its Oscillation Using a New β-Cell Cluster Model

The oscillatory insulin release is fundamental to normal glycemic control. The basis of the oscillation is the intercellular coupling and bursting synchronization of β cells in each islet. The functional role of islet β cell mass organization with respect to its oscillatory bursting is not well understood. This is of special interest in view of the recent finding of islet cytoarchitectural differences between human and animal models. In this study we developed a new hexagonal closest packing (HCP) cell cluster model. The model captures more accurately the real islet cell organization than the simple cubic packing (SCP) cluster that is conventionally used. Using our new model we investigated the functional characteristics of β-cell clusters, including the fraction of cells able to burst fb, the synchronization index λ of the bursting β cells, the bursting period Tb, the plateau fraction pf, and the amplitude of intracellular calcium oscillation [Ca]. We determined their dependence on cluster architectural parameters including number of cells nβ, number of inter-β cell couplings of each β cell nc, and the coupling strength gc. We found that at low values of nβ, nc and gc, the oscillation regularity improves with their increasing values. This functional gain plateaus around their physiological values in real islets, at nβ∼100, nc∼6 and gc∼200 pS. In addition, normal β-cell clusters are robust against significant perturbation to their architecture, including the presence of non-β cells or dead β cells. In clusters with nβ>∼100, coordinated β-cell bursting can be maintained at up to 70% of β-cell loss, which is consistent with laboratory and clinical findings of islets. Our results suggest that the bursting characteristics of a β-cell cluster depend quantitatively on its architecture in a non-linear fashion. These findings are important to understand the islet bursting phenomenon and the regulation of insulin secretion, under both physiological and pathological conditions

Estimation of Glucose-Mediated Glucose Disposal in Type 1 Diabetic Subjects using MINMOD

Since its first introduction in 1979 by Bergman et al, Minimal Model (MINMOD) has become an important research tool in the investigation of glucose regulation. It has provided insight into the secretion and action of insulin and the effectiveness of glucose itself in regulating glucose tolerance. More than 500 research papers have been published since, reporting experimental results and MlNMOD analyses in humans and dogs. Because insulin resistance and impaired glucose effectiveness contribute to the patho-physiology of Non Insulin-Dependent Diabetes Mellitus (NIDDM or Type 2 Diabetes (T2D)), a quantitative assessment of these properties is of utmost importance. As a consequence, MINMOD has been very frequently applied to analyze FSIVGTT (Frequently Sampled Intravenous Glucose Tolerance Test) data of T2D subjects and great success has been achieved. In particular the Disposition Index (DD derived using MINMOD has been found to be an excellent prognostic marker for T2D. However, very few studies have been carried out to quantify the effects of insulin and glucose in glucose regulation in Type I Diabetes (TlD) subjects. Although glucose utilization is impaired in TID subjects, it is unclear whether this is due to reductions in Insulin Sensitivity (Si) and/or glucose-mediated glucose disposal (SG). TID subjects lacked endogenous insulin secretion and any experimental protocol involved in the study of individual contributions of glucose and insulin in these subjects involves risk. During the course of these studies, MINMOD has come under criticism that it is under-modeled due to the assumption of single compartment of glucose, and that this led to the overestimation of SG in subjects with impaired insulin secretion. Our long term goal is to develop a robust model of B-cell (pancreatic cell that secrets insulin) mass and functionality coupled with MINMOD. As a first step in this thesis project, we set to resolve the problems in MINMOD, evaluate the known reports on TlD subjects, examine the reaons for discrepancies and implement MINMOD in Matlab..

The hyperbolic effect of density and strength of inter beta-cell coupling on islet bursting: a theoretical investigation

<p>Abstract</p> <p>Background</p> <p>Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP) model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each <it>β</it>-cell is coupled to, <it>n</it>_c, and the coupling strength, <it>g</it>_c.</p> <p>Results</p> <p><it>β</it>-cell clusters of different sizes with number of <it>β</it>-cells <it>n</it>_{<it>β </it>}ranging from 1–343, <it>n</it>_cfrom 0–12, and <it>g</it>_cfrom 0–1000 pS, were simulated. Three functional measures of islet bursting characteristics – fraction of bursting <it>β</it>-cells <it>f</it>_b, synchronization index <it>λ</it>, and bursting period <it>T</it>_b, were quantified. The results revealed a hyperbolic dependence on the combined effect of <it>n</it>_cand <it>g</it>_c. From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures <it>f</it>_b, <it>λ </it>and <it>T</it>_bincreasing monotonically with CCI when it is small, and plateau around CCI = 1.</p> <p>Conclusion</p> <p>CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet <it>β</it>-cell mass and function.</p

SCP and HCP β-cell clusters.

<p>In a 2D cluster <i>n</i>_c = 4 for SCP (a) and <i>n</i>_c = 6 for HCP (b). In 3D the numbers become <i>n</i>_c = 6 for SCP (c) and <i>n</i>_c = 12 for HCP (d).</p

Threshold of β-cell loss that would lead to complete loss of bursting synchronization.

<p>Threshold of β-cell loss that would lead to complete loss of bursting synchronization.</p

Scheme of cell labeling in an HCP β-cell cluster.

<p>Scheme of cell labeling in an HCP β-cell cluster.</p

Function of β-cell clusters versus intercellular coupling strength <i>g</i>_c.

<p>Function of β-cell clusters versus intercellular coupling strength <i>g</i>_c.</p