Comparing the Efficacy of Various Insulin Types: Pharmacokinetic and Pharmacodynamic Modeling of Glucose Clamp Effects in Healthy Volunteers

This study compares the pharmacokinetics and efficacy of various subcutaneously (SC) dosed insulin analogs, including rapid-acting, intermediate-acting, long-acting, and regular human insulin, using mechanistic pharmacokinetic (PK) and pharmacodynamic (PD) models. These models were applied to data from euglycemic clamp studies in healthy volunteers, where insulin pharmacokinetics and its effects on glucose utilization were monitored. Data from published studies were digitized and modeled using MONOLIX (Version 2024). The PK model described insulin absorption via sequential first-order processes and linear elimination. The PD effects were captured using a model combination of biophase, indirect, and receptor down-regulation components. While PK parameters-especially absorption rates-varied between insulin types, a common set of nonlinear PD parameters was sought to account for dose-related differences in glucose utilization. The maximum glucose stimulation (S max ${{{\mathrm{S}}}_{{\mathrm{max}}}}$ ) was 163, and the insulin concentration for a half-maximal effect (S C 50 ${\mathrm{S}}{{{\mathrm{C}}}_{50}}$ ) were 1156 pmol/L for insulin lispro, regular human insulin, neutral protamine hagedorn (NPH) insulin, and insulin glargine; 674 pmol/L for insulin aspart; and 5335 pmol/L for insulin detemir. Insulin detemir showed similar overt effects as the other insulin types but with smaller clearances and lower potency. This mechanism-based glucose-insulin model demonstrated that most insulin analogs exhibit similar receptor- and transporter-related parameters. The model, with specific PK but unified PD parameters, may enable clinical optimization of insulin therapy by highlighting differences in pharmacokinetics and operating common intrinsic glucose utilization parameters.

Model-based simulation of glycaemic effect and body weight loss when switching from semaglutide or dulaglutide to once weekly tirzepatide

OBJECTIVE

To evaluate the efficacy endpoints of HbA1c and body weight loss after switching from the GLP-1 receptor agonists, semaglutide or dulaglutide, to treatment with the GIP/GLP-1 receptor agonist (RA) tirzepatide.

METHODS

Models were developed and validated to describe the HbA1c and weight loss time course for semaglutide (SUSTAIN 1-10), dulaglutide (AWARD-11) and tirzepatide (SURPASS 1-5, phase 3 global T2D program). The impact of switching from once weekly GLP-1 RAs to tirzepatide was described by simulating the efficacy time course. Semaglutide and dulaglutide doses were escalated in accordance with their respective labels.

RESULTS

Model-predicted mean decreases from baseline in HbA1c and body weight for semaglutide 0.5 mg, 1 mg, and 2 mg were 1.22 to 1.79% and 3.62 to 6.87 kg respectively, at Week 26. Model-predicted mean decreases from baseline in HbA1c and body weight for dulaglutide 1.5 mg, 3 mg and 4.5 mg were 1.53 to 1.84% and 2.55 to 3.71 kg respectively, at Week 26. After switching to tirzepatide 5, 10 and 15 mg HbA1c reductions were predicted to range between 1.95 to 2.46% and body weight reductions between 6.50 to 12.1 kg by Week 66.

CONCLUSION

In this model-based simulation, switching from approved maintenance doses of semaglutide or dulaglutide to tirzepatide, even at the lowest approved maintenance dose of 5 mg, showed the potential to further improve HbA1c and body weight reductions.

Periodic insulin stimulation of Akt: Dynamic steady states and robustness

The periodic secretion of insulin is a salient feature of the blood glucose control system in vivo. Insulin levels in the blood exhibit oscillations on multiple time scales - rapid, ultradian, and circadian - and the improved metabolic regulation resulting from pulsatile insulin release has been well established. Although numerous mathematical models investigating the causal mechanisms of insulin oscillations have appeared in the literature, to date there has been comparatively little attention given to the influence of periodic insulin stimulation on downstream components of the insulin signalling pathway. In this paper, we explore the effect of high frequency periodic insulin stimulation on Akt (also known as PKB), a crucial crosstalk node in the insulin signalling pathway that coordinates metabolic and mitogenic processes in the cell. We analyse a mathematical model of Akt translocation to the plasma membrane under both single step insulin perturbations and periodic insulin stimulation with an emphasis on - but not limited to - the physiological range of parameter values. It was shown that the system rapidly attains a robust dynamic steady state entrained to the periodic insulin stimulation. Moreover, the translocation of Akt to the plasma membrane in the model permits a sufficient level of phosphorylation to trigger downstream metabolic regulators. However, the modelling also indicated that further investigation of this activation process is required to determine whether the response of Akt is a key determinant of the enhanced metabolic control observed under periodic insulin stimulation.

Insulin Signaling Pathway Model in Adipocyte Cells

BACKGROUND

Worldwide, type 2 diabetes mellitus (T2DM) is one of the most pervasive and fastgrowing disorders, bringing long-term adverse effects. T2DM arises from pancreatic β-cells deficiency to produce enough insulin or when the body cannot effectively use the insulin produced by such cells. Accordingly, early diagnosis will decrease the long-term effects and high-healthcare costs of diabetes.

OBJECTIVE

The objective is developing an integrated mathematical model of the insulin signaling network based on Brännmark's model, which can simulate the signaling events more comprehensively with the added key components.

METHODS

In this study, a thorough mathematical model of the insulin signaling network was developed by expanding the previously validated model and incorporating the glycogen synthesis module. Parameters (69 parameters) of the integrated model were evaluated by a genetic algorithm by fitting the model predictions to eighty percent of experimental data from the literature. Twenty percent of the experimental data were used to evaluate the final optimized model.

