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

경구최소모델을 기반으로 한 포도당 대사에서의 최적화와 제어

학위논문 (석사)-- 서울대학교 대학원 : 의학과 의공학전공, 2016. 8. 김성완.In the mathematical models to describe physiological phenomena, optimization problem and control tactics are important. Because optimal parameters to represent status of subjects should be estimated and biological variables beyond the normal range should be recovered by using of the pertinent control or interventions. For this objective, the model is required to be validated based on clinical data and the optimal algorithm for each subject is able to be designed. The oral minimal model is the mathematical system to understand glycemic control in vivo, which can be helpful to evaluate the beta-cell function and insulin sensitivity. In this study, 10 healthy subjects with normal glucose tolerance and 14 patients with type 2 diabetes mellitus participated. In the results, firstly, blood glucose concentration level, C-peptide level, and Insulin response can be predicted by using of the oral minimal model. Secondly, insulin sensitivity and disposition indices are lower in type 2 diabetes group than normal group. Thirdly, the oral minimal model indices are well correlated with pre-existing clinical indices. Therefore the oral minimal model could be applied to the Korean. Furthermore, a proportional-integral-derivative (PID) controller and optimal control using dynamic programming can be used to establish algorithms to control blood glucose level in type 2 diabetes mellitus. PID controller showed capability to lower glucose level efficiently and the level of the glucose was continuously lowered without fluctuation. An optimal control scheme with two simplified additional insulin loading profiles also could lower blood glucose level efficiently, and the barrier term in the cost function could prevent too low blood glucose level. Among 14 T2DM patients, immediate injections of two insulin loadings were recommended in most cases for effective control of the glucose level. Based on this model and tactics, it is expected that latent interactions in glucose metabolism are clarified, and the models and efficient control algorithms for the artificial pancreas could be developed.1. Introduction 1 1.1.The mathematical modeling in glucose metabolism 1 1.2.The necessity of the simulation study 2 2. Optimization and control problems in the oral minimal model 4 2.1.Concepts of the oral minimal model 4 2.2.The mathematical systems in the oral minimal model 7 2.3.Optimization problems in the oral minimal model 11 2.4.Control problems in the oral minimal model 13 3. Method 15 3.1.Subjects and ethical statement 15 3.2.Study procedure in clinical experiments 15 3.3.Parameter estimation 16 3.4.Calculation for indices 17 3.5.Statistical analysis 21 3.6.Simulation of control procedures 21 4. Results 24 4.1.Clinical characteristics of the subjects 24 4.2.Simulation of plasma glucose level and C-peptide secretion 26 4.3.Insulin sensitivity, beta-cell responsivity indices and hepatic insulin extraction ratios 29 4.4.Disposition indices between NGT and T2DM groups 31 4.5.Correlation between other indices of insulin secretion or insulin action and the oral minimal model indices 35 4.6.Correlation between glucose levels and the oral minimal model indices 37 4.7.Simulation of glucose control tactics via additional insulin 39 5. Discussion 46 6. Conclusion 52 References 53 Abstract in Korean 60Maste

Sensitivity analysis in systems biology modelling and its application to a multi-scale model of blood glucose homeostasis

Biological systems typically consist of large numbers of interacting components and involve processes at a variety of spatial, temporal and biological scales. Systems biology aims to understand such systems by integrating information from all functional levels into a single cohesive model. Mathematical and computational modelling is a key part of the systems biology approach and can be used to produce composite models which describe systems across multiple scales. One of the major diculties in constructing models of biological systems is the lack of precise parameter values which are often associated with a high degree of uncertainty. This uncertainty in parameter values can be incorporated into the modelling process using sensitivity analysis, the systematic investigation of the relationship between uncertain model inputs and the resulting variation in the model outputs. This thesis discusses the use of global sensitivity analysis in systems biology modelling and addresses two main problem areas: the application of sensitivity analysis to time dependent model outputs and the analysis of multi-scale models. An approach to the analysis of time dependent model outputs which makes use of principal component analysis to extract the key modes of variation from the data, is presented. The analysis of multi-scale models is addressed using group-based sensitivity analysis which enables the identication of the most important sub-processes in the model. Together these methods provide a new methodology for sensitivity analysis in multi-scale systems biology modelling. The methodology is applied to a composite model of blood glucose homeostasis that combines models of processes at the sub-cellular, cellular and organ level to describe the physiological system. The results of the analysis suggest three main points about the system: the mobilisation of calcium by glucagon plays a minor role in the regulation of glycogen metabolism; auto-regulation of hepatic glucose production by glucose is important in regulating blood glucose levels; time-delays between changes in blood glucose levels, the release of insulin by the pancreas and the eect of the hormone on hepatic glucose production are important in the possible onset of ultradian glucose oscillations. These results suggest possible directions for further study into the regulation of blood glucose

Consistency of compact and extended models of glucose-insulin homeostasis: The role of variable pancreatic reserve

