The concept of Finite Absorption Time (FAT) for oral drug administration is set to affect pharmacokinetic analyses, Physiologically-based Pharmacokinetics simulations, and Pharmacometrics.

To date, mechanistic modeling of oral drug absorption has been achieved via the use of physiologically based pharmacokinetic (PBPK) modeling, and more specifically, physiologically based biopharmaceutics model (PBBM). The concept of finite absorption time (FAT) has been developed recently and the application of the relevant physiologically based finite time pharmacokinetic (PBFTPK) models to experimental data provides explicit evidence that drug absorption terminates at a specific time point. In this manuscript, we explored how PBBM and PBFTPK models compare when applied to the same dataset. A set of six compounds with clinical data from immediate-release formulation were selected. Both models resulted in absorption time estimates within the small intestinal transit time, with PBFTPK models generally providing shorter time estimates. A clear relationship between the absorption rate and the product of permeability and luminal concentration was observed, in concurrence with the fundamental assumptions of PBFTPK models. We propose that future research on the synergy between the two modeling approaches can lead to both improvements in the initial parameterization of PBPK/PBBM models but to also expand mechanistic oral absorption concepts to more traditional pharmacometrics applications.

The infinite time of oral drug absorption was conceived from the first day of the birth of pharmacokinetics when H. Dost introduced the term pharmacokinetics in his book published in 1953. He adopted the function developed by H. Bateman back in 1908 for the decay of the nuclei isotopes to describe oral drug absorption as a first-order process. We unveiled this false hypothesis relying on common wisdom i.e. drugs are absorbed in finite time. This false assumption had dramatic effects on the evolution of oral pharmacokinetics but most importantly on the bioavailability and bioequivalence concepts and metrics. This work focuses on the finite absorption time (FAT) concept, the relevant Physiologically Based Finite Time (PBFTPK) models developed and their applications in oral pharmacokinetics, bioavailability and bioequivalence. The crux of the matter is that drug absorption from the gastrointestinal tract takes place under sink conditions because of the high blood flow rate in the vena cava. The termination of oral, pulmonary and intranasal drug absorption at a specific time point, calls for regulatory changes in bioavailability and bioequivalence studies in terms of the study design and metrics used for the bioequivalence assessment.

Purpose To develop physiologically based finite time pharmacokinetic (PBFTPK) models for the analysis of oral pharmacokinetic data. Methods The models are based on the passive drug diffusion mechanism under the sink conditions principle. Up to three drug successive input functions of constant rate operating for a total time tau are considered. Differential equations were written for all these models assuming linear one- or two-compartment-model disposition. The differential equations were solved and functions describing the concentration of drug as a function of time for the central and the peripheral compartment were derived. The equations were used to generate simulated data and they were also fitted to a variety of experimental literature oral pharmacokinetic data. Results The simulated curves resemble real life data. The end of the absorption processes tau is either equal to t(max) or longer than t(max) at the descending portion of the concentration time curve. Literature oral pharmacokinetic data of paracetamol, ibuprofen, almotriptan, cyclosporine (a total of four sets of data), and niraparib were analyzed using the PBFTPK models. Estimates for tau corresponding to a single or two or three different in magnitude input rates were derived along with the other model parameters for all data analyzed. Conclusions The PBFTPK models are a powerful tool for the analysis of oral pharmacokinetic data since they rely on the physiologically sound concept of finite absorption time.

Objective The current study aimed to develop a novel milk-based formulation of docetaxel, a sparingly soluble antineoplastic agent, administered so far exclusively by the intravenous route and evaluate its oral bioavailability. Methods Pre-formulation studies included the determination of docetaxel solubility in water-alcohol mixtures as well as short-term content uniformity experiments of the final formulation. The pharmacokinetic (PK) performance of the developed milk-based formulations was further evaluated in vivo in mice using ritonavir, a potent P-glycoprotein inhibitor, as an absorption enhancer of docetaxel and the marketed intravenous docetaxel formulation, Taxotere (R), as a control. Results In vivo PK results in mice showed that all the administered oral docetaxel formulations had limited absorption in the absence of ritonavir. On the contrary, ritonavir co-administration given as pre-treatment significantly enhanced oral bioavailability of both the marketed and milk-based docetaxel formulations; an even more marked increase in drug exposure was observed when ritonavir was incorporated within the docetaxel milk-based formulation. The fixed-dose combination also showed a more prolonged absorption of the drug compared to separate administrations. Conclusions The current study provides insights for the discovery of a novel milk-based formulation that could potentially serve as an alternative, non-toxic and patient-friendly carrier for an acceptable docetaxel oral chemotherapy.

Purpose o explore the application of the parameters of the physiologically based finite time pharmacokinetic (PBFTPK) models subdivided in first-order (PBFTPK)(1) and zero-order (PBFTPK)(0) models to bioavailability and bioequivalence. To develop a methodology for the estimation of absolute bioavailability, F, from oral data exclusively. Methods Simulated concentration time data were generated from the Bateman equation and compared with data generated from the (PBFTPK)(1) and (PBFTPK)(0) models. The blood concentration C-b(tau) at the end of the absorption process tau, was compared to C-max; the utility of AUC(0)(tau) and (AUC)(t)(infinity) in bioequivalence assessment was also explored. Equations for the calculation of F from oral data were derived for the (PBFTPK)(1) and (PBFTPK)(0) models. An estimate for F was also derived from an areas proportionality using oral data exclusively. Results The simulated data of the (PBFTPK)(0) models exhibit rich dynamics encountered in complex drug absorption phenomena. Both (PBFTPK)(1) and (PBFTPK)(0) models result either in C-max = C-b(tau) or C-max > C-b(tau) for rapidly- and not rapidly-absorbed drugs, respectively; in the latter case, C-b(tau) and tau are meaningful parameters for drug's rate of exposure. For both (PBFTPK)(1) and (PBFTPK)(0) models, (AUC)(0)(tau) or portions of it cannot be used as early exposure rate indicators. (AUC)(tau)(infinity) is a useful parameter for the assessment of extent of absorption for very rapidly absorbed drugs. An estimate for F for theophylline formulations was found close to unity. Conclusion The (PBFTPK)(1) and (PBFTPK)(0) models are more akin to in vivo conditions. Estimates for F can be derived from oral data exclusively.

AbsractPurposeTo demonstrate that oral drug absorption is terminated in finite time. To develop models based on biopharmaceutical/physiological and finite absorption time concepts.MethodsThe models are based on i) the passive drug diffusion mechanism under the sink conditions principle ii) the rate limiting role of the drug's properties solubility and permeability and iii) the relevant restrictions associated with the gastrointestinal transit times of drug in the stomach, the small intestines and the colon. Two input functions of constant rate are considered for the absorption of drug from i) the stomach/small intestines with an upper limit of 5 h and ii) the colon with an upper limit of 30 h. Branched differential equations were written for the time course of drug in the body.ResultsSimulations were performed using different scenarios, assuming a variety of drug properties and limited or non-existent absorption from the colon. Literature oral data of cephradine, ibuprofen, flurbiprofen and itraconazole were analyzed. For all drugs examined, nice fittings of the branched differential equations to the experimental data were observed.ConclusionsFor all drugs the absorption process was terminated in the small intestine. The meaning of partial AUCs, Cmax, tmax are questioned. Applications of these models to IVIVC are anticipated.

The COVID-19 pandemic has already had a shocking impact on the lives of everybody on the planet. Here, we present a modification of the classical SI model, the Fractal Kinetics SI model which is in excellent agreement with the disease outbreak data available from the World Health Organization. The fractal kinetic approach that we propose here originates from chemical kinetics and has successfully been used in the past to describe reaction dynamics when imperfect mixing and segregation of the reactants is important and affects the dynamics of the reaction. The model introduces a novel epidemiological parameter, the ``fractal{''} exponenthwhich is introduced in order to account for the self-organization of the societies against the pandemic through social distancing, lockdowns and flight restrictions.

This work aims to explore the unphysical assumptions associated with i) the homogeneity of the well mixed compartments of pharmacokinetics and ii) the diffusion limited model of drug dissolution. To this end, we i) tested the homogeneity hypothesis using Monte Carlo simulations for a reaction and a diffusional process that take place in Euclidean and fractal media, ii) re-considered the flip-flop kinetics assuming that the absorption rate for a one-compartment model is governed by an instantaneous rate coefficient instead of a rate constant, and, iii) re-considered the extent of drug absorption as a function of dose using an in vivo reaction limited model of drug dissolution with integer and non-integer stoichiometry values. We found that drug diffusional processes and reactions are slowed down in heterogeneous media and the environmental heterogeneity leads to increased fluctuations of the measurable quantities. Highly variable experimental literature data with measurements in intrathecal space and gastrointestinal fluids were explained accordingly. Next, by applying power law and Weibull input functions to a one-compartment model of disposition we show that the shape of concentration-time curves is highly dependent on the time exponent of the input functions. Realistic examples based on PK data of three compounds known to exhibit flip-flop kinetics are analyzed. The need to use time dependent coefficients instead of rate constants in PBPK modeling and virtual bioequivalence is underlined. Finally, the shape of the fraction absorbed as a function of dose plots, using an in vivo reaction limited model of drug dissolution were found to be dependent on the stoichiometry value and the solubility of drug. Ascending and descending limbs were observed for the higher stoichiometries (2.0 and 1.5) with the low solubility drug. In contrast, for the more soluble drug, a continuous increase of fraction absorbed as a function of dose is observed when the higher stoichiometries are used (2.0 and 1.5). For both drugs, the fraction absorbed for the lower values of stoichiometry (0.7 and 1.0) exhibit a non-dependency on dose profile. Our results give an insight into the complex picture of in vivo drug dissolution since diffusion-limited and reaction-limited processes seem to operate under in vivo conditions concurrently.

The recent impact of the Biopharmaceutics Classification System (BCS) and the Biopharmaceutics Drug Disposition Classification System (BDDCS) on relevant scientific advancements is discussed. The major advances associated with the BCS concern the extensive work on dissolution of poorly absorbed BCS class II drugs in nutritional liquids (e.g. milk, peanut oil) and biorelevant media for the accurate prediction of the rate and the extent of oral absorption. The use of physiologically based pharmacokinetic (PBPK) modeling as predictive tool for bioavailability is also presented. Since recent dissolution studies demonstrate that the two mechanisms (diffusion- and reaction-limited dissolution) take place simultaneously, the neglected reaction-limited dissolution models are discussed, regarding the biopharmaceutical classification of drugs. Solubility- and dissolution-enhancing formulation strategies based on the supersaturation principle to enhance the extent of drug absorption, along with the applications of the BDDCS to the understanding of disposition phenomena are reviewed. Finally, recent classification systems relevant either to the BCS or the BDDCS are presented. These include: i) a model independent approach based on %metabolism and the fulfilment (or not) of the current regulatory dissolution criteria, ii) the so called AB Gamma system, a continuous version of the BCS, and iii) the so-called Extended Clearance Classification System (ECCS). ECCS uses clearance concepts (physicochemical properties and membrane permeability) to classify compounds and differentiates from BDDCS by bypassing the measure of solubility (based on the assumption that since it inter-correlates with lipophilicity, it is not directly relevant to clearance mechanisms or elimination).

We compare two of the most successful models for the description and analysis of drug release data. The fractal kinetics approach leading to release profiles described by a Weibull function and the fractional kinetics approach leading to release profiles described by a Mittag-Leffler function. We used Monte Carlo simulations to generate artificial release data from euclidean and fractal substrates. We have also used real release data from the literature and found that both models are capable in describing release data up to roughly 85% of the release. For larger times both models systematically overestimate the number of particles remaining in the release device.

The aim of this work is to develop a gastrointestinal (GI) drug absorption model based on a reaction limited model of dissolution and consider its impact on the biopharmaceutic classification of drugs. Estimates for the fraction of dose absorbed as a function of dose, solubility, reaction/dissolution rate constant and the stoichiometry of drug-GI fluids reaction/dissolution were derived by numerical solution of the model equations. The undissolved drug dose and the reaction/dissolution rate constant drive the dissolution rate and determine the extent of absorption when high-constant drug permeability throughout the gastrointestinal tract is assumed. Dose is an important element of drug-GI fluids reaction/dissolution while solubility exclusively acts as an upper limit for drug concentrations in the lumen. The 3D plots of fraction of dose absorbed as a function of dose and reaction/dissolution rate constant for highly soluble and low soluble drugs for different ``stoichiometries{''} (0.7, 1.0, 2.0) of the drug-reaction/dissolution with the GI fluids revealed that high extent of absorption was found assuming high drug-reaction/dissolution rate constant and high drug solubility. The model equations were used to simulate in vivo supersaturation and precipitation phenomena. The model developed provides the theoretical basis for the interpretation of the extent of drug's absorption on the basis of the parameters associated with the drug-GI fluids reaction/dissolution. A new paradigm emerges for the biopharmaceutic classification of drugs, namely, a model independent biopharmaceutic classification scheme of four drug categories based on either the fulfillment or not of the current dissolution criteria and the high or low % drug metabolism.

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.

Dry powder inhalers containing the budesonide/formoterol combination have currently a well-established position among other inhaled products. Even though their efficacy mainly depends on the local concentrations of the drug they deliver within the lungs, their safety profile is directly related to their total systemic exposure. The aim of the present investigation was to explore the absorption and disposition kinetics of the budesonide/formoterol combination delivered via two different dry powder inhalers in asthma patients. Plasma concentration time data were obtained from a single-dose, crossover bioequivalence study in asthma patients. Non compartmental and population compartmental approaches were applied to the available datasets. The non compartmental analysis allowed for an initial characterization of the primary pharmacokinetic (PK) parameters of the two inhaled drugs and subsequently the bioequivalence assessment of the two different dry powder inhalers. The population pharmacokinetic analysis further explored the complex absorption and disposition characteristics of the two drugs. In case of inhaled FOR, a five-compartment PK model including an enterohepatic re-circulation process was developed. For inhaled BUD, the incorporation of two parallel first-order absorption rate constants (fast and slow) for lung absorption in a two-compartment PK model emphasized the importance of pulmonary anatomical features and underlying physiological processes during model development. The role of potential covariates on the variability of the PK parameters was also investigated.

