Extrapolation of lung pharmacokinetics of antitubercular drugs from preclinical species to humans using PBPK modelling

OBJECTIVES

To develop physiologically based pharmacokinetic (PBPK) models for widely used anti-TB drugs, namely rifampicin, pyrazinamide, isoniazid, ethambutol and moxifloxacin lung pharmacokinetics (PK)-regarding both healthy and TB-infected tissue (cellular lesion and caseum)-in preclinical species and to extrapolate to humans.

METHODS

Empirical models were used for the plasma PK of each species, which were connected to multicompartment permeability-limited lung models within a middle-out PBPK approach with an appropriate physiological parameterization that was scalable across species. Lung's extracellular water (EW) was assumed to be the linking component between healthy and infected tissue, while passive diffusion was assumed for the drug transferring between cellular lesion and caseum.

RESULTS

In rabbits, optimized unbound fractions in intracellular water of rifampicin, moxifloxacin and ethambutol were 0.015, 0.056 and 0.08, respectively, while the optimized unbound fractions in EW of pyrazinamide and isoniazid in mice were 0.25 and 0.17, respectively. In humans, all mean extrapolated daily AUC and Cmax values of various lung regions were within 2-fold of the observed ones. Unbound concentrations in the caseum were lower than unbound plasma concentrations for both rifampicin and moxifloxacin. For rifampicin, unbound concentrations in cellular rim are slightly lower, while for moxifloxacin they are significantly higher than unbound plasma concentrations.

CONCLUSIONS

The developed PBPK approach was able to extrapolate lung PK from preclinical species to humans and to predict unbound concentrations in the various TB-infected regions, unlike empirical lung models. We found that plasma free drug PK is not always a good surrogate for TB-infected tissue unbound PK.

Donepezil Brain and Blood Pharmacokinetic Modeling after Nasal Film and Oral Solution Administration in Mice

Intranasal delivery is a non-invasive mode of administration, gaining popularity due to its potential for targeted delivery to the brain. The anatomic connection of the nasal cavity with the central nervous system (CNS) is based on two nerves: olfactory and trigeminal. Moreover, the high vasculature of the respiratory area enables systemic absorption avoiding possible hepatic metabolism. Due to these physiological peculiarities of the nasal cavity, compartmental modeling for nasal formulation is considered a demanding process. For this purpose, intravenous models have been proposed, based on the fast absorption from the olfactory nerve. However, most of the sophisticated approaches are required to describe the different absorption events occurring in the nasal cavity. Donepezil was recently formulated in the form of nasal film ensuring drug delivery in both bloodstream and the brain. In this work, a three-compartment model was first developed to describe donepezil oral brain and blood pharmacokinetics. Subsequently, using parameters estimated by this model, an intranasal model was developed dividing the administered dose into three fractions, corresponding to absorption directly to the bloodstream and brain, as well as indirectly to the brain expressed through transit compartments. Hence, the models of this study aim to describe the drug flow on both occasions and quantify the direct nose-to-brain and systemic distribution.

Implementation of non-linear mixed effects models defined by fractional differential equations

Fractional differential equations (FDEs), i.e. differential equations with derivatives of non-integer order, can describe certain experimental datasets more accurately than classic models and have found application in pharmacokinetics (PKs), but wider applicability has been hindered by the lack of appropriate software. In the present work an extension of NONMEM software is introduced, as a FORTRAN subroutine, that allows the definition of nonlinear mixed effects (NLME) models with FDEs. The new subroutine can handle arbitrary user defined linear and nonlinear models with multiple equations, and multiple doses and can be integrated in NONMEM workflows seamlessly, working well with third party packages. The performance of the subroutine in parameter estimation exercises, with simple linear and nonlinear (Michaelis-Menten) fractional PK models has been evaluated by simulations and an application to a real clinical dataset of diazepam is presented. In the simulation study, model parameters were estimated for each of 100 simulated datasets for the two models. The relative mean bias (RMB) and relative root mean square error (RRMSE) were calculated in order to assess the bias and precision of the methodology. In all cases both RMB and RRMSE were below 20% showing high accuracy and precision for the estimates. For the diazepam application the fractional model that best described the drug kinetics was a one-compartment linear model which had similar performance, according to diagnostic plots and Visual Predictive Check, to a three-compartment classic model, but including four less parameters than the latter. To the best of our knowledge, it is the first attempt to use FDE systems in an NLME framework, so the approach could be of interest to other disciplines apart from PKs.

Pharmacokinetic/Pharmacodynamic Determination of Systemic MIC Breakpoints for Intermittent, Extended, and Continuous Infusion Dosage Regimens of Mecillinam

Intravenous mecillinam has been used for the treatment of urosepsis at several dosing regimens, including a dose of 1,000 mg three times a day (TID). In the current pharmacokinetic/pharmacodynamic (PK/PD) study, we analyzed intermittent, extended, and continuous infusion regimens of mecillinam to provide dosage recommendations to treat infections caused by Enterobacterales exhibiting relatively higher mecillinam MICs than the wild-type strains. Monte Carlo simulation studies indicated that regimens of 1,000 mg TID and 1,000 to 1,200 mg four times a day (QID) are efficacious against wild-type and extended-spectrum β-lactamase-producing Enterobacterales, respectively. Prolonged infusion regimens (extended and continuous) could cover carbapenemase producers with a higher range of MICs (2 to 8 mg/L). IMPORTANCE Previous studies have shown that intravenous mecillinam might be suitable for treatment of urosepsis. Since multidrug-resistant Enterobacterales are common pathogens in such infections, an effort was made to delineate intermittent, extended, and continuous infusion regimens that could cover pathogens exhibiting relatively higher mecillinam MICs than the wild-type strains. Our PK/PD analysis has shown that mecillinam might be considered a valuable therapeutic option for the treatment of systemic infections caused by extended-spectrum β-lactamase- and carbapenemase-producing Enterobacterales exhibiting mecillinam MICs up to 8 mg/L.

