Panos Macheras

Quantitative Biopharmaceutics Classification System: The Central Role of Dose/Solubility Ratio

AbstractPurpose. 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 drugs dissolution and permeability characteristics. Results. The QBCS developed relies on a (permeability, dose/solubility ratio) plane with cutoff points 2 × 10−6-10−5cm/s for the permeability and 0.5-1 (unitless) for the dose/solubility ratio axes. Permeability estimates, Papp 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 (Papp> 10−5cm/s, q ≤ 0.5), II (Papp> 10−5cm/s, q >1), III (Papp< 2 × 10−6cm/s, q ≤0.5), and IV (Papp< 2 × 10−6cm/s, q >1). A region for borderline drugs (2 × 10−6< Papp< 10−5cm/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 drugs 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.

A Reappraisal of Drug Release Laws Using Monte Carlo Simulations: The Prevalence of the Weibull Function

AbstractPurpose. 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.

Fractal kinetics in drug release from finite fractal matrices

We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde et al. [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.

Analysis of Dissolution Data Using Modified Versions of Noyes–Whitney Equation and the Weibull Function

PurposeThe 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.MethodsThe 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.ResultsThe 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.ConclusionThe 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.

Fractional kinetics in drug absorption and disposition processes

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

Gastrointestinal Drug Absorption: Is It Time to Consider Heterogeneity as Well as Homogeneity?

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 underin vivoconditions. The implications associated with the use of strict statistical criteria in bioequivalence studies for heterogeneous drugs are also pointed out.

Analysis of Case II drug transport with radial and axial release from cylinders

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.

The mean dissolution time depends on the dose/solubility ratio

AbstractPurpose. 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 under 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 of 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.

Advanced Pharmacokinetic Models Based on Organ Clearance, Circulatory, and Fractal Concepts

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.

A Report from the Pediatric Formulations Task Force: Perspectives on the State of Child-Friendly Oral Dosage Forms

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.