Physiologically motivated time-delay model to account for mechanisms underlying enterohepatic circulation of piroxicam in human beings

Physiologically based pharmacokinetic (PBPK) modeling of piroxicam with regard to CYP2C9 genetic polymorphism

Piroxicam is a non-steroidal anti-inflammatory drug used to alleviate symptoms of osteoarthritis and rheumatoid arthritis. CYP2C9 genetic polymorphism significantly influences the pharmacokinetics of piroxicam. The objective of this study was to develop and validate the piroxicam physiologically based pharmacokinetic (PBPK) model related to CYP2C9 genetic polymorphism. PK-Sim^® version 10.0 was used for the PBPK modeling. The PBPK model was evaluated by predicted and observed plasma concentration-time profiles, fold errors of predicted to observed pharmacokinetic parameters, and a goodness-of-fit plot. The turnover number (k_cat) of CYP2C9 was adjusted to capture the pharmacokinetics of piroxicam in different CYP2C9 genotypes. The population PBPK model overall accurately described and predicted the plasma concentration-time profiles in different CYP2C9 genotypes. In our simulations, predicted AUC_inf in CYP2C9*1/*2, CYP2C9*1/*3, and CYP2C9*3/*3 genotypes were 1.83-, 2.07-, and 6.43-fold higher than CYP2C9*1/*1 genotype, respectively. All fold error values for AUC, C_max, and t_1/2 were included in the acceptance criterion with the ranges of 0.57-1.59, 0.63-1.39, and 0.65-1.51, respectively. The range of fold error values for predicted versus observed plasma concentrations was 0.11-3.13. 93.9% of fold error values were within the two-fold range. Average fold error, absolute average fold error, and root mean square error were 0.93, 1.27, and 0.72, respectively. Our model accurately captured the pharmacokinetic alterations of piroxicam according to CYP2C9 genetic polymorphism.

Square root law model for the delivery and intestinal absorption of drugs: a case of hydrophilic captopril

The in vivo release and absorption of drugs are dependent on the interplay between many factors related to compound, formulation, and physiological properties. The mathematical models of oral drug absorption attempt to strike a balance between a complete description that takes into consideration as many independent factors as possible, and simple models that operate with fewer parameters, based mainly on critical factors. The latter models are by far more robust and easier to apply to predict the extent and sometimes even the rate of absorption. The present paper attempted to develop a simple model to describe the time course of absorption of the hydrophilic drug captopril (CPT) at the early phases of absorption, with implications mainly in the induction and early stages of achieving its therapeutic effect. As a phenomenological model, the instantaneous release of CPT was considered in the gastrointestinal fluid, leading to a constant drug concentration for a prolonged time, followed by a ‘long path diffusion’ inside the intestinal wall and a very low concentration at the interface intestinal wall-blood. These conditions regarding CPT concentration were translated into initial and boundary mathematical conditions for the diffusion equation in the intestinal wall. The solution of the diffusion equation led in the end to a square root law describing the dependence between the fraction of the drug absorbed and time. The model was successfully applied to data obtained in five bioequivalence studies: three comparing plasma levels achieved after the administration of a single dose of CPT 50 mg, one evaluating CPT pharmacokinetics after a 100 mg dose, and a fifth comparing CPT pharmacokinetics of two fixed-dose combinations of CPT 50 mg and hydrochlorothiazide 25 mg.

Estimation of the In Vivo Release of Amiodarone From the Pharmacokinetics of Its Active Metabolite and Correlation With Its In Vitro Release

Due to its very low water solubility and complex pharmacokinetics, a reliable point-to-point correlation of its in vitro release with its pharmacokinetics has not been achieved so far with amiodarone. The correlation of the in vitro dissolution of a drug with the pharmacokinetics of one of its metabolites was recently proposed by the authors of the article as an additional or alternative analysis to the usual in vitro correlations in vivo, mainly in the case of fast-absorbing drugs that have metabolites with a significant therapeutic effect. The model proposed by the authors considers that amiodarone has a slow dissolution, rapid absorption, and rapid metabolism, and before returning to the blood from other compartments, its pharmacokinetics is determined mainly by the kinetics of release in the intestine from the pharmaceutical formulation. Under these conditions, the rate of apparition of desethylamiodarone in the blood is a metric of the release of amiodarone in the intestinal fluid. Furthermore, it has been shown that such an estimated in vivo dissolution is similar, after time scaling, to the dissolution measured experimentally in vitro. Dissolution data of amiodarone and the pharmacokinetic data of its active metabolite desethylamiodarone were obtained in a bioequivalence study of 24 healthy volunteers. The elimination constant of the metabolite from plasma was estimated as the slope of the linear regression of logarithmically transformed data on the tail of plasma levels. Because the elimination of desethylamiodarone was shown to follow a monoexponential model, a Nelson–Wagner-type mass equilibrium model could be applied to calculate the time course of the “plasma metabolite fraction.” After Levi-type time scaling for imposing the in vitro–in vivo correlation, the problem became that of the correlation between in vitro dissolution time and in vivo dissolution time, which was proven to follow a square root model. To validate the model, evaluations were performed for the reference drug and test drug separately. In both cases, the scaled time for in vivo dissolution, t*, depended approximately linearly on the square root of the in vitro dissolution time t, with the two regression lines being practically parallel.

