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OBJECTIVE Endogenous insulin clearance (EIC) is physiologically reduced at increasing insulin secretion rate (ISR). Computing EIC at the prevailing ISR does not distinguish the effects of hypersecretion from those of other mechanisms of glucose homeostasis. We aimed to measure EIC in standardized ISR conditions (i.e., at fixed ISR levels) and to analyze its associations with relevant physiologic factors. RESEARCH DESIGN AND METHODS We estimated standardized EIC (EICISR) by mathematical modeling in nine different studies with insulin and glucose infusions (N = 2,067). EICISR association with various traits was analyzed by stepwise multivariable regression in studies with both euglycemic clamp and oral glucose tolerance test (OGTT) (N = 1,410). We also tested whether oral glucose ingestion, as opposed to intravenous infusion, has an independent effect on EIC (N = 1,555). RESULTS Insulin sensitivity (as M/I from the euglycemic clamp) is the strongest determinant of EICISR, approximately four times more influential than insulin resistance–related hypersecretion. EICISR independently associates positively with M/I, fasting and mean OGTT glucose or type 2 diabetes, and β-cell glucose sensitivity and negatively with African American or Hispanic race, female sex, and female age. With oral glucose ingestion, an ISR-independent ∼10% EIC reduction is necessary to explain the observed insulin concentration profiles. CONCLUSIONS Based on EICISR, we posit the existence of two adaptive processes involving insulin clearance: the first reduces EICISR with insulin resistance (not with higher BMI per se) and is more relevant than the concomitant hypersecretion; the second reduces EICISR with β-cell dysfunction. These processes are dysregulated in type 2 diabetes. Finally, oral glucose ingestion per se reduces insulin clearance.

Aims: Hypertriglyceridemia is associated with an increased risk of type 2 diabetes. We aimed to comprehensively examine the effects of hypertriglyceridemia on major glucose homeostatic mechanisms involved in diabetes progression.Methods: In this randomized, cross-over, single-blinded study, two dual-labeled, 3-hour oral glucose tolerance tests were performed during 5-hour intravenous infusions of either 20 % Intralipid or saline in 12 healthy subjects (age 27.9 ± 2.6 years, 11 men, BMI 22.6 ± 1.4 kg/m2) to evaluate lipid-induced changes in insulin metabolism and glucose kinetics. Insulin sensitivity, β cell secretory function, and insulin clearance were assessed by modeling glucose, insulin and C-peptide data. Intestinal glucose absorption, endogenous glucose production, and glucose clearance were assessed from glucose tracers. The effect of triglycerides on β-cell secretory function was examined in perifusion experiments in murine pseudoislets and human pancreatic islets.Results: Mild acute hypertriglyceridemia impaired oral glucose tolerance (mean glucose: +0.9 [0.3, 1.5] mmol/L, p = 0.008) and whole-body insulin sensitivity (Matsuda index: -1.67 [-0.50, -2.84], p = 0.009). Post-glucose hyperinsulinemia (mean insulin: +99 [17, 182] pmol/L, p = 0.009) resulted from reduced insulin clearance (-0.16 [-0.32, -0.01] L min-1 m-2, p = 0.04) and enhanced hyperglycemia-induced total insulin secretion (+11.9 [1.1, 22.8] nmol/m2, p = 0.02), which occurred despite a decline in model-derived β cell glucose sensitivity (-41 [-74, -7] pmol min-1 m-2 mmol-1 L, p = 0.04). The analysis of tracer-derived glucose metabolic fluxes during lipid infusion revealed lower glucose clearance (-96 [-152, -41] mL/kgFFM, p = 0.005), increased 2-hour oral glucose absorption (+380 [42, 718] μmol/kgFFM, p = 0.04) and suppressed endogenous glucose production (-448 [-573, -123] μmol/kgFFM, p = 0.005). High-physiologic triglyceride levels increased acute basal insulin secretion in murine pseudoislets (+11 [3, 19] pg/aliquot, p = 0.02) and human pancreatic islets (+286 [59, 512] pg/islet, p = 0.02).Conclusion: Our findings support a critical role for hypertriglyceridemia in the pathogenesis of type 2 diabetes in otherwise healthy individuals and dissect the glucose homeostatic mechanisms involved, encompassing insulin sensitivity, β cell function and oral glucose absorption.

