Mathematical modeling of the glucose–insulin system: A review

Glucose Transporters Are Key Components of the Human Glucostat

Mouse models are extensively used in metabolic studies. However, inherent differences between the species, notably their blood glucose levels, hampered data translation into clinical settings. In this study, we confirmed GLUT1 to be the predominantly expressed glucose transporter in both adult and fetal human β-cells. In comparison, GLUT2 is detected in a small yet significant subpopulation of adult β-cells and is expressed to a greater extent in fetal β-cells. Notably, GLUT1/2 expression in INS+ cells from human stem cell-derived islet-like clusters (SC-islets) exhibited a closer resemblance to that observed in fetal islets. Transplantation of primary human islets or SC-islets, but not murine islets, lowered murine blood glucose to the human glycemic range, emphasizing the critical role of β-cells in establishing species-specific glycemia. We further demonstrate the functional requirements of GLUT1 and GLUT2 in glucose uptake and insulin secretion through chemically inhibiting GLUT1 in primary islets and SC-islets and genetically disrupting GLUT2 in SC-islets. Finally, we developed a mathematical model to predict changes in glucose uptake and insulin secretion as a function of GLUT1/2 expression. Collectively, our findings illustrate the crucial roles of GLUTs in human β-cells, and identify them as key components in establishing species-specific glycemic set points.

ARTICLE HIGHLIGHTS

Leveraging continuous glucose monitoring for personalized modeling of insulin-regulated glucose metabolism

Continuous glucose monitoring (CGM) is a promising, minimally invasive alternative to plasma glucose measurements for calibrating physiology-based mathematical models of insulin-regulated glucose metabolism, reducing the reliance on in-clinic measurements. However, the use of CGM glucose, particularly in combination with insulin measurements, to develop personalized models of glucose regulation remains unexplored. Here, we simultaneously measured interstitial glucose concentrations using CGM as well as plasma glucose and insulin concentrations during an oral glucose tolerance test (OGTT) in individuals with overweight or obesity to calibrate personalized models of glucose-insulin dynamics. We compared the use of interstitial glucose with plasma glucose in model calibration, and evaluated the effects on model fit, identifiability, and model parameters' association with clinically relevant metabolic indicators. Models calibrated on both plasma and interstitial glucose resulted in good model fit, and the parameter estimates associated with metabolic indicators such as insulin sensitivity measures in both cases. Moreover, practical identifiability of model parameters was improved in models estimated on CGM glucose compared to plasma glucose. Together these results suggest that CGM glucose may be considered as a minimally invasive alternative to plasma glucose measurements in model calibration to quantify the dynamics of glucose regulation.

A mathematical model of obesity-induced type 2 diabetes and efficacy of anti-diabetic weight reducing drug

The dominant paradigm for modeling the obesity-induced T2DM (type 2 diabetes mellitus) today focuses on glucose and insulin regulatory systems, diabetes pathways, and diagnostic test evaluations. The problem with this approach is that it is not possible to explicitly account for the glucose transport mechanism from the blood to the liver, where the glucose is stored, and from the liver to the blood. This makes it inaccurate, if not incorrect, to properly model the concentration of glucose in the blood in comparison to actual glycated hemoglobin (A1C) test results. In this paper, we develop a mathematical model of glucose dynamics by a system of ODEs. The model includes the mechanism of glucose transport from the blood to the liver, and from the liver to the blood, and explains how obesity is likely to lead to T2DM. We use the model to evaluate the efficacy of an anti-T2DM drug that also reduces weight.

An extended minimal model of OGTT: estimation of α- and β-cell dysfunction, insulin resistance, and the incretin effect

Loss of insulin sensitivity, α- and β-cell dysfunction, and impairment in incretin effect have all been implicated in the pathophysiology of type 2 diabetes (T2D). Parsimonious mathematical models are useful in quantifying parameters related to the pathophysiology of T2D. Here, we extend the minimum model developed to describe the glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment to the oral glucose tolerance test (OGTT). The extended model describes glucose and hormone dynamics in OGTT including the contribution of the incretin hormones, glucose-dependent insulinotropic polypeptide (GIP), and glucagon-like peptide-1 (GLP-1), to insulin secretion. A new function describing glucose arrival from the gut is introduced. The model is fitted to OGTT data from eight individuals with T2D and eight weight-matched controls (CS) without diabetes to obtain parameters related to insulin sensitivity, β- and α-cell function. The parameters, i.e., measures of insulin sensitivity, a1, suppression of glucagon secretion, k1, magnitude of glucagon secretion, γ2, and incretin-dependent insulin secretion, γ3, were found to be different between CS and T2D with P values < 0.002, <0.017, <0.009, <0.004, respectively. A new rubric for estimating the incretin effect directly from modeling the OGTT is presented. The average incretin effect correlated well with the experimentally determined incretin effect with a Spearman rank test correlation coefficient of 0.67 (P < 0.012). The average incretin effect was found to be different between CS and T2D (P < 0.032). The developed model is shown to be effective in quantifying the factors relevant to T2D pathophysiology.NEW & NOTEWORTHY A new extended model of oral glucose tolerance test (OGTT) has been developed that includes glucagon dynamics and incretin contribution to insulin secretion. The model allows the estimation of parameters related to α- and β-cell dysfunction, insulin sensitivity, and incretin action. A new function describing the influx of glucose from the gut has been introduced. A new rubric for estimating the incretin effect directly from the OGTT experiment has been developed. The effect of glucose dose was also investigated.