In Silico Dosimetry Study of Tc99m-Tetrofosmin in Children Using a Novel PBPK Model in Humans Built from SPECT Imaging Data

PURPOSE

The aim of this work is to develop a Physiologically Based Pharmacokinetic model (PBPK) for the radiopharmaceutical Tc99m-Tetrofosmin in humans, from literature SPECT imaging data, to carry out in-silico dosimetry studies in children and extrapolate dosing.

METHODS

A whole body PBPK model was developed from literature data from humans of Tc99m-Tetrofosmin tissue distribution. A data driven approach to estimate partition coeffects, permeability parameters and clearances was carried out, while some parameters were determined using a standard in silico PBPK method. Paediatric PK data for all tissues were simulated by changing the physiological parameters from the adult to paediatric values. Absorbed and effective doses for children of all ages were calculated using S-values from literature of Tc99m that have been computed from anthropomorphic phantoms.

RESULTS

Using the results from each tissue, satisfactory goodness-of-fit was achieved, assessed by visual inspection and a coefficient of determination of R² = 0.965 while all estimated parameters had good standard errors. Paediatric simulations of Tetrofosmin distribution showed that paediatric profiles are not very different to the those of adults. The effective doses per unit of administered activity for 15 yo, 10 yo, 5 yo and 1 yo children were calculated to be 1.2, 1.7, 2.6 and 4.8 times higher, respectively than the adult value. Based on these calculations maximum administered activity scale more than proportionately to body weight.

CONCLUSIONS

A PBPK model of tetrofosmin in adults has been developed from SPECT imaging data and was extrapolated to conduct in-silico dosimetry studies in children of all ages.

General clinical and methodological considerations on the extrapolation of pharmacokinetics and optimization of study protocols for small molecules and monoclonal antibodies in children

Pharmacometric modelling plays a key role in both the design and analysis of regulatory trials in paediatric drug development. Studies in adults provide a rich source of data to inform the paediatric investigation plans, including knowledge on drug pharmacokinetics (PK), safety and efficacy. In children, drug disposition differs widely from birth to adolescence but extrapolating adult to paediatric PK, safety and efficacy either with pharmacometric or physiologically based approaches can help design or in some cases reduce the need for clinical studies. Aspects to consider when extrapolating PK include the maturation of drug metabolizing enzyme expression, glomerular filtration, drug excretory systems, and the expression and activity of specific transporters in conjunction with other drug properties such as fraction unbound. Knowledge of these can be used to develop extrapolation tools such as allometric scaling plus maturation functions or physiologically based PK. PK/pharmacodynamic approaches and well-designed clinical trials in children are of key importance in paediatric drug development. In this white paper, state-of-the-art of current methods used for paediatric extrapolation will be discussed. This paper is part of a conect4children implementation of innovative methodologies including pharmacometric and physiologically based PK modelling in clinical trial design/paediatric drug development through dissemination of expertise and expert advice. The suggestions arising from this white paper should define a minimum set of standards in paediatric modelling and contribute to the regulatory science.

Pharmacokinetic Characteristics of Nebulized Colistimethate Sodium Using Two Different Types of Nebulizers in Critically Ill Patients with Ventilator-Associated Respiratory Infections

Background: Rising antimicrobial resistance has led to a revived interest in inhaled colistin treatment in the critically ill patient with ventilator-associated respiratory infection (VARI). Nebulization via vibrating mesh nebulizers (VMNs) is considered the current standard-of-care, yet the use of generic jet nebulizers (JNs) is more widespread. Few data exist on the intrapulmonary pharmacokinetics of colistin when administered through VMNs, while there is a complete paucity regarding the use of JNs. Methods: In this study, 18 VARI patients who received 2 million international units of inhaled colistimethate sodium (CMS) through a VMN were pharmacokinetically compared with six VARI patients who received the same drug dose through a JN, in the absence of systemic CMS administration. Results: Surprisingly, VMN and JN led to comparable formed colistin exposures in the epithelial lining fluid (ELF) (median (IQR) AUC0-24: 86.2 (46.0-185.9) mg/L∙h with VMN and 91.5 (78.1-110.3) mg/L∙h with JN). The maximum ELF concentration was 10.4 (4.7-22.6) mg/L and 7.4 (6.2-10.3) mg/L, respectively. Conclusions: Based on our results, JN might be considered a viable alternative to the theoretically superior VMN. Therapeutic drug monitoring in the ELF can be advised due to the observed low exposure, high variability, and appreciable systemic absorption.

Efficacy and safety of Mydriatic Microdrops for Retinopathy Of Prematurity Screening (MyMiROPS): study protocol for a non-inferiority crossover randomized controlled trial

Background

Retinopathy of prematurity (ROP) eye examination screening presupposes adequate mydriasis for an informative fundoscopy of preterm infants at risk, on a weekly basis. Systemic absorption of the instilled mydriatic regimens has been associated with various adverse events in this fragile population. This report aims to present the fully developed protocol of a full-scale trial for testing the hypothesis that the reduced mydriatic drop volume achieves adequate mydriasis while minimizing systemic adverse events.