OBJECTIVE We investigated the processes underlying glycemic deterioration in type 2 diabetes (T2D). RESEARCH DESIGN AND METHODS A total of 732 recently diagnosed patients with T2D from the Innovative Medicines Initiative Diabetes Research on Patient Stratification (IMI DIRECT) study were extensively phenotyped over 3 years, including measures of insulin sensitivity (OGIS), β-cell glucose sensitivity (GS), and insulin clearance (CLIm) from mixed meal tests, liver enzymes, lipid profiles, and baseline regional fat from MRI. The associations between the longitudinal metabolic patterns and HbA1c deterioration, adjusted for changes in BMI and in diabetes medications, were assessed via stepwise multivariable linear and logistic regression. RESULTS Faster HbA1c progression was independently associated with faster deterioration of OGIS and GS and increasing CLIm; visceral or liver fat, HDL-cholesterol, and triglycerides had further independent, though weaker, roles (R2 = 0.38). A subgroup of patients with a markedly higher progression rate (fast progressors) was clearly distinguishable considering these variables only (discrimination capacity from area under the receiver operating characteristic = 0.94). The proportion of fast progressors was reduced from 56% to 8–10% in subgroups in which only one trait among OGIS, GS, and CLIm was relatively stable (odds ratios 0.07–0.09). T2D polygenic risk score and baseline pancreatic fat, glucagon-like peptide 1, glucagon, diet, and physical activity did not show an independent role. CONCLUSIONS Deteriorating insulin sensitivity and β-cell function, increasing insulin clearance, high visceral or liver fat, and worsening of the lipid profile are the crucial factors mediating glycemic deterioration of patients with T2D in the initial phase of the disease. Stabilization of a single trait among insulin sensitivity, β-cell function, and insulin clearance may be relevant to prevent progression.

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.

AIMS: Sleeping oxygen saturation (SaO(2)) and sleep stage duration have been linked with prediabetic alterations but the pathogenic pathways are not well understood. This study of insulin sensitive and resistant adults examined the effect on postprandial metabolic regulation of repeated mixed-meal challenges of different carbohydrate loading. The aim was to examine whether the relationship between lower sleeping oxygen saturation (SaO(2)) and poorer fasting and postprandial metabolic function may be linked with reduced slow wave sleep (SWS) and rapid eye movement (REM) duration, independent of age, sex and total adiposity. METHODS: The 24 men and women, aged 25–54 years, had no diabetes or other diagnosed conditions, were evaluated with polysomnography to derive indices of SaO(2) and sleep architecture. In addition, an OGTT and two 14-hour serial mixed-meal tests were administered over 3 successive in-patient days. The carbohydrate content of the mixed-meals was manipulated to compare a standard-load day with a double-load day (300 vs. 600 kcal/meal). Quantitative modeling was applied to derive β-cell glucose sensitivity (β-GS), early insulin secretion rate sensitivity (ESRS), and total postprandial insulinemia (AUC(INS)). RESULTS: Analyses showed that, for the 14-hour tests, the SaO(2) relationship with metabolic outcomes was associated significantly with percent time spent in REM but not SWS, independent of age, sex and total adiposity. Specifically, indirect pathways indicated that lower SaO(2) was related to shorter REM duration, and shorter REM was respectively associated with higher β-GS, ESRS, and AUC(INS) for the 300- and 600-load days (300 kcal/meal: β=−8.68, p

