Does the dose-solubility ratio affect the mean dissolution time of drugs?

Coupling Drug Dissolution with BCS

PURPOSE

The purpose of this study is to develop a Temporal Biopharmaceutic Classification System (T-BCS), linking Finite Dissolution Time (F.D.T.) and Mean Dissolution Time (M.D.T.) for Class I/III drugs and Mean Dissolution Time for saturation (M.D.T.s.) for Class II/IV drugs.

METHODS

These parameters are estimated graphically or by fitting dissolution models to experimental data and coupled with the dose-to-solubility ratio (q) for each drug normalized in terms of the actual volume of dissolution medium (900 mL).

RESULTS

Class I/III drugs consistently exhibited q values less than 1, aligning with expectations based on their solubility, while some Class II/IV drugs presented a deviation from anticipated q values, with observations of q < 1. This irregularity was rendered to the dissolution volume of 250 mL used for biopharmaceutical classification purposes instead of 900 mL applied as well as the dual classification of some sparingly soluble drugs. Biowaivers were also analyzed in terms of M.D.T., F.D.T. estimates and the regulatory dissolution time limits for rapidly and very-rapidly dissolved drugs.

CONCLUSIONS

The T-BCS is useful for establishing correlations and assessing the magnitude of M.D.T., F.D.T., or M.D.T.s. for inter- and intra-class comparisons of different drugs and provide relationships between these parameters across all the models that were utilized.

Semi-mechanistic reduced order model of pharmaceutical tablet dissolution for enabling Industry 4.0 manufacturing systems

We propose a generalization of the Weibull dissolution model, referred to as generalized Weibull dissolution model, that seamlessly captures all three fractional dissolution rates experimentally observed in pharmaceutical solid tablets, namely decreasing, increasing, and non-monotonic rates. This is in contrast to traditional reduced order models, which capture at most two fractional dissolution rates and, thus, are not suitable for a wide range of product formulations hindering, for example, the adoption of knowledge management in the context of Industry 4.0. We extend the generalized Weibull dissolution model further to capture the relationship between critical process parameters (CPPs), critical materials attributes (CMAs), and dissolution profile to, in turn, facilitate real-time release testing (RTRT) and quality-by-control (QbC) strategies. Specifically, we endow the model with multivariate rational polynomials that interpolate the mechanistic limiting behavior of tablet dissolution as CPPs and CMAs approach certain values of physical significance (such as the upper and lower bounds of tablet porosity or lubrication conditions), thus the semi-mechanistic nature of the reduced order model. Restricting attention to direct compaction and using various case studies from the literature, we demonstrate the versatility and the capability of the semi-mechanistic ROM to estimate changes in dissolution due to process disturbances in tablet weight, porosity, lubrication conditions (i.e., the total amount of shear strain imparted during blending), and moisture content in the powder blend. In all of the cases considered in this work, the estimations of the model are in remarkable agreement with experimental data.

A Simple One-Parameter Percent Dissolved Versus Time Dissolution Equation that Accommodates Sink and Non-sink Conditions via Drug Solubility and Dissolution Volume

In vitro dissolution generally involves sink conditions, so dissolution equations generally do not need to accommodate non-sink conditions. Greater use of biorelevant media, which are typically less able to provide sink conditions than pharmaceutical surfactants, necessitates equations that accommodate non-sink conditions. One objective was to derive an integrated, one-parameter dissolution equation for percent dissolved versus time that accommodates non-sink effects via drug solubility and dissolution volume parameters, including incomplete solubility. A second objective was to characterize the novel equation by fitting it to biorelevant dissolution profiles of tablets of two poorly water-soluble drugs, as well as by conducting simulations of the effect of dose on dissolution profile. The Polli dissolution equation was derived, [Formula: see text], where M₀ is the drug dose (mg), c_s is drug solubility (mg/ml), V is dissolution volume (ml), and k_d is dissolution rate coefficient (ml/mg per min). Maximum allowable percent dissolved was determined by drug solubility and not a fitted extent of dissolution parameter. The equation fit tablet profiles in the presence and absence of sink conditions, using a single fitted parameter, k_d, and where solubility ranged over a 1000-fold range. k_d was generally smaller when c_s was larger. FeSSGF provided relatively small k_d values, reflecting FeSSGF colloids are large and slowly diffusing. Simulations showed impact of non-sink conditions, as well as plausible k_d values for various c_s scenarios, in agreement with observed k_d values. The equation has advantages over first-order and z-factor dissolution rate equations. An Excel file for regression is provided.

Systematic evaluation of the impact of solid-state polymorphism on the bioavailability of thalidomide