A Quantitative Systems Pharmacology Model of the Incretin Hormones GIP and GLP1, Glucagon, Glucose, Insulin, and the Small Molecule DPP-4 Inhibitor, Linagliptin

In the current study, we established a comprehensive quantitative systems pharmacology (QSP) model using linagliptin as the model drug, where drug disposition, drug intervention on dipeptidyl peptidase-4 (DPP-4), glucose-dependent insulinotropic peptide (GIP), Glucagon-like peptide-1 (GLP-1), glucagon, glucose, and insulin are integrated together with the cross talk and feedback loops incorporated among the whole glycemic control system. In the final linagliptin QSP model, the complicated disposition of linagliptin was characterized by a 2-compartment pharmacokinetic (PK) model with an enterohepatic cycling (EHC) component as well as target-mediated drug disposition (TMDD) processes occurring in both tissues and plasma, and the inhibitory effect of linagliptin on DPP-4 was determined by the linagliptin-DPP-4 complex in the central compartment based on target occupancy principle. The integrated GIP-GLP1-glucagon-glucose-insulin system contains five indirect response models as the "skeleton" structure with 12 feedback loops incorporated within the glucose control system. Our model adequately characterized the substantial nonlinear PK of linagliptin, time course of DPP-4 inhibition, as well as the kinetics of GIP, GLP-1, glucagon, and glucose simultaneously in humans. Our model provided valuable insights on linagliptin pharmacokinetics/pharmacodynamics and complicated glucose homeostasis. Since the glucose regulation modeling framework within the QSP model is "drug-independent", our model can be easily adopted by others to evaluate the effect of other DPP-4 inhibitors on the glucose control system. In addition, our QSP model, which contains more components than other reported glucose regulation models, can potentially be used to evaluate the effect of combination antidiabetic therapy targeting different components of glucose control system.

Steady solution and its stability of a mathematical model of diabetic atherosclerosis

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.

A Mathematical Model of the Disruption of Glucose Homeostasis in Cancer Patients

In this paper, we investigate the disruption of the glucose homeostasis at the whole-body level by the presence of cancer disease. Of particular interest are the potentially different responses of patients with or without hyperglycemia (including diabetes mellitus) to the cancer challenge, and how tumor growth, in turn, responds to hyperglycemia and its medical management. We propose a mathematical model that describes the competition between cancer cells and glucose-dependent healthy cells for a shared glucose resource. We also include the metabolic reprogramming of healthy cells by cancer-cell-initiated mechanism to reflect the interplay between the two cell populations. We parametrize this model and carry out numerical simulations of various scenarios, with growth of tumor mass and loss of healthy body mass as endpoints. We report sets of cancer characteristics that show plausible disease histories. We investigate parameters that change cancer cells' aggressiveness, and we exhibit differing responses in diabetic and non-diabetic, in the absence or presence of glycemic control. Our model predictions are in line with observations of weight loss in cancer patients and the increased growth (or earlier onset) of tumor in diabetic individuals. The model will also aid future studies on countermeasures such as the reduction of circulating glucose in cancer patients.

Altered glucose-dependent secretion of glucagon and ACTH is associated with insulin resistance, assessed by population analysis

This study aimed to characterize how the dysregulation of counter-regulatory hormones can contribute to insulin resistance and potentially to diabetes. Therefore, we investigated the association between insulin sensitivity and the glucose- and insulin-dependent secretion of glucagon, adrenocorticotropic hormone (ACTH), and cortisol in non-diabetic individuals using a population model analysis. Data, from hyperinsulinemic-hypoglycemic clamps, were pooled for analysis, including 52 individuals with a wide range of insulin resistance (reflected by glucose infusion rate 20-60 min; GIR20-60min). Glucagon secretion was suppressed by glucose and, to a lesser extent, insulin. The GIR20-60min and BMI were identified as predictors of the insulin effect on glucagon. At normoglycemia (5 mmol/L), a 90% suppression of glucagon was achieved at insulin concentrations of 16.3 and 43.4 µU/mL in individuals belonging to the highest and lowest quantiles of insulin sensitivity, respectively. Insulin resistance of glucagon secretion explained the elevated fasting glucagon for individuals with a low GIR20-60min. ACTH secretion was suppressed by glucose and not affected by insulin. The GIR20-60min was superior to other measures as a predictor of glucose-dependent ACTH secretion, with 90% suppression of ACTH secretion by glucose at 3.1 and 3.5 mmol/L for insulin-sensitive and insulin-resistant individuals, respectively. This difference may appear small but shifts the suppression range into normoglycemia for individuals with insulin resistance, thus, leading to earlier and greater ACTH/cortisol response when the glucose falls. Based on modeling of pooled glucose-clamp data, insulin resistance was associated with generally elevated glucagon and a potentiated cortisol-axis response to hypoglycemia, and over time both hormonal pathways may therefore contribute to dysglycemia and possibly type 2 diabetes.