Summary The presentation and underlying pathophysiology of type 2 diabetes (T2D) is complex and heterogeneous. Recent studies attempted to stratify T2D into distinct subgroups using data-driven approaches, but their clinical utility may be limited if categorical representations of complex phenotypes are suboptimal. We apply a soft-clustering (archetype) method to characterize newly diagnosed T2D based on 32 clinical variables. We assign quantitative clustering scores for individuals and investigate the associations with glycemic deterioration, genetic risk scores, circulating omics biomarkers, and phenotypic stability over 36 months. Four archetype profiles represent dysfunction patterns across combinations of T2D etiological processes and correlate with multiple circulating biomarkers. One archetype associated with obesity, insulin resistance, dyslipidemia, and impaired β cell glucose sensitivity corresponds with the fastest disease progression and highest demand for anti-diabetic treatment. We demonstrate that clinical heterogeneity in T2D can be mapped to heterogeneity in individual etiological processes, providing a potential route to personalized treatments., Graphical abstract, Highlights • Soft clustering based on 32 phenotypes identified 4 quantitative archetypes • These reflect different patterns of dysfunction across T2D etiological processes • The four archetypes are different in disease progression, GRSs, and omics signals • Some patients are dominated by one archetype, but many have etiological combinations, Wesolowska-Andersen et al. represent the clinical heterogeneity of newly diagnosed T2D as four quantitative archetype profiles reflecting patterns of dysfunction in disease etiological processes, rather than clustering individuals into categorical subgroups as attempted by others. The archetype profiles differ in genetic risk scores, disease progression, and circulating omics biomarkers.

To explore the effects of a single dose of the DPP-4 inhibitor sitagliptin on glucose-standardized insulin secretion and β-cell glucose sensitivity after meal ingestion, 12 healthy and 12 drug-naive, well-controlled type 2 diabetes (T2D) subjects (mean HbA1c 43mmol/mol, 6.2%) received sitagliptin (100mg) or placebo before a meal (525kcal). β-cell function was measured as the insulin secretory rate at a standardized glucose concentration and the β-cell glucose sensitivity (the slope between glucose and insulin secretory rate). Incretin levels were also monitored. Sitagliptin increased standardized insulin secretion, in both healthy and T2D subjects, compared to placebo, but without increasing β-cell glucose sensitivity. Sitagliptin also increased active glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1) and reduced total (reflecting the secretion) GIP, but not total GLP-1 levels. We conclude that a single dose of DPP-4 inhibition induces dissociated effects on different aspects of β-cell function and incretin hormones after meal ingestion in both healthy and well-controlled T2D subjects. (Less)

PharmML is an XML-based exchange format created with a focus on nonlinear mixed-effect (NLME) models used in pharmacometrics, but providing a very general framework that also allows describing mathematical and statistical models such as single-subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility.

Recent work on Model Informed Drug Discovery and Development (MID3) has noted the need for clarity in model description used in quantitative disciplines such as pharmacology and statistics. 1-3 Cur ...

Background: Glucose is a natural ligand for sweet taste receptors (STRs) that are expressed on the tongue and in the gastrointestinal tract. Whether STRs directly contribute to the regulation of glucose homeostasis in response to glucose ingestion is unclear.Objective: We sought to determine the metabolic effects of the pharmacologic inhibition of STRs in response to an oral glucose load in healthy lean participants.Design: Ten healthy lean participants with a body mass index (in kg/m2) of 22.4 ± 0.8 were subjected to an oral-glucose-tolerance test (OGTT) on 4 separate days with the use of a randomized crossover design. Ten minutes before the 75-g OGTT, participants consumed a preload solution of either 300 parts per million (ppm) saccharin or water with or without the addition of 500 ppm lactisole, a human-specific inhibitor of STRs. When present, lactisole was included in both the preload and OGTT solutions. We assessed plasma responses of glucose, insulin, C-peptide, glucagon, glucagon-like peptides 1 and 2, gastric inhibitory peptide, acetaminophen, and 3-O-methylglucose. With the use of mathematical modeling, we estimated gastric emptying, glucose absorption, β-cell function, insulin sensitivity and clearance, and the portal insulin:glucagon ratio.Results: The addition of lactisole to the OGTT caused increases in the plasma responses of insulin (P = 0.012), C-peptide (P = 0.004), and the insulin secretory rate (P = 0.020) compared with the control OGTT. The addition of lactisole also caused a slight reduction in the insulin sensitivity index independent of prior saccharin consumption (P < 0.025). The ingestion of saccharin before the OGTT did not alter any of the measured variables but eliminated the effects of lactisole on the OGTT.Conclusion: The pharmacologic inhibition of STRs in the gastrointestinal tract alters insulin responses during an oral glucose challenge in lean healthy participants. This trial was registered at clinicaltrials.gov as NCT02835859.