RESULTS

The time-response curves indicate that the GS phosphorylation reaches its maximum in response to 10^-7 M insulin after 4 min, while the maximum phosphorylated GSK3 is attained within ~50 min. The doseresponse curves for the GSP and GSK3 of the insulin signaling intermediaries in response to the increased concentration of insulin, after 10 min, in the input from 0-100 nM exhibits a decreasing trend, whereas an increasing trend was observed for the GS and GSK3P. The GSK and GS phosphorylation sensitivity was enhanced by increasing the initial insulin concentration level from 0.001 to 100 nM. However, the sensitivity of GSK3 to insulin concentration changes (from 0.001 to 100 nM) was 3-fold higher than GS sensitivity.

CONCLUSION

Considerably, the trends of all signaling components simulated by the expanded model shows high compatibility with experimental data (R2 ≥ 0.9), which approves the accuracy of the proposed model. The proposed mathematical model can be used in many biological systems and combined with the whole-body model of the blood glucose regulation system for a better understanding of the causes and potential treatment of type 2 diabetes. Although, this model is not a complete description of insulin signaling, yet it can make profound contributions to improvements regarding other important components and signaling branches such as epidermal growth factor (EGF) signaling, as well as signaling in other cell types in the model structure of future works.

Pharmacometrics: The Already-Present Future of Precision Pharmacology

The use of mathematical modeling to represent, analyze, make predictions or providing information on data obtained in drug research and development has made pharmacometrics an area of great prominence and importance. The main purpose of pharmacometrics is to provide information relevant to the search for efficacy and safety improvements in pharmacotherapy. Regulatory agencies have adopted pharmacometrics analysis to justify their regulatory decisions, making those decisions more efficient. Demand for specialists trained in the field is therefore growing. In this review, we describe the meaning, history, and development of pharmacometrics, analyzing the challenges faced in the training of professionals. Examples of applications in current use, perspectives for the future, and the importance of pharmacometrics for the development and growth of precision pharmacology are also presented.

Utilization of Pharmacokinetic/Pharmacodynamic Modeling in Pharmacoepidemiological Studies: A Systematic Review on Antiarrhythmic and Glucose-Lowering Medicines

Introduction: In human pharmacology, there are two important scientific branches: clinical pharmacology and pharmacoepidemiology. Pharmacokinetic/pharmacodynamic (PK/PD) modeling is important in preclinical studies and randomized control trials. However, it is rarely used in pharmacoepidemiological studies on the effectiveness and medication safety where the target population is heterogeneous and followed for longer periods. The objective of this literature review was to investigate how far PK/PD modeling is utilized in observational studies on glucose-lowering and antiarrhythmic drugs.

Method: A systematic literature search of MEDLINE, Embase, and Web of Science was conducted from January 2010 to 21 February 2020. To calculate the utilization of PK/PD modeling in observational studies, we followed two search strategies. In the first strategy, we screened a 1% random set from 95,672 studies on glucose-lowering and antiarrhythmic drugs on inclusion criteria. In the second strategy, we evaluated the percentage of studies in which PK/PD modeling techniques were utilized. Subsequently, we divided the total number of included studies in the second search strategy by the total number of eligible studies in the first search strategy.

Results: The comprehensive search of databases and the manual search of included references yielded a total of 29 studies included in the qualitative synthesis of our systematic review. Nearly all 29 studies had utilized a PK model, whereas only two studies developed a PD model to evaluate the effectiveness of medications. In total, 16 out of 29 studies (55.1%) used a PK/PD model in the observational setting to study effect modification. The utilization of PK/PD modeling in observational studies was calculated as 0.42%.

Conclusion: PK/PD modeling techniques were substantially underutilized in observational studies of antiarrhythmic and glucose-lowering drugs during the past decade.

A model-based simulation of glycaemic control and body weight when switching from semaglutide to 3.0- and 4.5-mg doses of once-weekly dulaglutide

AIM

To evaluate HbA1c and body weight changes when semaglutide 0.5- or 1.0-mg once-weekly (QW) is switched to dulaglutide 3.0- or 4.5-mg QW via exposure-response modelling.

METHODS

HbA1c and body weight time-course models were developed and validated with data from the SUSTAIN 1 to 10 trials for semaglutide and the AWARD-11 trial for dulaglutide. Simulations were conducted for HbA1c and body weight over 52 weeks. In the initial 26 weeks, semaglutide was initiated at 0.25-mg and titrated to 0.5- or 1.0-mg QW via 4-weekly stepwise titration, followed by 26 weeks of dulaglutide initiated at 0.75- or 1.5-mg QW and escalated to 3.0- or 4.5-mg QW via 4-weekly stepwise titration.

RESULTS

At 26 weeks, model-predicted mean changes from baseline in HbA1c and weight for semaglutide 0.5 mg were up to -1.55% and -3.44 kg, respectively. After switching to dulaglutide 3.0 mg, further reductions were 0.19% and 1.40 kg, respectively, at 52 weeks. Predicted mean HbA1c and weight changes for semaglutide 1.0 mg at 26 weeks were -1.84% and -4.96 kg, respectively; after switching to dulaglutide 4.5 mg, HbA1c was maintained with additional weight reduction of up to 0.57 kg at 52 weeks. Glycaemic control was preserved when switching from semaglutide 1.0 mg to dulaglutide 3.0 mg.

CONCLUSION

Switching from semaglutide 0.5 mg to dulaglutide 3.0 or 4.5 mg with dose escalation potentially yields additional HbA1c and weight reductions; switching from semaglutide 1.0 mg to dulaglutide 4.5 mg may enhance weight loss.