A mathematical model of the disruption of glucose homeostasis in cancer patients

In this paper we investigate the disruption of the glucose homeostasis at the whole-body level by the presence of cancer disease. Of particular interest are the potentially different responses of patients with or without hyperglycemia (including Diabetes Mellitus) to the cancer challenge, and how tumor growth, in turn, responds to hyperglycemia and its medical management. We propose a mathematical model that describes the competition between cancer cells and glucosedependent healthy cells for a shared glucose resource. We also include the metabolic reprogramming of healthy cells by cancer-cell-initiated mechanism to reflect the interplay between the two cell populations. We parametrize this model and carry out numerical simulations of various scenarios, with growth of tumor mass and loss of healthy body mass as endpoints. We report sets of cancer characteristics that show plausible disease histories. We investigate parameters that change cancer cells’ aggressiveness, and we exhibit differing responses in diabetic and non-diabetic, in the absence or presence of glycemic control. Our model predictions are in line with observations of weight loss in cancer patients and the increased growth (or earlier onset) of tumor in diabetic individuals. The model will also aid future studies on countermeasures such as the reduction of circulating glucose in cancer patients.

Comparable Hemodilution with Hypertonic Glucose in Patients with and without Type-2 Diabetes Mellitus during Hemodialysis

(1) Background: It was examined whether glucose-induced changes in the relative blood volume are suitable to identify subjects with and without type-2 diabetes mellitus (T2D) during hemodialysis. (2) Methods: The relative blood volume was continuously recorded during hemodialysis and perturbed by the infusion of glucose comparable to the dose used for intravenous glucose tolerance tests. Indices of glucose metabolism were determined by the homeostatic model assessment (HOMA). Body composition was measured by a bioimpedance analysis. The magnitude and the time course of hemodilution were described by a modified gamma variate model and five model parameters. (3) Results: A total of 34 subjects were studied, 14 with and 20 without T2D. The magnitude of the hemodilution and the selected model parameters correlated with measures of anthropometry, body mass index, absolute and relative fat mass, volume excess, baseline insulin concentration, and HOMA indices such as insulin resistance and glucose disposition in a continuous analysis, but were not different in a dichotomous analysis of patients with and without T2D. (4) Conclusions: Even though the parameters of the hemodilution curve were correlated with measures of impaired glucose metabolism and body composition, the distinction between subjects with and without T2D was not possible using glucose-induced changes in the relative blood volume during hemodialysis.

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.

A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment

Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6–36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)−1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)−1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (−0.79, 0.002), (−0.73,.007), (−0.86,.0003)) respectively).

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS WITH ADVANCED GLYCATION END-PRODUCTS

Atherosclerosis is a leading cause of death worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. The pathophysiology of diabetic vascular disease is generally understood. Dyslipidemia with increased levels of atherogenic LDL, hyperglycemia, oxidative stress and increased inflammation are factors that increase the risk and accelerate development of atherosclerosis. In a recent paper [53], we have developed mathematical model that includes the effect of hyperglycemia and insulin resistance on plaque growth. In this paper, we propose a more comprehensive mathematical model for diabetic atherosclerosis which include more variables; in particular it includes the variable for Advanced Glycation End-Products (AGEs)concentration. Hyperglycemia trigger vascular damage by forming AGEs, which are not easily metabolized and may accelerate the progression of vascular disease in diabetic patients. The model is given by a system of partial differential equations with a free boundary. We also establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS

Atherosclerosis is a leading cause of death in the United States and worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 21 million Americans have diabetes, a disease where patients' cells cannot efficiently take in dietary sugar, causing it to build up in the blood. In part because diabetes increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. Past work has shown that hyperglycemia and insulin resistance alter function of multiple cell types, including endothelium, smooth muscle cells and platelets, indicating the extent of vascular disarray in this disease. Although the pathophysiology of diabetic vascular disease is generally understood, there is no mathematical model to date that includes the effect of diabetes on plaque growth. In this paper, we propose a mathematical model for diabetic atherosclerosis; the model is given by a system of partial differential equations with a free boundary. We establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

Multi-step ahead predictive model for blood glucose concentrations of type-1 diabetic patients

Continuous monitoring of blood glucose (BG) levels is a key aspect of diabetes management. Patients with Type-1 diabetes (T1D) require an effective tool to monitor these levels in order to make appropriate decisions regarding insulin administration and food intake to keep BG levels in target range. Effectively and accurately predicting future BG levels at multi-time steps ahead benefits a patient with diabetes by helping them decrease the risks of extremes in BG including hypo- and hyperglycemia. In this study, we present a novel multi-component deep learning model BG-Predict that predicts the BG levels in a multi-step look ahead fashion. The model is evaluated both quantitatively and qualitatively on actual blood glucose data for 97 patients. For the prediction horizon (PH) of 30 mins, the average values for root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and normalized mean squared error (NRMSE) are [Formula: see text] mg/dL, 16.77 ± 4.87 mg/dL, [Formula: see text] and [Formula: see text] respectively. When Clarke and Parkes error grid analyses were performed comparing predicted BG with actual BG, the results showed average percentage of points in Zone A of [Formula: see text] and [Formula: see text] respectively. We offer this tool as a mechanism to enhance the predictive capabilities of algorithms for patients with T1D.