Plasma proteins can provide valuable insights on human health and disease states. Within the framework of the EU IMI project DIRECT (https://www.direct-diabetes.org), we used a set of affinity proteomic methods to profile > 3100 study participants at baseline. Multiplexed assays quantified more than 600 unique proteins in EDTA plasma from this multi-center cohort that included 2300 subjects at risk of developing T2D (HbA1c ~ 6-6.5%) as well as 800 with early T2D (HbA1c > 6.5%). Using extensive clinical and other omics metadata available, the aim of the investigation was to identify plasma proteins associated with baseline traits. An initial analysis highlighted the importance of considering sample-related and pre-analytical variables as possible confounders in the data analysis. Hence, we used linear mixed models that included several parameters such as age, sex, study center and collection date. Next, we defined proteins associating with any of the >50 quantitative clinical traits at baseline. We found more than 300 proteins in plasma that were associated with diabetes related traits (adjusted p-value < 0.0001), many of which were prominently associated with BMI. The shortlisted candidates included leptin which associates with waist circumference and BMI; IGFBP1 and IGFBP2 to Matsuda; adiponectin to basal insulin secretion rate and fasting HDL; LDL receptor proteins to fasting triglycerides; APOM to fasting cholesterol; or IL8 and MCP-1 to fasting AST. In addition, we performed pQTL analysis to assess any connection between the protein values in plasma and genetic variants. We observed >400 cis-pQTLs (q-value < 0.05), such as for APOM (rs2736163, p = 5.15 e-24), which illustrated that many of the studied protein profiles are affected by a genetic component. With follow-up samples collected 3-4 years after starting the study, the baseline values will serve as valuable indicators of progression and allow study of how each participant's disease phenotype changes over time or due to treatment. Disclosure M. Hong: None. A. Viñuela: None. R.S. Häussler: None. M. Dale: None. R.W. Koivula: None. J. Fernandez-Tajes: None. A. Mahajan: None. R. Bizzotto: Research Support; Self; GlaxoSmithKline plc. A. Mari: Consultant; Self; Eli Lilly and Company. Research Support; Self; Boehringer Ingelheim International GmbH. E. Dermitzakis: Advisory Panel; Self; DNAnexus LTD. Board Member; Self; Hybridstat LTD. M. McCarthy: Advisory Panel; Self; European Association for the Study of Diabetes, Pfizer Inc. Consultant; Self; Eli Lilly and Company, Merck & Co., Inc. Consultant; Spouse/Partner; Merck & Co., Inc. Research Support; Self; AbbVie Inc., Boehringer Ingelheim International GmbH. Research Support; Spouse/Partner; Diabetes UK. Research Support; Self; Janssen Pharmaceuticals, Inc., Merck & Co., Inc., National Institutes of Health. Research Support; Spouse/Partner; National Institutes of Health. Research Support; Self; Novo Nordisk A/S. Research Support; Spouse/Partner; Novo Nordisk A/S. Research Support; Self; Novo Nordisk Foundation, Roche Pharma, Sanofi-Aventis, Servier, Takeda Pharmaceutical Company Limited. P.W. Franks: Board Member; Self; Zoe Ltd. Research Support; Self; AstraZeneca, Boehringer Ingelheim International GmbH, Lilly Diabetes, Novo Nordisk A/S, Novo Nordisk Foundation, Sanofi, Servier. E. Pearson: None. J.M. Schwenk: None. Funding Innovative Medicines Initiative Joint Undertaking (115317)