Methods

A non-inferiority crossover randomized controlled trial will be performed to study the efficacy and safety of combined phenylephrine 1.67% and tropicamide 0.33% microdrops compared with standard drops in a total of 93 preterm infants requiring ROP screening. Primary outcome will be the pupil diameter at 45 (T45) min after instillation. Pupil diameter at T90 and T120 will constitute secondary efficacy endpoints. Mixed-effects linear regression models will be developed, and the 95% confidence interval approach will be used for assessing non-inferiority. Whole blood samples will be analyzed using hydrophilic liquid chromatography–tandem mass spectrometry method (HILIC–MS/MS), for gathering pharmacokinetic (PK) data on the instilled phenylephrine, at nine specific time points within 3 h from mydriasis. Pooled PK data will be used due to ethical restrictions on having a full PK profile per infant. Heart rate, oxygen saturation, blood pressure measurements, and 48-h adverse events will also be recorded.

Discussion

This protocol is designed for a study powered to assess non-inferiority of microdrops compared with standard dilating drops. If our hypothesis is confirmed, microdrops may become a useful tool in ROP screening.

Trial registration

ClinicalTrials.govNCT05043077. Registered on 2 September 2021

Population pharmacokinetics of cyclophosphamide and 4-hydroxycyclophosphamide metabolite in patients with autoimmune glomerulonephritis

OBJECTIVES

To develop a simultaneous population pharmacokinetic model of cyclophosphamide (CY) and 4-hydroxycyclophosphamide (4-OH) in patients with glomerulonephritis.

METHODS

In total, 23 patients participated in a pharmacokinetic evaluation using dense plasma sampling. A population pharmacokinetic model was developed in Monolix Suite 2020R1 that simultaneously describes the kinetics of CY and 4-OH. Several structural and residual error models were evaluated and patient variables were tested as potential covariates. The final model was selected based on visual predictive check and bootstrap. Simulations of plasma concentrations for various doses were conducted.

KEY FINDINGS

A model including two compartments for CY and one for 4-OH was found to best describe the data. A proportional error model for both compounds was chosen. The following estimates were found for the main CY pharmacokinetic parameters: total clearance, 13.3 l/h with inter-individual variability (IIV) 32%, and central volume of distribution, 59.8 l with IIV 12%. The metabolite elimination rate constant was 4.3 h-1 with IIV 36% and the proportion of metabolism 64%. Sex was a significant covariate on the central volume of CY, with females exhibiting 25% lower value than males.

CONCLUSIONS

A population pharmacokinetic model was developed for CY and 4-OH in patients with autoimmune glomerulonephritis. Simulations using various dose regimens allow for informed dosing before the initiation of therapy.

Intrapulmonary pharmacokinetics of high doses of tigecycline in patients with ventilator-associated pneumonia

Tigecycline is commonly used for infections by multidrug-resistant bacteria. However, it is not approved for ventilator-associated pneumonia (VAP) as increased mortality has been reported in VAP patients treated with conventional doses. The purpose of this study was to prospectively evaluate the intrapulmonary pharmacokinetics of off-label high-dose tigecycline in patients with VAP. Nine mechanically ventilated patients received tigecycline intravenously (loading dose 200 mg followed by 100 mg every 12 h). After ≥5 doses, two bronchoscopies were performed in each patient on consecutive days and eight blood samples were collected. Tigecycline concentrations in plasma and bronchoalveolar lavage fluid were determined by liquid chromatography. The urea dilution method was used to calculate epithelial lining fluid (ELF) concentrations. A two-compartmental pharmacokinetic (PK) model with linear elimination was used to estimate PK parameters. Mean patient age was 69 ± 11.86 years and mean APACHE II score was 21. The estimated population mean PK parameters (relative standard error) were: clearance, 11.64 L/h (54%); volume of distribution in central compartment, 79.01 L (37%); volume of distribution in peripheral compartment, 92.95 L (17%); intercompartmental clearance, 62.81 L/h (34%); and ELF penetration ratio, 2.41 (40%). C_max, C_min, plasma AUC_0-12, plasma fAUC_0-12 and ELF AUC_0-12 were 1.99 ± 1.82 μg/mL, 0.81 ± 1.27 μg/mL, 12.89 ± 17.25 μg•h/mL, 3.24 ± 3.09 μg•h/mL and 7.13 ± 2.61 μg•h/mL, respectively. The increased plasma and ELF AUC_0-12 achieved with a 200 mg daily tigecycline dose, combined with high ELF penetration, support the effectiveness of off-label high-dose tigecycline in VAP.

Dose individualization of intravenous busulfan in pediatric patients undergoing bone marrow transplantation: impact and in vitro evaluation of infusion lag-time

OBJECTIVES

To apply therapeutic drug monitoring and dose-individualization of intravenous Busulfan to paediatric patients and evaluate the impact of syringe-pump induced Busulfan infusion lag-time after in vitro estimation.

METHODS

76 children and adolescents were administered 2 h intravenous Busulfan infusion every 6 h (16 doses). Busulfan plasma levels, withdrawn by an optimized sampling scheme and measured by a validated HPLC-PDA method, were used to estimate basic PK parameters, AUC, Cmax, kel, t1/2, applying Non-Compartmental Analysis. In vivo infusion lag-time was simulated in vitro and used to evaluate its impact on AUC estimation.

