Wake dynamics in buoyancy-driven flows: Steady-state-Hopf-mode interaction with O(2) symmetry revisited.

We present a detailed mathematical study of a truncated normal form relevant to the bifurcations observed in wake flow past axisymmetric bodies, with and without thermal stratification. We employ abstract normal form analysis to identify possible bifurcations and the corresponding bifurcation diagrams in parameter space. The bifurcations and the bifurcation diagrams are interpreted in terms of symmetry considerations. Particular emphasis is placed on the presence of attracting robust heteroclinic cycles in certain parameter regimes. The normal form coefficients are computed for several examples of wake flows behind buoyant disks and spheres, and the resulting predictions compared with the results of direct numerical flow simulations. In general, satisfactory agreement is obtained.

Population Pharmacokinetic Modeling and Determination of Individual Exposure to Avalglucosidase Alfa in Adolescent and Adult Patients With Late-Onset Pompe Disease: Analysis of Pooled Data From Phase I to III Clinical Trials.

BACKGROUND: Pompe disease is a rare genetic disorder caused by a deficiency of a lysosomal enzyme called acid alpha-glucosidase and is classified into infantile and late-onset forms. Since 2006, an enzyme replacement therapy involving alglucosidase alfa has been available. In 2021, a new enzyme replacement therapy involving avalglucosidase alfa demonstrated improved clinical benefits. In this article, the authors describe the pharmacokinetics of avalglucosidase alfa using a population pharmacokinetic approach. METHODS: The population pharmacokinetic model was developed using a data set that included 75 patients and 2042 plasma drug concentrations determined through enzymatic activity assay from 3 studies (phases I/II and III) and involved 3 dose levels (5, 10, and 20 mg/kg). The analysis was performed using NONMEM software. RESULTS: Two sequences were observed in the plasma drug concentration profile: the first kinetic driving exposure, and after 12 hours postdose, a slight rebound addressing very low concentrations that lasted up to 2 weeks. Following model screening, a model with a central compartment with parallel linear and nonlinear elimination and 2 concatenated peripheral compartments was proposed. A putative back-redistribution of a marginal fraction of the drug from the second peripheral compartment to the central compartment may explain the slight rebound in concentration. The final model's mean bias and precision for individual predictions were -2.66% and 30.7%, respectively, and -0.433% and 38.9%, respectively, for population predictions. CONCLUSIONS: A concatenated 3-compartment model was developed to describe the avalglucosidase alfa concentrations in patients with late-onset Pompe disease. None of the covariates tested could explain the interindividual variability.

Population pharmacokinetic modeling and dosing simulation of avalglucosidase alfa for selecting alternative dosing regimen in pediatric patients with late-onset pompe disease.

Avalglucosidase alfa (AVAL) was approved in the United States (2021) for patients with late-onset Pompe disease (LOPD), aged ≥ 1 year. In the present study, pharmacokinetic (PK) simulations were conducted to propose alternative dosing regimens for pediatric LOPD patients based on a bodyweight cut-off. Population PK (PopPK) analysis was performed using nonlinear mixed effect modeling approach on pooled data from three clinical trials with LOPD patients, and a phase 2 study (NCT03019406) with infantile-onset Pompe disease (IOPD: 1-12 years) patients. A total of 2257 concentration-time points from 91 patients (LOPD, n = 75; IOPD, n = 16) were included in the analysis. The model was bodyweight dependent allometric scaling with time varying bodyweight included on clearance and distribution volume. Simulations were performed for two dosing regimens (20 mg/kg or 40 mg/kg) with different bodyweight cut-off (25, 30, 35 and 40 kg) by generating virtual pediatric (1-17 years) and adult patients. Corresponding simulated individual exposures (maximal concentration, Cmax and area under the curve in the 2-week dosing interval, AUC2W), and distributions were calculated. It was found that dosing of 40 mg/kg and 20 mg/kg in pediatric patients < 30 kg and ≥ 30 kg, respectively, achieved similar AVAL exposure (based on AUC2W) to adult patients receiving 20 mg/kg. PK simulations conducted on the basis of this model provided supporting data for the currently approved US labelling for dosing adapted bodyweight in LOPD patients ≥ 1 year by USFDA.