It is known that for a given insulin level glucose clearance depends on glucose concentration. However, a quantitative representation of the concomitant effects of hyperinsulinemia and hyperglycemia on glucose clearance, necessary to describe heterogeneous tests such as euglycemic and hyperglycemic clamps and oral tests, is lacking. Data from five studies (123 subjects) using a glucose tracer and including all the above tests in normal and diabetic subjects were collected. A mathematical model was developed in which glucose utilization was represented as a Michaelis-Menten function of glucose with constant Kmand insulin-controlled Vmax, consistently with the basic notions of glucose transport. Individual values for the model parameters were estimated using a population approach. Tracer data were accurately fitted in all tests. The estimated Kmwas 3.88 (2.83–5.32) mmol/l [median (interquartile range)]. Median model-derived glucose clearance at 600 pmol/l insulin was reduced from 246 to 158 ml·min−1·m−2when glucose was raised from 5 to 10 mmol/l. The model reproduced the characteristic lack of increase in glucose clearance when moderate hyperinsulinemia was accompanied by hyperglycemia. In all tests, insulin sensitivity was inversely correlated with BMI, as expected ( R2= 0.234, P = 0.0001). In conclusion, glucose clearance in euglycemic and hyperglycemic clamps and oral tests can be described with a unifying model, consistent with the notions of glucose transport and able to reproduce the suppression of glucose clearance due to hyperglycemia observed in previous studies. The model may be important for the design of reliable glucose homeostasis simulators.

Objective To develop a population pharmacokinetic model for propofol target-controlled infusion (TCI) in dogs and to evaluate its performance for use in the clinical setting. Study design Prospective clinical study. Animals A group of 40 client-owned dogs undergoing general anaesthesia for magnetic resonance imaging. Methods Propofol was administered to 26 premedicated dogs and arterial blood samples were collected during the infusion and over 240 minutes after terminating the infusion. Propofol concentrations were measured by high-performance liquid chromatography. A population pharmacokinetic analysis was performed using a nonlinear mixed-effects modelling approach, allowing inter- and intra-individual variability estimation and quantitative evaluation of the influence of the following covariates: weight, body condition score, age, size-related age (Age_size), sex, premedication type, size and contrast agent administration. A final model was obtained using a stepwise approach in which individual covariate effects on each pharmacokinetic variable were incorporated. The performance of the developed TCI model was subsequently evaluated while inducing and maintaining anaesthesia in 14 premedicated dogs and assessed by comparing predicted and measured concentrations at specific time points. Results Propofol pharmacokinetics was best described by a three-compartment model. Weight, Age_size, premedication and sex showed significant pharmacokinetic effects. Addition of the significant covariate/variable associations to the final model resulted in a reduction of the objective function value from 285.53 to –22.34. The median values of prediction error and absolute performance error were 3.1% and 28.4%, respectively. Induction targets between 4.0 and 6.5 μg mL–1 allowed intubation within 5.0 ± 0.9 minutes. Anaesthesia was achieved with targets between 3.0 and 6.5 μg mL–1. Mean time to extubation was 9.7 ± 2.6 minutes. All dogs recovered smoothly and without complications. Conclusions and clinical relevance Overall predictive performance of the pharmacokinetic model-driven infusion developed was clinically acceptable for administering propofol to dogs in routine anaesthesia.

Pharmacologically induced glycosuria elicits adaptive responses in glucose homeostasis and hormone release. In type 2 diabetes (T2D), along with decrements in plasma glucose and insulin levels and increments in glucagon release, sodium–glucose cotransporter 2 (SGLT2) inhibitors induce stimulation of endogenous glucose production (EGP) and a suppression of tissue glucose disposal (TGD). We measured fasting and postmeal glucose fluxes in 25 subjects without diabetes using a double glucose tracer technique; in these subjects and in 66 previously reported patients with T2D, we also estimated lipolysis (from [2H5]glycerol turnover rate and circulating free fatty acids, glycerol, and triglycerides), lipid oxidation (LOx; by indirect calorimetry), and ketogenesis (from circulating β-hydroxybutyrate concentrations). In both groups, empagliflozin administration raised EGP, lowered TGD, and stimulated lipolysis, LOx, and ketogenesis. The pattern of glycosuria-induced changes was similar in subjects without diabetes and in those with T2D but quantitatively smaller in the former. With chronic (4 weeks) versus acute (first dose) drug administration, glucose flux responses were attenuated, whereas lipid responses were enhanced; in patients with T2D, fasting β-hydroxybutyrate levels rose from 246 ± 288 to 561 ± 596 µmol/L (P < 0.01). We conclude that by shunting substantial amounts of carbohydrate into urine, SGLT2-mediated glycosuria results in a progressive shift in fuel utilization toward fatty substrates. The associated hormonal milieu (lower insulin-to-glucagon ratio) favors glucose release and ketogenesis.

