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

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

Sources of outlier data in the bioanalytical and clinical part of a piroxicam bioequivalence study.

OBJECTIVE: This paper analyzes the potential outliers in the bioanalytical and clinical part of a bioequivalence study, the effect on bioequivalence decisions whether or not it is appropriate to eliminate them from the statistical evaluation of bioequivalence. MATERIALS AND METHODS: The clinical part was a cross-over, two periods, two sequences bioequivalence study concerning two piroxicam formulations, on healthy subjects. A simulation study evaluated the influence of 10% errors on the percent bias of calculated concentrations from nominal ones. RESULTS: In bioequivalence studies, it is not possible to distinguish between relevant types of outliers based only on statistical criteria. The "problem" is particularly acute when the omission of outliers leads to a bias in the decision concerning bioequivalence from rejection to acceptance. In such cases, there is the suspicion of subjective analysis and torture of data. The effect of analytical errors at high plasma levels was criticized for the calculated concentrations in the neighborhood of lower limit of quantification. Errors at low concentrations have a less significant effect. In the pharmacokinetic analysis, several types of outliers were shown: single points, curves, pairs of curves corresponding to the same subject, intrasubject ratios of areas under curves and maximum concentrations. These pharmacokinetic outliers could have had, at the same time, bioanalytical, physiological and physicochemical causes. CONCLUSION: Considering the results, it was proposed the following algorithm in the analysis of outlier data and outlier subjects in bioequivalence studies: evaluation of the implications of the decision concerning elimination of outliers on the decision concerning bioequivalence; application of the statistic tests for detection of outliers data; evaluations from the point of view of physiological pharmacokinetics, final decision concerning elimination of outliers.

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

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

Effect of a New Synergistic Combination of Low Doses of Acetylsalicylic Acid, Caffeine, Acetaminophen, and Chlorpheniramine in Acute Low Back Pain.

The present paper continues a more complex research related to the increased synergism in terms of both anti-inflammatory and analgesic effect obtained by the addition of chlorpheniramine (CLF) to the common acetylsalicylic acid (ASA), acetaminophen (PAR), and caffeine (CAF) combination. This synergistic effect was previously highlighted both in vitro in rat models and in vivo in the treatment of migraine. The aim of the research was to further evaluate the analgesic effect of a synergistic low-dose ASA-PAR-CAF-CLF combination in the treatment of low back pain, in a parallel, multiple-dose, double-blind, active controlled clinical trial. A number of 89 patients with low back pain of at least moderate intensity were randomly assigned to receive Algopirin® (ALG), a combinational product containing 125 mg ASA, 75 mg PAR, 15 mg CAF, and 2 mg CLF, or PAR 500 mg, a drug recognized by American Pain Society as "safe and effective" in the treatment of low back pain. One tablet of the assigned product was administered three times a day for seven consecutive days. The patients evaluated their pain level using a Visual Analog Scale prior to administration, and at 1, 2, 4, and 6 h after the morning dose. Time course of effect was similar in structure and size for both treatments. Pain relief appeared rapidly and steadily increased over 4 h after drug administration. Differential pain curves of ALG and PAR were very similar and comparable with the previously determined ALG analgesia pattern in migraine. Differences between the daily mean pain scores were not statistically significant for the two treatments. Similar results were obtained for the Sum of Pain Intensity Differences (SPID) for 0-4 h and 0-6 h intervals as well as for the time course of the proportion of patients with at least 30% and at least 50% pain relief. In conclusion, in spite of very small doses of active components, ALG proved equally effective to the standard low back pain treatment and therefore a viable therapeutic alternative, mainly for patients with gastrointestinal and hepatic sensitivity. Trial Registration: www.ClinicalTrials.gov, identifier EudraCT No.: 2015-002314-74.

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

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

Mathematical Modeling of Release Kinetics from Supramolecular Drug Delivery Systems.

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

Chlorpheniramine Potentiates the Analgesic Effect in Migraine of Usual Caffeine, Acetaminophen, and Acetylsalicylic Acid Combination.

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.