Salmeterol (SAL) is a long-acting beta 2-adrenergic agonist, which is widely used in the therapy of asthma. The aim of this study was to investigate the pharmacokinetics (PK) of inhaled salmeterol in asthma patients using two different dry powder inhalers. This analysis was based on data from 45 subjects who participated in a two-sequence, four-period crossover bioequivalence (BE) study after single administration of the test (T) and reference (R) products. In order to mimic more closely the real treatment conditions, activated charcoal was not co-administered. Plasma concentration-time (C-t) data were initially analysed using classic non-compartmental PK approaches, while the main objective of the study was to apply population PK modeling. The relative fraction of the dose absorbed via the lungs (R-L) was set as a parameter in the structural model. The plasma C-t profiles of salmeterol showed a biphasic time course indicating a parallel pulmonary and gastrointestinal (GI) absorption. A two-compartment disposition model with first order absorption from the GI and very rapid absorption from lungs (like an i.v. bolus) was found to describe successfully the C-t profiles of salmeterol. The estimated R-L value was 13% suggesting a high gut deposition of inhaled salmeterol. Women were found to exert less capability to eliminate salmeterol than men, while body weight (in allometric form) was found to be an important covariate on the peripheral volume of distribution.

Fractional-order dynamical systems were recently introduced in the field of pharmacokinetics where they proved powerful tools for modeling the absorption, disposition, distribution and excretion of drugs which are liable to anomalous diffusion, deep tissue trapping and other nonlinear phenomena. In this paper we present several ways to simulate such fractional order pharmacokinetic models and we evaluate their accuracy and complexity on a fractional order pharmacokinetic model of Amiodarone, an anti-arrhythmic drug. We then propose an optimal administration scheduling scheme and evaluate it on a population of patients. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

The biopharmaceutics classification system (BCS) was based on the tube model of the intestinal lumen. This model considers constant drug permeability along the intestines, a plug flow fluid with the suspended drug particles moving with the fluid, and dissolution in the small particle limit. Since then the research work focusing on drug gastrointestinal (GI) absorption phenomena and processes rely on the classical laws of transport, diffusion and kinetics; however, the homogeneous assumptions associated with the well-stirred Euclidean media, where the classical laws of diffusion and kinetics apply, have been questioned in the past In this work we explore the biopharmaceutic classification of drugs using a heterogeneous pseudo steady-state model of oral drug absorption. The fraction of dose absorbed (F-abs) was expressed as a function of two time-dependent processes where time dependent coefficients govern drug absorption and non-absorption processes. Fundamental drug properties like the absorption potential are correlated with F-abs and allow the biopharmaceutic classification of drugs taking into account the heterogeneous aspects of oral drug absorption. This analysis reveals that for Class I drugs no time dependency is expected for both absorption and non absorption processes since the gastric emptying is controlling the absorption of Class I drugs while the completion of absorption (F-abs > 90%) is terminated along the first part of the jejunum. Due to the biopharmaceutical properties of Class II, III and IV drugs, these drugs travel throughout the GI tract and therefore both absorption and non absorption processes will exhibit time dependency. Thus, the calculation of F-abs (<90%) for Class II, III and IV is dependent on the estimates of the time exponents of time dependent coefficients controlling drug absorption e.g. dissolution, uptake or non absorption e.g. precipitation. (C) 2016 Elsevier B.V. All rights reserved.

This work discusses the scientific aspects of the definition of dose as the `highest single oral IR dose' recommended for administration in the SmPC (summary of product characteristics) in the current European Medicines Agency (EMA) 2010 Guideline, for the purpose of biopharmaceutics classification system (BCS)-based biowaiver decision making. Analysis of theoretical and experimental data dealing with drug dissolution and biopharmaceutic drug classification reveals that the drug dose is an important parameter for both drug dissolution and biopharmaceutic classification. The relevant implications for the dose considerations in bioequivalence studies are also discussed briefly. It is suggested that the concept of ``the highest single dose oral IR dose recommended for administration in the SmPC{''} of the EMA 2010 Guideline be abolished. It is advisable, each dose strength be considered separately Le., whether or not it meets the solubility-dissolution regulatory criteria. (C) 2014 Elsevier B.V. All rights reserved.

The combination of fluticasone propionate (FLP) and salmeterol (SAL) is often used in clinical practice for the treatment of pulmonary disorders. The purpose of this study was to explore the pharmacokinetics (PK) of inhaled FLP and SAL, after concomitant administration, in healthy male and female subjects using two dry powder inhalers. Plasma concentration (C)-time (t) data were obtained from a single dose, two-sequence, two-period, crossover (2 x 2) bioequivalence (BE) study. Activated charcoal was co-administered in order to prohibit absorption from the gastrointestinal tract. A number of 60 subjects were recruited, while 57 of them completed the study and were included in the PK analysis. Initially, PK parameters of FLP and SAL were estimated using the classic non-compartmental methods. Subsequently, BE assessment was applied to the estimated PK parameters of the two dry powder inhalers. Special focus was placed on the population PK analysis of the C-t data, which were pooled together. `Treatment' (i.e., test or reference) and `period' of the BE study were considered as covariates. A variety of structural and residual error models were tested to find the one which best described the plasma C-t data of FLP and SAL. Demographic data were also evaluated for their impact on the PK parameters. Several goodness-of-fit criteria were utilized. The non-compartmental PK estimates of this study were in agreement with previously reported values. The population PK analysis showed that FLP data were described by a two compartment model with first-order absorption and elimination kinetics. Body weight was found to affect significantly absorption rate constant, inter-compartmental clearance, and volume of distribution of the peripheral compartment. As body weight increases, the values of these PK parameters also rise. For SAL, the best results were obtained when a two-compartment disposition model was used assuming very rapid absorption kinetics (like intravenous bolus) and first-order elimination kinetics. Gender was found to be a significant covariate on clearance, with men exhibiting higher clearance than women. (C) 2015 Elsevier B.V. All rights reserved.

In the case of pediatric medicinal products the selection of an appropriate and palatable liquid dosage form can make the difference between treatment success and failure. Since the recent adoption of Pediatric Regulations in the U.S. and E.U., there is a greater demand for age-appropriate medicines for children. Extended research on the use of milk on drug administration in pediatric population has shown the multiple benefits of its use. Milk exhibits great solubilizing, gastroprotective and taste masking properties, which are very important characteristics in the case of insoluble, irritating and bitter-tasting active compounds. Milk-based formulations rely on a novel, simple and user-friendly approach for the delivery of ionized and unionized lipophilic drugs. In parallel they can provide critical nutritive elements and a wide range of biologically active peptides, very important elements especially for pediatric patients. (C) 2015 Elsevier B.V. All rights reserved.

Introduction Generic products of antiepileptic drugs (AEDs) are currently a controversial topic as neurologists and patients are reluctant to switch from brand products to generics and to switch between generics. Objective The aim of this study was to provide enlightenment on issues of bioequivalence (BE) and interchangeability of AED products. Methods Monte Carlo simulations of the classic 2 x 2 BE studies were performed to study the effect of sample size, within-subject variability, and the true difference in pharmacokinetic values of the products under comparison on BE acceptance of generic AED products. Simulations were extended to study the comparative performance of two generic AED products against the same innovative product. The simulated results are compared with literature data on AEDs. Results The question with regard to bioavailability (BA) is whether two formulations are different, while for BE the question is whether two formulations are sufficiently similar in terms of extent and rate of absorption. Therefore, the criteria for BA and BE and the statistical analysis involved in their analysis are different. Two generic formulations that meet regulatory approval requirements for generics by being bioequivalent to the same innovative AED may not be bioequivalent to one another and therefore should not be regarded as equal or as therapeutically equivalent products. A switch from a standard or an immediate-release formulation to a modified-release product, which comprises extended-release or delayed-release formulations, should not be regarded as a switch between generics, but rather as a switch between different formulation types. Discussions Switches between bioequivalent generic AED products could potentially lead to larger changes in plasma levels and exposure than the brand-to-generic switch. The simulation work verified the clinical findings that not all generic AED products bioequivalent to the same innovative product are bioequivalent to one another. Conclusions Two generic formulations that meet regulatory approval requirements for generics, by being bioequivalent to the innovative AED, may not be bioequivalent to one another. Additional BE criteria are needed for a formulation switch, particularly in epilepsy, where a breakthrough seizure may change a patient's status from seizure-free to refractory.

ObjectivesTwo-stage clinical designs are currently recommended by the regulatory authorities for the assessment of bioequivalence (BE). A specific statistical methodology was recently proposed by the European Medicines Agency (EMA). The aims of this article are to elaborate on the suggested statistical design from the EMA and to compare it with the existing statistical methods reported in the literature. MethodsMonte Carlo simulations were used to simulate the conditions of a two-stage BE design. The starting sample size was either 24 or 48, whereas the coefficient of variation of the within-subject variability was equal to 20% and 40%. Several geometric mean ratio levels of the BE metric were considered. Under each condition, 1000000 studies were simulated. Key findingsThe overall performance, in terms of percentage of BE acceptance, is identical. The additional term, sequencexstage', suggested in the EMA method is in most cases nonsignificant. The same results were obtained regardless of the type (fixed or random) of the effect applied to the subjects' term. ConclusionsAny BE study either finished or in progress which relies on the existing literature methodology leads to the same percentage of BE acceptance as if it was analysed with the recently proposed EMA method.

The purpose of the present work is to develop a non-binary biopharmaceutical classification system the so called AB Gamma system. The original mathematical model used for the development of BCS, appropriately modified, was applied to estimate the limiting values of drug solubility and permeability when the fraction of dose absorbed, Fa, was 0.90 or 0.20. The AB Gamma system is based on the fraction of dose absorbed and relies on permeability, solubility plane. The first category (A, alpha) includes drugs with Fa = 0.90, whereas the B (beta) category consists of drugs with Fa = 0.20. The area lying between the two boundaries of A and B defines the third category (gamma), Gamma, (0.20 < Fa < 0.90). For comparative purposes, the BCS classes I-IV were co-plotted together with the AB Gamma system. Most of the BCS classes II and III are included in category Gamma which mainly consists of drugs with properties like moderate or low solubility and permeability. Due to the dynamic character of dissolution and uptake processes, category A is expanded toward BCS Class II. The AB Gamma system allows the classification of all compounds into three categories (A, B, Gamma) in terms of the fraction of dose absorbed. (C) 2014 Elsevier B. V. All rights reserved.

This review starts with an introduction on the theoretical aspects of biopharmaceutics and developments in this field from mid-1950s to late 1970s. It critically addresses issues related to fundamental processes in oral drug absorption such as the complex interplay between drugs and the gastrointestinal system. Special emphasis is placed on drug dissolution and permeability phenomena as well as on the mathematical modeling of oral drug absorption. The review ends with regulatory aspects of oral drug absorption focusing on bioequivalence studies and the US Food and Drug Administration and European Medicines Agency guidelines dealing with Biopharmaceutics Classification System and Biopharmaceutic Drug Disposition Classification System. (C) 2013Wiley Periodicals, Inc. and the American Pharmacists Association

Despite the fact that a significant percentage of the population is unable to swallow tablets and capsules, these dosage forms continue to be the default standard. These oral formulations fail many patients, especially children, because of large tablet or capsule size, poor palatability, and lack of correct dosage strength. The clinical result is often lack of adherence and therapeutic failure. The American Association of Pharmaceutical Scientists formed a Pediatric Formulations Task Force, consisting of members with various areas of expertise including pediatrics, formulation development, clinical pharmacology, and regulatory science, in order to identify pediatric, manufacturing, and regulatory issues and areas of needed research and regulatory guidance. Dosage form and palatability standards for all pediatric ages, relative bioavailability requirements, and small batch manufacturing capabilities and creation of a viable economic model were identified as particular needs. This assessment is considered an important first step for a task force seeking creative approaches to providing more appropriate oral formulations for children.

Unveil the properties of a two-stage design (TSD) for bioequivalence (BE) studies. A TSD with an upper sample size limit (UL) is described and analyzed under different conditions using Monte Carlo simulations. TSD was split into three branches: A, B1, and B2. The first stage included branches A and B1, while stage two referred to branch B2. Sample size re-estimation at B2 relies on the observed GMR and variability of stage 1. The properties studied were % BE acceptance, % uses and % efficiency of each branch, as well as the reason of BE failure. No inflation of type I error was observed. Each TSD branch exhibits different performance. Stage two exhibits the greatest % BE acceptances when highly variable drugs are assessed with a low starting number of subjects (N-1) or when formulations differ significantly. Branch A is more frequently used when variability is low, drug products are similar, and a large N-1 is included. BE assessment at branch A is very efficient. The overall acceptance profile of TSD resembles the typical pattern observed in single-stage studies, but it is actually different. Inclusion of a UL is necessary to avoid inflation of type I error.

Assessment of bioequivalence (BE) for highly variable drugs is challenging. As within-subject variability increases, it becomes more difficult to prove BE, unless a large number of subjects is recruited. In order to face this problem, several approaches have been proposed. Among them, scaled BE limits (BEL) have recently attracted special attention because the European Medicines Agency and the US Food and Drug Administration adopted scaled approaches. Scaled BELs expand with variability using specific mathematical functions while include additional regulatory criteria in some cases. The aim of this study is twofold: (1) to provide a deeper insight into the dependence of scaled BELs on variability and (2) to unveil the underlying mathematical relationships. The comparative analysis of these BELs is implemented through algebraic manipulations and graphic illustrations. Special emphasis is placed on the ``absolute change{''} of each BEL and the ``relative change,{''} reflecting the portion of the relative to the maximum expansion of a BEL. This analysis reveals the causal differences between the different BELs on the mode of ``absolute{''} and ``relative{''} change. The results derived from this study are in agreement with the observed different performances of the various scaled BE approaches. (C) 2012 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 102:296-301, 2013

Purpose: The purpose of this work was to assess the colloidal stability of novel milk-based formulations. Methods: Milk-based formulations were prepared in situ by adding into milk alkaline- or ethanolic-drug solutions containing an array of drugs namely; ketoprofen, tolfenamic acid, meloxicam, tenoxicam and nimesulide, mefenamic acid, cyclosporine A, danazol and clopidogrel besylate. The produced formulations were characterized by means of dynamic lightscattering, zeta-potential studies, atomic force microscopy, fluorescence spectroscopy, Raman spectroscopy complemented with ab initio calculations and stability studies. Results: The presence of the drugs did not induce significant changes in most cases to the particle size and zeta-potential values of the emulsions pointing to the colloidal stability of these formulations. Raman spectroscopy studies revealed interactions of the drugs and the milk at the intermolecular level. Complementary analysis with ab initio calculations confirmed the experimental observations obtained by Raman spectroscopy. Finally the produced drug containing alkaline/ethanolic solutions exhibited stability over a period of up to 12 months. Conclusions: The current data demonstrate that milk is a promising drug carrier. (C) 2013 Elsevier B. V. All rights reserved.