When, how, and why the path of an air bubble rising in pure water becomes unstable.

Recently, [Herrada, M. A. and Eggers, J. G., Proc. Natl. Acad. Sci. U.S.A. 120, e2216830120 (2023)] reported predictions for the onset of the path instability of an air bubble rising in water and put forward a physical scenario to explain this intriguing phenomenon. In this Brief Report, we review a series of previously established results, some of which were overlooked or misinterpreted by the authors. We show that this set of findings provides an accurate prediction and a consistent explanation of the phenomenon that invalidates the suggested scenario. The instability mechanism actually at play results from the hydrodynamic fluid-body coupling made possible by the unconstrained motion of the bubble which behaves essentially, in the relevant size range, as a rigid, nearly spheroidal body on the surface of which water slips freely.

Combined Semi-mechanistic Target-Mediated Drug Disposition and Pharmacokinetic-Pharmacodynamic Models of Alirocumab, PCSK9, and Low-Density Lipoprotein Cholesterol in a Pooled Analysis of Randomized Phase I/II/III Studies.

BACKGROUND AND OBJECTIVES: Alirocumab is a cholesterol-lowering monoclonal antibody targeting proprotein convertase subtilisin kexin type 9 (PCSK9) indicated in the prevention of cardiovascular risk and exhibiting target-mediated drug disposition (TMDD). The aim of this work was to develop an integrated pharmacokinetic-pharmacodynamic model to describe the interaction of alirocumab with PCSK9 and its impact on the evolution of low-density lipoprotein cholesterol (LDL-C) levels and explore labeling specification for subpopulations. METHODS: Using data collected from nine phase I/II/III clinical studies (n = 527, subcutaneous or intravenous administration), a TMDD model considering the quasi-steady-state approximation was developed to characterize the interaction dynamics of alirocumab and PCSK9, combined with an indirect pharmacodynamic model describing the inhibition of LDL-C by PCSK9 in a one-step approach using nonlinear-mixed effects modeling. A "full fixed effects modeling" strategy was implemented to quantify parameter-covariate relationships. RESULTS: The model captures the interaction between alirocumab and its target PCSK9 and how this mechanism drives LDL-C depletion, with an estimation of the associated between-subject variability of model parameters and the quantification of clinically relevant parameter-covariate relationships. Co-administration of statins was found to increase the central volume of distribution of alirocumab by 1.75-fold (5.6 L versus 3.2 L) and allow for a 14% greater maximum lipid-lowering effect (88% versus 74%), highlighting the synergy of action between anti-PCSK9 therapeutic antibodies and statins toward lowering LDL-C plasma levels. Baseline levels of PCSK9 were found to be related to the amplitude of LDL-C variations by increasing the concentration of free PCSK9 necessary to reach half its capacity of inhibition of LDL-C degradation. CONCLUSION: The maximum effect of alirocumab is achieved when free PCSK9 concentration is close to zero, as seen mostly after 150 mg every 2 weeks (Q2W) or 300 mg every 4 weeks (Q4W), indicating that there would be no additional clinical benefit of increasing the dose higher than these recommended dosing regimens.

Prior information for population pharmacokinetic and pharmacokinetic/pharmacodynamic analysis: overview and guidance with a focus on the NONMEM PRIOR subroutine.

Population pharmacokinetic analysis is used to estimate pharmacokinetic parameters and their variability from concentration data. Due to data sparseness issues, available datasets often do not allow the estimation of all parameters of the suitable model. The PRIOR subroutine in NONMEM supports the estimation of some or all parameters with values from previous models, as an alternative to fixing them or adding data to the dataset. From a literature review, the best practices were compiled to provide a practical guidance for the use of the PRIOR subroutine in NONMEM. Thirty-three articles reported the use of the PRIOR subroutine in NONMEM, mostly in special populations. This approach allowed fast, stable and satisfying modelling. The guidance provides general advice on how to select the most appropriate reference model when there are several previous models available, and to implement and weight the selected parameter values in the PRIOR function. On the model built with PRIOR, the similarity of estimates with the ones of the reference model and the sensitivity of the model to the PRIOR values should be checked. Covariates could be implemented a priori (from the reference model) or a posteriori, only on parameters estimated without prior (search for new covariates).