A compartmental approach to isosteviol's disposition in Sprague-Dawley rats

Isosteviol has been reported to reverse hypertrophy and related inflammatory responses in in vitro models representative of cardiac muscle cells. The disposition of isosteviol is, however, characterized by secondary peaks and long plasma residence time despite reports of a relatively short half-life in liver fractions. The present study describes a compartmental approach to modelling the secondary peaks characteristic of isosteviol's concentration-time data in Sprague-Dawley rats. Oral (4 mg/kg) and intravenous (4 mg/kg) doses of isosteviol were administered to male and female Sprague-Dawley rats. Plasma samples collected between 0 and 72 h, and total bile secreted in 24 h, were analysed for isosteviol content with LC-MS/MS techniques. The disposition of isosteviol was, thereafter, described with a structural model that accounted for the sampling, liver and biliary secretion compartments, with a gap-time characterizing the accumulation and subsequent emptying of isosteviol for re-absorption. The half-life of isosteviol following oral dosing was about 103% greater in female rats than in the male, and the model-derived area under the concentration-time curve (AUC) in 72 h was about 756% greater in female animals than in males. Following the administration of intravenous doses of isosteviol, half-life and AUC in 24 h were about 332% and 595%, respectively, higher in female rats than in males. Isosteviol equivalent secreted into bile over 24 h accounted for about 94% of orally administered dose in male rats, and about 59% of oral dose in females. These findings show a differential systemic removal of isosteviol in Sprague-Dawley rats, likely explainable by gender-related differences in the glucuronidation-capacity of isosteviol.

Modelling gastric emptying: A pharmacokinetic model simultaneously describing distribution of losartan and its active metabolite EXP-3174

Losartan presents multiple peaks in the concentration-time profile. This characteristic can be attributed to gastric emptying, which is known to significantly affect the disposition of highly soluble and permeable compounds. The aim of this study was to develop a population pharmacokinetic model for losartan and its active metabolite (EXP-3174) in order to describe the effect of gastric emptying on their disposition. Population pharmacokinetic analysis was performed using concentration-time data derived from a crossover bioequivalence study in 31 volunteers after a single oral dose of 100 mg losartan potassium in the fasted state. Delay differential equations (DDEs) were explored for the description of losartan absorption and EXP-3174 formation, since when solved they result in oscillatory behaviour. A two-compartment model preceded by a pre-absorption compartment (referring to small intestine) adequately described the observed concentration-time profiles of losartan. In the final model, a sinusoidal equation was used for the description of gastric emptying in view of its simplicity, leading to enhanced stability of the model and its capacity to describe periodicity. In case of EXP-3174, a one-compartment model, with a delayed first-order formation rate from losartan's central compartment, best described its disposition. Using the model developed, it was shown through simulations that changes in gastric emptying parameters lead to changes in the C-t profiles of both compounds. In particular, plasma oscillations can be enhanced or completely suppressed, simply by changing parameters affecting gastric emptying.

In Vitro-In Vivo Correlations Based on In Vitro Dissolution of Parent Drug Diltiazem and Pharmacokinetics of its Metabolite

In this study a novel type of in vitro-in vivo correlation (IVIVC) is proposed: The correlation of the in vitro parent drug dissolution data with the in vivo pharmacokinetic data of drug's metabolite after the oral administration of the parent drug. The pharmacokinetic data for the parent drug diltiazem (DTZ) and its desacetyl diltiazem metabolite (DTZM) were obtained from an in vivo study performed in 19 healthy volunteers. The pharmacokinetics of the parent drug and its metabolite followed a pseudomono-compartmental model and deconvolution of the DTZ or DTZM plasma concentration profiles was performed with a Wagner-Nelson-type equation. The calculated in vivo absorption fractions were correlated with the in vitro DTZ dissolution data obtained with USP 2 apparatus. A linear IVIVC was obtained for both DTZ and DTZM, with a better correlation observed for the case of the metabolite. This type of correlation of the in vitro data of the parent compound with the in vivo data of the metabolite could be useful for the development of drugs with active metabolites and prodrugs.

Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems

Embedding of active substances in supramolecular systems has as the main goal to ensure the controlled release of the active ingredients. Whatever the final architecture or entrapment mechanism, modeling of release is challenging due to the moving boundary conditions and complex initial conditions. Despite huge diversity of formulations, diffusion phenomena are involved in practically all release processes. The approach in this paper starts, therefore, from mathematical methods for solving the diffusion equation in initial and boundary conditions, which are further connected with phenomenological conditions, simplified and idealized in order to lead to problems which can be analytically solved. Consequently, the release models are classified starting from the geometry of diffusion domain, initial conditions, and conditions on frontiers. Taking into account that practically all solutions of the models use the separation of variables method and integral transformation method, two specific applications of these methods are included. This paper suggests that "good modeling practice" of release kinetics consists essentially of identifying the most appropriate mathematical conditions corresponding to implied physicochemical phenomena. However, in most of the cases, models can be written but analytical solutions for these models cannot be obtained. Consequently, empiric models remain the first choice, and they receive an important place in the review.

