Advancing our understanding of the glucose system via modeling: a perspective

A Glucose-Only Model to Extract Physiological Information from Postprandial Glucose Profiles in Subjects with Normal Glucose Tolerance

BACKGROUND

Current mathematical models of postprandial glucose metabolism in people with normal and impaired glucose tolerance rely on insulin measurements and are therefore not applicable in clinical practice. This research aims to develop a model that only requires glucose data for parameter estimation while also providing useful information on insulin sensitivity, insulin dynamics and the meal-related glucose appearance (GA).

METHODS

The proposed glucose-only model (GOM) is based on the oral minimal model (OMM) of glucose dynamics and substitutes the insulin dynamics with a novel function dependant on glucose levels and GA. A Bayesian method and glucose data from 22 subjects with normal glucose tolerance are utilised for parameter estimation. To validate the results of the GOM, a comparison to the results of the OMM, obtained by using glucose and insulin data from the same subjects is carried out.

RESULTS

The proposed GOM describes the glucose dynamics with comparable precision to the OMM with an RMSE of 5.1 ± 2.3 mg/dL and 5.3 ± 2.4 mg/dL, respectively and contains a parameter that is significantly correlated to the insulin sensitivity estimated by the OMM (r = 0.7) Furthermore, the dynamic properties of the time profiles of GA and insulin dynamics inferred by the GOM show high similarity to the corresponding results of the OMM.

CONCLUSIONS

The proposed GOM can be used to extract useful physiological information on glucose metabolism in subjects with normal glucose tolerance. The model can be further developed for clinical applications to patients with impaired glucose tolerance under the use of continuous glucose monitoring data.

Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials

Several models have been proposed to describe the glucose system at whole-body, organ/tissue and cellular level, designed to measure non-accessible parameters (minimal models), to simulate system behavior and run in silico clinical trials (maximal models). Here, we will review the authors' work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models-building on the classical intravenous glucose tolerance test minimal models-to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.

Modeling the Effect of Subcutaneous Lixisenatide on Glucoregulatory Endocrine Secretions and Gastric Emptying in Type 2 Diabetes to Simulate the Effect of iGlarLixi Administration Timing on Blood Sugar Profiles

BACKGROUND

As type 2 diabetes (T2D) progresses, intensification to combination therapies, such as iGlarLixi (a fixed-ratio GLP-1 RA and basal insulin combination), may be required. Here a simulation study was used to assess the effect of iGlarLixi administration timing (am vs pm) on blood sugar profiles.

METHODS

Models of lixisenatide were built with a selection procedure, optimizing measurement fits and model complexity, and were included in a pre-existing T2D simulation platform containing glargine models. With the resulting tool, a simulated trial was conducted with 100 in-silico participants with T2D. Individuals were given iGLarLixi either before breakfast or before an evening meal for 2 weeks and daily glycemic profiles were analyzed. In the model, breakfast was considered the largest meal of the day.

RESULTS

A similar percentage of time within 24 hours was spent with blood sugar levels between 70 to 180 mg/dL when iGlarLixi was administered pre-breakfast or pre-evening meal (73% vs 71%, respectively). Overall percent of time with blood glucose levels above 180 mg/dL within a 24-hour period was similar when iGlarLixi was administered pre-breakfast or pre-evening meal (26% vs 28%, respectively). Rates of hypoglycemia were low in both regimens, with a blood glucose concentration of below 70 mg/dL only observed for 1% of the 24-hour time period for either timing of administration.

CONCLUSIONS

Good efficacy was observed when iGlarlixi was administered pre-breakfast; however, administration of iGlarlixi pre-evening meal was also deemed to be effective, even though in the model the size of the evening meal was smaller than that of the breakfast.

An OGI model for personalized estimation of glucose and insulin concentration in plasma

Plasma glucose concentration (PGC) and plasma insulin concentration (PIC) are two essential metrics for diabetic regulation, but difficult to be measured directly. Often, PGC and PIC are estimated from continuous glucose monitoring and insulin delivery data. Nevertheless, the inter-individual variability and external disturbance (e.g. carbohydrate intake) bring challenges for accurate estimations. This study is to estimate PGC and PIC adaptively by identifying personalized parameters and external disturbances. An observable glucose-insulin (OGI) dynamic model is established to describe insulin absorption, glucose regulation, and glucose transport. The model parameters and disturbances can be extended to observable state variables and be identified dynamically by Bayesian filtering estimators. Two basic Gaussian noise based Bayesian filtering estimators, extended Kalman filtering (EKF) and unscented Kalman filtering (UKF), are implemented. Recognizing the prevalence of non-Gaussian noise, in this study, two new filtering estimators: particle filtering with Gaussian noise (PFG), and particle filtering with mixed non-Gaussian noise (PFM) are designed and implemented. The proposed OGI model in conjunction with the estimators is evaluated using the data from 30 in-silico subjects and 10 human participants. For in-silico subjects, the OGI with PFM estimator has the ability to estimate PIC and PGC adaptively, achieving RMSE of PIC 9.49±3.81 mU/L, and PGC 0.89±0.19 mmol/L. For human, the OGI with PFM has the promise to identify disturbances (95.46%±0.65% accurate rate of meal identification). OGI model provides a way to fully personalize the parameters and external disturbances in real time, and has potential clinical utility for artificial pancreas.

