Mathematical Modelling of Glucose-Dependent Insulinotropic Polypeptide and Glucagon-like Peptide-1 following Ingestion of Glucose.

The incretin hormones, glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1), play an important role in glucose homeostasis by potentiating glucose-induced insulin secretion. Furthermore, GLP-1 has been reported to play a role in glucose homeostasis by inhibiting glucagon secretion and delaying gastric emptying. As the insulinotropic effect of GLP-1 is preserved in patients with type 2 diabetes (T2D), therapies based on GLP-1 have been developed in recent years, and these have proven to be efficient in the treatment of T2D. The endogenous secretion of both GIP and GLP-1 is stimulated by glucose in the small intestine, and the release is dependent on the amount. In this work, we developed a semimechanistic model describing the release of GIP and GLP-1 after ingestion of various glucose doses in healthy volunteers and patients with T2D. In the model, the release of both hormones is stimulated by glucose in the proximal small intestine, and no differences in the secretion dynamics between healthy individuals and patients with T2D were identified after taking differences in glucose profiles into account.

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.

A reversible albumin-binding growth hormone derivative is well tolerated and possesses a potential once-weekly treatment profile.

CONTEXT: Human growth hormone (hGH) replacement therapy currently requires daily sc injections for years/lifetime, which may be both inconvenient and distressing for patients. NNC0195-0092 is a novel hGH derivative intended for once-weekly treatment of GH deficiency. A noncovalent albumin binding moiety is attached to the hGH backbone. Clearance is reduced as a consequence of a reversible binding to circulating serum albumin, which prolongs the pharmacodynamic (PD) effect. OBJECTIVE: To evaluate safety, local tolerability, pharmacokinetics (PK), and pharmacodynamics (PD) of a single dose (SD) and multiple doses (MD) of NNC0195-0092. SETTING AND DESIGN: Randomized, single-center, placebo-controlled, double-blind, SD/MD, dose-escalation trial of 105 healthy male subjects. NNC0195-0092 sc administration: Five cohorts of eight subjects received one dose of NNC0195-0092 (0.01-0.32 mg/kg) (n = 6) or placebo (n = 2). Sixteen subjects (equal numbers of Japanese and non-Asian) received once-weekly doses of NNC0195-0092 (0.02-0.24 mg/kg; n=12) or placebo (n=4) for 4 weeks. Blood samples were drawn for assessment of safety, PK, IGF-1, and IGF binding protein 3 profiles and anti-drug antibodies. RESULTS: SD and MD of NNC0195-0092 were well tolerated at all dose levels. No safety concerns or local tolerability issues were identified. A dose-dependent IGF-1 response was observed. IGF-1 profiles suggest that NNC0195-0092 may be suitable for once-weekly dosing, with a clinically relevant dose ≤0.08 mg/kg/week. No differences in PK and PD were observed between Japanese and non-Asian subjects. CONCLUSIONS: SD and MD of NNC0195-0092 administered to healthy Japanese and non-Asian male subjects were well tolerated at all doses. The present trial suggests that NNC0195-0092 has the potential for an efficacious, well-tolerated, once-weekly GH treatment.

Modeling of 24-hour glucose and insulin profiles in patients with type 2 diabetes mellitus treated with biphasic insulin aspart.

Insulin therapy for diabetes patients is designed to mimic the endogenous insulin response of healthy subjects and thereby generate normal blood glucose levels. In order to control the blood glucose in insulin-treated diabetes patients, it is important to be able to predict the effect of exogenous insulin on blood glucose. A pharmacokinetic/pharmacodynamic model for glucose homoeostasis describing the effect of exogenous insulin would facilitate such prediction. Thus the aim of this work was to extend the previously developed integrated glucose-insulin (IGI) model to predict 24-hour glucose profiles for patients with Type 2 diabetes following exogenous insulin administration. Clinical data from two trials were included in the analysis. In both trials, 24-hour meal tolerance tests were used as the experimental setup, where exogenous insulin (biphasic insulin aspart) was administered in relation to meals. The IGI model was successfully extended to include the effect of exogenous insulin. Circadian variations in glucose homeostasis were assessed on relevant parameters, and a significant improvement was achieved by including a circadian rhythm on the endogenous glucose production in the model. The extended model is a useful tool for clinical trial simulation and for elucidating the effect profile of new insulin products.