The Effect of Three Levels of Concentrate and Grain Processing on Feeding Behavior, Nutrient Digestibility, Blood Metabolites and Fecal pH Of Turkmen Horses

The aim of this study was to investigate, the effect of different levels of concentrates and grain processing on feeding behavior, nutrient digestibility, fecal pH and blood metabolites in the horse. Sixteen 5 to 11 years old Turkmen horses with an initial body weight 433±50 kg were used in this experiment based on completely randomized design. Four treatments were studied, in three treatments were used 20, 25 and 30% of concentrate containing processed grains (A20, A25 and A30, respectively), and in one treatment was used 25% of concentrate containing whole grain (B25). The amount of feed intake, chewing and swallowing rate and total intake for forage and concentrate were not affected by experimental treatments (P> .05). By increasing the concentrate level up to 30%, the digestibility coefficients of dry matter, organic matter, crude protein, ash-free neutral detergent fiber, ash-free acid detergent fiber and digestible energy increased. The highest digestibility coefficients were observed in A30 treatment (P< 0.05). The digestibility of organic matter, crude protein, ash-free neutral detergent fiber and digestible energy in A25 treatment significantly increased compared to B25 (P< 0.05). The concentration of total protein, triglycerides, cholesterol and low-density lipoprotein were not affected by experimental treatments (P> 0.05). The concentration of glucose increased with increasing concentrate for treatment A30 (P< 0.05). In conclusion, comparing the two levels of 25% concentrate showed that the use of processed grains compared to unprocessed grains had no effect on feeding behavior, fecal pH and blood parameters. The use of 30% concentrate containing processed grains improved digestion without adversely affecting feeding behavior and fecal pH.

Bayesian analysis of Glucose dynamics during the Oral Glucose Tolerance Test (OGTT)

This paper proposes a model that considers the action and timing of insulin and glucagon in glucose homeostasis after an oral stimulus. We use the Bayesian paradigm to infer kinetic rates, namely insulin and glucagon secretion, gastrointestinal emptying, and basal glucose concentration in blood. We identify two insulin scores related to glucose concentration in both blood and the gastrointestinal tract. The scores allow us to suggest a classification for individuals with impaired insulin sensitivity.

A Practical Perspective for a Conservative Estimate of Blood Glucose Level during Restaurant Dining and Supermarket Shopping

Foods today are so diverse and enjoyable, making healthy choices difficult. In this perspective, an in vitro-in silico approach for obtaining a conservative estimate of the postprandial blood glucose concentration, which is a realistic estimate nevertheless, after intake of a certain portion of meals is proposed. The rationales and feasibilities of the approach are described and discussed to an extent. The key idea is to first measure the maximum amount of glucose released in an in vitro test under standardized conditions from a specified serving size of a meal or dish or a packaged product sold in a supermarket. The value can then be translated by a literate consumer to the highest estimate of blood glucose rise prior to purchasing or eating through an established in silico blood glucose prediction model in the medical field. The strategy proposed here would help health conscious (diabetics included) and other life quality conscious individuals to make quantitative decisions on consuming the portions of different foods of desire. This strategy may be more effective in reality compared to the conventional GI (Glycemic Index) and GL (Glycemic Load) concepts.

The effects of processing barley and maize on metabolic and digestive responses in horses

The competition for customers increases the search for new grain processing methods for equine feed, but the effect on starch digestibility and metabolic responses varies. Therefore, to evaluate the effect of the processing methods, toasting and micronizing, on starch digestion and the effect on metabolic responses, the mobile bag technique (MBT) and plasma glucose and insulin concentrations in the blood were used to estimate nutrient disappearance and metabolic responses pre-cecally. Further, cecal pH, ammonium nitrogen (N), and short-chain fatty acid (SCFA) concentrations were used to estimate the metabolic response in the cecum. Four cecally cannulated horses (body weight [BW] 565 ± 35 kg) were used in a 4 × 4 Latin square design with four periods of 8 d of diet adaptation and 2 d of data collection. Diets were formulated using hay and processed grains: micronized barley (MB), toasted barley (TB), micronized maize (MM), and toasted maize (TM) and were balanced to provide 1 g starch/kg BW in the morning meal. On day 9 in each period, blood and cecal fluid samples were taken before the morning meal and hourly thereafter for 8 h. On day 10 in each period, 15 bags of either MB, TB, MM, or TM (1 × 1 × 12 cm; 15 μm pore size; 1 g feed) were placed in the stomach, respectively. The dry matter disappearance was highest for the MM at all time points compared with the other feedstuffs (P < 0.001). Maize and micronizing had the highest starch disappearance (P = 0.048) compared with barley and toasting. No treatment effect was measured for any of the glucose and insulin parameters. No feed effect was measured for the insulin parameters. Plasma glucose peaked later (P = 0.045) for maize than for barley, and TB had a larger area under the curve for glucose than MB, MM, and TM (P = 0.015). The concentration of total SCFA increased after feeding (P < 0.001), with a higher concentration for barley than for maize (P = 0.044). No treatment or feed effects were measured for ammonium N or pH, but both were affected by time (P < 0.001). In conclusion, toasting was not as efficient as micronizing to improve pre-cecal starch digestibility; therefore, the preferred processing method for both barley and maize is micronizing. Further, the amount of starch escaping enzymatical digestion in the small intestine was higher than expected.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Driver versus navigator causation in biology: the case of insulin and fasting glucose

BACKGROUND

In biomedicine, inferring causal relation from experimental intervention or perturbation is believed to be a more reliable approach than inferring causation from cross-sectional correlation. However, we point out here that even in interventional inference there are logical traps. In homeostatic systems, causality in a steady state can be qualitatively different from that in a perturbed state. On a broader scale there is a need to differentiate driver causality from navigator causality. A driver is essential for reaching a destination but may not have any role in deciding the destination. A navigator on the other hand has a role in deciding the destination and the path but may not be able to drive the system to the destination. The failure to differentiate between types of causalities is likely to have resulted into many misinterpretations in physiology and biomedicine.