KEY FINDINGS

Mean (%CV) Busulfan AUC, Cmax, clearance and t1/2 for pediatric population were found 962.3 μm × min (33.1), 0.95 mg/L (41.4), 0.27 L/h/kg (33.3), 2.2 h (27.8), respectively. TDM applied to 76 children revealed 6 (7.9%) being above and 25 (32.9%) below therapeutic-range (AUC: 900-1350 μm × min). After dose correction, all patients were measured below toxic levels (AUC < 1500 μm × min), no patient below 900 μm × min. Incorporation of infusion lag-time revealed lower AUCs with 17.1% more patients and 23.1% more younger patients, with body weight <16 kg, being below the therapeutic-range.

CONCLUSIONS

TDM, applied successfully to 76 children, confirmed the need for Busulfan dose-individualization in paediatric patients. Infusion lag-time was proved clinically significant for younger, low body-weight patients and those close to the lower therapeutic-range limit.

Population pharmacokinetics of micafungin over repeated doses in critically ill patients: a need for a loading dose?

OBJECTIVES

To study the population pharmacokinetics of micafungin in critically ill patients, evaluate and optimize dosage regimens.

METHODS

An HPLC-fluorescence bioassay for micafungin was developed, fully validated and applied to a pharmacokinetic study conducted in 14 ICU patients. Dense blood sampling was performed from days 1 to 7. A population pharmacokinetic model accounting for interindividual (IIV) and interoccasion variability (IOV) of the PK parameters was developed. Simulations were performed to estimate the probability of target attainment (PTA) for several dosing regimens.

KEY FINDINGS

A two-compartment pharmacokinetic model best described the data, with population clearance CL = 1.31 L/h and central volume V1 = 14.2 L. The relatively high IOV observed (45% for CL, 27% for V1) sets limits for the dose individualization in this population. The low PTA on the first day of treatment suggests the need of a loading dose. PTA and CFR estimates show that the current micafungin dosage may be insufficient for the treatment of borderline susceptible Candida strains.

CONCLUSIONS

A loading dose of up to 300 mg of micafungin is needed for the treatment of invasive candidiasis in ICU patients while a maintenance dose of up to 200 mg can be considered in empirical antifungal treatment.

Population pharmacokinetics of anidulafungin in ICU patients assessing inter- and intrasubject variability

AIMS

The population pharmacokinetics (PK) of anidulafungin in critically ill patients hospitalized in intensive care units (ICUs) was explored with the intention of evaluating and optimizing dosing regimens.

METHODS

A PK study was conducted in a cohort of 13 patients treated with anidulafungin using intensive sampling during multiple periods per patient and the high-performance liquid chromatography method for drug quantification. A population PK model was developed to describe the concentration-time course of anidulafungin and the inter-individual (IIV) and interoccasion variability (IOV) of the PK parameters. Model-based PK simulations have been performed to estimate the probability of target attainment (PTA), given the pharmacokinetic/pharmacodynamic target of free 24-hour area under the free drug concentration-time curve over minimum inhibitory concentration for several dosing regimens.

RESULTS

A two-compartment PK model, with first-order elimination, best described the data with population clearance (CL) and central/peripheral volume of distribution (V1/V2) of 0.778 L/h and 10.2/21.1 L, respectively, and a mean ± s.d. AUC_0-24 of 119.97 ± 46.23 mg·h/L. Pronounced IIV and IOV variability was found for CL (38% and 31%) and V1 (47% and 30%), respectively. Sequential Organ Failure Assessment (SOFA) and Body Mass Index (BMI) were found to be covariates on CL and V1, respectively. Low PTA values were calculated for borderline Clinical & Laboratory Standards Institute (CLSI)-susceptible Candida strains.

CONCLUSIONS

Although anidulafungin exposure was found comparable to that in healthy volunteers, elevated interindividual and significant interoccasion variability was found in critically ill ICU patients, which resulted in reduced PTA values in these patients.

Minocycline susceptibility breakpoints for Acinetobacter baumannii: do we need to re-evaluate them?

Minocycline is an old broad-spectrum tetracycline indicated for the treatment of various infections, including those due to minocycline-susceptible Acinetobacter spp. Susceptibility data worldwide are showing increasing rates of resistance of Acinetobacter baumannii to almost all antimicrobial classes, whereas minocycline seems to remain relatively potent against this significant pathogen. Since no new effective drugs have been released against MDR A. baumannii, minocycline is an attractive choice. Tracing back minocycline CLSI susceptibility breakpoints, it is evident that they have been based on old pharmacokinetic approaches. In an attempt to integrate the scarce new pharmacodynamic data, a Monte Carlo simulation was performed. It seems that the currently used breakpoints are, 8-fold elevated according to the approved dosage regimen, giving erroneously higher rates of minocycline susceptibility of A. baumannii. Therefore, current minocycline breakpoints merit re-evaluation in order to deliver reliable susceptibility profiles for selecting the appropriate therapy.