Insulin degludec: pharmacokinetic properties in subjects with hepatic impairment.

BACKGROUND AND OBJECTIVE: Insulin degludec is a basal insulin with a slow and distinct absorption mechanism resulting in an ultra-long, flat, and stable pharmacokinetic profile in patients with diabetes mellitus. The aim of this study was to examine the effect of hepatic impairment on the single-dose pharmacokinetics of insulin degludec. METHODS: Twenty-four subjects, allocated to one of four groups (n=6 per group) based on level of hepatic impairment (normal hepatic function, Child-Pugh grade A, B, or C), were administered a single subcutaneous dose of 0.4 U/kg insulin degludec. Blood samples up to 120 h post-dose and fractionated urine samples were collected to measure pharmacokinetic parameters. RESULTS: No difference was observed in pharmacokinetic parameters [area under the 120-h serum insulin degludec concentration-time curve (AUC120 h), maximum insulin degludec concentration (C max), and apparent clearance (CL/F)] for subjects with impaired versus normal hepatic function after a single dose of insulin degludec. The geometric mean [coefficient of variation (CV) %] AUC120 h values were 89,092 (16), 83,327 (15), 88,944 (23), and 79,846 (19) pmol·h/L for normal hepatic function and mild, moderate, and severe hepatic impairment, respectively. Simulated steady-state insulin degludec pharmacokinetic profiles showed an even distribution of exposure across a 24-h dosing interval regardless of hepatic function status. CONCLUSIONS: The ultra-long pharmacokinetic properties of insulin degludec were preserved in subjects with hepatic impairment and there were no statistically significant differences in absorption or clearance compared with subjects with normal hepatic function.

Insulin degludec: pharmacokinetics in patients with renal impairment.

BACKGROUND: Insulin degludec is a new-generation basal insulin with an ultra-long duration of action. We evaluated the pharmacokinetic properties of insulin degludec in subjects with normal renal function; mild, moderate or severe renal impairment; or end-stage renal disease (ESRD) undergoing hemodialysis. METHODS: Thirty subjects (n = 6 per group) received a single subcutaneous dose of 0.4 U/kg insulin degludec. Blood samples up to 120 h post-dose and fractionated urine samples were collected. RESULTS: The ultra-long pharmacokinetic properties of insulin degludec were preserved in subjects with renal impairment, with no statistically significant differences in absorption or clearance, compared with subjects with normal renal function. In subjects with ESRD, pharmacokinetic parameters were similar whether the insulin degludec pharmacokinetic assessment period included hemodialysis or not, and total exposure was comparable to subjects with normal renal function. Simulated mean steady-state pharmacokinetic profiles were comparable between groups. CONCLUSION: This study indicated dose adjustments due to impaired renal function should not be required for insulin degludec.

Determination of myosin filament orientations in electron micrographs of muscle cross sections.

An automated image analysis system for determining myosin filament azimuthal rotations, or orientations, in electron micrographs of muscle cross sections is described. The micrographs of thin sections intersect the myosin filaments which lie on a triangular lattice. The myosin filament profiles are variable and noisy, and the images exhibit a variable contrast and background. Filament positions are determined by filtering with a point spread function that incorporates the local symmetry of the lattice. Filament orientations are determined by correlation with a template that incorporates the salient filament characteristics, and the orientations are classified using a Gaussian mixture model. The precision of the technique is assessed by application to a variety of micrographs and comparison with manual classification of the orientations. The system provides a convenient, robust, and rapid means of analysing micrographs containing many filaments to study the distribution of filament orientations.

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.