Generics are usually considered to exhibit comparable in vivo properties in terms of efficacy and safety and for this reason are intended to be interchangeable with the reference product. The aim of this study is to provide a quantitative picture of the switchability problem between two generics and to introduce the concept of conditional probability of bioequivalence (BE) acceptance. Monte Carlo simulations were performed to examine all possible relationships between the tested products. Four types of percent BE acceptances are defined and evaluated: (a) % BA1, when generic T-1 is compared to the R product, (b) % BA2, in cases of comparison of generic T-2 with the R product, (c) % BA21, when generic T-2 is compared to another generic T-1, and finally (d) % BA21C which is the conditional probability of percent bioequivalence acceptance of generic T(2)versus another generic T-1 given that both T-1 and T-2 are declared bioequivalent to the same R formulation. The simulations were expanded to study concomitantly the performance of T-1 and T-2 when compared to the same R formulation. In each case, the 2 x 2 cross-over design was used and evaluation of BE was based on the classic BE limits (0.80-1.25) and the stricter BE limits (0.90-1.11) for narrow therapeutic index (NTI) drugs. A number of 24 and 48 subjects were assumed to participate in the simulated trials, while the coefficient of variation for the within-subject variability (CVw) was 20% and 40%. A number 40,000 BE trials were simulated under each condition. The T-1/R and T-2/R ratios ranged from 0.80 to 1.25 using a step of 0.05. Even though two generics (T-1 and T-2) can be declared bioequivalent to the same R product, this does not ensure that they are always mutually bioequivalent. On the contrary, two generic products which differ substantially from the R product can still have a high probability to be truly interchangeable. The two generics (T-1 and T-2) can be switched from one to another when the T-1/R and T-2/R ratios are close to the same value, the CVw of the drug is low, and each BE study of T-1-R and T-2-R was conducted using a relatively large number of subjects. In the same context, two generic NTI drugs which differ more than 10% from the R product can still be declared bioequivalent to one another depending on the relative T-1/R and T-2/R ratios. Switchability between generics assessed at the 0.90-1.11 interval is safer, but not always ensured. (C) 2013 Elsevier B.V. All rights reserved.

Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. (C) 2013 Elsevier B.V. All rights reserved.

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

The number of options available to drug discovery scientists to enhance the solubility of poorly soluble compounds by conventional formulation approaches is limited. In most cases, drug formulation is oriented toward the creation of a supersaturated solution upon contact with aqueous environment, often combined with solubilizing agents and precipitation inhibitors. The most popular formulations for achieving this target are the lipid-based formulations called self-emulsifying and self-microemulsifying drug delivery systems, SEDDS and SMEDDS, respectively. They offer enhanced absorption and hence enhanced oral bioavailability of lipophilic drugs, presenting the drug in solubilized form in vivo, avoiding dissolution, which can be the rate limiting step in drug absorption for sparingly soluble drugs. The production of high energy or rapid dissolving solid state formulations using drug particle engineering to enhance drug solubility and bioavailability is also applied. These formulations include solid dispersions, nanoparticles, co-ground mixtures etc. Furthermore, the development of prodrugs is also a useful strategy to improve the physicochemical, biopharmaceutical or pharmacokinetic properties of pharmacologically potent compounds, and thereby increase the developability and usefulness of a potential drug. Up to now, most medications were made for adults and children's requirements were not taken into account. Since the recent adoption of Paediatric Regulations in the U.S. and E.U., there is a greater demand for age-appropriate medicines for children. The challenges in paediatric formulation development are mostly associated with the difficulty in defining design requirements for the intended dosage form that is most appropriate for the target patient population, due to the diversity of the paediatric population (range of ages, physical size and capabilities) that varies significantly from birth to age 12 yrs old along with the dosage flexibility. The last years there has been an effort to develop solid paediatric formulations that deliver the appropriate dose in a ``user friendly{''} way and to find alternative drug delivery vehicles, such as mini-tablets, dairy products, and new taste masking techniques in order to improve drug acceptability. In addition, alternative routes of administration have been proposed such as inhalation and nasal administration.

Introduction: Nowadays, reducing medication costs is vital for health care agencies. Prescription of generic drug products can help lower these expenses. A generally accepted assumption is that therapeutic equivalence, between a generic and a brand-name medication, can be claimed if bioequivalence is demonstrated. Areas covered: This article reviews the current regulatory procedures on bioequivalence testing. Special focus is placed on the guidelines recommended by the European Medicines Agency and the US Food and Drug administration. The authors also describe the evolution of these issues and the alternatives proposed in the literature. Expert opinion: Defining bioequivalence, as the condition of no significant differences in the extent and rate of absorption between the generic and the brand-name medication, sounds simple. However, the scientific and regulatory basis of bioequivalence appears rather complicated in practice. Even though the regulatory authorities have elucidated many issues, several aspects of bioequivalence assessment are still unresolved. Examples, of these open questions, in bioequivalence, include the assessment of complex drugs, such as biologics and iron-carbohydrates, the assessment of immunosuppressive agents as well as the role that pharmacogenomics plays in bioequivalence.

To explore the comparative performance of the recently proposed bioequivalence (BE) approaches, FDA(s) and EMA(s), by the FDA working group on highly variable drugs and the EMA, respectively; to compare the impact of the GMR-constraint on the two approaches; and to provide representative plots of % BE acceptance as a function of geometric mean ratio, sample size and variability. Simulated BE studies and extreme GMR versus CV plots were used. Three sequence, three period crossover studies with two treatments were simulated using four levels of within-subject variability. The FDA(s) and EMA(s) approaches were identical when variability was < 30%. In all other cases, the FDA(s) method was more permissive than EMA(s). The major discrepancy was observed for variability values > 50%. The GMR-constraint was necessary for FDA(s), especially for drugs with high variabilities. For EMA(s), the GMR-constraint only became effective when sample size was large and variability was close to 50%. A significant discrepancy in the performances of FDA(s) and EMA(s) was observed for high variability values. The GMR-constraint was essential for FDA(s), but it was of minor importance in case of the EMA(s).

We highlight some physical and mathematical aspects relevant to the derivation and use of the Higuchi equation. More specifically, the application of the Higuchi equation to different geometries is discussed and Monte Carlo simulations to verify the validity of Higuchi law in one and two dimensions, as well as the derivation of the Higuchi equation under alternative boundary conditions making use of fractional calculus, are presented. (C) 2010 Elsevier B.V. All rights reserved.

Early prediction of human intestinal absorption is important in selection of potential orally administered drugs. Various computational models for prediction of the fraction of dose absorbed, Fa, have been developed. In 1989, a sigmoidal relationship between Fa and drug absorption potential was shown. Since then various physicochemical descriptors of molecules (lipophilicity, polar surface area, hydrogen bond descriptors) have been found to correlate with human intestinal absorption and various attempts in estimating Fa have been reported. Most studies rely on the presupposition that Fa is mainly dependent on drug's solubility, which drives the dissolution rate in the gastrointestinal (GI) fluids, and the rate of passive drug transport across the intestinal membrane. In the same vein, the biopharmaceutics classification system (BCS) and the relevant FDA guideline classify drugs in four categories according to their aqueous solubility and permeability. However, the biopharmaceutics drug disposition classification system (BDDCS) revealed the poor predictability of permeability estimates for Fa and the major role of transporters for GI uptake of drugs. The role of solubility in the reaction limited model of dissolution and the ubiquitous presence of supersaturated solubility-dissolution phenomena in the GI lumen, call for a more physiologically relevant consideration of GI absorption.

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 (R)) 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 (R) at 10, 25 and 37 degrees C. Dissolution studies were carried out using Tegretol (R) 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 degrees 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 degrees 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.

Areas covered in this review: In this review, we present the classic approach of bioequivalence assessment, some situations of special importance such as the role of metabolites and highly variable drugs, and the current regulatory state in North America and Europe. Special emphasis is given to the methods proposed for solving the problems caused by high variability such as multiple-dose studies, replicate designs, individual bioequivalence and the widening of bioequivalence limits. Other issues discussed include the concept of biowaivers and the rising field of the equivalence of biologicals (biosimilars). What the reader will gain: The reader will gain an understanding of why bioequivalence assessment is necessary, how it is performed and what one should be aware of when planning to conduct a bioequivalence study. Take home message: The aim of bioequivalence studies is to ensure comparable in vivo performance of two drug products. This is accomplished by performing an appropriate clinical study which should be capable of ensuring the drug's safety and efficacy for consumers with less human exposure and costs of producing.

Recently, the European Medicines Agency (EMA) issued a new guideline on the investigation of bioequivalence (BE). In case of highly variable drugs, this guideline proposes that the acceptance limits for C-max can gradually be expanded as a function of within-subject variability (CVWR). Actually, these BE limits exhibit leveling-off properties since they are not allowed to scale continuously, but only up to CVWR = 50%. To avoid the risk of accepting two drug products which may differ significantly, this EMA guideline also proposes the use of a secondary constraint criterion on the geometric mean ratio (GMR) of the two products under comparison. Aim of this study was to explore the leveling-off properties of the new EMA limits in comparison to other approaches, as well as to assess the impact of the complementary GMR criterion on the ability to declare bioequivalence. Simulated bioequivalence studies and extreme GMR plots were used to assess the performance of the EMA limits. Three sequence, three period (3 x 3) crossover studies with two treatments (T and R) were simulated. The R product was considered to be administered twice, while the T only once (i.e., TRR/RTR/RRT). Among others, this study revealed the leveling-off properties of the new EMA limits. It was also shown that the complementary GMR-constraint is only effective when a large sample size is used and at regions of CVWR close to 50%. This GMR-criterion begins to be effective at sample sizes around 60 and becomes more prominent as the number of subjects participating in the BE study increases. For CVWR values lower than 50%, the GMR-constraint has no role. In case of within-subject variabilities greater than 50%, the impact of the GMR-constraint diminishes due to the leveling-off properties of the EMA limits. Compared to the classic 0.80-1.25 or the extended 0.75-1.33 criteria, the new EMA limits are more liberal at high CVWR values and allow greater differences between the two drug products to be declared bioequivalent. Finally, this study showed that the use of an approximate value (0.760) on the scaling factor proposed by EMA, has no impact on the performance of the new BE limits compared to other more accurate approaches. (C) 2011 Elsevier B.V. All rights reserved.

The diffusion layer model of drug dissolution is used for the simulation of oral drug absorption as well as for the analysis of experimental data. The governing role of saturation solubility in the rate of dissolution makes this parameter predominant for biopharmaceutical classification purposes. The hypothesis models and criteria associated with the use of solubility and dissolution for the biopharmaceutical classification of compounds and marketed drugs are reviewed in this article. The complex hydrodynamics in the in vitro dissolution apparatuses as well as the motility in the gastrointestinal tract do not allow the application of the diffusion layer model in these systems, as this has been built and verified in the rotating disk device. The solubilizing capacity of gastrointestinal fluids media is higher than the aqueous saturation solubility usually reported and used for biopharmaceutical purposes. Emphasis is given on the reaction-limited model of dissolution which provides a useful alternative not based on diffusion principles. Model independent dissolution parameters are more useful for regulators as our knowledge for the dissolution mechanism(s) under in vivo conditions is limited.

Purpsoe. Investigate the role of metabolites in bioequivalence (BE) assessment. Methods. Sets of ordinary differential equations are used to generate concentration - time data for both parent drug (P) and metabolite (M). The calculations include 24 subjects, two different formulations (Test, Reference), and a range of Test/Reference ratios for the fraction of dose absorbed and the rate of absorption. A summarized view of these results is made through the construction of three dimensional power curves. The criteria for the choice of the preferred analyte (P or M) are based on a sensitivity analysis of the bioequivalence measure (AUC, C-max). The latter depends on the relative ability of P and M to reflect better the changes of the pharmacokinetic parameters and variability. Results. The different sensitivity properties of P and M were reflected on the power curves. For AUC, the performance of metabolite is very similar to that of the parent drug for all scenarios and models examined. A more complex behaviour is evident for C-max. In most of these cases, metabolite data show higher permissiveness in the percentages of acceptance. This attribute is more evident when P exhibits high elimination rate and/or the formation of M occurs rapidly. When the Test and Reference products have similar absorption profiles, metabolite data are preferable for the determination of bioequivalence. Parent drug has the advantage for detecting better the differences in the absorption rate of two drugs. The latter is counterbalanced by the increased sensitivity of P data to the variability of the data. Conclusions. Both parent drug and metabolite share the same ability to declare BE when AUC is used as a bioequivalence measure. In case of C-max, metabolite data exhibit better performance when the T and R products are truly bioequivalent or the two formulations differ in their extent of absorption. For the pharmacokinetic scenarios studied, parent drug data were found to be more sensitive to detect differences in the rate of absorption. However, in such cases, their information is much influenced by the increased variability.

Most correlations between in vitro and in vivo data (IVIVC) rely on linear relationships. However, non-linear IVIVC can be also observed, justified and validated. The purpose of the present work was the development of a methodology for power law IVIVC, which mirror power law kinetics under in vitro and in vivo conditions. Fractional calculus was used to justify power law kinetics for zero-order processes in disordered media. Power law kinetics was observed in a large number of in vitro data sets. When ``zero-order{''} release and absorption is considered in terms of fractional calculus the following power law IVIVC between the fraction released F-r and the fraction absorbed F-alpha, is obtained: F-alpha = mu F-r(lambda) - beta, where mu is a constant related to the rate constants and the orders of the release/absorption kinetics, lambda is the ratio of the orders of the kinetics under in vitro and in vivo conditions and 13 accounts for a time shift between the in vitro and in vivo processes; We used literature data to develop power law IVIVC and derive estimates for mu, lambda and beta; the simulated pharmacokinetic profiles using the in vitro release data and the IVIVC developed compared well with the actual in vivo data. (C) 2010 Elsevier B.V. All rights reserved.

Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order alpha < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems.

The aim of this study is to develop milk-based formulations for ionized and unionized lipophilic drugs. Solubility studies of the following non-steroidal anti-inflammatory drugs (NSAIDs): mefenamic acid, tolfenamic acid, ketoprofen, meloxicam, tenoxicam and nimesulide in phosphate- and glycine-NaOH buffers at nominal pH 8-12. were performed. The solubilities of cyclosporine and danazol in water-ethanol solutions were studied. NSAIDs-, cyclosporine-, danazol-, aspirin-milk oral liquid formulations were prepared by adding the appropriate volume of (i) NSAIDs-alkaline buffer solutions, (ii) water-ethanol solutions of cyclosporine and danazol and (iii) aspirin aqueous solution to 150-200 ml of milk. All the non-steroidal anti-inflammatory drugs exhibited increased solubility in the alkaline buffers. The actual pH values (range 6.7-7.7) of the final NSAIDs-milk formulations were very close to milk pH. The higher ethanol content in ethanol-water mixtures increased the solubility of danazol and cyclosporine. A 15 mg meloxicam-, a 100 mg cyclosporine- and a 500 mg aspirin-milk formulation was administered orally to healthy volunteers. All these formulations showed a satisfactory in vivo performance. The strong buffering capacity of milk that was observed and the high solubility of unionized drugs in ethanol allow the preparation of drug-milk formulations with enhanced pharmacokinetic properties. (C) 2010 Elsevier B.V. All rights reserved.

Praziquantel (PZQ), the primary drug of choice in the treatment of schistosomiasis, is a highly lipophilic drug that possesses high permeability and low aqueous solubility and is, therefore, classified as a Class II drug according to the Biopharmaceutics Classification System (BCS). In this work, beta-cyclodextrin (beta-CD) and hydroxypropyl-beta-cyclodextrin (HP-beta-CD) were used in order to determine whether increasing the aqueous solubility of a drug by complexation with CDs, a BCS-Class II compound like PZQ could behave as BCS-Class I (highly soluble/highly permeable) drug. Phase solubility and the kneading and lyophilization techniques were used for inclusion complex preparation; solubility was determined by UV spectroscopy. The ability of the water soluble polymer polyvinylpyrolidone (PVP) to increase the complexation and solubilization efficiency of beta-CD and HP-beta-CD for PZQ was examined. Results showed significant improvement of PZQ solubility in the presence of both cyclodextrins but no additional effect in the presence of PVP. The solubility/dose ratios values of PZQ-cyclodextrin complexes calculated considering the low (150 mg) and the high dose (600 mg) of PZQ, used in practice, indicate that PZQ complexation with CDs may result in drug dosage forms that would behave as a BCS-Class I depending on the administered dose.

Therapeutic proteins are a diverse class of drugs consisting of naturally occurring or modified proteins, and due to their size and physico-chemical properties, they can pose challenges for the pharmacokinetic and pharmacodynamic studies. Physiologically-based pharmacokinetics (PBPK) modelling has been effective for early in silico prediction of pharmacokinetic properties of new drugs. The aim of the present workshop was to discuss the feasibility of PBPK modelling of macromolecules. The classical PBPK approach was discussed with a presentation of the successful example of PBPK modelling of cyclosporine A. PBPK model was performed with transport of the cyclosporine across cell membranes, affinity to plasma proteins and active membrane transporters included to describe drug transport between physiological compartments. For macromolecules, complex PBPK modelling or permeability-limited and/or target-mediated distribution was discussed. It was generally agreed that PBPK modelling was feasible and desirable. The role of the lymphatic system should be considered when absorption after extravascular administration is modelled. Target-mediated drug disposition was regarded as an important feature for generation of PK models. Complex PK-models may not be necessary when a limited number of organs are affected. More mechanistic PK/PD models will be relevant when adverse events/toxicity are included in the PK/PD modelling.

To compare the performance of the reference scaled average bioequivalence(scABE(R)) method proposed by FDA scientists {[}Haidar et al., 2008. Pharm. Res. 25,237-241] with other approaches focusing on the human exposure expressed as the product sample size x periods of drug administration. Simulated bioequivalence studies were generated assuming the partial replicate 3-way crossover design and the classic (2 x 2) crossover design. Intrasubject variability (CV(W)) values ranged from 15% to 60% and sample sizes from 16 to 54. The procedures examined include: the scABER method. the classic 0.80-1.25 approach, a levelling-off scaled BE limit (BELscW), and some other scaled bioequivalence lit-nits. To assess the performance of the aforementioned approaches, the typical as well as novel three-dimensional modified power curves were constructed. A new index, termed %Mean Relative Difference (MRD%). was introduced in order to quantitatively compare the performance of the bioequivalence limits. The recently proposed scABER approach showed the lowest producer risk in particular for highly variable drugs. When exposure was taken into account scABER resulted in a desired behaviour when CV(W) was low. For high CV(W) values the overall performance diminished when geometric mean ratio (GMR) substantially deviated from unity. Application of the MRD% index clearly revealed that the effect of lowering the producer risk at GMR = I was totally Counterbalanced by the rise of consumer risk at high GMR values. The classic 0.80-1.25 limits were favoured at low intrasubject variability and high exposure, whereas the levelling-off limits demonstrated a preferred overall performance when variability was high and exposure was limited. (C) 2009 Elsevier B.V. All rights reserved.

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.

A reaction-limited model for drug dissolution is developed assuming that the reaction at the solid-liquid interface is controlling the rate of dissolution. The dissolution process is considered as a bidirectional chemical reaction of the undissolved drug species with the free solvent molecules, yielding the dissolved species of drug complex with solvent. This reaction was considered in either sink conditions, where it corresponds to the unidirectional case and the entire amount of the drug is dissolved, or reaching chemical equilibrium, which corresponds to saturation of the solution. The model equation was fitted successfully to dissolution data sets of naproxen and nitrofurantoin formulations measured in the paddle and basket apparatuses, respectively, under various experimental conditions. For comparative purposes these data were also analyzed using three functions based on the diffusion layer model. All functions failed to reveal the governing role of saturation solubility in the dissolution process associated with the diffusion layer model when the conditions for the valid estimation of saturation solubility, established theoretically in this study, were met by the experimental set up employed. Overall, the model developed provides an interesting alternative to the classic approaches of drug dissolution modeling, quantifying the case of reaction-limited dissolution of drugs. (c) 2007 Elsevier B.V. All rights reserved.

We have studied drug release from matrices with periodic layers of high and low diffusivity using Monte Carlo simulations. Despite the fact, that the differential equations relevant to this process have a form that is quite different from the classical diffusion equation with constant diffusion coefficient, we have found that the Weibull model continues to describe the release process as well as in the case of the ``classical{''} diffusion controlled drug release. We examine the similarities and differences between release from matrices with periodic layers and matrices with random mixtures of high and low diffusivity area and show that the periodic geometrical arrangement of the low diffusivity areas has an influence in the release profile which is negligible for low diffusivity ratios, but becomes important in the case of high diffusivity ratios and for intermediate values of the periodic ``length{''}. Such an arrangement in periodic layers leads to Weibull exponent a which are lower than those of the corresponding random arrangement and exponents b which are higher than those of the random case. (C) 2007 Elsevier B.V. All rights reserved.

This is a summary report of the EUFEPS & COST B25 conference on Bioavailability and Bioequivalence which focused on physiological factors and variability. This conference was held at The Royal Olympic Hotel in the centre of Athens (Greece) during the 1-2 of October in 2007. The issues discussed in the conference involved physiological factors affecting drug absorption, the role of pre-systemic effects on bioavailability (BA), the impact of variability in bioequivalence (BE) studies, and a final closing panel session on unresolved issues in BA/BE regulations. Several important aspects of drug absorption were highlighted. It was presented how the complexity of gastrointestinal (GI) physiology and the site dependent absorption can impact on drug BA. Similarly, the effects of food and formulation were also studied. The second session focused on integrating the complexities of GI into modeling the inter-individual variability of absorption and the prediction of first-pass metabolism from in-vitro data. The necessity to measure metabolites, the value of Biopharmaceutical Classification System (BCS), and the more recently proposed Biopharmaceutical Drug Disposition Classification System (BDDCS) were assessed as well. This session closed with presentations of pharmacokinetic software delegates. In the second day of the conference, the problem of high intra-subject variability in BE studies was analyzed. Study design considerations, the use of multiple-dose studies and the role of statistics in BE were also highlighted. Finally, the current thinking of regulatory authorities (EMEA and US-FDA) was presented. The conference closed with a last session on unresolved issues in the regulatory level.

Drug absorption is a complex process dependent upon drug properties such as solubility and permeability, formulation factors, and physiological variables including regional permeability differences, pH, luminal and mucosal enzymes, and intestinal motility, among others. Despite this complexity, various qualitative and quantitative approaches have been proposed for the estimation of oral drug absorption. These approaches are reviewed in this article with particular emphasis on drug dissolution modelling, dynamic systems for oral absorption and absorption models based on structure. The regulatory aspects of oral drug absorption and in particular the biopharmaceutic classification of drugs are also discussed. Models for drug dissolution and release describe adequately the in vitro data, and models for oral drug absorption provide reasonable results. The development of in vitro-in vivo correlations based on the official compendia specifications are facilitated using commercial computer packages.

We use Monte Carlo simulations in order to study diffusion controlled drug release from matrices consisting of random mixtures of high and low diffusivity areas (random mixing), and from matrices covered by a thin film of low diffusivity (ordered mixing). We compared our results with the Weibull model for drug release and found that it provides an adequate description of the release process in all cases of random mixing and most cases of ordered mixing. We have studied the dependence of the Weibull parameters on the diffusion coefficient and, in most cases, found a rather simple linear dependence. Moreover, our results indicate that a device covered by a thin film with diffusion coefficient three orders of magnitude lower that the coefficient of the rest of the device, will release drug at constant rate for most of the release process. This last result may have considerable practical applications. (C) 2007 Elsevier B.V. All rights reserved.

Three advanced models of pharmacokinetics are described. In the first class are physiologically based pharmacokinetic models based on in vitro data on transport and metabolism. The information is translated as transporter and enzyme activities and their attendant heterogeneities into liver and intestine models. Second are circulatory models based on transit time distribution and plasma concentration time curves. The third are fractal models for nonhomogeneous systems and non-Fickian processes are presented. The usefulness of these pharmacokinetic models, with examples, is compared.

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. 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. 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. 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.

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 modem trends on drug dissolution research and their regulatory implications. (c) 2006 Elsevier B.V. All rights reserved.

The competitive binding of diflunisal and three well-known uraemic toxins (3-indoxyl sulfate, indole-3-acetic acid and hippuric acid) to bovine serum albumin (BSA), human serum albumin (HSA) and human plasma was studied by direct potentiometry. The method used the potentiometric drug ion-probe technique with a home-made ion sensor (electrode) selective to the drug anion. The site-oriented Scatchard model was used to describe the binding of diflunisal to BSA, HSA and human plasma, while the general competitive binding model was used to calculate the binding parameters of the three uraemic toxins to BSA. Diflunisal binding parameters, number of binding sites, n(i) and association constants for each class of binding site, K-i, were calculated in the absence and presence of uraemic toxins. Although diflunisal exhibits high binding affinity for site I of HSA and the three uraemic toxins bind primarily to site II, strong interaction was observed between the drug and the three toxins, which were found to affect the binding of diflunisal on its primary class of binding sites on both BSA and HSA molecules and on human plasma. These results are strong evidence that the decreased binding of diflunisal that occurs in uraemic plasma may not be solely attributed to the lower albumin concentration observed in many patients with renal failure. The uraemic toxins that accumulate in uraemic plasma may displace the drug from its specific binding sites on plasma proteins, resulting in increased free drug plasma concentration in uraemic patients.

Purpose: (1) To develop novel scaled bioequivalence (BE) limits with levelling-off properties based solely on variability considerations and (2) to evaluate their performance in comparison to the classic unscaled BE limits 0.80-1.25, the expanded BE limits 0.75-1.33 and the recently proposed Geometric Mean Ratio (GMR)-dependent scaled BE limits BELscW (Karalis et al., Eur. J. Pharm. Sci., 26:54-61, 2005). Materials and Methods: Two model functions were used to ensure the gradual change of the BE limits from a starting value towards a predefined plateau value. Plots of the new BE limits and extreme GMR values ensuring BE as a function of the coefficient of variation (CV) were constructed. Two-period crossover BE studies with 12, 24, or 36 subjects were simulated assuming CV values from 10 to 60%. Power curves were constructed by recording the percentage of accepted BE studies as the true GMR was raised from 1.00 to 1.50. The percentage of the true GMR within the simulated BE limits vs. true GMR was used to evaluate the estimation accuracy of the scaled methods. Results: Depending on the parameters' values of the model functions, the scaled BE limits exhibit different performance. Four new scaled BE limits, showing favourable performance for the evaluation of average BE are presented. At low variability levels two of the novel BE limits show similar performance to the 0.80-1.25 criterion, while the other two (as expected from their design) appear to be less permissive. At high CV values (30, 40%) all new BE limits exhibit much higher statistical power than the 0.80-1.25 criterion. They show almost identical behavior with the expanded 0.75-1.33 limits and appear to be less permissive than BELscW. Finally, the percentage of the true GMR within the simulated BE limits vs. true GMR shows a sharp decline. Due to the absence of the GMR factor in the model functions a more accurate estimation of the new scaled BE limits, compared to BELscW, is observed. Conclusions: The new scaled BE limits appear to be highly effective at all levels of variation investigated and present satisfactory estimation accuracy.

Previous findings from our group based on Monte Carlo simulations indicated that Fickian drug release from Euclidian or fractal matrices can be described with the Weibull function. In this study, the entire drug release kinetics of various published data and experimental data from commercial or prepared controlled release formulations of diltiazem and diclofenac are analyzed using the Weibull function. The exponent of time b of the Weibull function is linearly related to the exponent n of the power law derived from the analysis of the first 60% of the release curves. The value of the exponent b is an indicator of the mechanism of transport of a drug through the polymer matrix. Estimates for b < 0.75 indicate Fickian diffusion in either fractal or Euclidian spaces while a combined mechanism (Fickian diffusion and Case 11 transport) is associated with b values in the range 0.75 < b < 1. For values of b higher than 1, the drug transport follows a complex release mechanism. (c) 2005 Elsevier B.V. All rights reserved.

