Interaction of fast and slow dynamics in endocrine control systems with an application to β-cell dynamics

Endocrine dynamics spans a wide range of time scales, from rapid responses to physiological challenges to with slow responses that adapt the system to the demands placed on it. We outline a non-linear averaging procedure to extract the slower dynamics in a way that accounts properly for the non-linear dynamics of the faster time scale and is applicable to a hierarchy of more than two time scales, although we restrict our discussion to two scales for the sake of clarity. The procedure is exact if the slow time scale is infinitely slow (the dimensionless epsilon-quantity is the period of the fast time scale fluctuation times an upper bound to the slow time scale rate of change). However, even for an imperfect separation of time scales we find that this construction provides an excellent approximation for the slow-time dynamics at considerably reduced computational cost. Besides the computation advantage, the averaged equation provided a qualitative insight into the interaction of the time scales. We demonstrate the procedure and its advantages by applying the theory to the model described by Tolic et al. [I.M. Tolic, E. Mosekilde, J. Stuns, Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion, J. Theor. Biol. 207 (2000) 361-375.] for ultradian dynamics of the glucose-insulin homeostasis feedback system, extended to include beta-cell dynamics. We find that the dynamics of the beta-cell mass are dependent not only on the glycemic load (amount of glucose administered to the system), but also on the way this load is applied (i.e. three meals daily versus constant infusion), effects that are lost in the inappropriate methods used by the earlier authors. Furthermore, we find that the loss of the protection against apoptosis conferred by insulin that occurs at elevated levels of insulin has a functional role in keeping the beta-cell mass in check without compromising regulatory function. We also find that replenishment of beta-cells from a rapidly proliferating pool of cells, as opposed to the slow turn-over which characterises fully differentiated beta-cells, is essential to the prevention of type 1 diabetes

Population Pharmacokinetics and Exposure-Response Relationships of Astegolimab in Patients With Severe Asthma

Astegolimab is a fully human immunoglobulin G2 monoclonal antibody that binds to the ST2 receptor and blocks the interleukin-33 signaling. It was evaluated in patients with uncontrolled severe asthma in the phase 2b study (Zenyatta) at doses of 70, 210, and 490 mg subcutaneously every 4 weeks for 52 weeks. This work aimed to characterize astegolimab pharmacokinetics, identify influential covariates contributing to its interindividual variability, and make a descriptive assessment of the exposure-response relationships. A population pharmacokinetic model was developed using data from 368 patients in the Zenyatta study. Predicted average steady-state concentration was used in the subsequent exposure-response analyses, which evaluated efficacy (asthma exacerbation rate) and biomarker end points including forced expiratory volume in 1 second, fraction exhaled nitric oxide, blood eosinophils, and soluble ST2. A 2-compartment disposition model with first-order elimination and first-order absorption best described the astegolimab pharmacokinetics. The relative bioavailability for the 70-mg dose was 15.3% lower. Baseline body weight, estimated glomerular filtration rate, and eosinophils were statistically correlated with pharmacokinetic parameters, but only body weight had a clinically meaningful influence on the steady-state exposure (ratios exceeding 0.8-1.25). The exposure-response of efficacy and biomarkers were generally flat with a weak trend in favor of the highest dose/exposure. This study characterized astegolimab pharmacokinetics in patients with asthma and showed typical pharmacokinetic behavior as a monoclonal antibody-based drug. The exposure-response analyses suggested the highest dose tested in the Zenyatta study (490 mg every 4 weeks) performed close to the maximum effect, and no additional response may be expected above it

Population repeated time-to-event analysis of exacerbations in asthma patients : A novel approach for predicting asthma exacerbations based on biomarkers, spirometry, and diaries/questionnaires

Identification of covariates, including biomarkers, spirometry, and diaries/questionnaires, that predict asthma exacerbations would allow better clinical predictions, shorter phase II trials and inform decisions on phase III design, and/or initiation (go/no-go). The objective of this work was to characterize asthma-exacerbation hazard as a function of baseline and time-varying covariates. A repeated time-to-event (RTTE) model for exacerbations was developed using data from a 52-week phase IIb trial, including 502 patients with asthma randomized to placebo or 70 mg, 210 mg, or 490 mg astegolimab every 4 weeks. Covariate analysis was performed for 20 baseline covariates using the full random effects modeling approach, followed by time-varying covariate analysis of nine covariates using the stepwise covariate model (SCM) building procedure. Following the SCM, an astegolimab treatment effect was explored. Diary-based symptom score (difference in objective function value [dOFV] of -83.7) and rescue medication use (dOFV = -33.5), and forced expiratory volume in 1 s (dOFV = -14.9) were identified as significant time-varying covariates. Of note, time-varying covariates become more useful with more frequent measurements, which should favor the daily diary scores over others. The most influential baseline covariates were exacerbation history and diary-based symptom score (i.e., symptom score was important as both time-varying and baseline covariate). A (nonsignificant) astegolimab treatment effect was included in the final model because the limited data set did not allow concluding the remaining effect size as irrelevant. Without time-varying covariates, the treatment effect was statistically significant (p < 0.01). This work demonstrated the utility of a population RTTE approach to characterize exacerbation hazard in patients with severe asthma