Optimization of a paediatric fixed dose combination mini-tablet and dosing regimen for the first line treatment of tuberculosis

We aim to optimize the paediatric dosing regimen of isoniazid, rifampicin and pyrazinamide for the first-line treatment of tuberculosis, based on a fixed dose combination (FDC) mini-tablet using simulations. An optimization problem was set up to determine the 3 strengths of the drugs of the mini-tablet and 4 cutoff points that define the weight bands of a dosing chart, simultaneously. Using Monte Carlo simulations, first, exposure targets were determined for the 3 drugs, from published population pharmacokinetic models for adults, assuming that the approved doses for adults are de facto efficacious. Then optimal strengths and cutoff points were determined by matching children exposures generated from population pharmacokinetic models to the adults targets. The optimal dosing strengths of the FDC tablet were found to be 95 mg of rifampicin, 200 mg of pyrazinamide and 75 mg of isoniazid, and the 4 body weight bands for 1 to 4 mini-tablets, respectively were: 4 to 8 kg, 8 to 12 kg, 12 to 18 kg and 18 to 28 kg. Children with body weight ≥ 28 kg will be treated with adult dosages. The higher doses proposed were evaluated to be much closer to the adult targets compared to the existing recommended by WHO paediatric doses.

Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim

The aim of this study is to benchmark two Bayesian software tools, namely Stan and GNU MCSim, that use different Markov chain Monte Carlo (MCMC) methods for the estimation of physiologically based pharmacokinetic (PBPK) model parameters. The software tools were applied and compared on the problem of updating the parameters of a Diazepam PBPK model, using time-concentration human data. Both tools produced very good fits at the individual and population levels, despite the fact that GNU MCSim is not able to consider multivariate distributions. Stan outperformed GNU MCSim in sampling efficiency, due to its almost uncorrelated sampling. However, GNU MCSim exhibited much faster convergence and performed better in terms of effective samples produced per unit of time.

Fractional calculus in pharmacokinetics

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics". The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.

Extrapolation of enalapril efficacy from adults to children using pharmacokinetic/pharmacodynamic modelling

OBJECTIVES

To extrapolate enalapril efficacy to children 0-6 years old, a pharmacokinetic/pharmacodynamic (PKPD) model was built using literature data, with blood pressure as the PD endpoint.

METHODS

A PK model of enalapril was developed from literature paediatric data up to 16 years old. A PD model of enalapril was fitted to adult literature response vs time data with various doses. The final PKPD model was validated with literature paediatric efficacy observations (diastolic blood pressure (DBP) drop after 2 weeks of treatment) in children of age 6 years and higher. The model was used to predict enalapril efficacy for ages 0-6 years.

KEY FINDINGS

A two-compartment PK model was chosen with weight, reflecting indirectly age as a covariate on clearance and central volume. An indirect link PD model was chosen to describe drug effect. External validation of the model's capability to predict efficacy in children was successful. Enalapril efficacy was extrapolated to ages 1-11 months and 1-6 years finding the mean DBP drop 11.2 and 11.79 mmHg, respectively.

CONCLUSIONS

Mathematical modelling was used to extrapolate enalapril efficacy to young children to support a paediatric investigation plan targeting a paediatric-use marketing authorization application.

Serum and tissue pharmacokinetics of silibinin after per os and i.v. administration to mice as a HP-β-CD lyophilized product

Silibinin, the main active component of Silybum marianum is a hepatoprotective and antioxidant agent with antitumor effect, exhibiting very low aqueous solubility and oral bioavailability limiting its use in therapeutics. We characterized serum and tissue pharmacokinetics of SLB, calculated its absolute bioavailability and developed an open loop physiologically based pharmacokinetic (PBPK) model, after oral (per os, p.o) and intravenous (i.v.) administration in mice as water-soluble silibinin-hydroxypropyl-beta-cyclodextrin (SLB-HP-β-CD) lyophilized product. 60 C57Bl/6J mice were divided into groups of 5, each group representing one sampling time point. SLB-HP-β-CD lyophilized product was administered orally (50mg/kg) and i.v. (20mg/kg) after reconstitution with water for injection. Blood and tissue samples were collected at selected time points after animal sacrificed, properly treated and analyzed with HPLC-PDA for non-metabolized and total SLB. NONMEM pharmacokinetic analysis revealed a 2-compartment PK model to describe serum SLB pharmacokinetics, with zero order absorption after oral administration and was applied as forcing function to an open loop PBPK model incorporating heart, liver, kidneys and lungs. Tissue/plasma Kp values were estimated using i.v. data and can be used to predict tissue SLB distribution after oral administration. Absolute oral bioavailability of SLB from the lyophilized SLB-HP-β-CD product was 10 times higher than after administration of pure SLB.

Elucidating the role of dose in the biopharmaceutics classification of drugs: the concepts of critical dose, effective in vivo solubility, and dose-dependent BCS

PURPOSE

To develop a dose dependent version of BCS and identify a critical dose after which the amount absorbed is independent from the dose.

METHODS

We utilized a mathematical model of drug absorption in order to produce simulations of the fraction of dose absorbed (F) and the amount absorbed as function of the dose for the various classes of BCS and the marginal cases in between classes.

RESULTS

Simulations based on the mathematical model of F versus dose produced patterns of a constant F throughout a wide range of doses for drugs of Classes I, II and III, justifying biowaiver claim. For Classes I and III the pattern of a constant F stops at a critical dose Dose(cr) after which the amount of drug absorbed, is independent from the dose. For doses higher than Dose(cr), Class I drugs become Class II and Class III drugs become Class IV. Dose(cr) was used to define an in vivo effective solubility as S(eff) = Dose(cr)/250 ml. Literature data were used to support our simulation results.

CONCLUSIONS

A new biopharmaceutic classification of drugs is proposed, based on F, separating drugs into three regions, taking into account the dose, and Dose(cr), while the regions for claiming biowaiver are clearly defined.