First-in-Human, Single-Ascending Dose and Food Effect Studies to Assess the Safety, Tolerability, Pharmacokinetics and Pharmacodynamics of Cetagliptin, a Dipeptidyl Peptidase-4 Inhibitor for the Treatment of Type 2 Diabetes Mellitus

BACKGROUND AND OBJECTIVES

Cetagliptin is a highly selective dipeptidyl peptidase-4 inhibitor under development to treat type 2 diabetes mellitus. This first-in-human study was conducted to characterise the pharmacokinetics, pharmacodynamics and tolerability of single-ascending oral doses of cetagliptin in healthy subjects. In addition, the effect of food on pharmacokinetics was evaluated.

METHODS

Study 1 enrolled 66 healthy subjects in a double-blind, randomised, placebo-controlled, single-dose escalation study; sitagliptin was employed as a positive open-label control. Forty-four subjects were assigned to seven cohorts (cetagliptin 12.5, 25, 50, 100, 200, 300 or 400 mg); 12 subjects were assigned to the placebo group. The remaining ten subjects received sitagliptin 100 mg as the positive control. Blood, urine and faeces were collected for the pharmacokinetic analysis and determination of plasma dipeptidyl peptidase-4 inhibition, active glucagon-like peptide-1, glucose and insulin levels. In Study 2, 14 healthy subjects were assigned to a randomised, open-label, two-period crossover study, and received a single oral dose of cetagliptin 100 mg in the fasted state or after a high-fat meal, with a 14-day washout period between treatments. Blood samples were collected to evaluate the effects of food on the pharmacokinetics of cetagliptin.

RESULTS

Following administration of a single oral dose, cetagliptin was rapidly absorbed, presenting a median time to maximum concentration of 1.0-3.25 h. The terminal half-life ranged between 25.8 and 41.3 h, which was considerably longer than that of sitagliptin. The area under the plasma concentration-time curve was approximately dose proportional between 25 mg and 400 mg, and the increase in maximum concentration was greater than dose proportional. The unchanged drug was mainly excreted in the urine (27.2-46.2% of dose) and minimally via the faeces (1.4% of dose). Dipeptidyl peptidase-4 inhibition, an increase in active glucagon-like peptide-1 and a slight decrease in blood glucose were observed, whereas insulin was not significantly altered when compared with placebo. The weighted average dipeptidyl peptidase-4 inhibition by cetagliptin 100 mg was higher than that mediated by sitagliptin 100 mg. Cetagliptin was well tolerated up to a single oral dose of 400 mg. No food effects were noted.

CONCLUSIONS

Cetagliptin inhibited plasma dipeptidyl peptidase-4 activity, increased levels of active glucagon-like peptide-1 and was well tolerated at single doses up to 400 mg, eliciting no dose-limiting toxicity in healthy volunteers. Food did not affect the pharmacokinetics of cetagliptin.

CLINICAL TRIAL REGISTRATION

The studies were registered at http://www.chinadrugtrials.org.cn (Nos. CTR20180167 and CTR20181331).

Machine learning-guided, big data-enabled, biomarker-based systems pharmacology: modeling the stochasticity of natural history and disease progression

The incidence of systemic and metabolic co-morbidities increases with aging. The purpose was to investigate a novel paradigm for modeling the orchestrated changes in many disease-related biomarkers that occur during aging. A hybrid strategy that integrates machine learning and stochastic modeling was evaluated for modeling the long-term dynamics of biomarker systems. Bayesian networks (BN) were used to identify quantitative systems pharmacology (QSP)-like models for the inter-dependencies for three disease-related datasets of metabolic (MB), metabolic with leptin (MB-L), and cardiovascular (CVB) biomarkers from the NHANES database. Biomarker dynamics were modeled using discrete stochastic vector autoregression (VAR) equations. BN were used to derive the topological order and connectivity of a data driven QSP model structure for inter-dependence of biomarkers across the lifespan. The strength and directionality of the connections in the QSP models were evaluated using bootstrapping. VAR models based on QSP model structures from BN were assessed for modeling biomarker system dynamics. BN-restricted VAR models of order 1 were identified as parsimonious and effective for characterizing biomarker system dynamics in the MB, MB-L and CVB datasets. Simulation of annual and triennial data for each biomarker provided good fits and predictions of the training and test datasets, respectively. The novel strategy harnesses machine learning to construct QSP model structures for inter-dependence of biomarkers. Stochastic modeling with the QSP models was effective for predicting the age-varying dynamics of disease-relevant biomarkers over the lifespan.

Effect of Nigella sativa oil on pharmacokinetics and pharmacodynamics of gliclazide in rats

Nigella sativa oil (NSO) has been used widely for its putative anti-hyperglycemic activity. However, little is known about its potential effect on the pharmacokinetics and pharmacodynamics of antidiabetic drugs, including gliclazide. This study aimed to investigate herb-drug interactions between gliclazide and NSO in rats. Plasma concentrations of gliclazide (single oral and intravenous dose of 33 and 26.4 mg/kg, respectively) in the presence and absence of co-administration with NSO (52 mg/kg per oral) were quantified in healthy and insulin resistant rats (n = 5 for each group). Physiological and treatment-related factors were evaluated as potential influential covariates using a population pharmacokinetic modeling approach (NONMEM version 7.4). Clearance, volume of distribution and bioavailability of gliclazide were unaffected by disease state (healthy or insulin resistant). The concomitant administration of NSO resulted in higher systemic exposures of gliclazide by modulating bioavailability (29% increase) and clearance (20% decrease) of the drug. A model-independent analysis highlighted that pre-treatment with NSO in healthy rats was associated with a higher glucose lowering effect by up to 50% compared with that of gliclazide monotherapy, but not of insulin resistant rats. Although a similar trend in glucose reductions was not observed in insulin resistant rats, co-administration of NSO improved the sensitivity to insulin of this rat population. Natural product-drug interaction between gliclazide and NSO merits further evaluation of its clinical importance.