In this study, novel approaches for the design of bioequivalence (BE) limits are developed. The new BE limits scale with intrasubject variability but only until a geometric mean ratio (GMR)-dependent plateau value and combine the classic (0.80-1.25) and expanded (0.70-1.43) BE limits into a single criterion. Plots of the extreme GMR values accepted as a function of coefficient of variation (CV) have a convex shape, similar to the classic unscaled 0.80-1.25 limits. The performance of the novel approaches in comparison to the classic unscaled 0.80-1.25 limits as well as the two expanded BE limits, i.e., 0.70-1.43 and 0.75-1.33 was assessed using simulated data. Two-period crossover BE investigations with 12, 24 or 36 subjects were simulated with assumptions of CV 10%, 20%, 30% or 40%. At low CV values, the performance of the novel BE limits is almost identical to the 0.80-1.25 criterion. On the contrary, the expanded BE limits are very permissive even at high GMR values. For high CV% values (30% and 40%), the new BE limits show a much greater probability of declaring BE when GMR = 1 in comparison to the classic 0.80-1.25 limits. In addition, when the drug products differ more than 25%, the new BE limits show much lower percentage of acceptance than the expanded 0.70-1.43 limits. One of the major advantages of the new BE limits is their gradual expansion with variability until a GMR-dependent plateau value. Finally, the continuity and leveling-off properties of the new BE limits make them suitable for the assessment of BE studies, irrespective of the level of variability encountered. (c) 2005 Elsevier B.V. All rights reserved.

{The pharmacokinetics of tobramycin was studied in adult patients (N = 151) admitted either for initial suspicion of Gram-negative infection or for prophylaxis. In addition to age, weight, height and creatinine clearance (CrCL), a range of other covariates were also analysed, including type of pathology, co-medication, fever, sex and ethnicity (Basque or not). All patients received 100 mg tobramycin every 8 h and samples were collected at three time points after the first dose and at two time points after the fourth dose and assayed with a fluorescence polarisation immunoassay. The population mixed effects bicompartmental parameters were obtained from 725 concentration measurements using NONMEM, FOCE method, and were: systemic clearance

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.

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.

Two different approaches were used to study the kinetics of the enzymatic reaction under heterogeneous conditions to interpret the unusual nonlinear pharmacokinetics of mibefradil. Firstly, a detailed model based on the kinetic differential equations is proposed to study the enzymatic reaction under spatial constraints and in vivo conditions. Secondly, Monte Carlo simulations of the enzyme reaction in a two-dimensional square lattice, placing special emphasis on the input and output of the substrate were applied to mimic in vivo conditions. Both the mathematical model and the Monte Carlo simulations for the enzymatic reaction reproduced the classical Michaelis-Menten ( MM) kinetics in homogeneous media and unusual kinetics in fractal media. Based on these findings, a time-dependent version of the classic MM equation was developed for the rate of change of the substrate concentration in disordered media and was successfully used to describe the experimental plasma concentration-time data of mibefradil and derive estimates for the model parameters. The unusual nonlinear pharmacokinetics of mibefradil originates from the heterogeneous conditions in the reaction space of the enzymatic reaction. The modified MM equation can describe the pharmacokinetics of mibefradil as it is able to capture the heterogeneity of the enzymatic reaction in disordered media.

Purpose. i) To develop novel approaches for the construction of bio-equivalence ( BE) limits incorporating both the intrasubject variability and the geometric mean ratio (GMR), and ii) to assess the performance of the novel approaches in comparison to several scaled BE procedures and the classic unscaled average BE. Methods. Plots of the BE limits or the extreme GMR values accepted as a function of the coefficient of variation ( CV) were constructed for published and the developed scaled procedures. Two-period crossover BE investigations with 12, 24, or 36 subjects were simulated with assumptions of a CV 10%, 20%, 30%, or 40%. The decline in the percentage of accepted studies was recorded as the true GMR for the two formulations was raised from 1.00 to 1.50. Acceptance of BE was evaluated by published and the developed scaled procedures, and, for comparison, by the unscaled average BE. Results. Two GMR-dependent BE limits are proposed for the evaluation of average BE: i) BELscG1 with Ln(Upper, Lower BE limit) = +/-{[}(5-4GMR)0.496s + Ln(1.25)], and ii) BELscG2 with Ln(Upper, Lower BE limit) = +/-{[}(3-2GMR)(0.496s + Ln(1.25))], where s is the square root of the intrasubject variance. The range of BE limits becomes narrower as GMR values deviate from unity, and increases with variability. The two new approaches exhibit the highest statistical power at low CV values. At high levels of variability, BELscG1 and BELscG2 show high statistical power, as well as the lowest percentages of acceptance among the scaled methods when GMR = 1.25. The latter becomes more obvious when a large number of subjects is incorporated in the studies. Conclusions. The GMR and CV estimates of the BE study can be used in conjunction with the GMR vs. CV plot for the assessment of average BE. The new approaches, BELscG1 and BELscG2, appear to be highly effective at all levels of variation investigated.

{Purpose. Better dosing is needed for antibiotics, including teicoplanin (TEI), to prevent emergence of resistant bacterial strains. Here, we assess the TEI pharmacokinetics (PK) related to a 10 mg/l minimum inhibitory concentration (MIC) target in ICU children (4 to 120 months; n=20) with gram+infections. Methods. Standard administration of TEI was with three 10 mg/kg Q12h, loading infusions, and maintainance with 10 mg/kg or 15 mg/kg Q24h. During maintenance, 9 samples (3/day) were collected per patient and the PK analyzed with Nonlinear Mixed Effects Model (NONMEM). Results. Thirty-five percent of concentrations in older children (greater than or equal to2 months) vs. 8% in younger infants (<12 months) were below the target MIC. The global bicompartmental population PK parameters were {[}mean (interindividual CV%)] CL=0.23 l/h {[}72%]

Advances in mathematics and physics that deal with fractal geometry, fractal kinetics and chaotic dynamics have offered new insights for complex, kinetic and dynamical phenomena. These concepts can be applied to describe the heterogeneous nature of drug processes in the human body. Using these concepts, all processes related to gastrointestinal drug absorption (i.e. dissolution or release, transit and uptake) are considered to take place in non-homogeneous, disordered media. In pharmacokinetic modeling, fractal spaces and branching transport networks, or stochastic models, replace the classical compartmental models. Classical pharmacodynamics relies on the suppression or amplification of a steady-state baseline; however, the underlying physiological systems are often much more complex. Therefore, tools of nonlinear dynamics are used to analyze the drug effect.

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.

We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde {[}J. Chem. Phys. 83, 5909 (1985)]. A certain population of particles diffuses on a fractal structure, and as particles reach the boundaries of the structure they are removed from the system. We find that the number of particles that escape from the matrix as a function of time can be approximated by a Weibull (stretched exponential) function, similar to the case of release from Euclidean matrices. The earlier result that fractal release rates are described by power laws is correct only at the initial stage of the release, but it has to be modified if one is to describe in one picture the entire process for a finite system. These results pertain to the release of drugs, chemicals, agrochemicals, etc., from delivery systems. (C) 2003 American Institute of Physics.

This study, explores the utility of quantitative structure-pharmacokinetic relationship models of the disposition parameters: clearance (CL), apparent volume of drug distribution (V-ap), fractal clearance (CLf), and fractal volume (v(f)), for a series of 23 cephalosporins used in therapeutics. Data for CL, V-ap and elimination half-life were obtained from literature, whereas CL, and vf were calculated from the literature data for CL and V-ap, respectively. A variety of descriptors expressing acidity/basicity, lipophilicity, molecular size and hydrogen bonding properties were estimated using computer packages. For each pharmacokinetic parameter, projection to latent structures (PLS) was applied to the total dataset. Adequate PLS models, with one principal component, were derived for CL, CLf, V-ap and v(f). Identical descriptors were found to be significant for the two clearance as well as for the two volume of distribution terms. CL and CLf expressed similar performance while the predictive performance of v(f) was much higher than that of V-ap. Multiple linear and non-linear regression models were developed. The regression results were in agreement with the PLS models. The non-linear models were superior to the relevant linear relationships. The worst models found were for V-ap (R-2 = 0.523 and R-2 = 0.571 for the linear and non-linear model, respectively) and the best models found were for v(f) (R-2 = 0.729 and R-2 = 0.824 for the linear and non-linear model, respectively). (C) 2003 Elsevier B.V. All fights reserved.

This study addresses the utility of pharmacodynamic considerations to the assessment of bioequivalence (BE) studies. A novel methodology was developed and the performance of classic, nonclassic and novel BE indices was evaluated using extensive simulations of BE trials generated from a classic pharmacokinetic (PK)/pharmacodynamic (PD) model. Three novel indices based on drug's pharmacodynamics were developed and served as criteria for the assessment of all BE indices. Modified power curves were constructed and used for the analysis of BE trials from a PD point of view. All BE indices of either purely PK or PD nature were classified in a semiquantitative manner according to their strictness in declaring BE. The partial area until the peak concentration followed by the two newly proposed metrics (MARD, MARD(w1)) exhibited the most strict performance in declaring BE irrespective of the PK scenarios examined. The study opens new avenues in BE assessment since it places more emphasis on the PD aspects of the formulations. (C) 2003 Elsevier Science B.V. All rights reserved.

Analysis is presented for Case II drug transport with axial and radial release from cylinders. The previously reported {[}J. Control Release 5 (1987) 37] relationships for radial release from films and slabs are special cases of the general solution derived in this study. The widely used exponential relation M-t/M-infinity = kt(n) describes nicely the first 60% of the fractional release curve when Case II drug transport with axial and radial release from cylinders is operating. (C) 2003 Elsevier Science B.V. All rights reserved.

Purpose. To investigate the relationship between mean dissolution time (MDT) and dose/solubility ratio (q) using the diffusion layer model. Methods. Using the classic Noyes-Whitney equation and considering a finite dose, we derived an expression for MDT as a function of q various conditions. q was expressed as a dimensionless quantity by taking into account the volume of the dissolution medium. Our results were applied to in vitro and in vivo data taken from literature. Results. We found that MDT depends on q when q < 1 and is infinite when q > 1 and that the classic expression of MDT = 1/k, where k is the dissolution rate constant, holds only in the special case of q = 1. For the case of perfect sink conditions, MDT was found to be proportional to dose. Using dissolution data from literature with q < 1, we found better estimates of MDT when dependency on dose/solubility ratio was considered than with the classic approach. Prediction dissolution limited absorption was achieved for some of the in vivo drug examples examined. Conclusion. The mean dissolution time of a drug depends on dose/solubility ratio, even when the model considered is the simplest possible. This fact plays an important role in drug absorption when absorption is dissolution limited.

Materials are distributed throughout the body of mammals by fractal networks of branching tubes. Based on the scaling laws of the fractal structure, the vascular tree is reduced to an equivalent one-dimensional, tube model. A dispersion-convection partial differential equation with constant coefficients describes the heterogeneous concentration profile of an intravascular tracer in the vascular tree. A simple model for the mammalian circulatory system is built in entirely physiological terms consisting of a ring shaped, one-dimensional tube which corresponds to the arterial, venular, and pulmonary trees, successively. The model incorporates the blood flow heterogeneity of the mammalian circulatory system. Model predictions are fitted to published concentration-time data of indocyanine green injected in humans and dogs. Close agreement was found with parameter values within the expected physiological range. (C) 2003 Biomedical Engineering Society. {[}DOI: 10.1114/1.1555627].

Purpose. To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. Methods. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. Results. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Conclusions. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Purpose. To develop a quantitative biopharmaceutics drug classification system (QBCS) based on fundamental parameters controlling rate and extent of absorption. Methods. A simple absorption model that considers transit flow, dissolution, and permeation processes stochastically was used to illustrate the primary importance of dose/solubility ratio and permeability on drug absorption. Simple mean time considerations for dissolution, uptake, and transit were used to identify relationships between the extent of absorption and a drug's dissolution and permeability characteristics. Results. The QBCS developed relies on a ( permeability, dose/ solubility ratio) plane with cutoff points 2 x 10(-6) - 10(-5) cm/s for the permeability and 0.5 - 1 (unitless) for the dose/ solubility ratio axes. Permeability estimates, P-app are derived from Caco-2 studies, and a constant intestinal volume content of 250 ml is used to express the dose/ solubility ratio as a dimensionless quantity, q. A physiologic range of 250 - 500 ml was used to account for variability in the intestinal volume. Drugs are classified into the four quadrants of the plane around the cutoff points according to their Papp, q values, establishing four drug categories, i.e., I (P-app > 10(-5) cm/s, q less than or equal to 0.5), II (P-app > 10(-5) cm/s, q > 1), III (P-app < 2 x 10(-6) cm/s, q <= 0.5), and IV (P-app < 2 x 10(-6) cm/s, q > 1). A region for borderline drugs (2 x 10(-6) < P-app < 10(-5) cm/s, 0.5 < q < 1) was defined too. For category I, complete absorption is anticipated, whereas categories II and III exhibit dose/ solubility ratio - limited and permeability-limited absorption, respectively. For category IV, both permeability and dose/ solubility ratio are controlling drug absorption. Semiquantitative predictions of the extent of absorption were pointed out on the basis of mean time considerations for dissolution, uptake, and transit in conjunction with drug's dose/ solubility ratio and permeability characteristics. A set of 42 drugs were classified into the four categories, and the predictions of intestinal drug absorption were in accord with the experimental observations. Conclusions. The QBCS provides a basis for compound classification into four explicitly defined drug categories using the fundamental biopharmaceutical properties, permeability, and dose/ solubility ratio. Semiquantitative predictions for the extent of absorption are essentially based on these drug properties, which either determine or are strongly related to the in vivo kinetics of drug dissolution and intestinal wall permeation.

The purposes of this study were to (i) re-examine the relevance of Higuchi equation and the power la Using both simulated and experimental release data in conjunction with the linearized. in tern's of t(1/2). percent of drug release plots. (ii) demonstrate that the power law describes the entire drug release profile of several experimental data, and (iii) point out a physically based hypothesis for the Successful Use Of power law in describing the entire drug release profile. Simulated data generated from the equation of power law were further analyzed using linear regression analysis in accord with the Higuchi equation. The analysis revealed that data generated from the equation Of power law can be misinterpreted as obeying the Higuchi equation. The use of power law in describing the entire drug release curie from HPMC-based matrix tablets is validated by direct fit of power law equation to published data of other authors. A hypothesis based on the nonclassical diffusion of the solutes in the HPMC matrices is used to interpret the successful use of the power law in describing the entire release profile. (C) 2003 Elsevier Science B.V, All rights reserved.