Pharmacokinetics of doripenem in CSF of patients with non-inflamed meninges

OBJECTIVES

To investigate intact blood-brain barrier (BBB) penetration by doripenem and characterize doripenem pharmacokinetics in CSF using a pharmacokinetic model.

PATIENTS AND METHODS

Thirty-eight neurological patients with no active neurological disease or CNS infection received a single 500 mg doripenem dose before pump implantation surgery, or lumbar puncture, for intrathecal baclofen administration. In most cases single CSF and blood samples were collected per patient and analysed for doripenem with HPLC. A two-stage pharmacokinetic analysis was performed to estimate: (i) empirical Bayesian estimates (EBEs) of individual doripenem plasma pharmacokinetic parameters, using plasma doripenem concentrations and literature population priors for a two-compartment model; and (ii) doripenem CSF pharmacokinetic parameters using simulated plasma concentrations from stage (i) as a forcing function. The mean values of the structural model parameters, k(CSF) (distribution rate constant) and PC (CSF/plasma partition coefficient), and the residual variability were estimated.

RESULTS

The mean estimates of the parameters were k(CSF)= 0.105 h(-1) and PC= 0.053, corresponding to mean steady-state doripenem CSF concentrations of 0.20 mg/L and 0.40 mg/L for regimens of 3 × 500 mg daily and 3 × 1000 mg daily, respectively, and a mean equilibrium half-life of 6.6 h. The model was validated internally using a visual predictive check (VPC) and bootstrap. Simulating two dosing scenarios gave doripenem levels in the CSF above or close to the literature MIC values.

CONCLUSIONS

The present NONMEM software analysis shows that doripenem crosses intact BBB significantly and suggests that the drug should be further evaluated as a candidate to treat certain CNS infections, since drug penetration through BBB is enhanced by meningeal inflammation.

Supersaturated dissolution data and their interpretation: the TPGS–carbamazepine model case

Objectives

This study was undertaken to investigate the effect of d-alpha-tocopheryl polyethylene glycol 1000 succinate (vitamin E TPGS) on the dissolution of carbamazepine (CBZ) commercial tablets (Tegretol®) as a function of temperature and to modify the reaction-limited model of dissolution for the description of classical supersaturated dissolution data.

Methods

Solubility studies were performed using various concentrations of (i) TPGS and (ii) silicon dioxide and microcrystalline cellulose, which are excipients of Tegretol® at 10, 25 and 37°C. Dissolution studies were carried out using Tegretol® tablets, 200 mg/tab.

Key findings

The solubility of CBZ in the presence of TPGS was found to increase in a concentration-dependent manner at all temperatures studied. Classical supersaturated dissolution curves with concentration maxima higher than the corresponding solubility values in the presence of TPGS were observed only at 10°C. The model developed was based on a time-dependant expression for the forward microconstant of the CBZ-TPGS reaction at the solid–liquid interface and it was fitted successfully to the dissolution data of CBZ in the presence of TPGS at 10°C.

Conclusions

Vitamin E TPGS increased the solubility of CBZ at all temperatures studied. The modification of the reaction-limited model of dissolution allowed us to describe classical supersaturated dissolution curves.

Application of optimal design methodologies in clinical pharmacology experiments

Pharmacokinetics and pharmacodynamics data are often analysed by mixed-effects modelling techniques (also known as population analysis), which has become a standard tool in the pharmaceutical industries for drug development. The last 10 years has witnessed considerable interest in the application of experimental design theories to population pharmacokinetic and pharmacodynamic experiments. Design of population pharmacokinetic experiments involves selection and a careful balance of a number of design factors. Optimal design theory uses prior information about the model and parameter estimates to optimize a function of the Fisher information matrix to obtain the best combination of the design factors. This paper provides a review of the different approaches that have been described in the literature for optimal design of population pharmacokinetic and pharmacodynamic experiments. It describes options that are available and highlights some of the issues that could be of concern as regards practical application. It also discusses areas of application of optimal design theories in clinical pharmacology experiments. It is expected that as the awareness about the benefits of this approach increases, more people will embrace it and ultimately will lead to more efficient population pharmacokinetic and pharmacodynamic experiments and can also help to reduce both cost and time during drug development.

A method for robust model order reduction in pharmacokinetics

We present a Bayesian automated method to reduce by lumping, a large system described by differential equations which takes into account parameter variability. Model reduction is a potentially useful tool to simplify large systems but suffers from lack of robustness over the model parameter values. With the present method we address this problem by incorporating a prior parameter distribution in the determination of the optimal lumping scheme in a Bayesian manner. Applications of this method may include PBPK models for the drug distribution and/or Systems Biology models for the drug action. The method builds on our previously published algorithm for lumping that works stepwise, reducing the system's dimension by one at each step and where each successive step is conditional to the previous ones. We applied the methodology to a PBPK model for barbiturates taken from the literature. An arbitrary variability of 20% CV was added to the nominal reported parameter values. The Bayesian method performed better than the method which ignored the parameter variability, producing a lumping scheme which, while not optimal for any parameter value, was optimal on average. On the other hand the simple, non-Bayesian method produced a lumping scheme which while optimal for the nominal parameter values, was very poor for most other values within the prior distribution. Further, we discuss the generality of a lumping strategy to reduce a model and we argue that this is more powerful than elimination of states, with the latter being almost a special case of lumping.

Proper lumping in systems biology models

An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system's states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-B signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-B signalling pathways and were found to be in agreement, in terms of the identified key species for the system's kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.

Fractional kinetics in drug absorption and disposition processes

We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the "zero-" and "first-order" processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag-Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag-Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data.