Published compact and extended models of the glucose-insulin physiologic control system are compared, in order to understand why a specific functional form of the compact model proved to be necessary for a satisfactory representation of acute perturbation experiments such as the Intra Venous Glucose Tolerance Test (IVGTT). A spectrum of IVGTT’s of virtual subjects ranging from normal to IFG to IGT to frank T2DM were simulated using an extended model incorporating the population-of-controllers paradigm originally hypothesized by Grodsky, and proven to be able to capture a wide array of experimental results from heterogeneous perturbation procedures. The simulated IVGTT’s were then fitted with the Single-Delay Model (SDM), a compact model with only six free parameters, previously shown to be very effective in delivering precise estimates of insulin sensitivity and secretion during an IVGTT. Comparison of the generating, extended-model parameter values with the obtained compact model estimates shows that the functional form of the nonlinear insulin-secretion term, empirically found to be necessary for the compact model to satisfactorily fit clinical observations, captures the pancreatic reserve level of the simulated virtual patients. This result supports the validity of the compact model as a meaningful analysis tool for the clinical assessment of insulin sensitivity

Modelling endocrine regulation of glycaemic control in animal models of diabetes

This thesis is concerned with mathematical modelling of the glucose-insulin homeostatic system, with the specific aim of mathematically modelling diabetes and diabetes-like conditions in animals. Existing models were examined and critiqued in this thesis. Additionally, structural identifiability analysis of the most widely-used model in the field, the Minimal Model, was performed using Taylor series and similarity transformation approaches. It was shown under certain assumptions that it was theoretically possible to obtain a unique set of parameters for the model from only measuring glucose. C-peptide deconvolution was performed using the WinNonLin algorithm and Maximum Entropy technique implemented in MATLAB. This was used to calculate insulin secretion, the percentage of insulin appearing in the periphery and insulin clearance rate. This was then further developed to model insulin appearance and clearance based on hepatic blood flow changes. A short-term model of the glucose-insulin and C-peptide system was initially formulated using a PID controller concept and later refined to reduce the number of model parameters. Structural identifiability analysis was performed using the Lie symmetries approach, followed by parameter estimation on rat and mice data from IVGTTs, OGTTs and hyperglycaemic clamps and sensitivity analysis. This short-term model was integrated into a long-term model to analyse Zucker and ZDF rat data to create a single model to cater for both short- and long-term dynamics. Finally, a software tool was developed to allow non-mathematical scientists to use and access the benefits of the model

Hyperprolactinemia induced by hCG leads to metabolic disturbances in female mice

The metabolic syndrome is a growing epidemic; it increases the risk for diabetes, cardiovascular disease, fatty liver, and several cancers. Several reports have indicated a link between hormonal imbalances and insulin resistance or obesity. Transgenic (TG) female mice overexpressing the human chorionic gonadotropin β-subunit (hCGβ+ mice) exhibit constitutively elevated levels of hCG, increased production of testosterone, progesterone and prolactin, and obesity. The objective of this study was to investigate the influence of hCG hypersecretion on possible alterations in the glucose and lipid metabolism of adult TG females. We evaluated fasting serum insulin, glucose, and triglyceride levels in adult hCGβ+ females and conducted intraperitoneal glucose and insulin tolerance tests at different ages. TG female mice showed hyperinsulinemia, hypertriglyceridemia, and dyslipidemia, as well as glucose intolerance and insulin resistance at 6 months of age. A 1-week treatment with the dopamine agonist cabergoline applied on 5-week-old hCGβ+ mice, which corrected hyperprolactinemia, hyperandrogenism, and hyperprogesteronemia, effectively prevented the metabolic alterations. These data indicate a key role of the hyperprolactinemia-induced gonadal dysfunction in the metabolic disturbances of hCGβ+ female mice. The findings prompt further studies on the involvement of gonadotropins and prolactin on metabolic disorders and might pave the way for the development of new therapeutic strategies.Fil: Ratner, Laura Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Stevens, Guillermina. Gobierno de la Ciudad de Buenos Aires. Hospital General de Agudos "Ramos Mejía"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Bonaventura, Maria Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Lux, Victoria Adela R.. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Poutanen, Matti. University of Turku; FinlandiaFil: Calandra, Ricardo Saul. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Huhtaniemi, Ilpo T.. University of Turku; FinlandiaFil: Rulli, Susana Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentin

Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.Comment: Accepted for publication in PLOS ON

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells

open5noMost endocrine cells secrete hormones as a result of Ca(2+)-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca(2+) channels, and the resulting Ca(2+) influx elevate the intracellular Ca(2+) concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca(2+) dynamics, which depends on the particular pattern of electrical activity as well as Ca(2+) channel kinetics, exocytosis is dependent on the spatial arrangement of Ca(2+) channels and secretory granules. For example, the creation of local Ca(2+) microdomains, where the Ca(2+) concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca(2+) diffusion have provided important insight into the interplay between electrical activity, Ca(2+) channel kinetics, and the location of granules and Ca(2+) channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca(2+) regulated exocytosis of hormone-containing granules.openPedersen, Morten Gram; Tagliavini, Alessia; Cortese, Giuliana; Riz, Michela; Montefusco, FrancescoPedersen, MORTEN GRAM; Tagliavini, Alessia; Cortese, Giuliana; Riz, Michela; Montefusco, Francesc