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.

An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments

One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.

Swarm hybrid optimization for a piecewise model fitting applied to a glucose model

Purpose

The purpose of this paper is to study insulin pump therapy and accurate monitoring of glucose levels in diabetic patients, which are current research trends in diabetology. Both problems have a wide margin for improvement and promising applications in the control of parameters and levels involved.

Design/methodology/approach

The authors have registered data for the levels of glucose in diabetic patients throughout a day with a temporal resolution of 5 minutes, the amount and time of insulin administered and time of ingestion. The estimated quantity of carbohydrates is also monitored. A mathematical model for Type 1 patients was fitted piecewise to these data and the evolution of the parameters was analyzed.

Findings

They have found that the parameters for the model change abruptly throughout a day for the same patient, but this set of parameters account with precision for the evolution of the glucose levels in the test patients. This fitting technique could be used to personalize treatments for specific patients and predict the glucose-level variations in terms of hours or even shorter periods of time. This way more effective insulin pump therapies could be developed.

Originality/value

The proposed model could allow for the development of improved schedules on insulin pump therapies.

Crosstalk in transition: the translocation of Akt

Akt/PKB is an important crosstalk node at the junction between a number of major signalling pathways in the mammalian cell. As a significant nutrient sensor, Akt plays a central role in many cellular processes, including cell growth, cell survival and glucose metabolism. The dysregulation of Akt signalling is implicated in the development of many diseases, from diabetes to cancer. The translocation of Akt from cytosol to plasma membrane is a crucial step in Akt activation. Akt is initially synthesized on the endoplasmic reticulum, but translocates to the plasma membrane (PM) in response to insulin stimulation, where it may be activated. The Akt is then recycled to the cytoplasm. The activated Akt may propagate signals to downstream substrates both at the PM and in the cytosol, hence understanding the translocation dynamics is an important step in dissecting the signalling system. At the present time, however, knowledge concerning the translocation of either activated and unactivated Akt is scant. Here we present a simple, deterministic, three-compartment ordinary differential equation model of Akt translocation in vitro. This model can reproduce the salient features of Akt translocation in a manner consistent with the experimental data. Furthermore, we demonstrate that this system is equivalent to a damped harmonic oscillator, and analyse the steady state and transient behaviour of the model over the entire parameter space.

Modeling of Diabetes and Its Clinical Impact

Understanding all aspects of diabetes treatment is hindered by the complexity of this chronic disease and its multifaceted complications and comorbidities, including social and financial impacts. In vivo studies as well as clinical trials provided invaluable information for unraveling not only metabolic processes but also risk estimations of, for example, complications. These approaches are often time- and cost-consuming and have frequently been supported by simulation models. Simulation models provide the opportunity to investigate diabetes treatment from additional viewpoints and with alternative objectives. This review presents selected models focusing either on metabolic processes or risk estimations and financial outcomes to provide a basic insight into this complex subject. It also discusses opportunities and challenges of modeling diabetes.

In silico drug absorption tract: An agent-based biomimetic model for human oral drug absorption

Background

An agent-based modeling approach has been suggested as an alternative to traditional, equation-based modeling methods for describing oral drug absorption. It enables researchers to gain a better understanding of the pharmacokinetic (PK) mechanisms of a drug. This project demonstrates that a biomimetic agent-based model can adequately describe the absorption and disposition kinetics both of midazolam and clonazepam.

Methods

An agent-based biomimetic model, in silico drug absorption tract (ISDAT), was built to mimic oral drug absorption in humans. The model consisted of distinct spaces, membranes, and metabolic enzymes, and it was altogether representative of human physiology relating to oral drug absorption. Simulated experiments were run with the model, and the results were compared to the referent data from clinical equivalence trials. Acceptable similarity was verified by pre-specified criteria, which included 1) qualitative visual matching between the clinical and simulated concentration-time profiles, 2) quantitative similarity indices, namely, weighted root mean squared error (RMSE), and weighted mean absolute percentage error (MAPE) and 3) descriptive similarity which requires less than 25% difference between key PK parameters calculated by the clinical and the simulated concentration-time profiles. The model and its parameters were iteratively refined until all similarity criteria were met. Furthermore, simulated PK experiments were conducted to predict bioavailability (F). For better visualization, a graphical user interface for the model was developed and a video is available in Supporting Information.

Results

Simulation results satisfied all three levels of similarity criteria for both drugs. The weighted RMSE was 0.51 and 0.92, and the weighted MAPE was 5.99% and 8.43% for midazolam and clonazepam, respectively. Calculated PK parameter values, including area under the curve (AUC), peak plasma drug concentration (C_max), time to reach C_max (T_max), terminal elimination rate constant (Kel), terminal elimination half life (T_1/2), apparent oral clearance (CL/F), and apparent volume of distribution (V/F), were reasonable compared to the referent values. The predicted absolute oral bioavailability (F) was 44% for midazolam (literature reported value, 31–72%) and 93% (literature reported value, ≥ 90%) for clonazepam.

Conclusion

The ISDAT met all the pre-specified similarity criteria for both midazolam and clonazepam, and demonstrated its ability to describe absorption kinetics of both drugs. Therefore, the validated ISDAT can be a promising platform for further research into the use of similar in silico models for drug absorption kinetics.