METHODS

We illustrate this by critically re-examining a specific case of the causal role of insulin in glucose homeostasis using five different approaches (1) Systematic review of tissue specific insulin receptor knock-outs, (2) Systematic review of insulin suppression and insulin enhancement experiments, (3) Differentiating steady state and post-meal state glucose levels in streptozotocin treated rats in primary experiments, (4) Mathematical and theoretical considerations and (5) Glucose-insulin relationship in human epidemiological data.

RESULTS

All the approaches converge on the inference that although insulin action hastens the return to a steady state after a glucose load, there is no evidence that insulin action determines the steady state level of glucose. Insulin, unlike the popular belief in medicine, appears to be a driver but not a navigator for steady state glucose level. It is quite likely therefore that the current line of clinical action in the field of type 2 diabetes has limited success largely because it is based on a misinterpretation of glucose-insulin relationship. The insulin-glucose example suggests that we may have to carefully re-examine causal inferences from perturbation experiments and set up revised norms for experimental design for causal inference.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and β-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients

This study designs a robust closed-loop control algorithm for elevated blood glucose level stabilisation in type 1 diabetic patients. The control algorithm is based on a novel control action resulting from integrating algebraic meal disturbance estimator with back-stepping integral sliding mode control (BISMC) technique. The estimator shows finite time convergence leading to accurate and fast estimation of meal disturbance. Moreover, compensation of the estimated disturbance in controller provides significant reduction in chattering phenomenon, which is inherent drawback of sliding mode control (SMC). The controller is applied to one of the most reliable models of type 1 diabetic patients, named Bergman's minimal model. The effectiveness and superiority of the designed controller is shown by comparing it to classical SMC and super-twisting sliding mode control. The designed controller is subject to three different cases for detailed analysis of the controller's robustness against meal disturbance. The three cases considered are hyperglycaemia, hyperglycaemia combined with meal disturbance and three meal disturbance. The simulation results confirm superior performance of algebraic disturbance estimator based BISMC controller for all the cases mentioned above.

Homeostasis as a proportional-integral control system

According to medical guidelines, the distinction between "healthy" and "unhealthy" patients is commonly based on single, discrete values taken at an isolated point in time (e.g., blood pressure or core temperature). Perhaps a more robust and insightful diagnosis can be obtained by studying the functional interdependence of such indicators and the homeostasis that controls them. This requires quasi-continuous measurements and a procedure to map the data onto a parsimonious control model with a degree of universality. The current research illustrates this approach using glucose homeostasis as a target. Data were obtained from 41 healthy subjects wearing over-the-counter glucose monitors, and projected onto a simple proportional-integral (PI) controller, widely used in engineering applications. The indicators quantifying the control function are clustered for the great majority of subjects, while a few outliers exhibit less responsive homeostasis. Practical implications for healthcare and education are further discussed.

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.

Modelling of energy-driven switch for glucagon and insulin secretion

We present a mathematical model of the energy-driven metabolic switch for glucagon and insulin secretion from pancreatic alpha and beta cells, respectively. The energy status related to hormone secretion is studied for various glucose concentrations. Additionally, the physiological response is studied with regards to the presence of other metabolites, particularly the free-fatty acids. At low glucose, the ATP production in alpha cells is high due to free-fatty acids oxidation in mitochondria, which enables glucagon secretion. When the glucose concentration is elevated above the threshold value, the glucagon secretion is switched off due to the contribution of glycolytic ATP production, representing an "anaerobic switch". On the other hand, during hypoglycemia, the ATP production in beta cells is low, reflecting a "waiting state" for glucose as the main metabolite. When glucose is elevated above the threshold value, the oxidative fate of glucose in mitochondria is the main source of energy required for effective insulin secretion, i.e. the "aerobic switch". Our results show the importance of well-regulated and fine-tuned energetic processes in pancreatic alpha and beta cells required for efficient hormone secretion and hence effective blood glucose regulation. These energetic processes have to be appropriately switched on and off based on the sensing of different metabolites by alpha and beta cells. Our computational results indicate that disturbances in cell energetics (e.g. mitochondrial dysfunction), and dysfunctional metabolite sensing and distribution throughout the cell might be related to pathologies such as metabolic syndrome and diabetes.

Mathematical model of diabetes and lipid metabolism linked to diet, leptin sensitivity, insulin sensitivity and VLDLTG clearance predicts paths to health and type II diabetes

An original model of diabetes linked to carbohydrate and lipid intake is presented and applied to predict the effects on biomarkers of various diets. The variables (biomarkers) are concentrations of fasting plasma glucose, insulin, leptin, glucagon, non-esterified fatty acids (NEFA) and very low density lipoprotein triglyceride (VLDLTG), as well as muscle lipids, hepatic lipids, pancreatic lipids, fat mass and mass of β-cells. The model predicts isocaloric high carbohydrate low fat (HCLF) diet and low carbohydrate high fat (LCHF) diet trajectories to health which vary in fat mass by at most a few kilograms at steady state. The LCHF trajectories to health are faster than isocaloric HCLF trajectories with respect to fat mass loss, although these trajectories may be slower initially if parameters are adjusting from HCLF values. On LC diets, leptin sensitivity and VLDLTG clearance are thought to increase. Increasing leptin sensitivity and VLDLTG clearance is predicted to lower lipids including fat mass and VLDLTG. The model predicts that changes in VLDLTG due to a change in diet happen rapidly, approaching steady state values after a few weeks, reflecting leptin sensitivity and VLDLTG clearance which are much harder to measure. The model predicts that if only insulin sensitivity increases on a LC diet, steady state fat mass would increase slightly. If leptin and insulin sensitivities increase concurrently, the combined effect could be a decrease in fat mass, consistent with the fact that increasing insulin sensitivity is often associated with fat mass loss in trials. The model predicts trajectories to fat type II diabetes with hypertriglyceridemia due to high carbohydrate moderate fat diets, on which insulin rises before falling, as ectopic fat deposits increase; made fatter and more diabetic by higher lipid consumption. It predicts trajectories to non-diabetic states with raised fat mass, VLDLTG and muscle, hepatic and pancreatic lipids due to moderate carbohydrate high fat diets. The model predicts paths to lean type II diabetes, on a diet of moderate energy but low β-cell replication rate or high death rate.