Thalidomide (TLD) is used to treat erythema nodosum leprosum (ENL), multiple myeloma, aphthous ulceration and wasting syndrome in HIV patients. The API can be found in two crystalline habits known as α-TLD and β-TLD. The saturation solubility (C_s) and the dissolution profiles under non-sink and sink conditions of both polymorphs were assessed. In addition, mini-capsules containing α-TLD or β-TLD without excipients were orally given (10 mg/kg) to Wistar rats. An intravenous (i.v.) dose was also administrated (5 mg/kg). The C_s values for α-TLD and β-TLD were not significantly different (α = 56.2 ± 0.5 μg·mL^-1; β = 55.2 ± 0.2 μg·mL^-1). However, the dissolution profile of α-TLD presented the fastest rate and the largest extension of drug dissolution than that from β-TLD (80% in 4 h versus 55% in 4 h). The α-TLD provided a more favorable pharmacokinetic than the β-TLD (maximum plasma concentration - C_max: 5.4 ± 0.90 μg·mL^-1versus 2.6 ± 0.2 μg·mL^-1; area under the curve of the concentration-time profile from time zero to infinity - AUC_0-∞: 44.3 ± 8.8 μg·h·mL^-1versus 33.9 ± 4.7 μg·h·mL^-1; absolute bioavailability - F: 92.2 ± 18.5% versus 70.5 ± 9.9%, respectively). Drug suppliers and pharmaceutical companies should strictly control the technological processes involved in the TLD API synthesis as well as in the production of the pharmaceutical dosage form in order to guarantee the inter-batch homogeneity and therefore, product compliance.

The Biopharmaceutics Classification System (BCS) and the Biopharmaceutics Drug Disposition Classification System (BDDCS): Beyond guidelines

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 ΑΒΓ 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).

On the unphysical hypotheses in pharmacokinetics and oral drug absorption: Time to utilize instantaneous rate coefficients instead of rate constants

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.

Scientific considerations concerning the EMA change in the definition of "dose" of the BCS-based biowaiver guideline and implications for bioequivalence

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 i.e., whether or not it meets the solubility-dissolution regulatory criteria.

Keeping a critical eye on the science and the regulation of oral drug absorption: a review

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.

Homogeneous diffusion layer model of dissolution incorporating the initial transient phase

Purpose of this paper is to describe characteristic features of dissolution data by using homogeneous model of dissolution with initial transient phase. To achieve the goal we consider a random lag time before the homogeneous phase of the dissolution begins. The resulting dissolution profiles are characterized by sigmoidal shape commonly observed in empirical dissolution data. Furthermore, probability distribution of repeated measurements at fixed time is deduced from the model and function describing variability of the data in dependency on time is proposed. Three examples with normal, exponential and gamma probability distribution of the lag time are presented. All the models are pairwise compared with the Weibull function with high similarity between them. The result offers an alternative interpretation for the frequently found fit of the Weibull model to experimental data.

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 century of dissolution research: from Noyes and Whitney to the biopharmaceutics classification system

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 modern trends on drug dissolution research and their regulatory implications.

Modeling and Monte Carlo simulations in oral drug absorption

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.

A stochastic differential equation model for drug dissolution and its parameters

A stochastic differential equation describing the process of drug dissolution is presented. This approach generalizes the classical deterministic first-order model. Instead of assuming a constant fractional dissolution rate, it is considered here that the rate is corrupted by a white noise. The half-dissolution time is investigated for the model. The maximum likelihood and Bayes methods for the estimation of the parameters of the model are developed. The method is illustrated on experimental data. As expected, due to the nonlinear relationship between the fractional dissolution rate and the dissolution time, the estimates of the dissolution rate obtained from this stochastic model are systematically lower than the rate calculated from the deterministic model.

Role of heterogeneity in deterministic models of drug dissolution and their statistical characteristics

Dissolution of drugs is one of the crucial factors determining their global action in a body, and thus for any new solid dosage form its dissolution characteristics have to be established. A variety of empirical and semi-empirical models for drug dissolution is reviewed in this article. Their properties are investigated, the parameters are discussed and the role of drug heterogeneity is studied.

Classification of dissolution profiles in terms of fractional dissolution rate and a novel measure of heterogeneity

Dissolution profiles are classified in accordance with the shape of fractional dissolution rate function. This function is constant in time for the classical first-order model and, in this case, the dissolution is described by a monoexponential function. Therefore, any deviation of the fractional dissolution rate from the constant level suggests the presence of different (nonlinear/nonhomogenous) mechanisms in the dissolution process. The shapes of the fractional dissolution rate depend on the type of the model of dissolution; thus, classification with respect to this function is proposed as a tool for model selection. The Kullback-Leibler information distance is proposed for measuring similarity between two different drug dissolution profiles. The method is applied mainly to compare the first-order model, which characterizes a homogenous dosage form, with other common descriptors of dissolution and with experimental data.

The mean dissolution time depends on the dose/solubility ratio

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 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.

Modeling heterogeneity of properties and random effects in drug dissolution

PURPOSE

To investigate new models characterizing dissolution data obtained for heterogenous materials (model I) and under randomly time-varying conditions (model II).

METHODS

In model I, the heterogeneity of the dissolving substance introduces variation of the fractional dissolution rate. In model II, the fractional dissolution rate evolves randomly, and thus the dissolution has the characteristics of a stochastic process. This situation is studied for the constant and time-dependent means of the dissolution rate.

RESULTS

The time dynamics of the dissolved fraction is presented for model I. The standard characteristics of dissolution are derived under general conditions and for several examples. One of them is in accordance with a function found empirically (1). A duality between the time-dependency of the fractional dissolution rate and the heterogeneity of the substance is investigated. The mean and variance of the dissolved fraction are calculated for model II. A method for estimating the mean dissolution rate is proposed and illustrated using Monte-Carlo experiments.

CONCLUSIONS

It follows from model I that the heterogeneity, with the same mean properties, slows down the dissolution with respect to the homogeneous case. The second approach permits predictions about the role of the stochastic fluctuations of the dissolution rate and to establish the boundaries for the dissolution profiles.