Influence of Meals and Glycemic Changes on QT Interval Dynamics

Thorough QT/QTc studies have become an integral part of early drug development programs, with major clinical and regulatory implications. This analysis expands on existing pharmacodynamic models of QT interval analysis by incorporating the influence of glycemic changes on the QT interval in a semimechanistic manner. A total of 21 healthy subjects enrolled in an open-label phase 1 pilot study and provided continuous electrocardiogram monitoring and plasma glucose and insulin concentrations associated with a 24-hour baseline assessment. The data revealed a transient decrease in QTc, with peak suppression occurring approximately 3 hours after the meal. A semimechanistic modeling approach was applied to evaluate temporal delays between meals and subsequent changes that might influence QT measurements. The food effect was incorporated into a model of heart rate dynamics, and additional delayed effects of the meal on QT were incorporated using a glucose-dependent hypothetical transit compartment. The final model helps to provide a foundation for the future design and analysis of QT studies that may be confounded by meals. This study has significant implications for QT study assessment following a meal or when a cohort is receiving a medication that influences postprandial glucose concentrations.

Impact of demographics and disease progression on the relationship between glucose and HbA1c

CONTEXT

Several studies have shown that the relationship between mean plasma glucose (MPG) and glycated haemoglobin (HbA1c) may vary across populations. Especially race has previously been referred to shift the regression line that links MPG to HbA1c at steady-state (Herman & Cohen, 2012).

OBJECTIVE

To assess the influence of demographic and disease progression-related covariates on the intercept of the estimated linear MPG-HbA1c relationship in a longitudinal model.

DATA

Longitudinal patient-level data from 16 late-phase trials in type 2 diabetes with a total of 8927 subjects was used to study covariates for the relationship between MPG and HbA1c. The analysed covariates included age group, BMI, gender, race, diabetes duration, and pre-trial treatment. Differences between trials were taken into account by estimating a trial-to-trial variability component.

PARTICIPANTS

Participants included 47% females and 20% above 65years. 77% were Caucasian, 9% were Asian, 5% were Black and the remaining 9% were analysed together as other races.

ANALYSIS

Estimates of the change in the intercept of the MPG-HbA1c relationship due to the mentioned covariates were determined using a longitudinal model.

RESULTS

The analysis showed that pre-trial treatment with insulin had the most pronounced impact associated with a 0.34% higher HbA1c at a given MPG. However, race, diabetes duration and age group also had an impact on the MPG-HbA1c relationship.

CONCLUSION

Our analysis shows that the relationship between MPG and HbA1c is relatively insensitive to covariates, but shows small variations across populations, which may be relevant to take into account when predicting HbA1c response based on MPG measurements in clinical trials.

Characterizing the dynamic interaction among gastric emptying, glucose absorption, and glycemic control in nondiabetic obese adults

The effects of altered gastric emptying on glucose absorption and kinetics are not well understood in nondiabetic obese adults. The aim of this work was to develop a physiology-based model that can characterize and compare interactions among gastric emptying, glucose absorption, and glycemic control in nondiabetic obese and lean healthy adults. Dynamic glucose, insulin, and gastric emptying (measured with breath test) data from 12 nondiabetic obese and 12 lean healthy adults were available until 180 min after an oral glucose tolerance test (OGTT) with 10, 25, and 75 g of glucose. A physiology-based model was developed to characterize glucose kinetics applying nonlinear mixed-effects modeling with NONMEM7.3. Glucose kinetics after OGTT was described by a one-compartment model with an effect compartment to describe delayed insulin effects on glucose clearance. After the interactions between individual gastric emptying and glucose absorption profiles were accounted for, the glucose absorption rate was found to be similar in nondiabetic obese and lean controls. Baseline glucose concentration was estimated to be only marginally higher in nondiabetic obese subjects (4.9 vs. 5.2 mmol/l), whereas insulin-dependent glucose clearance in nondiabetic obese subjects was found to be cut in half compared with lean controls (0.052 vs. 0.029 l/min) and the insulin concentration associated with 50% of insulin-dependent glucose elimination rate was approximately twofold higher in nondiabetic obese subjects compared with lean controls (7.1 vs. 15.3 μU/ml). Physiology-based models can characterize and compare the dynamic interaction among gastric emptying, glucose absorption and glycemic control in populations of interest such as lean healthy and nondiabetic obese adults.

The variability in beta-cell function in placebo-treated subjects with type 2 diabetes: application of the weight-HbA1c-insulin-glucose (WHIG) model

AIM

The weight-glycosylated haemoglobin (HbA1C)-insulin-glucose (WHIG) model describes the effects of changes in weight on insulin sensitivity (IS) in newly diagnosed, obese subjects receiving placebo treatment. This model was applied to a wider population of placebo-treated subjects, to investigate factors influencing the variability in IS and β-cell function.

METHODS

The WHIG model was applied to the WHIG dataset (Study 1) and two other placebo datasets (Studies 2 and 3). Studies 2 and 3 consisted of nonobese subjects and subjects with advanced type 2 diabetes mellitus (T2DM). Body weight, fasting serum insulin (FSI), fasting plasma glucose (FPG) and HbA1c were used for nonlinear mixed-effects modelling (using NONMEM v7.2 software). Sources of interstudy variability (ISV) and potential covariates (age, gender, diabetes duration, ethnicity, compliance) were investigated.

RESULTS

An ISV for baseline parameters (body weight and β-cell function) was required. The baseline β-cell function was significantly lower in subjects with advanced T2DM (median difference: Study 2: 15.6%, P < 0.001; Study 3: 22.7%, P < 0.001) than in subjects with newly diagnosed T2DM (Study 1). A reduction in the estimated insulin secretory response in subjects with advanced T2DM was observed but diabetes duration was not a significant covariate.