Chatteringfree hybrid adaptive neuro-fuzzy inference system-particle swarm optimisation data fusion-based BG-level control

In this study, a closed-loop control scheme is proposed for the glucose-insulin regulatory system in type-1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose-insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well-studied. Higher-order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non-linear property of glucose-insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro-fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG-level tracking and chattering reduction in the presence of daily glucose-level disturbances is verified.

On the Possibility of Predicting Glycaemia 'On the Fly' with Constrained IoT Devices in Type 1 Diabetes Mellitus Patients

Type 1 Diabetes Mellitus (DM1) patients are used to checking their blood glucose levels several times per day through finger sticks and, by subjectively handling this information, to try to predict their future glycaemia in order to choose a proper strategy to keep their glucose levels under control, in terms of insulin dosages and other factors. However, recent Internet of Things (IoT) devices and novel biosensors have allowed the continuous collection of the value of the glucose level by means of Continuous Glucose Monitoring (CGM) so that, with the proper Machine Learning (ML) algorithms, glucose evolution can be modeled, thus permitting a forecast of this variable. On the other hand, glycaemia dynamics require that such a model be user-centric and should be recalculated continuously in order to reflect the exact status of the patient, i.e., an ‘on-the-fly’ approach. In order to avoid, for example, the risk of being disconnected from the Internet, it would be ideal if this task could be performed locally in constrained devices like smartphones, but this would only be feasible if the execution times were fast enough. Therefore, in order to analyze if such a possibility is viable or not, an extensive, passive, CGM study has been carried out with 25 DM1 patients in order to build a solid dataset. Then, some well-known univariate algorithms have been executed in a desktop computer (as a reference) and two constrained devices: a smartphone and a Raspberry Pi, taking into account only past glycaemia data to forecast glucose levels. The results indicate that it is possible to forecast, in a smartphone, a 15-min horizon with a Root Mean Squared Error (RMSE) of 11.65 mg/dL in just 16.15 s, employing a 10-min sampling of the past 6 h of data and the Random Forest algorithm. With the Raspberry Pi, the computational effort increases to 56.49 s assuming the previously mentioned parameters, but this can be improved to 34.89 s if Support Vector Machines are applied, achieving in this case an RMSE of 19.90 mg/dL. Thus, this paper concludes that local on-the-fly forecasting of glycaemia would be affordable with constrained devices.

A novel fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the Diabetes Prevention Program

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

Mathematical modeling of the glucagon challenge test

A model for the homeostasis of glucose through the regulating hormones glucagon and insulin is described. It contains a subsystem that models the internalization of the glucagon receptor. Internalization is a mechanism in cell signaling, through which G-protein coupled receptors are taken from the surface of the cell to the endosome. The model is used to interpret data from a glucagon challenge test in which subjects have been under treatment with a novel glucagon receptor anti-sense drug which is aimed at reducing the number of receptors in the liver. It is shown how the receptor internalization results in tolerance of the blood glucose concentration to glucagon-induced hyperglycemia. We quantify the reduction of the number of receptors using the model and the data before and after treatment.

Computational Modeling of Glucose Uptake in the Enterocyte

Absorption of glucose across the epithelial cells of the small intestine is a key process in human nutrition and initiates signaling cascades that regulate metabolic homeostasis. Validated and predictive mathematical models of glucose transport in intestinal epithelial cells are essential for interpreting experimental data, generating hypotheses, and understanding the contributions of and interactions between transport pathways. Here we report on the development of such a model that, in contrast to existing models, incorporates mechanistic descriptions of all relevant transport proteins and is implemented in the CellML framework. The model is validated against experimental and simulation data from the literature. It is then used to elucidate the relative contributions of the sodium-glucose cotransporter (SGLT1) and the glucose transporter type 2 (GLUT2) proteins in published measurements of glucose absorption from human intestinal epithelial cell lines. The model predicts that the contribution of SGLT1 dominates at low extracellular glucose concentrations (<20 mM) and short exposure times (<60 s) while the GLUT2 contribution is more significant at high glucose concentrations and long durations. Implementation in CellML permitted a modular structure in which the model was composed by reusing existing models of the individual transporters. The final structure also permits transparent changes of the model components and parameter values in order to facilitate model reuse, extension, and customization (for example, to simplify, or add complexity to specific transporter/pathway models, or reuse the model as a component of a larger framework) and carry out parameter sensitivity studies.