To study the integrative impact of macronutrients on postprandial glycaemia, β-cell function, glucagon and incretin hormones in humans.Macronutrients were ingested alone (glucose 330 kcal, protein 110 kcal or fat 110 kcal) or together (550 kcal) by healthy subjects (n = 18) and by subjects with drug-naïve type 2 diabetes (T2D; n = 18). β-cell function and insulin clearance were estimated by modelling glucose, insulin and C-peptide data. Secretion of glucose-dependent insulinotropic polypeptide (GIP) and glucagon-like peptide-1 (GLP-1) were measured, and paracetamol was administered to estimate gastric emptying.In both groups, the mixed-meal challenge diminished glucose excursion compared with glucose challenge alone, and insulin levels, but not C-peptide levels, rose more than after the mixed meal than after glucose alone. β-cell function was augmented, insulin clearance was reduced and glucagon levels were higher after the mixed meal compared with glucose alone. GLP-1 and GIP levels increased after all challenges and GIP secretion was markedly higher after the mixed meal than after glucose alone. The appearance of paracetamol was delayed after the mixed-meal challenge compared with glucose alone.Adding protein and fat macronutrients to glucose in a mixed meal diminished glucose excursion. This occurred in association with increased β-cell function, reduced insulin clearance, delayed gastric emptying and augmented glucagon and GIP secretion. This suggests that the macronutrient composition regulates glycaemia through both islet and extra-islet mechanisms in both healthy subjects and in subjects with T2D.

High-carbohydrate diets have been associated with β-cell strain, dyslipidemia, and endothelial dysfunction. We examined how β-cell and endothelial function adapt to carbohydrate overloading and the influence of insulin resistance. On sequential days in randomized order, nondiabetic subjects (classified as insulin-sensitive [IS] [n = 64] or insulin-resistant [IR] [n = 79] by euglycemic clamp) received four mixed meals over 14 h with either standard (300 kcal) or double carbohydrate content. β-Cell function was reconstructed by mathematical modeling; brachial artery flow-mediated dilation (FMD) was measured before and after each meal. Compared with IS, IR subjects showed higher glycemia and insulin hypersecretion due to greater β-cell glucose and rate sensitivity; potentiation of insulin secretion, however, was impaired. Circulating free fatty acids (FFAs) were less suppressed in IR than IS subjects. Baseline FMD was reduced in IR, and postprandial FMD attenuation occurred after each meal, particularly with high carbohydrate, similarly in IR and IS. Throughout the two study days, higher FFA levels were significantly associated with lower (incretin-induced) potentiation and impaired FMD. In nondiabetic individuals, enhanced glucose sensitivity and potentiation upregulate the insulin secretory response to carbohydrate overloading. With insulin resistance, this adaptation is impaired. Defective suppression of endogenous FFA is one common link between impaired potentiation and vascular endothelial dysfunction.