CONCLUSION

The WHIG model can be used to describe the changes in weight, IS and β-cell function in the diabetic population. IS remained relatively stable between subjects but a large ISV in β-cell function was observed. There was a trend towards decreasing β-cell responsiveness with diabetes duration, and further studies, incorporating subjects with a longer history of diabetes, are required.

Disease Progression Modeling: Key Concepts and Recent Developments

Disease modeling involves the use of mathematical functions to describe quantitatively the time course of disease progression. In order to characterize the natural progression of disease, these models generally incorporate longitudinal data for some biomarker(s) of disease severity or can incorporate more direct measures of disease severity. Disease models are also often linked to pharmacokinetic-pharmacodynamic models so that the influence of drug treatment on disease progression can be quantified and evaluated. Regulatory agencies have embraced disease progression models as powerful tools that can be used to improve drug development productivity. This article provides a brief overview of key concepts in disease progression modeling followed by illustrative examples from models for Alzheimer's disease. Finally, recent novel applications in which disease progression models have been linked to cost-effectiveness analysis and genomic analysis are described.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

Evaluation of the long-term durability and glycemic control of fasting plasma glucose and glycosylated hemoglobin for pioglitazone in Japanese patients with type 2 diabetes

BACKGROUND

This study applied a pharmacodynamic model-based approach to evaluate the long-term durability and glycemic control of pioglitazone in comparison with other oral glucose-lowering drugs in Japanese type 2 diabetes mellitus (T2DM) patients.

SUBJECTS AND METHODS

Japanese T2DM patients were enrolled in a prospective, randomized, open-label, blinded-end point study and received pioglitazone with or without other oral glucose-lowering drugs (excluding another thiazolidinedione [TZD]) (n=293) or oral glucose-lowering drugs excluding TZD (n=294). Treatment was adjusted to achieve glycosylated hemoglobin (HbA1c) <6.9%, and samples for fasting plasma glucose (FPG) and HbA1c were collected over 2.5-4 years. A simultaneous cascading indirect response model structure was applied to describe the time course of FPG and HbA1c. HbA1c levels were described using both an FPG-dependent and an FPG-independent function. To account for titration, drug effects for both treatment groups were implemented using a time-dependent Emax model.

RESULTS

Pioglitazone was superior in both time to maximum effect and the magnitude of reduction achieved in FPG and HbA1c. A greater reduction in median FPG (-21 mg/dL vs. -9 mg/dL) was observed with pioglitazone (P<0.05). Maximum drug effect for FPG was predicted to occur earlier (11 months) for pioglitazone than for the control group (14 months). The simulated additional reduction in FPG and HbA1c achieved with pioglitazone was predicted to be maintained beyond the currently observed study duration.

CONCLUSIONS

Pioglitazone was found to result in improved glycemic control and durability compared with control treatment. This model-based approach enabled the quantification of differences in FPG and HbA1c for both treatment groups and simulation to evaluate longer-term durability on FPG and HbA1c.

A receptor state space model of the insulin signalling system in glucose transport

Insulin is a potent peptide hormone that regulates glucose levels in the blood. Insulin-sensitive cells respond to insulin stimulation with the translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM), enabling the clearance of glucose from the blood. Defects in this process can give rise to insulin resistance and ultimately diabetes. One widely cited model of insulin signalling leading to glucose transport is that of Sedaghat et al. (2002) Am. J. Physiol. Endocrinol. Metab. 283, E1084-E1101. Consisting of 20 deterministic ordinary differential equations (ODEs), it is the most comprehensive model of insulin signalling to date. However, the model possesses some major limitations, including the non-conservation of key components. In the current work, we detail mathematical and sensitivity analyses of the Sedaghat model. Based on the results of these analyses, we propose a reduced state space model of the insulin receptor subsystem. This reduced model maintains the input-output relation of the original model but is computationally more efficient, analytically tractable and resolves some of the limitations of the Sedaghat model.

Using physiologically-based pharmacokinetic-guided "body-on-a-chip" systems to predict mammalian response to drug and chemical exposure

The continued development of in vitro systems that accurately emulate human response to drugs or chemical agents will impact drug development, our understanding of chemical toxicity, and enhance our ability to respond to threats from chemical or biological agents. A promising technology is to build microscale replicas of humans that capture essential elements of physiology, pharmacology, and/or toxicology (microphysiological systems). Here, we review progress on systems for microscale models of mammalian systems that include two or more integrated cellular components. These systems are described as a "body-on-a-chip", and utilize the concept of physiologically-based pharmacokinetic (PBPK) modeling in the design. These microscale systems can also be used as model systems to predict whole-body responses to drugs as well as study the mechanism of action of drugs using PBPK analysis. In this review, we provide examples of various approaches to construct such systems with a focus on their physiological usefulness and various approaches to measure responses (e.g. chemical, electrical, or mechanical force and cellular viability and morphology). While the goal is to predict human response, other mammalian cell types can be utilized with the same principle to predict animal response. These systems will be evaluated on their potential to be physiologically accurate, to provide effective and efficient platform for analytics with accessibility to a wide range of users, for ease of incorporation of analytics, functional for weeks to months, and the ability to replicate previously observed human responses.