Purpose. (i) Evaluate the predictive performance of the fractal volume of drug distribution, v(f), (Pharm. Res.18, 1056, 2001), (ii) develop the concept of the fractal clearance, CLf, which is the clearance analogue of v(f), (iii) examine the utility of CLf in allometric studies, (iv) develop allometric relationships for the elimination half-life, t(1/2), and (v) evaluate the use of v(f) and CLf in predicting the volume of drug distribution, V-ap, clearance, CL, and elimination half-life, t(1/2). Methods. Estimates for v(f) of various drugs were obtained and correlated with body mass using data only from animal species. A comparison was made between the predicted and actual v(f) values for humans. For a variety of animal species CLf values were estimated from the equation: CLf = v(f)/V-ap CL The allometric equations developed using CLf were compared with other allometric approaches. Allometric equations were also developed for t(1)/2 utilizing the allometric relationships of v(f) and CLf. Results. The predicted estimates of v(f) were very close to the actual values and the correlation exhibited favorable statistical properties. The values of the allometric exponents for CLf were found to be close to 0.75. The predictive performance for CL using the allometric equations for CLf in conjuction with the rule of exponents was found to be better than the currently considered most accurate allometric approaches. The values of the allometric exponents for t(1)/2 were found to be close to 0.25. Conclusion. The predictive ability of v(f) is high; predictions for V(a)p based on v(f) values are better than the current approaches. CLf expressed a good behavior both in prospective and retrospective analysis. The allometric exponents, 0.75, 0.25 for CLf and t(1/2), respectively, agree with the theoretical expected values.

Purpose. To explore the quantitative structure pharmacokinetic relationships of the disposition parameters: clearance (CL), apparent volume of drug distribution (V-ap), fractal clearance (CLf), and fractal volume (v(f)) for 272 structurally unrelated drugs used in therapeutics. Methods. Literature data were used for CL and V-ap whereas CLf and v(f) were estimated as described previously (Pharm. Res. 18, 1056, 2001 and 19, 697, 2002). A variety of molecular descriptors expressing lipophilicity, ionization, molecular size and hydrogen bonding capacity were estimated using computer packages. The data were analyzed using multivariate statistics. For each disposition parameter (CL, V-ap, CLf, v(f)) PCA (principal component analysis) and PLS (projection to latent structures) were applied to the total set of data as well as to subsets of data. Results. Drugs were divided into two classes (I and II) according to their v(f) /V-ap ratio. Class I comprises 131 drugs with v(f) /V-ap >1, whereas class II 141 drugs with v(f) /V-ap < 1. After initial PLS analysis, class I was subdivided in subclusters I-a (30 drugs) and I-b (101 drugs). It was found that Ia included mostly acidic drugs with high protein binding, whereas class II comprises mainly basic, lipophilic compounds. No correlation was found between CL, V-ap, CLf and the used descriptors. Adequate PLS models were derived for v(f) considering subclusters I-a, I-b and class II separately. The low v(f) values of class I-a drugs were affected negatively from molecular size descriptors and non- polar surface area. For class I-b drugs with intermediate v(f) values, apparent lipophilicity contributed positively, although molecular size descriptors and polarity were inhibitory factors. The high v(f) values of class II drugs were positively dependent on intrinsic lipophilicity and increased basicity, whereas polarity entered with negative contribution. Conclusions. The parameters V-ap, CL, and CLf fail to reflect the physicochemical properties of drugs. The transformation of V-ap values to v(f) is the underlying cause for the valid models for v(f). These models allow a global consideration of molecular properties (lipophilicity, ionization, molecular size, polar surface area) which govern the distribution of drugs in the human body. The present study provides additional evidence for the physiologically sound concept of v(f)

The computational approach is one of the newest and fastest developing techniques in pharmacokinetics, ADME (absorption, distribution, metabolism, excretion) evaluation, drug discovery and toxicity. However, to date, the software packages devoted to ADME prediction, especially of metabolism, have not yet been adequately validated and still require improvements to be effective. Most are `open' systems, under constant evolution and able to incorporate rapidly, and often easily, new information from user or developer databases. Quantitative in silico predictions are now possible for several pharmacokinetic (PK) parameters, particularly absorption and distribution. The emerging consensus is that the predictions are no worse than those made using in vitro tests, with the decisive advantage that much less investment in technology, resources and time is needed. In addition, and of critical importance, it is possible to screen virtual compounds. Some packages are able to handle thousands of molecules in a few hours. However, common experience shows that, in part at least for essentially irrational reasons, there is currently a lack of confidence in these approaches. An effort should be made by the software producers towards more transparency, in order to improve the confidence of their consumers. It seems highly probable that in silico approaches will evolve rapidly, as did in vitro methods during the last decade. Past experience with the latter should be helpful in avoiding repetition of similar errors and in taking the necessary steps to ensure effective implementation. A general concern is the lack of access to the large amounts of data on compounds no longer in development, but still kept secret by the pharmaceutical industry. Controlled access to these data could be particularly helpful in validating new in silico approaches. (C) 2002 Elsevier Science B.V. All rights reserved.

The pharmacokinetics of cyclosporin (CsA) are unusual because of several heterogeneous features which include the presence of more than one conformer, considerable accumulation, in erythrocytes and lipoproteins, extensive plasma protein binding, distribution into deep tissues, biliary secretion and hepatic clearance involving a large number of metabolites. In this study, a stochastic compartmental model was developed to describe the heterogeneous elimination kinetics of CsA. This new approach relies on a probabilistic transfer model with a gamma distributed probability intensity coefficient for drug elimination. For comparative purposes both the stochastic model and compartmental deterministic models were fitted to real post infusion data from patients receiving CsA as a 2-hr intravenous infusion. The criteria for selecting the best model showed that the stochastic model, although simpler than the compartmental deterministic models, is more flexible and gives a better fit to the kinetic data of CsA than the compartmental deterministic models. The stochastic model with a random rate intensity coefficient adequately describes the heterogeneous pharmacokinetics of CsA.

Purpose, To develop the physiologically sound concept of fractal volume of drug distribution, nu (f) and evaluate its utility and applicability in interspecies pharmacokinetic scaling. Methods, Estimates for nu (f) of various drugs in different species were obtained from the relationship: nu (f) = (nu - V-pl) V-ap-V-pl/V-ap + Vpl where nu is the total volume of the species (equivalent to its total mass assuming a uniform density 1g/mL), V-pl is the plasma volume of the species and V-ap is the conventional volume of drug distribution. This equation was also used to calculate the fractal analogs of various volume terms of drug distribution (the volume of central compartment, V-c. the steady state volume of distribution, V-ss, and the volume of distribution following pseudodistribution equilibrium, V-z). The calculated fractal volumes of drug distribution were correlated with body mass of different mammalian species and allometric exponents and coefficients were determined. Results, The calculated values of nu (f) for selected drugs in humans provided meaningful and physiologically sound estimates for the distribution of drugs in the human body. For all fractal volume terms utilized, the allometric exponents were found to be either one or close to unity. The estimates of the allometric coefficients were found to be in the interval (0,1). These decimal values correspond to a fixed fraction of the fractal volume term relative to body mass in each one of the species. Conclusions. Fractal volumes of drug distribution scale proportionally to mass. This confirms the theoretically expected relationship between volume and mass in mammalian species.

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.

Four different parameter estimation criteria, the geometric mean functional relationship (GMFR), the maximum likelihood (ML), the perpendicular least-squares (PLS) and the non-linear weighted least squares (WLS), were used to fit a model to the observed data when both regression variables were subject to error. Performances of these criteria were evaluated by fitting the co-operative drug-protein binding Hill model on simulated data containing errors in both variables. Six types of data were simulated with known variances. Comparison of the criteria was done by evaluating the bias, the relative standard deviation (S.D.) and the root-mean-squared error (RMSE), between estimated and true parameter values. Results show that (1) for data with correlated errors, all criteria perform poorly; in particular, the GMFR and ML criteria. For data with uncorrelated errors, all criteria perform equally well with regard to the RMSE. (2) Use of GMFR and ML lead to lower values far S.D. but higher biases compared with WLS and PLS. (3) WLS performs less well when equal dispersion is applied to the two observed variables. Copyright (C) 2000 John Wiley & Sons, Ltd.

The aim was to study the ursodeoxycholic acid (UDC) effect on thr cyclosporin A (CsA) pharmacokinetics after oral administration of the microemulsion Formulation Neoral(R) (CsA-ME) in liver transplant recipients, and test the potential protective effect of this bile acid on liver and renal CsA-ME-induced toxicity. At entry into the study, 12 patients who underwent orthotopic liver transplantation received CsA-ME. for at least 6 months. They then received a cotreatment CsA-ME plus UDC (13.8 mg.kg (1).day(-1)) for three months. Blood concentrations of CsA were measured using a monoclonal antibody specific For the parent compound. The kinetic data were analysed by a mathematical model incorporating a time dependent rate coefficient for CsA intestinal absorption, before and after UDC treatment. Changes in serum markers of hepatic and renal injury were assessed. Individual serum bile acids were determined by chromatography. Serum levels of UDC increased from 3 to about 45 % of total serum bile acids after UDC treatment. The estimated model parameters indicate that UDC administration modulates CsA intestinal absorption. In the nine non-cholestatic patients, UDC reduced the absorption late and the bioavailability of CsA without modifying the elimination rate constant of CsA and the CsA pre-drug levels. In contrast, in the three cholestatic patients, the bioavailability tended to be higher and the absorption rate faster when CsA was combined with UDC. UDC significantly decreased elevated gamma -glutamyl transferase and creatinine serum levels and induced some clinical improvements such as disappearance of headaches in four patients. In conclusion, a 3-month UDC treatment modifies CsA intestinal absorption without affecting CsA elimination rate constant. On the other hand, UDC supplementation appears to improve CsA tolerability. (C) 2000 Editions scientifiques et medicales Elsevier SAS.

Purpose. To develop an approach based on computer simulations for the study of intestinal drug absorption. Methods. The drug flow in the gastrointestinal tract was simulated with a biased random walk model in the heterogeneous tube model (Pharm. Res. 16, 87-91, 1999), while probability concepts were used to describe the dissolution and absorption processes. An amount of drug was placed into the input end of the tube and allowed to flow, dissolve and absorb along the tube. Various drugs with a diversity in dissolution and permeability characteristics were considered. The fraction of dose absorbed (F-abs) was monitored as a function of time measured in Monte Carlo steps (MCS). The absorption number An was calculated from the mean intestinal transit time and the absorption rate constant adhering to each of the drugs examined. Results. A correspondence between the probability factor used to simulate drug absorption and the conventional absorption rate constant derived from the analysis of data was established. For freely soluble drugs, the estimates for F-abs derived from simulations using as an intestinal transit time 24500 MCS (equivalent to 4.5 h) were in accord with the corresponding data obtained from literature. For sparingly soluble drugs, a comparison of the normalized concentration profiles in the tube derived from the heterogeneous tube model and the classical macroscopic mass balance approach enabled the estimation of the dissolution probability factor for five drugs examined. The prediction of F-abs can be accomplished using estimates for the absorption and the dissolution probability factors. Conclusions. A fully computerized approach which describes the flow, dissolution and absorption of drug in the gastrointestinal tract in terms of probability concepts was developed. This approach can be used to predict F-abs for drugs with various solubility and permeability characteristics provided that probability factors for dissolution and absorption are available.

Phase plane plots are graphical expressions for differential equations ploting the state derivative dc/dt versus the state c. Using these plots, we developed a novel method for the estimation of the terminal slope from time-concentration data. The values of the derivatives used for the construction of the phase plane plots were calculated by two different methods of numerical differentiation. The first method (D1) is based on the classical calculation of slope of the line connecting two successive data points. The alternative method (D2) relies on an initial second-order polynomial interpolation utilizing three successive data points followed by the calculation of the derivative at each one of the concentration values. A forced-through-zero linear regression of the phase plane plot data is used to derive an estimate for the slope. For comparative purposes, the standard approach based on the semilogarithmic plot was also applied. For a hypothetical drug absorbed by first-order process into a one-compartment model, simulated time-concentration data disturbed by a Gaussian zero mean random error with various coefficients of variation were generated. Various sampling schedules, with two, three, four, or five data points, were utilized for the estimation of the terminal slope. Performances of the proposed methods on simulated data were expressed by means of root-mean-squared error, bias, and standard deviation. In all cases, D2 was superior to D1. The D2 method outperforms the standard method in that it furnishes estimates closer to the real values in all cases when two data points and in most cases when three data points were used. All methods behave similarly when four or five data points were used.

The interaction of diflunisal ion (DF) with beta-cyclodextrin (PCD), gamma-cyclodextrin (gamma CD), and hydroxypropyl-beta-cyclodextrin (HP beta CD) was studied in phosphate buffer, pH 7.4, at 5-37 degrees C and various CD concentrations using a home-made diflunisal ion-selective electrode. Typical direct binding plots and Scatchard plots were obtained with HP beta CD. The Scatchard model for one class of binding sites was used for the estimation of binding parameters for the DF/HP beta CD interaction. The estimates for n (number of binding sites per CD molecule) were in all cases very close to unity, indicating 1:1 complexation. The association constant (K) estimates decrease with increasing temperature. Sigmoidal direct binding plots and concave-downwards Scatchard plots were obtained with various beta CD or gamma CD concentrations. The Hill model was used for the estimation of the binding parameters for the DF/beta CD and DF/gamma CD interactions. Both the Hill coefficients and the binding constants were markedly dependent on the CD concentration. These findings indicate the cooperative character of DF/beta CD and DF/gamma CD interactions. The foe energy change, Delta G, and the thermodynamic parameters, Delta H and Delta S, were estimated for each of the interactions studied using the Van't Hoff equation. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

An isocratic reversed-phase HPLC method was developed to determine cefepime levels in plasma and vitreous fluid. Cefepime and the internal standard cefadroxil were separated on a Shandon Hypersil BDS C18 column by using a mobile phase of 25 mM sodium dihydrogen phosphate monohydrate (pH 3) and methanol (87:13, v/v). Ultraviolet detection was carried out at 270 nm. The retention times were 4.80 min for cefepime and 7.70 min for cefadroxil. This fast procedure which involves an efficient protein precipitation step (addition of HClO4), allows a quantification limit of 2.52 mu g ml(-1) and a detection limit of 0.83 mu g ml(-1). Recoveries and absolute recoveries of cefepime from plasma were 96.13-99.44% and 94-102.5% respectively. The intra-day and inter-day reproducibilities were less than 2% for cefepime at 10, 30, 50 mu g ml(-1) (n=10). The method was proved to be suitable for determining cefepime levels in human plasma and was modified to measure vitreous fluid samples. (C) 1999 Elsevier Science B.V. All rights reserved.