Translating glucose tolerance data from mice to humans: Insights from stable isotope labelled glucose tolerance tests

Objective

The glucose tolerance test (GTT) is widely used in human and animal biomedical and pharmaceutical research. Despite its prevalent use, particularly in mouse metabolic phenotyping, to the best of our knowledge we are not aware of any studies that have attempted to qualitatively compare the metabolic events during a GTT in mice with those performed in humans.

Methods

Stable isotope labelled oral glucose tolerance tests (siOGTTs; [6,6-²H₂]glucose) were performed in both human and mouse cohorts to provide greater resolution into postprandial glucose kinetics. The siOGTT allows for the partitioning of circulating glucose into that derived from exogenous and endogenous sources. Young adults spanning the spectrum of normal glucose tolerance (n = 221), impaired fasting (n = 14), and impaired glucose tolerance (n = 19) underwent a 75g siOGTT, whereas a 50 mg siOGTT was performed on chow (n = 43) and high-fat high-sucrose fed C57Bl6 male mice (n = 46).

Results

During the siOGTT in humans, there is a long period (>3hr) of glucose absorption and, accordingly, a large, sustained insulin response and robust suppression of lipolysis and endogenous glucose production (EGP), even in the presence of glucose intolerance. In contrast, mice appear to be highly reliant on glucose effectiveness to clear exogenous glucose and experience only modest, transient insulin responses with little, if any, suppression of EGP. In addition to the impaired stimulation of glucose uptake, mice with the worst glucose tolerance appear to have a paradoxical and persistent rise in EGP during the OGTT, likely related to handling stress.

Conclusions

The metabolic response to the OGTT in mice and humans is highly divergent. The potential reasons for these differences and their impact on the interpretation of mouse glucose tolerance data and their translation to humans are discussed.

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We compared the mechanisms governing glucose handling in humans and mice.

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Humans and mice underwent stable isotope labelled oral glucose tolerance tests.

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Metabolic responses between humans and mice were highly divergent.

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Unlike humans, most mice exhibit little EGP suppression or insulin response.

A phenomenological-based semi-physical model of the kidneys and its role in glucose metabolism

The kidneys play an important role in glucose homeostasis in three ways: Via endogenous glucose production from non-carbohydrate precursors (e.g. glutamine, lactate, alanine, glycerol) during both postprandial and post-absorptive states; via glucose filtration and reabsorption by the glomerulus and proximal tubule, respectively; and via glucose utilization and the elimination of its excess in the urine when glucose levels exceed 180mg/dl. The renal release of glucose into the circulation occurs mainly in the renal cortex and results from the glucose phosphorylating capacity of those renal cells, meaning that, cells in the renal cortex can form glucose-6-phosphate. Considering glucose filtration and reabsorption, the kidneys filtrate and reabsorb all circulating glucose, rendering the urine virtually glucose-free in a healthy person. Finally, the kidneys take up glucose from the circulation for energetic self-supply. Besides their role in glucose metabolism, the kidneys are the major site of insulin clearance from the systemic circulation, removing approximately 50% of peripheral insulin. In this regard, insulin clearance by kidneys occurs by degradation in the proximal tubule after being filtered in the glomerulus. All the aforementioned mechanisms affect the glucose concentration levels in the blood, preventing the parametrization of a mathematical model for patients with diabetes mellitus, in the implementation of an artificial pancreas. Aiming for a complete physiological model of the glucose homeostasis, a physiological submodel of the kidneys is presented in a way not described in the literature so far. This submodel is a phenomenological-based semi-physical model with a basic structure rooted in the conservation law and for which the parameters are interpretable. The model's results coincide well with the available clinical data reported for kidney functions associated with glucose and insulin.

A Glucose-Insulin Mixture Model and Application to Short-Term Hypoglycemia Prediction in the Night Time

OBJECTIVE

Insulin-induced hypoglycemia is recognized as a critical problem for diabetic patients, especially at night. To give glucose prediction and advance warning of hypoglycemia of at least 30 minutes, various glucose-insulin models have been proposed. Recognizing the complementary nature of the models, this research proposes a Glucose-Insulin Mixture (GIM) model to predict the glucose values for hypoglycemia detection, by optimally fusing different models with its adjusted parameters to address the inter- and intra-individual variability.