Meta-modeling of methylprednisolone effects on glucose regulation in rats

A retrospective meta-modeling analysis was performed to integrate previously reported data of glucocorticoid (GC) effects on glucose regulation following a single intramuscular dose (50 mg/kg), single intravenous doses (10, 50 mg/kg), and intravenous infusions (0.1, 0.2, 0.3 and 0.4 mg/kg/h) of methylprednisolone (MPL) in normal and adrenalectomized (ADX) male Wistar rats. A mechanistic pharmacodynamic (PD) model was developed based on the receptor/gene/protein-mediated GC effects on glucose regulation. Three major target organs (liver, white adipose tissue and skeletal muscle) together with some selected intermediate controlling factors were designated as important regulators involved in the pathogenesis of GC-induced glucose dysregulation. Assessed were dynamic changes of food intake and systemic factors (plasma glucose, insulin, free fatty acids (FFA) and leptin) and tissue-specific biomarkers (cAMP, phosphoenolpyruvate carboxykinase (PEPCK) mRNA and enzyme activity, leptin mRNA, interleukin 6 receptor type 1 (IL6R1) mRNA and Insulin receptor substrate-1 (IRS-1) mRNA) after acute and chronic dosing with MPL along with the GC receptor (GR) dynamics in each target organ. Upon binding to GR in liver, MPL dosing caused increased glucose production by stimulating hepatic cAMP and PEPCK activity. In adipose tissue, the rise in leptin mRNA and plasma leptin caused reduction of food intake, the exogenous source of glucose input. Down-regulation of IRS-1 mRNA expression in skeletal muscle inhibited the stimulatory effect of insulin on glucose utilization further contributing to hyperglycemia. The nuclear drug-receptor complex served as the driving force for stimulation or inhibition of downstream target gene expression within different tissues. Incorporating information such as receptor dynamics, as well as the gene and protein induction, allowed us to describe the receptor-mediated effects of MPL on glucose regulation in each important tissue. This advanced mechanistic model provides unique insights into the contributions of major tissues and quantitative hypotheses for the multi-factor control of a complex metabolic system.

Longitudinal Modeling of the Relationship Between Mean Plasma Glucose and HbA1c Following Antidiabetic Treatments

Late-phase clinical trials within diabetes generally have a duration of 12–24 weeks, where 12 weeks may be too short to reach steady-state glycated hemoglobin (HbA1c). The main determinant for HbA1c is blood glucose, which reaches steady state much sooner. In spite of this, few publications have used individual data to assess the time course of both glucose and HbA1c, for predicting HbA1c. In this paper, we present an approach for predicting HbA1c at end-of-trial (24–28 weeks) using glucose and HbA1c measurements up to 12 weeks. The approach was evaluated using data from 4 trials covering 12 treatment arms (oral antidiabetic drug, glucagon-like peptide-1, and insulin treatment) with measurements at 24–28 weeks to evaluate predictions vs. observations. HbA1c percentage was predicted for each arm at end-of-trial with a mean prediction error of 0.14% [0.01;0.24]. Furthermore, end points in terms of HbA1c reductions relative to comparator were accurately predicted. The proposed model provides a good basis to optimize late-stage clinical development within diabetes.

Population pharmacodynamic modeling of exenatide after 2-week treatment in STZ/NA diabetic rats

The purpose of this study is to investigate the effect of exenatide on glycemic control following two administration routes in a streptozotocin/nicotinamide (STZ/NA)-induced diabetic rat model, and to develop a pharmacodynamic model to better understand the disease progression and the action of exenatide in this experimental system. Two groups of STZ/NA-induced diabetic rats were treated for 2 weeks with 20 (μg/kg/day) of exenatide, either by continuous subcutaneous (SC) infusion or two SC injections daily. Disease progression was associated with slower glucose utilization. Fasting blood glucose was significantly reduced by 30 mg/dL in both treatment groups at the end of 2 weeks. A subsequent intravenous glucose tolerance test (IVGTT) confirmed an improved glucose tolerance in both treatment groups; however, overall glycemic control was similar between groups, likely due to the relatively low and short-term drug exposure. A population indirect response model was successfully developed to simultaneously describe the STZ/NA-induced disease progression, responses to an IVGTT, and exenatide effects on these systemic challenges. The unified model includes a single set of parameters, and the cumulative area under the drug-receptor concentration curve was used as a unique driving force to account for systemic effects long after drug elimination.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

Moving from basic toward systems pharmacodynamic models

Building upon many classical foundations of pharmacology, a diverse array of mechanistic pharmacokinetic-pharmacodynamic (PK/PD) models have emerged based on mechanisms of drug action and primary rate-limiting or turnover processes in physiology. An array of basic models can be extended to handle various complexities including tolerance and can readily be employed as building blocks in assembling enhanced PK/PD or small systems models. Our corticosteroid models demonstrate these concepts as well as elements of horizontal and vertical integration of molecular to whole-body processes. The potential advantages and challenges in moving PK/PD toward systems models are described.

Population PK/PD analysis of metformin using the signal transduction model

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT

Metformin, a biguanide glucose lowering agent, is commonly used to manage type 2 diabetes. The molecular mechanisms of metformin have not been fully identified, but turnover of biomarkers such as glucose and signalling pathways or translocation of glucose transporters are closely related to the glucose-lowering effects of metformin. The PK/PD of metformin have been investigated in healthy humans and patients with type 2 diabetes mellitus and modelling has been performed using an indirect response model.

WHAT THIS STUDY ADDS

The purpose of this investigation was to develop a population PK/PD model for metformin using a signal transduction model in healthy humans and predict the PK/PD profile in patients with type 2 diabetes. The aim was to compare a previous model (a biophase model) with the signal transduction model, and use a more appropriate model to follow the actions of metformin. Additionally, our developed model was appropriate to predict the time course of plasma metformin and fasting plasma glucose (FPG) concentrations in patients with type 2 diabetes. To our knowledge, this is the first published population PK/PD analysis using the signal transduction model for metformin. AIMS To develop a population pharmacokinetic (PK) and pharmacodynamic (PD) model for metformin (500 mg) using the signal transduction model in healthy humans and to predict the PK/PD profile in patients with type 2 diabetes.