A Simple, Realistic Stochastic Model of Gastric Emptying

Several models of Gastric Emptying (GE) have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations), considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.

Role of enterohepatic recirculation in drug disposition: cooperation and complications

Enterohepatic recirculation (EHC) concerns many physiological processes and notably affects pharmacokinetic parameters such as plasma half-life and AUC as well as estimates of bioavailability of drugs. Also, EHC plays a detrimental role as the compounds/drugs are allowed to recycle. An in-depth comprehension of this phenomenon and its consequences on the pharmacological effects of affected drugs is important and decisive in the design and development of new candidate drugs. EHC of a compound/drug occurs by biliary excretion and intestinal reabsorption, sometimes with hepatic conjugation and intestinal deconjugation. EHC leads to prolonged elimination half-life of the drugs, altered pharmacokinetics and pharmacodynamics. Study of the EHC of any drug is complicated due to unavailability of the apposite model, sophisticated procedures and ethical concerns. Different in vitro and in vivo methods for studies in experimental animals and humans have been devised, each having its own merits and demerits. Involvement of the different transporters in biliary excretion, intra- and inter-species, pathological and biochemical variabilities obscure the study of the phenomenon. Modeling of drugs undergoing EHC has always been intricate and exigent models have been exploited to interpret the pharmacokinetic profiles of drugs witnessing multiple peaks due to EHC. Here, we critically appraise the mechanisms of bile formation, factors affecting biliary drug elimination, methods to estimate biliary excretion of drugs, EHC, multiple peak phenomenon and its modeling.

System approach to modeling of liver glucose metabolism with physiologically interpreted model parameters outgoing from [18F]FDG concentrations measured by PET

New mathematical models from physiologically interpreted parameters capable of evaluating glucose metabolism within the liver and/or the whole body were developed. The group of pigs in a fasting state and the group of pigs with euglycemic supraphysiological hyperinsulinemia were scanned by positron emission tomography after a single dose of [(18)F]FDG tracer. Simultaneously frequent sampling of the dynamic data of [(18)F]FDG plasma concentration in artery, portal vein and hepatic vein was obtained. A system approach to the liver and/or the whole-body system by the tools of linear dynamic sysztem theory was used. Three kinds of structural models, single input and single output or multiple outputs and multiple inputs and single output, were identified. Differences between the group of fasting pigs and the group of pigs in euglycemic supraphysiological hyperinsulinemia were identified by estimated parameters of the structural models. The suitability of the structural mathematical models for the estimation of physiologically interpreted parameters from PET was validated.

Physiologically based structure of mean residence time

A mean residence time (MRT) is an important pharmacokinetic parameter. To the author's knowledge, however, a physiologically based structure of MRT (thereafter MRT structure) has not been published so far. Primarily this is because MRT structures cannot be identified by traditional pharmacokinetic methods used for the determination of MRT. Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. The MRT structure identified is physiologically meaningful. Accordingly, it seems that the MRT structure identified may contribute to already established knowledge about MRT.

Novel approach to bioequivalence assessment based on physiologically motivated model

The study was conducted to exemplify an approach capable of obtaining a new insight into bioequivalence (BE) assessment, by the use of a physiologically motivated model. Data from an oral BE study of two piroxicam (PXM) products was used as an example. The BE study was carried out with 24 healthy European subjects according to a two-sequence crossover-randomized design. The test and reference formulations were a PXM generic formulation (LaborMed Pharma, Romania) and Feldene (Pfizer, USA), respectively. Plasma concentrations of PXM were monitored by a validated high-performance liquid chromatography over a period of 144 h after administration. After the structure of the optimal model was selected, parameters that characterized the whole-body disposition behavior of PXM in the subjects were derived. The paired Student's t-test and Wilkoxon's test were performed on the derived parameters. The null hypothesis of no differences in the parameters of the whole-body disposition behavior of PXM related to the test and reference product was not rejected at 5% level of significance. This result suggested that the compared products were bioequivalent and could be used interchangeably in clinical setting. The presented approach might show a new way, worth incorporating in future BE guidelines.

Computer controlled sequential simulation method: reconsidering evaluation of measurements from frequently sampled intravenous glucose tolerance test

This work describes quantification of regulatory mechanisms glucose-insulin, using data from a frequently sampled intravenous glucose tolerance test (FSIVGTT) and a mechanistically motivated model with time delays. FSIVGTT was performed on 14 young healthy volunteers. The constructed model computationally takes into account the form of the short-time glucose infusion used. Estimated model parameters are used to derive relationships quantifying the following mechanisms of regulatory systems glucose-insulin of the volunteers enrolled: (1) glucose uptake by body cells; (2) cessation (suppression) of glucose output from liver; (3) glucose clearance. The model presented correctly approximates initial peaks and subsequent waves in plasma glucose concentration-time profiles after the glucose infusion. These results indicate that the model presented is an appropriate tool for assessing glucose behavior during a FSIVGTT.