Purpose. A Monte-Carlo computer simulation technique was employed to study the details of the small intestinal transit flow in the gastrointestinal (GI) tract. Methods. A heterogeneous tube model was constructed using a numerical computer simulation technique. The model was built from first principles and included several heterogeneous characteristics of the GI tract structure. We used a random, dendritic-type internal structure representing the villi of the GI tract. The small intestinal transit flow was simulated using two diffusion models, namely, the blind ant and the myopic ant models, which are different models to account the elapse of time, and which are both based on statistical properties of random walks. For each one of the models we utilize two types of biased random walk, placing different emphasis in the motion towards the output of the tube. We monitored the flow of the drug in terms of Monte-Carlo time steps (MCS) through the tube walls and dendritic villi present. Results. The frequency of the transit times was dependent on the structure of the dendritic villi and on the type of biased random walk. The small intestinal flow profile of literature data for a large number of drugs was well characterized by the heterogeneous model using, as parameters, a certain number of villi per unit length of the tube and specific characteristics for both types of the biased random walk. A correspondence between the MCS and real time units was achieved. Conclusions. The transit process of the oral dosage forms in the GI tract can be reproduced with the heterogeneous model developed. This model can be used to study GI absorption phenomena.

A displacement approach for competitive binding studies was developed. The method utilizes the potentiometric 1-anilino-8-naphthalene-sulfonate (ANS) probe technique and is applied to the binding study of several non-steroidal anti-inflammatory drugs (NSADs) to bovine serum albumin (BSA). A home-made ANS electrode was used to monitor the displaced free ANS probe from its binding sites on the protein molecule by the stepwise addition of the studied drug. To assess and compare quantitatively the displacing ability of the various drugs, the `ANS Displacement Index' is used. The possible interference of 19 ionizable drugs (NSADs, sulfonamides, etc.) to the ANS selective electrode at pH 7.4 was studied and their potentiometric selectivity coefficients (K-ANS,D(pot)) were determined. Correction procedures for the determination of the free ANS concentration are proposed in the case of interfering ionic drugs. A blank binding experiment in conjunction with the incorporation of K-ANS,D(pot) values in the `general competitive site oriented model' allows one to derive estimates for the drug binding parameters, i.e. the number of binding sites and association constants. (C) 1999 Elsevier Science B.V. All rights reserved.

A recursion equation which relies on the population growth model of dissolution is used for the analysis of supersaturated dissolution data. The concentration-time data of dissolution experiments are initially transformed to fractions of dose dissolved-generations by adopting an appropriate time interval as the time step of the recursion equation. A computer program is used to derive estimates for the maximum fraction of dose dissolved and the fraction of dose remaining in solution at steady state. Good fittings were observed when this equation was applied to phenytoin and nifedipine supersaturated dissolution data obtained from literature. (C) 1999 Elsevier Science B.V. All rights reserved.

Purpose. To develop a simple approach for investigating absorption kinetics, which does not require modeling assumptions or intravenous data. Methods. The concentration (C) -time (t) data are plotted as a phase plane plot (dC/dt versus C). Errorless C,t data were generated from one and two compartment models employing first-order, zero-order and Michaelis-Menten input kinetics, and the phase plane plots were constructed. A simple test based on the ratio of slopes of the separate linear regression analyses of absorption and elimination data of the phase plane plot is proposed to justify or not the presence of zero-order input kinetics. Errant data were used to assess the performance of the test developed. Literature data of theophylline and nitroglycerin formulations were analyzed using the phase plane plot. Input rate-time profiles were constructed for one compartment model drugs utilizing the data of the phase plane plot. Results. The geometric forms of the phase plane plots derived from the errorless data of the various pharmacokinetic models were found to be indicative of the absorption kinetics. Very good results were obtained when the test for the discernment of absorption kinetics was applied to errant data. Zero-order absorption kinetics were justified (i) for the transdermal absorption of nitroglycerin and (ii) only for a certain period of time, for the gastrointestinal absorption of theophylline. Conclusions. Investigation of absorption kinetics can be accomplished with the phase plane method. The cumulative character of the classical percent absorbed versus time plots can be misleading in justifying the presence of zero-order input kinetics.

The objectives of these studies were, first, to determine the effect of elevated luminal viscosity on the gastrointestinal absorption of four model drugs and, second, to identify the key processes influencing drug absorption under elevated viscosity conditions. Studies were conducted in vitro and in healthy female mongrel does under fasting conditions. In the canine model, both the rate and extent of paracetamol and hydrochlorothiazide absorption were significantly decreased by the coadministration of 15 g guar gum dissolved in 500 ml normal saline. In the case of cimetidine, the rate but not extent of absorption was decreased. Owing to the high variability in the data, no statistically based conclusion could be drawn about the effects of coadministered guar gum on the oral absorption of the poorly soluble mefenamic acid. Based on the in vitro data, it appears that substantial reductions in the dissolution rate of paracetamol, hydrochlorothiazide and cimetidine account for the effects observed in vivo. It is concluded that the effect of an elevation in the intraluminal viscosity on drug absorption is greatest for highly soluble drugs, and results from a combination of a decrease in dissolution rate and gastric emptying rate. (C) 1998 Elsevier Science B.V.

The objective of this study was to evaluate the effects which hydroxypropylmethylcellulose (HPMC) may exert on oral drug absorption, in cases where this soluble fiber is administered to regulate blood lipid levels. Studies were conducted in vitro and in healthy female mongrel dogs using two different grades of HPMC, i.e. K8515 HPMC and ultra high molecular weight (UHMW) HPMC. The maximum plasma concentration, C-max, of paracetamol and both the C-max and the area under the concentration-time curve, AUC, of cimetidine were significantly decreased by the coadministration of 10 g of K8515 HPMC or 7.5 g of UHMW HPMC dissolved in 500 mL normal saline under fasting conditions. No statistically significant effects were observed on hydrochlorothiazide or mefenamic acid absorption. Based on in vitro data and previous studies it appears that reductions in gastric emptying and dissolution rate of paracetamol account for the effect observed in vivo. For cimetidine, a drug which can be absorbed from both the small and the large intestine, the indigestibility of HPMC in the colon in addition to the great reduction of dissolution rate led to reductions of both the C-max and AUC values. The long T-max values, even in the absence of HPMCs and the more modest reduction of the dissolution rate of hydrochlorothiazide by the HPMCs are thought to have precluded the observation of any significant alterations in the in vivo absorption profile. Owing to its erratic absorption, no statistically based conclusion could be drawn about the effects of coadministered HPMC on the oral absorption of the poorly soluble mefenamic acid. It is concluded that the effects of HPMCs on drug absorption in dogs are most pronounced for compounds with absorption profiles that are dependent on gastric emptying, i.e. compounds that are highly water soluble and that exhibit short T-max values. Compounds with long absorption profiles appear to be less susceptible to changes in absorption behavior due to coadministration of HPMCs. (C) 1998 John Wiley & Sons, Ltd.

Purpose. To develop a new approach for describing drug dissolution which does not require the presuppositions of time continuity and Fick's law of diffusion and which can be applied to both homogeneous and heterogeneous media. Methods. The mass dissolved is considered to be a function of a discrete time index specifying successive `'generations'' (n). The recurrence equation: Phi(n+1) = Phi(n) + r(1 - Phi(n))(1 - Phi(n)X(0)/theta) was derived for the fractions of dose dissolved Phi(n) and Phi(n+1) between generations n and n + 1, where r is a dimensionless proportionality constant, X-0 is the dose and theta is the amount of drug corresponding to the drug's solubility in the dissolution medium. Results. The equation has two steady state solutions, Phi(ss) = 1 when (X-0/theta) less than or equal to 1 and Phi(ss) = theta/X-0 when (X-0/theta) > 1 and the usual behavior encountered in dissolution studies, i.e. a monotonic exponential increase of Phi(n) reaching asymptotically the steady state when either r < theta/X-0 < 1 or r < 1 < theta/X-0. Good fits were obtained when the model equation was applied to danazol data after appropriate transformation of the time scale to `'generations''. The dissolution process is controlled by the two dimensionless parameters theta/X-0 and r, which were found to be analogous to the fundamental parameters dose and dissolution number, respectively. The model was also used for the prediction of fraction of dose absorbed for highly permeable drugs. Conclusions. The model does not rely on diffusion principles and therefore it can be applied under both homogeneous and non-homogeneous conditions. This feature will facilitate the correlation of in vitro dissolution data obtained under homogeneous conditions and in vivo observations adhering to the heterogeneous milieu of the GI tract.

The current analysis of gastrointestinal absorption phenomena relies on the concept of homogeneity. However, drug dissolution, transit and uptake in the gastrointestinal tract are heterogeneous processes since they take place at interfaces of different phases under variable stirring conditions. Recent advances in physics and chemistry demonstrate that the geometry of the environment is of major importance for the treatment of heterogeneous processes. In this context, the heterogeneous character of in vivo drug dissolution, transit and uptake is discussed in terms of fractal concepts, Based on this analysis, drugs are classified in accordance with their gastrointestinal absorption characteristics into two broad categories i.e. homogeneous and heterogeneous. The former category includes drugs with satisfactory solubility and permeability which ensure the validity of the homogeneous hypothesis. Drugs with low solubility and permeability are termed heterogeneous since they traverse the entire gastrointestinal tract and therefore are more likely to exhibit heterogeneous dissolution, transit and uptake. The high variability of whole bowel transit and the unpredictability of conventional dissolution tests for heterogeneous drugs are interpreted on the basis of the fractal nature of these processes under in vivo conditions. The implications associated with the use of strict statistical criteria in bioequivalence studies for heterogeneous drugs are also pointed out.

Purpose. To point out the importance of heterogeneity in drug distribution processes and develop a noncompartmental approach for the description of the distribution of drug in the body. Methods. A dichotomous branching network of vessels for the arterial tree connected to a similar venous network was used to describe the heterogeneity of blood flow in the successive generations of the networks. The relevant kinetics of drug distribution in the well perfused and the deep tissues was considered to take place under well stirred (homogeneous) and understirred (heterogeneous) conditions, respectively. Results. A `'homogeneous model'' with classical kinetics (which is mathematically equivalent with the one-compartment model) was developed for these drugs which are confined to well perfused (''well stirred'') spaces. A `'heterogeneous model'' was proposed for the drugs reaching understirred spaces using a decreasing with time rate coefficient (fractal kinetics) to model the diffusion of drug under heterogeneous conditions. The analysis of the model equations revealed that the homogeneous model can be considered as a special case of the heterogeneous model. Concentration-time plots of multiexponential type were generated using the heterogeneous model equation. The empirically used power functions of time for the analysis of calcium clearance curves, were found to be similar to the equation adhering to the heterogeneous model. Fittings comparable to multiexponential models were obtained when the heterogeneous model equation with only one adjustable parameter was applied to six sets of long period calcium data. Conclusions. The heterogeneous processes of drug distribution in the body can obey the principles of fractal kinetics. Calcium clearance curves were analysed with the heterogeneous model. The validity of multicompartmental models which are based on the concept of homogeneity to describe drug distribution should be reconsidered.

A potentiometric method for the in vitro adsorption kinetic study of an ionic micromolecule to charcoal, based on the continuous direct monitoring of the micromolecule free concentration by means of an ion-selective electrode (ISE), has been developed. A chlorpromazine ISE was constructed and used to study the adsorption kinetics of the drug on pure activated charcoal and two commercial formulations (Ultracarbon tablets and Carbomix powder). The method consists of the rapid addition of a slurry containing the charcoal into the drug solution under stirring at pH 1.2 (to simulate a gastric fluid environment) and continuous recording of the electrode potential until the establishment of equilibrium The drug free concentration at appropriate time intervals was calculated from the recorded adsorption curve acid the apparent adsorption rate constant was estimated assuming first order kinetics. Within run RSD of the estimates ranged from 0.3 to 12% (mainly less than 5%), while between run RSD (n=3) ranged from 1 to 19% (mainly less than 10%). A linear relationship was found between the apparent adsorption rate constants and the amount of charcoal used with slopes following the rank order activated charcoal>Ultracarbon tablets>Carbomix powder. These results were explained on the basis of different surface areas of the adsorbents. The work proved the usefulness of ion-selective potentiometry in adsorption studies and can be extended to other ionic drugs for which selective electrodes can be constructed.

Background: This investigation war undertaken to study: a) the adsorption characteristics of chlorpromazine to activated charcoal and its formulations Carbomix(R) powder and Ultracarbon(R) tablets at gastric pH; b) the effect on chlorpromazine adsorption of polyethylene glycol and its combination with electrolyte lavage solution; c) the effect of the order of addition of polyethylene glycol-electrolyte lavage solution. Method: Ion selective electrode potentiometry, bared on the selective, direct and continuous response of a chlorpromazine-ion selective electrode to the concentration of the free drug, was used. Successive additions of microvolumes of a chlorpromazine solution were made into a charcoal slurry in acidic medium of pH 1.2 with measurement of the chlorpromazine-ion selective electrode potential at equilibrium Results: The maximum adsorption capacity values of activated charcoal, Carbomix and Ultracarbon, were 297, 563, and 382 mg/g respectively, while the affinity constant values were 40.2, 70.4, and 40.5 L/g, respectively. The adsorption of chlorpromazine to each of the Ultracarbon and Carbomix components was compared to the total adsorption of the formulations. The addition of polyethylene glycol-electrolyte lavage solution causes a slight desorption of chlorpromazine from activated charcoal at gastric pH, more pronounced when polyethylene glycol-electrolyte lavage solution follows the addition of activated charcoal, suggesting the possibility of a nonspecific binding of chlorpromazine to polyethylene glycol. The amount of chlorpromazine adsorbed to Carbomix and Ultracarbon was not significantly affected at gastric pH by the presence of polyethylene glycol or polyethylene glycol-electrolyte lavage solution added either concurrently or sequentially to these formulations.