METHODS

Two types of classic glucose-insulin models, the Ruan model, with single-compartment glucose kinetics, and the Hovorka model, with two-compartment glucose kinetics, are selected as two candidate models. Based on Bayesian inference, GIM is introduced with quantified contributions from the models with the associated parameters. GIM is then applied to predict the glucose values and hypoglycemia events.

RESULTS

The proposed model is validated by the nocturnal glucose data collected from 12 participants with type 1 diabetes. The GIM model has promising fitting of RMSE within 0.3465 mmol/L and predicting of RMSE within 0.5571 mmol/L. According to the literature, the hypoglycemia is defined as 3.9 mmol/L, and the GIM model shows good short-term hypoglycemia prediction performance with the data collected within the last hour (accuracy: 95.97%, precision: 91.77%, recall: 95.60%). In addition, the probability of hypoglycemia event in 30 minutes is inferred.

CONCLUSION

GIM, by fusing various glucose-insulin models via Bayesian inference, has the promise to capture glucose dynamics and predict hypoglycemia.

SIGNIFICANCE

GIM based short-term hypoglycemia prediction has potential clinical utility for timely intervention.

A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Clinical Impact of Blood Glucose Monitoring Accuracy: An In-Silico Study

BACKGROUND

Patients with diabetes rely on blood glucose (BG) monitoring devices to manage their condition. As some self-monitoring devices are becoming more and more accurate, it becomes critical to understand the relationship between system accuracy and clinical outcomes, and the potential benefits of analytical accuracy.

METHODS

We conducted a 30-day in-silico study in type 1 diabetes mellitus (T1DM) patients using continuous subcutaneous insulin infusion (CSII) therapy and a variety of BG meters, using the FDA-approved University of Virginia (UVA)/Padova Type 1 Simulator. We used simulated meter models derived from the published characteristics of 43 commercial meters. By controlling random events in each parallel run, we isolated the differences in clinical performance that are directly associated with the meter characteristics.

RESULTS

A meter's systematic bias has a significant and inverse effect on HbA1c ( P < .01), while also affecting the number of severe hypoglycemia events. On the other hand, error, defined as the fraction of measurements beyond 5% of the true value, is a predictor of severe hypoglycemia events ( P < .01), but in the absence of bias has a nonsignificant effect on average glycemia (HbA1c). Both bias and error have significant effects on total daily insulin (TDI) and the number of necessary glucose measurements per day ( P < .01). Furthermore, these relationships can be accurately modeled using linear regression on meter bias and error.

CONCLUSIONS

Two components of meter accuracy, bias and error, clearly affect clinical outcomes. While error has little effect on HbA1c, it tends to increase episodes of severe hypoglycemia. Meter bias has significant effects on all considered metrics: a positive systemic bias will reduce HbA1c, but increase the number of severe hypoglycemia attacks, TDI use, and number of fingersticks per day.

Data Based Prediction of Blood Glucose Concentrations Using Evolutionary Methods

Predicting glucose values on the basis of insulin and food intakes is a difficult task that people with diabetes need to do daily. This is necessary as it is important to maintain glucose levels at appropriate values to avoid not only short-term, but also long-term complications of the illness. Artificial intelligence in general and machine learning techniques in particular have already lead to promising results in modeling and predicting glucose concentrations. In this work, several machine learning techniques are used for the modeling and prediction of glucose concentrations using as inputs the values measured by a continuous monitoring glucose system as well as also previous and estimated future carbohydrate intakes and insulin injections. In particular, we use the following four techniques: genetic programming, random forests, k-nearest neighbors, and grammatical evolution. We propose two new enhanced modeling algorithms for glucose prediction, namely (i) a variant of grammatical evolution which uses an optimized grammar, and (ii) a variant of tree-based genetic programming which uses a three-compartment model for carbohydrate and insulin dynamics. The predictors were trained and tested using data of ten patients from a public hospital in Spain. We analyze our experimental results using the Clarke error grid metric and see that 90% of the forecasts are correct (i.e., Clarke error categories A and B), but still even the best methods produce 5 to 10% of serious errors (category D) and approximately 0.5% of very serious errors (category E). We also propose an enhanced genetic programming algorithm that incorporates a three-compartment model into symbolic regression models to create smoothed time series of the original carbohydrate and insulin time series.