Analytical expressions for combining population pharmacokinetic parameters from different studies

We provide a set of formulas that allow the combination of separately performed analyses of population pharmacokinetic (PK) studies, without any further computational effort. More specifically, given the point estimates and uncertainties of two population PK analyses, the formulas provide the point estimates and uncertainties of the combined analysis, including the mean population values, the between-subject variability, and the residual variability. To derive the formulas we considered distributional assumptions applicable for the conjugate priors of the Bayesian problem of "unknown mean and variance." In order to demonstrate the approach, the formulas were applied to an example involving the results of fitting two real experimental datasets. The formulas presented offer an easy-to-use method of combining different analyses particularly applicable to a combination of literature information.

Predictive models for oral drug absorption: from in silico methods to integrated dynamical models

Poor oral absorption is one of the most common reasons for a drug to be terminated during development. Oral drug absorption is a complex process affected by many competing factors related to the compound, the formulation and the gastrointestinal physiology. Throughout drug development, in silico, computational and mathematical models play important roles in the support of drug development and decision making in absorption-related issues. These models range from simple empirical rule of thumb tools to sophisticated dynamic systems. This article reviews the different computational methods for oral drug absorption for the various processes, with emphasis on solubility, permeability, dissolution and release rates, and gastrointestinal transit, but also on the modern integrated absorption prediction systems and computer software.

Bayesian Optimal Designs for Pharmacokinetic Models: Sensitivity to Uncertainty

We studied the sensitivity of the number of unique design points and their placement, in Bayesian optimal designs for pharmacokinetic models, with respect to the magnitude of prior uncertainty. We used two and three-parameter pharmacokinetic models with fixed and mixed effects and two Bayesian optimal design criteria, namely ED and API, using different error weighting schemes. We found that by increasing the magnitude of the uncertainty, in most cases, additional design points appear, compared to the corresponding local design, and this happens gradually, forming bifurcation patterns. These bifurcation patterns were interpreted as high sensitivity of the design from the magnitude of the uncertainty.

A Parenteral Econazole Formulation Using a Novel Micelle-to-Liposome Transfer Method: In Vitro Characterization and Tumor Growth Delay in a Breast Cancer Xenograft Model

PURPOSE

The aim of the study is to develop modified, branched versions of the Noyes-Whitney and the Weibull equations, including explicitly the solubility/dose parameter, for the analysis of dissolution data, which reach the plateau either at infinite or finite time.

METHODS

The modified Weibull function is applied to the analysis of experimental and literature dissolution data. To demonstrate the usefulness of the mathematical models, two model drugs are used: one highly soluble, metoprolol, and one relatively insoluble, ibuprofen.

RESULTS

The models were fitted successfully to the data performing better compared with their classic versions. The advantages of the use of the models presented are several. They fit better to a large range of datasets, especially for fast dissolution curves that reach complete dissolution at a finite time. Also, the modified Weibull presented can be derived from differential equations, and it has a physical meaning as opposed to the purely empirical character of the original Weibull equation. The exponent of the Weibull equation can be attributed to the heterogeneity of the process and can be explained by fractal kinetics concepts. Also, the solubility/dose ratio is present explicitly as a parameter and allows to obtain estimates of the solubility even when the dissolution data do not reach the solubility level.

CONCLUSION

The use of the developed branched equations gives better fittings and specific physical meaning to the dissolution parameters. Also, the findings underline the fact that even in the simplest, first-order case, the speed of the dissolution process depends on the dose, a fact of great importance in biopharmaceutic classification for regulatory purposes.

Propagation of population pharmacokinetic information using a Bayesian approach: comparison with meta-analysis

We investigated the propagation of population pharmacokinetic information across clinical studies by applying Bayesian techniques. The aim was to summarize the population pharmacokinetic estimates of a study in appropriate statistical distributions in order to use them as Bayesian priors in consequent population pharmacokinetic analyses. Various data sets of simulated and real clinical data were fitted with WinBUGS, with and without informative priors. The posterior estimates of fittings with non-informative priors were used to build parametric informative priors and the whole procedure was carried on in a consecutive manner. The posterior distributions of the fittings with informative priors where compared to those of the meta-analysis fittings of the respective combinations of data sets. Good agreement was found, for the simulated and experimental datasets when the populations were exchangeable, with the posterior distribution from the fittings with the prior to be nearly identical to the ones estimated with meta-analysis. However, when populations were not exchangeble an alternative parametric form for the prior, the natural conjugate prior, had to be used in order to have consistent results. In conclusion, the results of a population pharmacokinetic analysis may be summarized in Bayesian prior distributions that can be used consecutively with other analyses. The procedure is an alternative to meta-analysis and gives comparable results. It has the advantage that it is faster than the meta-analysis, due to the large datasets used with the latter and can be performed when the data included in the prior are not actually available.

A century of dissolution research: from Noyes and Whitney to the biopharmaceutics classification system

Dissolution research started to develop about 100 years ago as a field of physical chemistry and since then important progress has been made. However, explicit interest in drug related dissolution has grown only since the realisation that dissolution is an important factor of drug bioavailability in the 1950s. This review attempts to account the most important developments in the field, from a historical point of view. It is structured in a chronological order, from the theoretical foundations of dissolution, developed in the first half of the 20th century, and the development of a relationship between dissolution and bioavailability in the 1950s, going to the more recent developments in the framework of the Biopharmaceutics Classification System (BCS). Research on relevant fields of pharmaceutical technology, like sustained release formulations, where drug dissolution plays an important role, is reviewed. The review concludes with the modern trends on drug dissolution research and their regulatory implications.