The paper presents a method for the calculation of fractal reaction dimension, D-R, in dissolution studies of powdered substances with a given particle size distribution. An estimate for D-R can be directly obtained from dissolution experiments using the well known Hixson-Crowell equations in a modified form. The estimation is accomplished with a special computer program in BASIC which was developed and applied to simulated errorless and contaminated data with very good results. A practical demonstration of the method's usefulness was shown on experimental data taken from the literature.

Bioequivalence assessment of extended release (ER) dosage forms is usually carried out at steady-state, using area under the curve (AUG) to evaluate extent of absorption and maximum concentration (C-max) and % peak trough fluctuation ratio (%PTF) to evaluate rate of absorption. Other metrics such as C-max/AUC and partial AUCs have recently been proposed as alternatives for assessing the absorption rate of drugs from immediate release (IR) dosage forms under single dose conditions. The performances of these metrics were assessed using the results of two sets of simulated experiments of ER dosage forms at steady-state and 2 actual pharmacokinetic studies involving ER dosage forms of a Glaxo drug. In the first set of simulations there was no difference in bioavailability between the two formulations; in the second set of simulations the test formulation had a 50% greater absorption rate-constant (ka) than the reference formulation. The following conclusions were reached: 1. For ER dosage forms at steady-state, all the metrics, with the exception of %PTF, resulted in much smaller increases than the underlying 50% increase in ka. Although, %PTF gave the largest effect it was also the most imprecisely estimated. 2. In our studies, none of the metrics tested provided reliable information about changes in the underlying rate of absorption from ER dosage forms under steady-state conditions. 3. The current practice of comparing rate of absorption from ER dosage forms using steady-state C-max is inappropriate due to lack of sensitivity. The use of %PTF may require a widening in the currently accepted 80-125% permissible range set for C-max and AUC.

A model based on the fractal methodology is proposed for the kinetic study of carrier-mediated transport under heterogeneous conditions, i.e., when the drug-carrier interaction occurs at an interface with an effective dimensionality smaller than the embedding dimension of d = 2. A model equation is derived for the flux, based on a similar approach for an analogous equation for enzyme kinetics. It is shown that the total flux-solute concentration plots are curvilinear when the fractal dimension is smaller than unity while they become biexponential, with ascending and descending limbs, when the fractal dimension D is in the range 1 < D < 2. Nonlinear Lineweaver-Burk plots are obtained when this fractal kinetics approach is used. Good fittings are obtained when the fractal model is applied to literature data previously analysed with a combined transport mechanism, revealing experimental systems that display a D value in the range 1 < D < 2. It is suggested that transport studies should be carried out at a wider working solute concentration range and various agitation and incubation conditions in order to derive definite conclusions for the transport pathways.

A diflunisal ion selective electrode of the PVC membrane type with an ion-exchanger consisting of the tetraheptylammonium-diflunisal ion pair is described. The sensor exhibits a rapid, near-Nernstian, selective response to diflunisal anion in the pH range 7-10, with a (batch) detection limit of 1 x 10(-5) M. The ion sensor was used as a flow detector in an automated flow-injection analyzer to develop routine methods for assays (concentration range 1-50 x 10(-4) M, (flow) detection limit 2.6 x 10(-5) M), content uniformity, and dissolution studies of diflunisal formulations. No serious interference from common ions and tablet excipients was found, and the drug can be directly determined in colored samples without separation steps. Fourty measurements can be performed automatically per hour with a precision of 0.5-1.8% relative standard deviation. The automated method for the dissolution test provides a complete dissolution profile by the end of the experiment. Using the constructed ion sensor, the intramolecular hydrogen bonding of the diflunisal anion was studied, thereby revealing a new application of ion sensor potentiometry.

The application of flow-injection analysis (FIA) to automated dissolution studies of sustained-release formulations is described. The long-term stability of the dissolution-FIA analyser was checked during unattended operation for 42 h. The construction of multiple calibration curves with the so-called electronic dilution FIA procedure was used to extend the linear range of the determination. The computer-controlled FIA system and the principles of associated software are described and applied to dissolution studies of sustained-release formulations of iron(II) using its sensitive reaction with the colour reagent, ferrozine. The extended linear range of the determination is 1-130 ppm iron(II) and the precision (RSD) better than 3% (n = 3).

The aqueous solubility of cyclosporin A (CyA) in the presence of various concentrations of TPGS ranging from 0.01 to 0.50 mM was studied at three temperatures (5, 20, and 37-degrees-C). Compared to previously reported solubility data in triple distilled water, solubility in the presence of TPGS was significantly increased at all temperatures. Surface tension and light scattering measurements showed that solubilization in TPGS multimers is the main mechanism responsible for the increased CyA solubility at 20-degrees-C and 37-degrees-C. In contrast, the increased CyA solubility at 5-degrees-C appears to be mediated by other mechanism(s), such as association of TPGS with CyA. These data substantiate the view that the enhanced bioavailability of CyA, when coadministered with TPGS in patients suffering from cholestasis, is due to the increased solubility of CyA in the presence of TPGS.

The partial area method has been suggested for the assessment of the absorption rate in bioequivalence studies. This paper provides a theoretical basis for the estimation of the optimal cutoff time point of the partial areas for drugs with one compartment model disposition. The analysis is performed by using the appropriate equations which relate the normalized (in terms of the extent of absorption) partial areas with time expressed in terms of multiples of half-life. Provided that the quality of experimental data ensures precise estimation of the parameters, the t(max) of the formulation with the faster absorption characteristics is generally the most practical cutoff time point for calculation of the normalized partial areas, when a drug follows one compartment model disposition with linear absorption.

The binding of diflunisal to hydroxypropyl-beta-cyclodextrin (HPbetaCD), bovine serum albumin (BSA), human serum albumin (HSA), normal human plasma, and mixed solutions of HPbetaCD/protein was studied at 25-degrees-C, pH 7.4, by potentiometry using an electrode selective to diflunisal. The experimental data for diflunisal/HPbetaCD fit well to the 1:1 binding model. The binding of diflunisal with each of the studied proteins was compatible with a model having two independent classes of binding sites. The binding of diflunisal in mixed solutions HPbetaCD/BSA, HPbetaCD/HSA, and HPbetaCD/plasma increased considerably when the HPbetaCD concentration was increased. The binding behavior of the two biomolecules in the mixed solutions of HPbetaCD/BSA or HPbetaCD/HSA was described with an `'additive'' model formulated on the basis of the estimates of the binding parameters of diflunisal derived from the separate experiments with each one of the binders tested. The lower than theoretical binding observed in HPbetaCD/plasma solutions was ascribed to the competitive displacement of diflunisal from the HPbetaCD cavity by plasma cholesterol.

The binding of naproxen, ketoprofen, phenylbutazone, salicyclic acid, azapropazone, and indobufen to bovine serum albumin was studied by applying the potentiometric ion probe technique. An ion-selective electrode for the ion probe 1-anilino-8-naphthalenesulfonate was utilized for the purposes of this study. A modified site-oriented competitive binding model was used for the estimation of the drugs' binding parameters, considering different number of binding sites on the competing binding class(es) for the probe and the drug. Calculations v,ere based exclusively on the concentration data of the free probe. The model's ability for accurate estimations of binding parameters was evaluated by simulation studies. The following values of binding parameters were found at 25 degrees C for the drugs under study; naproxen, n(1) = 9.1, k(1) = 9.4 X 10(5) M(-1); ketoprofen, n(1) = 8.8, k(1) = 10.8 X 10(5) M(-1); phenylbutazone, n(1) = 3.2, k(1) = 1.4 X 10(5) M(-1); salicylic acid, n(1) = 2.6, k(1) = 1.8 X 10(5) M(-1), n(2) = 21.5, k(2) = 1.0 X 10(4) M(-1); azapropazone, n(1) = 0.5, k(1) = 7.8 X 10(5) M(-1), n(2) = 26.3, k(2) = 1.9 X 10(4) M(-1); indobufen, n(1) = 5.8, k(1) = 5.8 X 10(5) M(-1), n(2) = 19.9, k(2) = 3.8 X 10(5) M(-1), where n(i) the number of binding sites of the i class and k(i) the corresponding association constant.

A flow-injection dynamic dialysis technique is presented for the determination of binding parameters of drugs to cyclodextrins (CDs). The automated system consists of a flow-injection unit, the sample loop of which is the receiving compartment of a dialyser unit, and a home made timing module for operation control through two flow switching solenoid valves. The procedure of binding studies is rapid and yields reproducible results. Binding parameters of CD-micromolecule complexes was calculated using the Scatchard model. Typical examples of the binding of p-nitrophenol with alpha-CD(K-as=1.56x10(3) M(-1) at pH 7.4 and 2.06x10(3) M(-1) at pH 9.0), salicylic acid with beta-CD (K-as=3.8 x 10(2) M(-1) at pH 1.5 and 51 M(-1) at pH 7.4) and ibuprofen with beta-CD (K-as=2.2x10(2) M(-1) at pH 2.5) are presented and the binding constants obtained are compared to literature values. 1:1 stoichiometry was found in all cases and within run precision ranged from 2 to 14% R.S.D. The between run precision for the binding of p-nitrophenol to alpha-CD was 2% (n=3).

The binding of sulphafurazole, sulphamethizole and sulphamethoxazole to bovine serum albumin (BSA) and human plasma has been studied in-vitro by potentiometry using an electrode selective for the ion probe 1-anilino-8-napthalenesulphonate (ANS). The method requires two separate potentiometric titrations of the binder solution with ANS in the absence and in the presence of sulphonamides. ANS displaced sulphonamides from the first-class of binding sites of both binders. The binding constants for sulphonamide-BSA interactions were higher than those for sulphonamide-human plasma. The expansion of the least linear limit of the response curve of the electrode down to 10(-7) M in the presence of BSA was also demonstrated. The reverse reaction, i.e. the displacement of the probe from the binding sites induced by the sulphonamides, was also explored. The proposed method is suitable for studying competitive binding interactions in biological specimens.

The complexation of six tricyclic antidepressant drugs {[}amitriptylin (AMN), nortriptylin (NRN), imipramin (IMN), doxepin (DXN), protriptylin (PTN), and maprotilin (MPN)] with alpha-and-beta-cyclodextrins (CDs) using ion-selective electrodes (ISEs) as drug ion sensors is described. Binding parameters were calculated by nonlinear fitting of the model described by the Scatchard equation, to the experimental data of a titration of a CD solution with the ion of interest. One binding site (the CD cavity) was found in all cases with both CDs. The calculated association constants at 25-degrees-C using CD concentrations in the range of 0.0100-0.0010 M, varied from 4.81 x 10(3) M-1 (MPN) to 23.9 x 10(3) M-1 (AMN) in the case of beta-CD and from 50 M-1 (DXN) to 123 M-1 (MPN) in the case of alpha-CD. The precision for the estimation of the binding parameters was 0.1-5.0% (within-run RSD%) and 8-10% (between-run RSD%; n = 3). The complexation of the drugs with beta-CD was also examined as a function of temperature in the range of 5-37-degrees-C; it was found to decrease by increasing temperature. Van't Hoff analysis gave good correlations (r greater-than-or-equal-to 0.989) for all drug ions studied. The estimates of the thermodynamic parameters indicate that the formation of inclusion complexes is enthalpy driven. A compensation plot based on the thermodynamic parameters DELTA-H and DELTA-S resulted in a linear relationship, which is indicative of a common type of force involved in the complexation of drugs to beta-CD.

The appropriate Scatchard equation was developed for a system involving the formation of 1:1 and 1:2 substrate:cyclodextrin complexes. Simulation of this system was performed under the most common experimental conditions encountered in this type of study. The use of the equation allows for nonlinear least-squares estimation of the association constants. The interaction of the model compounds 1-anilino-8-naphthalenesulfonate (1,8-ANS) and 2(p-toluidinyl)-6-naphthalenesulfonate (2,6-TNS) with beta-cyclodextrin (beta-CD) was used to evaluate the theoretical model. Binding experiments were performed using either potentiometric titration or fluorimetric detection. The experimental data for 1,8-ANS/beta-CD fit well to the 1:1 binding model, with an association constant of 87 +/- 1 M-1. The association constants of the 1:1 and 1:2 2,6-TNS/beta-CD complexes utilizing direct potentiometry were 3737 +/- 6 and 149 +/- 2 M-1. It is shown that fluorimetry can give biased estimates for the association constants of the complexation 2,6-TNS/beta-CD, since the assumption of an equivalent quantum yield of bound species is not valid.

A compartmental approach for estimating the duration of the zero-order absorption was developed. For drugs obeying one-compartment model disposition, the estimation is based on an explicit relationship while an iterative process is required for drugs represented by two-compartment kinetics. A method based on a double graphical plot for ascertaining absorption kinetics for drugs exhibiting one-compartment model disposition was also developed.

The binding of 1-anilino-8-naphthalenesulfonate (ANS) to bovine serum albumin (BSA), human serum albumin (HSA), and human plasma has been studied by potentiometric titration utilizing a laboratory constructed ion selective electrode (ISE) of ANS. Three classes of ANS binding sites were found on BSA, HSA, and plasma at 25 and 37-degrees-C. Computer analysis of the data resulted in estimates for the association constants, number of binding sites (HSA, BSA), and binding capacity of each class. The association constants for the first class of binding sites at 25-degrees-C were found to be 7.53 (+/- 0.59) x 10(5), 2.70 (+/- 0.20) x 10(5), and 2.64 (+/- 0.26) x 10(5) M-1 for BSA, HSA, and plasma, respectively. Lower values for the association constants of all binding classes were estimated at the higher temperature (37-degrees-C). The binding capacity for ANS decreased in the order BSA, plasma, HSA.

The solubility of cyclosporin A was determined in water and in Sorensen buffers at pH 1.2 and 6.6 at temperatures ranging from 5 to 37-degrees-C. No differences in solubility behaviour were observed among the three aqeous media. Solubility was found to be inversely proportional to the temperature in each medium, indicating that the heat of solution was exothermic in each case.