A Novel Insulin/Glucose Model after a Mixed-Meal Test in Patients with Type 1 Diabetes on Insulin Pump Therapy

Current closed-loop insulin delivery methods stem from sophisticated models of the glucose-insulin (G/I) system, mostly based on complex studies employing glucose tracer technology. We tested the performance of a new minimal model (GLUKINSLOOP 2.0) of the G/I system to characterize the glucose and insulin dynamics during multiple mixed meal tests (MMT) of different sizes in patients with type 1 diabetes (T1D) on insulin pump therapy (continuous subcutaneous insulin infusion, CSII). The GLUKINSLOOP 2.0 identified the G/I system, provided a close fit of the G/I time-courses and showed acceptable reproducibility of the G/I system parameters in repeated studies of identical and double-sized MMTs. This model can provide a fairly good and reproducible description of the G/I system in T1D patients on CSII, and it may be applied to create a bank of “virtual” patients. Our results might be relevant at improving the architecture of upcoming closed-loop CSII systems.

Glucose Variability: Timing, Risk Analysis, and Relationship to Hypoglycemia in Diabetes

Glucose control, glucose variability (GV), and risk for hypoglycemia are intimately related, and it is now evident that GV is important in both the physiology and pathophysiology of diabetes. However, its quantitative assessment is complex because blood glucose (BG) fluctuations are characterized by both amplitude and timing. Additional numerical complications arise from the asymmetry of the BG scale. In this Perspective, we focus on the acute manifestations of GV, particularly on hypoglycemia, and review measures assessing the amplitude of GV from routine self-monitored BG data, as well as its timing from continuous glucose monitoring (CGM) data. With availability of CGM, the latter is not only possible but also a requirement-we can now assess rapid glucose fluctuations in real time and relate their speed and magnitude to clinically relevant outcomes. Our primary message is that diabetes control is all about optimization and balance between two key markers-frequency of hypoglycemia and HbA1c reflecting average BG and primarily driven by the extent of hyperglycemia. GV is a primary barrier to this optimization, including to automated technologies such as the "artificial pancreas." Thus, it is time to standardize GV measurement and thereby streamline the assessment of its two most important components-amplitude and timing.

A Model Approach: Mathematical modeling provides an increasingly clear picture of glucose and neural systems

Mathematical modeling of physiological systems is a fundamental milestone of biomedical engineering. Models allow for the quantitative understanding of the intimate functions of a biological system, estimating parameters that are not accessible to direct measurement and performing in silico trials by simulating and tracking a physiological system in case its function has been deranged. Modeling has always been central in the Italian biomedical engineering community. Here, we review the progress in two areas: glucose and neurocomputational modeling with an emphasis on their clinical impact.

Model-Based Quantification of the Systemic Interplay between Glucose and Fatty Acids in the Postprandial State

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30–45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease.

A Long-Term Model of the Glucose-Insulin Dynamics of Type 1 Diabetes

A new glucose-insulin model is introduced which fits with the clinical data from in- and outpatients for two days. Its stability property is consistent with the glycemia behavior for type 1 diabetes. This is in contrast to traditional glucose-insulin models. Prior models fit with clinical data for a few hours only or display some nonnatural equilibria. The parameters of this new model are identifiable from standard clinical data as continuous glucose monitoring, insulin injection, and carbohydrate estimate. Moreover, it is shown that the parameters from the model allow the computation of the standard tools used in functional insulin therapy as the basal rate of insulin and the insulin sensitivity factor. This is a major outcome as they are required in therapeutic education of type 1 diabetic patients.

Overexpression of sphingosine kinase 1 in liver reduces triglyceride content in mice fed a low but not high-fat diet

Hepatic insulin resistance is a major risk factor for the development of type 2 diabetes and is associated with the accumulation of lipids, including diacylglycerol (DAG), triacylglycerols (TAG) and ceramide. There is evidence that enzymes involved in ceramide or sphingolipid metabolism may have a role in regulating concentrations of glycerolipids such as DAG and TAG. Here we have investigated the role of sphingosine kinase (SphK) in regulating hepatic lipid levels. We show that mice on a high-fat high-sucrose diet (HFHS) displayed glucose intolerance, elevated liver TAG and DAG, and a reduction in total hepatic SphK activity. Reduced SphK activity correlated with downregulation of SphK1, but not SphK2 expression, and was not associated with altered ceramide levels. The role of SphK1 was further investigated by overexpressing this isoform in the liver of mice in vivo. On a low-fat diet (LFD) mice overexpressing liver SphK1, displayed reduced hepatic TAG synthesis and total TAG levels, but with no change to DAG or ceramide. These mice also exhibited no change in gluconeogenesis, glycogenolysis or glucose tolerance. Similarly, overexpression of SphK1 had no effect on the pattern of endogenous glucose production determined during a glucose tolerance test. Under HFHS conditions, normalization of liver SphK activity to levels observed in LFD controls did not alter hepatic TAG concentrations. Furthermore, DAG, ceramide and glucose tolerance were also unaffected. In conclusion, our data suggest that SphK1 plays an important role in regulating TAG metabolism under LFD conditions.