Population Pharmacokinetic Analysis of Alirocumab in Healthy Volunteers or Hypercholesterolemic Subjects Using a Michaelis-Menten Approximation of a Target-Mediated Drug Disposition Model-Support for a Biologics License Application Submission: Part I.

BACKGROUND: Alirocumab, a human monoclonal antibody, inhibits proprotein convertase subtilisin/kexin type 9 (PCSK9) to significantly reduce low-density lipoprotein cholesterol levels; pharmacokinetics (PK) are governed by non-linear, target-mediated drug disposition (TMDD). OBJECTIVES: We aimed to develop and qualify a population PK (PopPK) model to characterize the PK profile of alirocumab, evaluate the impact of covariates on alirocumab PK and on individual patient exposures, and estimate individual predicted concentrations for a subsequent PK/pharmacodynamic (PD) analysis. METHODS: Data from 13 phase I-III trials of 2799 healthy volunteers or patients with hypercholesterolemia treated with intravenous or subcutaneous alirocumab (13,717 alirocumab concentrations) were included; a Michaelis-Menten approximation of the TMDD model was used to estimate PK parameters and exposures. The final model comprised two compartments with first-order absorption. Elimination from the central compartment was described by linear (CLL) and non-linear Michaelis-Menten clearance (Vm and Km). The model was validated using visual predictive check and bootstrap methods. Patient exposures to alirocumab were computed using individual PK parameters. RESULTS: The PopPK model was well-qualified, with the majority of observed alirocumab concentrations in the 2.5th-97.5th predicted percentiles. Covariates responsible for interindividual variability were identified. Body weight and concomitant statin administration impacted CLL, whereas time-varying free PCSK9 concentrations and age affected Km and peripheral distribution volume (V3), respectively. No covariates were clinically meaningful, therefore no dose adjustments were needed. CONCLUSIONS: The model explained the between-subject variability, quantified the impact of covariates, and, finally, predicted alirocumab concentrations (subsequently used in a PopPK/PD model, see Part II) and individual exposures.

Population Pharmacokinetic/Pharmacodynamic Analysis of Alirocumab in Healthy Volunteers or Hypercholesterolemic Subjects Using an Indirect Response Model to Predict Low-Density Lipoprotein Cholesterol Lowering: Support for a Biologics License Application Submission: Part II.

BACKGROUND: Alirocumab, a human monoclonal antibody against proprotein convertase subtilisin/kexin type 9 (PCSK9), significantly lowers low-density lipoprotein cholesterol levels. OBJECTIVE: This analysis aimed to develop and qualify a population pharmacokinetic/pharmacodynamic model for alirocumab based on pooled data obtained from 13 phase I/II/III clinical trials. METHODS: From a dataset of 2799 individuals (14,346 low-density lipoprotein-cholesterol values), individual pharmacokinetic parameters from the population pharmacokinetic model presented in Part I of this series were used to estimate alirocumab concentrations. As a second step, we then developed the current population pharmacokinetic/pharmacodynamic model using an indirect response model with a Hill coefficient, parameterized with increasing low-density lipoprotein cholesterol elimination, to relate alirocumab concentrations to low-density lipoprotein cholesterol values. RESULTS: The population pharmacokinetic/pharmacodynamic model allowed the characterization of the pharmacokinetic/pharmacodynamic properties of alirocumab in the target population and estimation of individual low-density lipoprotein cholesterol levels and derived pharmacodynamic parameters (the maximum decrease in low-density lipoprotein cholesterol values from baseline and the difference between baseline low-density lipoprotein cholesterol and the pre-dose value before the next alirocumab dose). Significant parameter-covariate relationships were retained in the model, with a total of ten covariates (sex, age, weight, free baseline PCSK9, total time-varying PCSK9, concomitant statin administration, total baseline PCSK9, co-administration of high-dose statins, disease status) included in the final population pharmacokinetic/pharmacodynamic model to explain between-subject variability. Nevertheless, the high number of covariates included in the model did not have a clinically meaningful impact on model-derived pharmacodynamic parameters. CONCLUSIONS: This model successfully allowed the characterization of the population pharmacokinetic/pharmacodynamic properties of alirocumab in its target population and the estimation of individual low-density lipoprotein cholesterol levels.

