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

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

The World Health Organization (WHO) rules (1996) recommend in chapter 3 ''Technical data for regulatory assessment'' that information for marketing authorization should contain among others in-documentation, equivalence data (comparative bioavailability, pharmacodynamic or clinical studies), and comparative in vitro dissolution tests. European rules concerning evaluation of bioavailability and bioequivalence (CPMP/EWP/QWP/1401/98) specify in chapter 5.2: ''Dissolution studies are always necessary and consequently required. In vitro dissolution testing forms a part of the assessment of a bioequivalence waiver''. The consequence is that over the last years all over Europe dissolution studies were connected to bioequivalence studies and the natural tendency was to correlate the results obtained in the pair studies in order to obtain models allowing dissolution results as predictor for in vivo results.Let us consider only as a mnemotechnique, the living body as a ''mathematical operator'' which transforms parameters characterizing dissolution curves in pharmacokinetic parameters associated to plasma levels curves. y (dissolution) Ω pharmacokineticsIf we consider the two spaces as ordered metric spaces, a natural question is that the operator preserves the distances and order. For example, if we compare a tested drug T with a reference one R, we would be interested to know ifLess formally speaking we are interested to know if in vitro similarity implies bioequivalence and if a better dissolution implies a better bioavailablity. It is clear that the response depends on the active substance and physiopatological parameters but also on the particular metrics choiced for characterizing in vitro and in vivo curves as well as distances between its. The response is not so simple, first of all since due to the complexity of the phenomena studied, both metrics and order in vitro and in vivo are not well defined. The great number of dissolution and bioequivalence metrics (Enachescu et al. 2003) show that the problem is yet to be solved.In vitro dissolution tests. Dissolution tests were performed using the method indicated by USP or according to the specifications provided by the producers. As metrics of dissolution were considered the factors f 1 and f 2 .Clinical trials. Each study was performed on healthy volunteers. Experiments were of the standard type: cross-over, with two periods and two sequences.Analytical methods. Plasma levels of the drugs were evaluated using validated liquid chromatographic methods, with UV or mass spectometry detection.In judging the results it should be kept in mind that that in so-called in vitro/in vivo correlations, we practically jump over one step -in vivo dissolution, which is by far more variable and more complex than the in vitro dissolution. Since in vitro dissolution conditions are often far from the in vivo conditions, we have non-correlation between the two dissolutions.Similar dissolution and non-bioequivalence. This is the case for many acidic or basic drugs. Most representative is ...

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

Previous studies indicated that addition of the antihistaminic chlorpheniramine to the usual combination of acetylsalicylic acid, acetaminophen, and caffeine further increases their synergism both in terms of anti-inflammatory and analgesic effect. The present non-interventional study tested the superiority of two Algopirin® tablets, containing a total of 250 mg acetylsalicylic acid (ASA), 150 mg acetaminophen (paracetamol, PAR), 30 mg caffeine (CAF) and 4 mg chlorpheniramine (CLF) vs. a combination containing 250 mg ASA, 250 mg PAR, and 65 mg CAF recognized as “safe and effective” by FDA in treating migraine. Patients evaluated their pain intensity on the Visual Analog Scale—VAS(PI) before and 30, 60, 120, 180, and 240 min after drug intake. Interpretation of the pain curves as “survival pain curves” was considered as a method for direct comparison of the pain curves. This interpretation permitted the application of the log rank test for comparison of pain hazards. The results of the applied parametric and non-parametric statistical tests indicated significant differences between the main endpoints: both Areas Under Pain Curves and time to decrease of the pain intensity to less than 50% of the initial value comparisons highlighted that Algopirin® was more efficient in spite of smaller doses of PAR and CAF. Comparison of “survival of pain” led to the same conclusion concerning the superiority of Algopririn. Consequently, the addition of CLF permitted decreasing of ASA, PAR, and CAF doses as well as their potential side effects, without a loss of analgesic effect.