Blood Glucose Level Prediction for Diabetics Based on Nutrition and Insulin Administration Logs Using Personalized Mathematical Models

According to recent surveys, the current ways of diabetics trying to estimate their insulin need based on experience and conjecture are sometimes inefficient in practice. This paper proposes a prediction algorithm and presents the validation of the model in outpatient care. The algorithm consists of two state-of-the-art models that calculate nutrition absorption and glycaemia including insulin evolution. The combined model is extended with personalized parameter training including genetic algorithm and Nelder-Mead method, and a more realistic, diurnal parameter profile as a representation of the natural biorhythm. This method implemented in a user-friendly application can help diabetics calculate their insulin need. The tests were performed on a data set including a clinical trial involving more than 20 diabetic patients. We experienced 55% improvement in the results due to model training compared to the tests based on literature parameters. In the best case, 92.5% of the predicted blood glucose level values were in the range of clinically acceptable errors, which means around 2.8 mmol/l root mean square error. The results of the validation based on outpatient data are promising compared to others found in the literature. Handling other important factors such as physical activity and stress remains a challenge for future research.

Design principles of the paradoxical feedback between pancreatic alpha and beta cells

Mammalian glucose homeostasis is controlled by the antagonistic hormones insulin and glucagon, secreted by pancreatic beta and alpha cells respectively. These two cell types are adjacently located in the islets of Langerhans and affect each others’ secretions in a paradoxical manner: while insulin inhibits glucagon secretion from alpha cells, glucagon seems to stimulate insulin secretion from beta cells. Here we ask what are the design principles of this negative feedback loop. We systematically simulate the dynamics of all possible islet inter-cellular connectivity patterns and analyze different performance criteria. We find that the observed circuit dampens overshoots of blood glucose levels after reversion of glucose drops. This feature is related to the temporal delay in the rise of insulin concentrations in peripheral tissues, compared to the immediate hormone action on the liver. In addition, we find that the circuit facilitates coordinate secretion of both hormones in response to protein meals. Our study highlights the advantages of a paradoxical paracrine feedback loop in maintaining metabolic homeostasis.

Labile haemoglobin as a glycaemic biomarker for patient-specific monitoring of diabetes: mathematical modelling approach

Diabetes mellitus constitutes a major health problem and its clinical presentation and progression may vary considerably. A number of standardized diagnostic and monitoring tests are currently used for diabetes. They are based on measuring either plasma glucose, glycated haemoglobin or both. Their main goal is to assess the average blood glucose concentration. There are several sources of interference that can lead to discordances between measured plasma glucose and glycated haemoglobin levels. These include haemoglobinopathies, conditions associated with increased red blood cell turnover or the administration of some therapies, to name a few. Therefore, there is a need to provide new diagnostic tools for diabetes that employ clinically accessible biomarkers which, at the same time, can offer additional information allowing us to detect possible conflicting cases and to yield more reliable evaluations of the average blood glucose level concentration. We put forward a biomathematical model to describe the kinetics of two patient-specific glycaemic biomarkers to track the emergence and evolution of diabetes: glycated haemoglobin and its labile fraction. Our method incorporates erythrocyte age distribution and utilizes a large cohort of clinical data from blood tests to support its usefulness for diabetes monitoring.

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

Receptor/gene/protein-mediated signaling connects methylprednisolone exposure to metabolic and immune-related pharmacodynamic actions in liver

A multiscale pharmacodynamic model was developed to characterize the receptor-mediated, transcriptomic, and proteomic determinants of corticosteroid (CS) effects on clinically relevant hepatic processes following a single dose of methylprednisolone (MPL) given to adrenalectomized (ADX) rats. The enhancement of tyrosine aminotransferase (TAT) mRNA, protein, and enzyme activity were simultaneously described. Mechanisms related to the effects of MPL on glucose homeostasis, including the regulation of CCAAT-enhancer binding protein-beta (C/EBPβ) and phosphoenolpyruvate carboxykinase (PEPCK) as well as insulin dynamics were evaluated. The MPL-induced suppression of circulating lymphocytes was modeled by coupling its effect on cell trafficking with pharmacogenomic effects on cell apoptosis via the hepatic (STAT3-regulated) acute phase response. Transcriptomic and proteomic time-course profiles measured in steroid-treated rat liver were utilized to model the dynamics of mechanistically relevant gene products, which were linked to associated systemic end-points. While time-courses of TAT mRNA, protein, and activity were well described by transcription-mediated changes, additional post-transcriptional processes were included to explain the lack of correlation between PEPCK mRNA and protein. The immune response model quantitatively discerned the relative roles of cell trafficking versus gene-mediated lymphocyte apoptosis by MPL. This systems pharmacodynamic model provides insights into the contributions of selected molecular events occurring in liver and explores mechanistic hypotheses for the multi-factorial control of clinically relevant pharmacodynamic outcomes.

Integrated model of insulin and glucose kinetics describing both hepatic glucose and pancreatic insulin regulation

BACKGROUND AND OBJECTIVES

Modeling of glucose kinetics has to a large extent been based on models with plasma insulin as a known forcing function. Furthermore, population-based statistical methods for parameter estimation in these models have mainly addressed random inter-individual variations and not intra-individual variations in the parameters. Here we present an integrated whole-body model of glucose and insulin kinetics which extends the well-known two-compartment glucose minimal model. The population-based estimation technique allow for quantification of both random inter- and intra-individual variation in selected parameters using simultaneous data series on glucose and insulin.

METHODS

We extend the two-compartment glucose model into a whole-body model for both glucose and insulin using a simple model for the pancreas compartment which includes feedback of glucose on both insulin secretion and formation of insulin in pancreas. The model has 15 unknown parameters of which 8 have been selected for both intra- and inter-individual variations. The statistical technique for parameter estimation is based on first order conditional estimation.