METHODS

Following the oral administration of 500 mg metformin to healthy humans, plasma concentrations of metformin were measured using LC-MS/MS. A sequential modelling approach using NONMEM VI was used to facilitate data analysis. Monte Carlo simulation was performed to predict the antihyperglycaemic effect in patients with type 2 diabetes.

RESULTS

Forty-two healthy humans were included in the study. Population mean estimates (relative standard error, RSE) of apparent clearance, apparent volume of distribution and the absorption rate constant were 52.6 l h(-1) (4.18%), 113 l (56.6%) and 0.41 h(-1) , respectively. Covariate analyses revealed that creatinine clearance (CL(CR) ) significantly influenced metformin: CL/F= 52.6 × (CL(cr) /106.5)(0.782) . The signal transduction model was applied to describe the antihyperglycaemic effect of metformin. The population means for efficacy, potency, transit time and the Hill coefficient were estimated to be 19.8 (3.17%), 3.68 µg ml(-1) (3.89%), 0.5 h (2.89%) and 0.547 (9.05%), respectively. The developed model was used to predict the antihyperglycaemic effect in patients with type 2 diabetes. The predicted plasma glucose concentration value was similar to previous values.

CONCLUSIONS

The population signal transduction model was developed and evaluated for metformin use in healthy volunteers. Model evaluation by non-parametric bootstrap analysis suggested that the proposed model was robust and parameter values were estimated with good precision.

Pharmacometric Approaches to Guide Dose Selection of the Novel GPR40 Agonist TAK-875 in Subjects With Type 2 Diabetes Mellitus

The G-protein-coupled receptor 40 agonist (GPR40) TAK-875 is being developed as an adjunct to diet and exercise to improve glycemic control in patients with type 2 diabetes mellitus. Pharmacometric approaches such as model-based exposure-response and meta-analyses were applied to (i) characterize exposure/dose–efficacy responses of TAK-875, (ii) characterize the time course of glycosylated hemoglobin A1c (HbA1c) response with TAK-875 6.25 to 200 mg q.d. doses for 12 weeks, (iii) project and compare HbA1c response with dipeptidyl peptidase 4 (DPP-4) inhibitors and TAK-875 up to 24 weeks, and (iv) provide a quantitative rationale for dose selection in phase 3. On the basis of phase 2 data, relationships between TAK-875 concentrations and HbA1c were well characterized by exposure–response models. EC₅₀ and E_max of TAK-875 were estimated to be 3.16 µg/ml and 0.366, respectively. Model-based simulations over 24 weeks indicated that the 25- and 50-mg q.d. doses of TAK-875 achieve efficacy as comparable with or better than that of commonly used antidiabetic agents.

Assessment of glycemic response to an oral glucokinase activator in a proof of concept study: application of a semi-mechanistic, integrated glucose-insulin-glucagon model

A proof of concept study was conducted to investigate the safety and tolerability of a novel oral glucokinase activator, LY2599506, during multiple dose administration to healthy volunteers and subjects with Type 2 diabetes mellitus (T2DM). To analyze the study data, a previously established semi-mechanistic integrated glucose-insulin model was extended to include characterization of glucagon dynamics. The model captured endogenous glucose and insulin dynamics, including the amplifying effects of glucose on insulin production and of insulin on glucose elimination, as well as the inhibitory influence of glucose and insulin on hepatic glucose production. The hepatic glucose production in the model was increased by glucagon and glucagon production was inhibited by elevated glucose concentrations. The contribution of exogenous factors to glycemic response, such as ingestion of carbohydrates in meals, was also included in the model. The effect of LY2599506 on glucose homeostasis in subjects with T2DM was investigated by linking a one-compartment, pharmacokinetic model to the semi-mechanistic, integrated glucose-insulin-glucagon system. Drug effects were included on pancreatic insulin secretion and hepatic glucose production. The relationships between LY2599506, glucose, insulin, and glucagon concentrations were described quantitatively and consequently, the improved understanding of the drug-response system could be used to support further clinical study planning during drug development, such as dose selection.

Study reanalysis using a mechanism-based pharmacokinetic/pharmacodynamic model of pramlintide in subjects with type 1 diabetes

This report describes a pharmacokinetic/pharmacodynamic model for pramlintide, an amylinomimetic, in type 1 diabetes mellitus (T1DM). Plasma glucose and drug concentrations were obtained following bolus and 2-h intravenous infusions of pramlintide at three dose levels or placebo in 25 T1DM subjects during the postprandial period in a crossover study. The original clinical data were reanalyzed by mechanism-based population modeling. Pramlintide pharmacokinetics followed a two-compartment model with zero-order infusion and first-order elimination. Pramlintide lowered overall postprandial plasma glucose AUC (AUC(net)) and delayed the time to peak plasma glucose after a meal (T (max)). The delay in glucose T (max) and reduction of AUC(net) indicate that overall plasma glucose concentrations might be affected by differing mechanisms of action of pramlintide. The observed increase in glucose T (max) following pramlintide treatment was independent of dose within the studied dose range and was adequately described by a dose-independent, maximum pramlintide effect on gastric emptying of glucose in the model. The inhibition of endogenous glucose production by pramlintide was described using a sigmoidal function with capacity and sensitivity parameter estimates of 0.995 for I (max) and 23.8 pmol/L for IC(50). The parameter estimates are in good agreement with literature values and the IC(50) is well within the range of postprandial plasma amylin concentrations in healthy humans, indicating physiological relevance of the pramlintide effect on glucagon secretion in the postprandial state. This model may prove to be useful in future clinical studies of other amylinomimetics or antidiabetic drugs with similar mechanisms of action.