Linear and nonlinear perturbation analysis of the symmetry breaking in time-periodic propulsive wakes.

The two-dimensional and time-periodic wake flows produced by a pitching foil are investigated numerically for a fixed flapping amplitude. As the flapping frequency is increased, three regimes are identified in the time-marching nonlinear simulations. The first regime is characterized by nondeviated wake flows with zero time-averaged lift. In the second regime, the wake flow is slightly deviated from the streamwise direction and the time-averaged lift is slightly positive or negative. The third regime is characterized by larger deviations of the wake, associated with larger values of both the time-averaged lift and the thrust. The transition from the first to the second regime is examined by performing a Floquet stability analysis of the nondeviated wake. A specific method is introduced to compute the time-periodic, nondeviated wake when it is unstable. It is found that one synchronous antisymmetric mode becomes unstable at the critical frequency where deviation occurs. Investigation of its instantaneous and time-averaged characteristics show that it acts as a displacement mode translating the nondeviated wake away from the streamwise direction. Finally, it is demonstrated that the transition from the second to the third regime is linked to nonlinear effects that amplify both antisymmetric and symmetric perturbations around the foil.

Target-Mediated Drug Disposition Population Pharmacokinetics Model of Alirocumab in Healthy Volunteers and Patients: Pooled Analysis of Randomized Phase I/II/III Studies.

BACKGROUND AND OBJECTIVE: Proprotein convertase subtilisin/kexin type 9 inhibition with monoclonal antibodies such as alirocumab significantly reduces low-density lipoprotein-cholesterol levels ± other lipid-lowering therapies. We aimed to develop and qualify a population pharmacokinetics (PopPK) model for alirocumab in healthy subjects and patients, taking into account the mechanistic target-mediated drug disposition (TMDD) process. METHODS: This TMDD model was developed using a subset of the alirocumab clinical trial database, including nine phase I/II/III studies (n = 527); the model was subsequently expanded to a larger data set of 13 studies (n = 2870). Potential model parameters and covariate relationships were explored, and predictive ability was qualified using a visual predictive check. RESULTS: The TMDD model was built using the quasi-steady-state approximation. The final TMDD-quasi-steady-state model included a significant relationship between distribution volume of the central compartment and disease state: distribution volume of the central compartment was 1.56-fold higher in patients vs. healthy subjects. Separately, application of the model to the expanded data set revealed a significant relationship between linear clearance and statin co-administration: linear clearance was 1.27-fold higher with statins. The good predictive performance of the TMDD model was assessed based on graphical and numerical quality criteria, together with the visual predictive check and comparison of the predictions to those from a PopPK model with parallel linear and Michaelis-Menten clearances (i.e., simplification of the TMDD PopPK model). CONCLUSIONS: This mechanistic TMDD PopPK model integrates the interaction of alirocumab with its target and accurately predicts both alirocumab and total proprotein convertase subtilisin/kexin type 9 concentrations in healthy subjects and patients.

Ocular Drug Distribution After Topical Administration: Population Pharmacokinetic Model in Rabbits.