The statistical distributions of bout lengths for the different (macro) sleep states (wake, N1, N2, N3, and REM sleep) are essential to understanding whether any memory-free subcomponent (“micro state”) is involved in the organization of sleep. Micro state detection can be prevented by the fusion of data including various sources of variability, in particular by the differences in sleep architecture between individuals, along sleep time (or nighttime), or between different nights. In this analysis, a mathematical model of sleep was adopted to disentangle these features and advance the understanding of the dynamics and mechanisms of sleep and its states. The analysis involved 116 primary insomnia patients taking placebo before going to bed and undergoing polysomnography for one night. The individual sequences of macro sleep states had been previously modeled with a mixed-effect nonhomogeneous modified Markov chain model, from which individual conditional probability distributions for the bout durations were derived in this analysis as functions of sleep time. The probability distributions, affected by neither subject, night-time, nor multiple-night pooling, substantially changed at ¼ and ¾ sleep time, had modified exponential shape, and were best described as the sum of one to four exponentials, depending on the sleep state. The time constants and proportions of bouts contributing to each exponential were similar in the different subjects, changing over sleep time. Variability in bout durations thus indicated the presence of multiple memory-free sleep subcomponents whose mean residence times and access probabilities could be identified and shown to be consistent among the studied subjects.NEW & NOTEWORTHY We present a new methodology for deriving, from polysomnography data, the individual conditional probability for the duration of the bouts of wake, N1, N2, N3, and REM sleep. We evaluated the variability of this probability within and between primary insomnia patients and along sleep time. The multiexponential shapes of the probability distributions within the individuals revealed memory-free mechanisms and sleep subcomponents with consistent features in the studied population.

To establish whether incretin hormones affect insulin clearance, the aim of this study was to assess insulin clearance in mice with genetic deletion of receptors for both glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP), so called double incretin receptor knockout mice (DIRKO). DIRKO ( n = 31) and wild-type (WT) C57BL6J mice ( n = 45) were intravenously injected with d-glucose (0.35 g/kg). Blood was sampled for 50 min and assayed for glucose, insulin, and C-peptide. Data were modeled to calculate insulin clearance; C-peptide kinetics was established after human C-peptide injection. Assessment of C-peptide kinetics revealed that C-peptide clearance was 1.66 ± 0.10 10−3 1/min. After intravenous glucose administration, insulin clearance during first phase insulin secretion was markedly higher in DIRKO than in WT mice (0.68 ± 0.06 10−3 l/min in DIRKO mice vs. 0.54 ± 0.03 10−3 1/min in WT mice, P = 0.02). In contrast, there was no difference between the two groups in insulin clearance during second phase insulin secretion ( P = 0.18). In conclusion, this study evaluated C-peptide kinetics in the mouse and exploited a mathematical model to estimate insulin clearance. Results showed that DIRKO mice have higher insulin clearance than WT mice, following intravenous injection of glucose. This suggests that incretin hormones reduce insulin clearance at physiological, nonstimulated levels.

Previous work has shown that potentiation of insulin release is impaired in non-diabetic insulin resistance; we tested the hypothesis that this defect may be related to altered glucagon-like peptide-1 (GLP-1) release. On consecutive days, 82 non-diabetic individuals, classified as insulin sensitive (IS, n=41) or insulin resistant (IR, n=41) by the euglycaemic clamp, were given two sequential mixed meals with standard (75 g, LCD) or double (150 g, HCD) carbohydrate content. Plasma glucose, insulin, C-peptide, non-esterified fatty acids (NEFA) and GLP-1 concentrations were measured; β-cell function (glucose sensitivity and potentiation) was resolved by mathematical modelling. Fasting GLP-1 levels were higher in IR than IS (by 15%, P=0.006), and reciprocally related to insulin sensitivity after adjustment for sex, age, fat mass, fasting glucose or insulin concentrations. Mean postprandial GLP-1 responses were tightly correlated with fasting GLP-1, were higher for the second than the first meal, and higher in IR than IS subjects but only with LCD. In contrast, incremental GLP-1 responses were higher during (i) the second than the first meal, (ii) on HCD than LCD, and (iii) significantly smaller in IR than IS independently of meal and load. Potentiation of insulin release was markedly reduced in IR vs IS across meal and carbohydrate loading. In the whole dataset, incremental GLP-1 was directly related to potentiation, and both were inversely related to mean NEFA concentrations. We conclude that (a) raised GLP-1 tone may be inherently linked with a reduced GLP-1 response and (b) defective post-meal GLP-1 response may be one mechanism for impaired potentiation of insulin release in insulin resistance.