RESULTS

The model has been evaluated on two datasets: Study group 1 includes 13 healthy subjects with 3-5 repeated IVGTT series of simultaneous plasma glucose and insulin measurements and Study group 2 includes 26 obese patients (3 subgroups: 10 type 2 diabetes (T2D), 7 impaired glucose tolerance (IGT) and 9 normal glucose tolerance (NGT)) with a single IVGTT series. In general the estimated population parameters compares well with reported values in similar studies. Overall the model fits the data series well and the random variation in the 8 selected parameters can account for both intra- and inter-individual variations in the data series. Simulation studies perform reasonable in response to either a slow glucose infusion or a staircase experiment with increasing glucose infusion. Furthermore, the parameters related to the pancreas compartment add useful interpretations in relation to discrimination between populations with varying degree of glucose intolerance.

CONCLUSIONS

We report a new and improved whole-body model of glucose and insulin kinetics which performs robustly under differing conditions and adds useful interpretations in relation to glucose intolerance.

A closed-loop multi-level model of glucose homeostasis

BACKGROUND

The pathophysiologic processes underlying the regulation of glucose homeostasis are considerably complex at both cellular and systemic level. A comprehensive and structured specification for the several layers of abstraction of glucose metabolism is often elusive, an issue currently solvable with the hierarchical description provided by multi-level models. In this study we propose a multi-level closed-loop model of whole-body glucose homeostasis, coupled with the molecular specifications of the insulin signaling cascade in adipocytes, under the experimental conditions of normal glucose regulation and type 2 diabetes.

METHODOLOGY/PRINCIPAL FINDINGS

The ordinary differential equations of the model, describing the dynamics of glucose and key regulatory hormones and their reciprocal interactions among gut, liver, muscle and adipose tissue, were designed for being embedded in a modular, hierarchical structure. The closed-loop model structure allowed self-sustained simulations to represent an ideal in silico subject that adjusts its own metabolism to the fasting and feeding states, depending on the hormonal context and invariant to circadian fluctuations. The cellular level of the model provided a seamless dynamic description of the molecular mechanisms downstream the insulin receptor in the adipocytes by accounting for variations in the surrounding metabolic context.

CONCLUSIONS/SIGNIFICANCE

The combination of a multi-level and closed-loop modeling approach provided a fair dynamic description of the core determinants of glucose homeostasis at both cellular and systemic scales. This model architecture is intrinsically open to incorporate supplementary layers of specifications describing further individual components influencing glucose metabolism.

An Information Theoretical Analysis of Human Insulin-Glucose System Toward the Internet of Bio-Nano Things

Molecular communication is an important tool to understand biological communications with many promising applications in Internet of Bio-Nano Things (IoBNT). The insulin-glucose system is of key significance among the major intra-body nanonetworks, since it fulfills metabolic requirements of the body. The study of biological networks from information and communication theoretical (ICT) perspective is necessary for their introduction in the IoBNT framework. Therefore, the objective of this paper is to provide and analyze for the first time in the literature, a simple molecular communication model of the human insulin-glucose system from ICT perspective. The data rate, channel capacity, and the group propagation delay are analyzed for a two-cell network between a pancreatic beta cell and a muscle cell that are connected through a capillary. The results point out a correlation between an increase in insulin resistance and a decrease in the data rate and channel capacity, an increase in the insulin transmission rate, and an increase in the propagation delay. We also propose applications for the introduction of the system in the IoBNT framework. Multi-cell insulin glucose system models may be based on this simple model to help in the investigation, diagnosis, and treatment of insulin resistance by means of novel IoBNT applications.

Personalized glucose-insulin model based on signal analysis

Glucose plasma measurements for diabetes patients are generally presented as a glucose concentration-time profile with 15-60min time scale intervals. This limited resolution obscures detailed dynamic events of glucose appearance and metabolism. Measurement intervals of 15min or more could contribute to imperfections in present diabetes treatment. High resolution data from mixed meal tolerance tests (MMTT) for 24 type 1 and type 2 diabetes patients were used in our present modeling. We introduce a model based on the physiological properties of transport, storage and utilization. This logistic approach follows the principles of electrical network analysis and signal processing theory. The method mimics the physiological equivalent of the glucose homeostasis comprising the meal ingestion, absorption via the gastrointestinal tract (GIT) to the endocrine nexus between the liver, pancreatic alpha and beta cells. This model demystifies the metabolic 'black box' by enabling in silico simulations and fitting of individual responses to clinical data. Five-minute intervals MMTT data measured from diabetic subjects result in two independent model parameters that characterize the complete glucose system response at a personalized level. From the individual data measurements, we obtain a model which can be analyzed with a standard electrical network simulator for diagnostics and treatment optimization. The insulin dosing time scale can be accurately adjusted to match the individual requirements of characterized diabetic patients without the physical burden of treatment.

Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation

We study the effect of diabetic deficiencies on the production of an oscillatory ultradian regime using a deterministic nonlinear model which incorporates two physiological delays. It is shown that insulin resistance impairs the production of oscillations by dampening the ultradian cycles. Four strategies for restoring healthy regulation are explored. Through the introduction of an instantaneous glucose-dependent insulin response, explicit conditions for the existence of periodic solutions in the linearised model are formulated, significantly reducing the complexity of identifying an oscillatory regime. The model is thus shown to be suitable for representing the effect of diabetes on the oscillatory regulation and for investigating pathways to reinstating a physiological healthy regime.