Mathematical modeling of the glucagon challenge test

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.

Modeling the effect of glucagon on endogenous glucose production in type 1 diabetes: On the role of glucagon receptor dynamics

This paper validates a glucoregulatory model including glucagon receptors dynamics in the description of endogenous glucose production (EGP). A set of models from literature are selected for a head-to-head comparison in order to evaluate the role of glucagon receptors. Each EGP model is incorporated into an existing glucoregulatory model and validated using a set of clinical data, where both insulin and glucagon are administered. The parameters of each EGP model are identified in the same optimization problem, minimizing the root mean square error (RMSE) between the simulation and the clinical data. The results show that the RMSE for the proposed receptors-based EGP model was lower when compared to each of the considered models (Receptors approach: 7.13±1.71 mg/dl vs. 7.76±1.45 mg/dl (p=0.066), 8.45±1.38 mg/dl (p=0.011) and 8.99±1.62 mg/dl (p=0.007)). This raises the possibility of considering glucagon receptors dynamics in type 1 diabetes simulators.

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.

Mathematical Model of Glucagon Kinetics for the Assessment of Insulin-Mediated Glucagon Inhibition During an Oral Glucose Tolerance Test

Glucagon is secreted from the pancreatic alpha cells and plays an important role in the maintenance of glucose homeostasis, by interacting with insulin. The plasma glucose levels determine whether glucagon secretion or insulin secretion is activated or inhibited. Despite its relevance, some aspects of glucagon secretion and kinetics remain unclear. To gain insight into this, we aimed to develop a mathematical model of the glucagon kinetics during an oral glucose tolerance test, which is sufficiently simple to be used in the clinical practice. The proposed model included two first-order differential equations -one describing glucagon and the other describing C-peptide in a compartment remote from plasma - and yielded a parameter of possible clinical relevance (i.e., S_GLUCA(t), glucagon-inhibition sensitivity to glucose-induced insulin secretion). Model was validated on mean glucagon data derived from the scientific literature, yielding values for S_GLUCA(t) ranging from -15.03 to 2.75 (ng of glucagon·nmol of C-peptide^-1). A further validation on a total of 100 virtual subjects provided reliable results (mean residuals between -1.5 and 1.5 ng·L^-1) and a negative significant linear correlation (r = -0.74, p < 0.0001, 95% CI: -0.82 - -0.64) between S_GLUCA(t) and the ratio between the areas under the curve of suprabasal remote C-peptide and glucagon. Model reliability was also proven by the ability to capture different patterns in glucagon kinetics. In conclusion, the proposed model reliably reproduces glucagon kinetics and is characterized by sufficient simplicity to be possibly used in the clinical practice, for the estimation in the single individual of some glucagon-related parameters.

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.