Mixed-effect Markov chain models have been recently proposed to characterize the time course of transition probabilities between sleep stages in insomniac patients. The most recent one, based on multinomial logistic functions, was used as a base to develop a final model combining the strengths of the existing ones. This final model was validated on placebo data applying also new diagnostic methods and then used for the inclusion of potential age, gender, and BMI effects. Internal validation was performed through simplified posterior predictive check (sPPC), visual predictive check (VPC) for categorical data, and new visual methods based on stochastic simulation and estimation and called visual estimation check (VEC). External validation mainly relied on the evaluation of the objective function value and sPPC. Covariate effects were identified through stepwise covariate modeling within NONMEM VI. New model features were introduced in the model, providing significant sPPC improvements. Outcomes from VPC, VEC, and external validation were generally very good. Age, gender, and BMI were found to be statistically significant covariates, but their inclusion did not improve substantially the model’s predictive performance. In summary, an improved model for sleep internal architecture has been developed and suitably validated in insomniac patients treated with placebo. Thereafter, covariate effects have been included into the final model.

Hypnotic drug development calls for a better understanding of sleep physiology in order to improve and differentiate novel medicines for the treatment of sleep disorders. On this basis, a proper evaluation of polysomnographic data collected in clinical trials conducted to explore clinical efficacy of novel hypnotic compounds should include the assessment of sleep architecture and its drug-induced changes. This work presents a non-linear mixed-effect Markov-chain model based on multinomial logistic functions which characterize the time course of transition probabilities between sleep stages in insomniac patients treated with placebo. Polysomnography measurements were obtained from patients during one night treatment. A population approach was used to describe the time course of sleep stages (awake stage, stage 1, stage 2, slow-wave sleep and REM sleep) using a Markov-chain model. The relationship between time and individual transition probabilities between sleep stages was modelled through piecewise linear multinomial logistic functions. The identification of the model produced a good adherence of mean post-hoc estimates to the observed transition frequencies. Parameters were generally well estimated in terms of CV, shrinkage and distribution of empirical Bayes estimates around the typical values. The posterior predictive check analysis showed good consistency between model-predicted and observed sleep parameters. In conclusion, the Markov-chain model based on multinomial logistic functions provided an accurate description of the time course of sleep stages together with an assessment of the probabilities of transition between different stages.

Postprandial glucose homeostasis is regulated through the secretion of glucagon-like peptide 1 (GLP-1) through the stimulation of insulin secretion and inhibition of glucagon secretion. However, how these processes dynamically adapt to demands created by caloric challenges achieved during daily life is not known.The objective of the study was to explore the adaptation of incretin and islet hormones after mixed meals of increasing size in healthy subjects.Twenty-four healthy lean subjects ingested a standard breakfast after an overnight fast followed, after 4 hours, by a lunch of a different size (511, 743, and 1034 kcal) but with identical nutrient composition together with 1.5 g paracetamol. Glucose, insulin, C-peptide, glucagon, intact GLP-1, and glucose-dependent insulinotropic polypeptide (GIP) and paracetamol were measured after the meals.Area under the 180-minute curve (AUC) for insulin, C-peptide, glucagon, GLP-1, and GIP and model-derived β-cell function and paracetamol appearance were calculated.Glucose profiles were similar after the two larger meals, whereas after the smaller meal, there was a postpeak reduction below baseline to a nadir of 3.8 ± 0.1 mmol/L after 75 minutes (P.001). The AUC for GLP-1, GIP, insulin, and C-peptide were significantly higher by increasing the caloric load as was β-cell sensitivity to glucose. In contrast, the AUC glucagon was the same for all three meals, although there was an increase in glucagon after the postpeak glucose reduction in the smaller meal. The 0- to 20-minute paracetamol appearance was increased by increasing meal size.Mixed lunch meals of increasing size elicit a caloric-dependent insulin response due to increased β-cell secretion achieved by increased GIP and GLP-1 levels. The adaptation at larger meals results in identical glucose excursions, whereas after a lower caloric lunch, the insulin response is high, resulting in a postpeak suppression of glucose below baseline.