BACKGROUND AND OBJECTIVE: When eye diseases are treated by topical administration, the success of treatment lies in the effective drug concentration in the target tissue. This is why the drug's pharmacokinetic, in the different substructures of the eye, needs to be explored more accurately during drug development. The aim of the present analysis was to describe by rabbit model, the distribution of a drug after ocular instillation in the selected eye tissues and fluids. METHODS: By a top-down population approach, we developed and validated a population pharmacokinetics (PopPK) model, using tissue concentrations (tear, naso-lacrymal duct, cornea and aqueous humor) of a new src tyrosine kinase inhibitor (FV-60165) in each anterior segment's tissue and fluid of the rabbit eye. Inter-individual variability was estimated and the impact of the formulation (solution or nanosuspension) was evaluated. RESULTS: The model structure selected for the eye is a 4-compartment model with the formulation as a significant covariate on the first-order rate constant between tears and the naso-lacrymal duct. The model showed a good predictive performance and may be used to estimate the concentration-time profiles after single or repeated administration, in each substructure of the eye for each animal included in the analysis. CONCLUSIONS: This analysis allowed describing the distribution of a drug in the different selected tissues and fluids in the rabbit's eyes after instillation of the prodrug as a solution or nanosuspension.

Weakly nonlinear model with exact coefficients for the fluttering and spiraling motion of buoyancy-driven bodies.

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Physiologically based pharmacokinetic modeling for sequential metabolism: effect of CYP2C19 genetic polymorphism on clopidogrel and clopidogrel active metabolite pharmacokinetics.

Clopidogrel is a prodrug that needs to be converted to its active metabolite (clopi-H4) in two sequential cytochrome P450 (P450)-dependent steps. In the present study, a dynamic physiologically based pharmacokinetic (PBPK) model was developed in Simcyp for clopidogrel and clopi-H4 using a specific sequential metabolite module in four populations with phenotypically different CYP2C19 activity (poor, intermediate, extensive, and ultrarapid metabolizers) receiving a loading dose of 300 mg followed by a maintenance dose of 75 mg. This model was validated using several approaches. First, a comparison of predicted-to-observed area under the curve (AUC)0-24 obtained from a randomized crossover study conducted in four balanced CYP2C19-phenotype metabolizer groups was performed using a visual predictive check method. Second, the interindividual and intertrial variability (on the basis of AUC0-24 comparisons) between the predicted trials and the observed trial of individuals, for each phenotypic group, were compared. Finally, a further validation, on the basis of drug-drug-interaction prediction, was performed by comparing observed values of clopidogrel and clopi-H4 with or without dronedarone (moderate CYP3A4 inhibitor) coadministration using a previously developed and validated physiologically based PBPK dronedarone model. The PBPK model was well validated for both clopidogrel and its active metabolite clopi-H4, in each CYP2C19-phenotypic group, whatever the treatment period (300-mg loading dose and 75-mg last maintenance dose). This is the first study proposing a full dynamic PBPK model able to accurately predict simultaneously the pharmacokinetics of the parent drug and of its primary and secondary metabolites in populations with genetically different activity for a metabolizing enzyme.

Population pharmacokinetic analysis of fexofenadine in Japanese pediatric patients.

A population pharmacokinetic analysis was conducted to characterize the pharmacokinetics of fexofenadine in Japanese pediatric patients (6 months through 16 years) with perennial allergic rhinitis or atopic dermatitis. The dataset was composed of 515 patients (including 109 adults), for a total of 1,080 concentration-time points. The analysis was performed with NONMEM using the SAEM method. Several structural models and residual error models were evaluated. The relationship between the individual estimates and the potential covariates was then investigated: demographic and pathophysiologic characteristics were tested as potential model covariates (forward selection method). The qualification of the model was performed using visual predictive check and bootstrap. A two-compartment disposition model with first-order absorption best fitted the data. The inter-individual variability was modeled through an exponential error model for all parameters (except for ka for which no inter-individual term could be estimated), while a proportional error model was used to model the residual variability. The final model included two covariates on elimination clearance and one on the intercompartmental clearance. CL/F was related to BSA and patient's age (expressed in months) Q/F was also related to BSA. Once the model was correctly qualified, exposure parameters such as Cmax and AUCτ were computed and compared between each age sub-group and between Japanese and Caucasians patients. These comparisons did not reveal any major difference (less than 50 %) between subgroups.