Propagation of population PK and PD information using a Bayesian approach: dealing with non-exchangeability

The aim of this work is to implement a conservative prior that safeguards against population non-exchangeability of prior and data likelihood, in the framework of population pharmacokinetic/pharmacodynamic analysis, incorporating multi-level hierarchical modelling. Three different exercises were performed: (i) we investigated the use of parametric priors in the multilevel hierarchical modelling framework; (ii) we assessed the average performance of the multilevel hierarchical model compared to the standard mixed effect model, considering also some interesting extreme cases and (iii) we implemented an application with a small Proof of Principle (PoP) study, which demonstrates the propagation of information across PD studies using multilevel modelling. Fitting with the 4-level model and informative parametric priors performed similar to a meta-analysis of the test datasets combined with the datasets that the priors came from, demonstrating that parametric priors can be used alternatively to meta-analysis. Further, the 4-level model gave posterior distributions which had larger uncertainty but at the same time were unbiased, compared to the 3-level model, and therefore implements a more conservative prior in a formal way, which is appropriate when the prior and the test populations are not exchangeable. For the application with the PoP study, the statistical power of detecting the difference in potency between two drugs, when inter-study variability was present, was greater when an extra level in the hierarchical model to account for it, was used. In conclusion, by applying the prior one hierarchical level above the level of the parameters of interest, we implemented a more conservative prior, compared to applying the prior directly on the parameters of interest. The approach is equivalent to Bayesian individualization, offers a safeguard against bias from the prior and also avoids the danger of the data being overwhelmed by a strong prior.

Modeling and Monte Carlo simulations in oral drug absorption

Drug dissolution, release and uptake are the principal components of oral drug absorption. All these processes take place in the complex milieu of the gastrointestinal tract and they are influenced by physiological (e.g. intestinal pH, transit time) and physicochemical factors (e.g. dose, particle size, solubility, permeability). Due to the enormous complexity issues involved, the models developed for drug dissolution and release attempt to capture their heterogeneous features. Hence, Monte Carlo simulations and population methods have been utilized since both dissolution and release processes are considered as time evolution of a population of drug molecules moving irreversibly from the solid state to the solution. Additionally, mathematical models have been proposed to determine the effect of the physicochemical properties, solubility/dose ratio and permeability on the extent of absorption for regulatory purposes, e.g. biopharmaceutics classification. The regulatory oriented approaches are based on the tube model of the intestinal lumen and apart from the drug's physicochemical properties, take into account the formulation parameters the dose and the particle size.

Identification of Biowaivers Among Class II Drugs: Theoretical Justification and Practical Examples

PURPOSE

To set up a theoretical basis for identifying biowaivers among Class II drugs and apply the methodology developed to nonsteroidal anti-inflammatory drugs (NSAIDs).

METHODS

The dynamics of the two consecutive drug processes dissolution and wall permeation are considered in the time domain of the physiologic transit time using a tube model of the intestinal lumen. The model considers constant permeability along the intestines, a plug flow fluid with the suspended particles moving with the fluid, and dissolution in the small particle limit. The fundamental differential equation of drug dissolution-uptake in the intestines is expressed in terms of the fraction of dose dissolved.

RESULTS

The fundamental parameters, which define oral drug absorption in humans resulting from this analysis, are i) the formulation-related factors, dose, particle radius size, and ii) the drug-related properties, dimensionless solubility/dose ratio (1/q), and effective permeability. Plots of dose as a function of (1/q) for various particle sizes unveil the specific values of these meaningful parameters, which ensure complete absorption for Class II drugs [(1/q) < 1]. A set of NSAIDs were used to illustrate the application of the approach in identifying biowaivers among the NSAIDs.

CONCLUSIONS

The underlying reason for a region of fully absorbed drugs in Class II originates from the dynamic character of the dissolution-uptake processes. The dynamic character of the approach developed allows identification of biowaivers among Class II drugs. Several biowaivers among the NSAIDs were identified using solubility data at pH 5.0 and in fed-state-simulated intestinal fluid at pH 5.0. The relationships of formulation parameters, dose, particle radius, and the drug properties, dimensionless solubility/dose ratio (1/q), and permeability with the fraction of dose absorbed for drugs with low 1/q values [(1/q) < 1] can be used as guidance for the formulation scientist in the development phase.

A Physiologically Based Approach for the Estimation of Recirculatory Parameters

Indicator dilution studies are used to provide estimates for several physiological parameters such as cardiac output as well as intra- and extravascular volumes. This study introduces a novel technique for the estimation of recirculatory parameters. A mathematical model based on a dispersion-convection partial differential equation (PDE), derived from the fractal geometry of the vascular tree and the hydrodynamics of the blood flow, is used to describe the spatiotemporal profile of tracers in the circulatory system. Initially, the equation is fitted to concentration-time (C,t) data of a tracer to derive the parameter estimates of the model equation; in a subsequent step, these estimates along with appropriate changes of the parameters of the PDE are used to generate the early concentration-time profile of a hypothetical appropriate tracer without recirculation. Thus, the area under the concentration-time curve of the first passage of the tracer is calculated and used for the estimation of various physiological parameters, including cardiac output, miscellaneous partial blood volumes, and the corresponding mean transit times. The procedure was applied successfully to literature data of various tracers from humans and dogs.