Modeling heterogeneity of properties and random effects in drug dissolution

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.

Biorelevant dissolution of poorly soluble weak acids studied by UV imaging reveals ranges of fractal-like kinetics

Much pharmaceutical research has been invested into drug dissolution testing and its mathematical modeling. Even today, there is no complete understanding of the dissolution process but novel imaging tools have been introduced into pharmaceutics that may spur further scientific advancement. We used UV imaging to study the intrinsic dissolution of various poorly soluble acidic model drugs to understand the effects of heterogeneity on early intrinsic drug dissolution using a biorelevant medium: celecoxib, ketoprofen, naproxen, and sulfathiazole. All compounds were characterized using X-ray powder diffraction and thermal analysis. Raman spectroscopy and scanning electron microscopy were employed before and after the initial dissolution phase. As a result, ranges of fractal-like dissolution behavior were found with all model compounds. Intrinsic dissolution rate exhibited a power law mainly at early time points. Subsequently, after several minutes, pseudo-equilibrium was reached with a nearly constant dissolution rate. Further research should investigate whether compounds other than acids demonstrate similar early dissolution kinetics in biorelevant media. The observed fractal-like intrinsic dissolution behavior has several pharmaceutical implications. This study primarily helps us to better understand in vitro dissolution testing, particularly on a miniaturized scale. This improved understanding of early dissolution events may advance future correlations with in vivo data. Therefore, fractal-like dissolution should be considered during biopharmaceutical modeling.

On the estimate of the rate constant in the homogeneous dissolution model

The aim is to determine how well the rate parameter of the homogeneous model of dissolution can be estimated in dependency on the chosen times to measure the empirical data. The approach is based on the theory of Fisher information. We show that if the probability distribution of the measurement errors is known, the data should be collected at a single time instant or its close proximity in order to obtain the best estimate. This is in sharp contrast with commonly used experimental protocols. Further, from the properties of the Fisher information we deduce how suitable is the model of measurement error and we show that asymmetric distribution of data close to the time origin is unavoidable.

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.

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.

Immediate Drug Release from Solid Oral Dosage Forms

Fast drug release from solid dosage forms requires a very fast contact of the vast majority of the drug particles with the solvent; this, however, is particularly delayed in tablets and granulations. Starch and cellulose substances favor the matrix disintegration during the starting phase and the generation of the effective dissolution surface of the drug substance, thereby. To investigate the very complex interrelation between the functionality of commonly used excipients and the structural effects of the production processes, wettability, porosity, water uptake, and drug release rates of several ketoprofen-excipient preparations (powder blends, granulations, tablets) were measured. Significant linear correlation between these parameters, however, was not achieved; only qualitative tendencies of the effects could be detected. In consequence, a general mathematical model describing the mechanistic steps of drug dissolution from solid dosage forms in a fully correct way was not realized. However, the time-dependent change of the effective dissolution surface follows stochastic models: a new dissolution equation is based on the differential Noyes-Whitney equation combined with a distribution function, e.g. the lognormal distribution, and numerically solved with the software system EASY-FIT by fitting to the observations. This new model coincides with the data to a considerably higher degree of accuracy than the Weibull function alone, particularly during the starting, matrix disintegration, and end phases. In combination with a procedure continuously quantifying the dissolved drug, this mathematical model is suitable for the characterization and optimization of immediate drug release by the choice and modification of excipients and unit operations. The interdependence of some characteristic effects of excipients and production methods is discussed.

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.