Comparison and analysis of theoretical models for diffusion-controlled dissolution

Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation

The dissolution testing method described in the United States Pharmacopeia (USP) Chapter ⟨711⟩ is widely used for assessing the release of active pharmaceutical ingredients from solid dosage forms. However, extensive use over the years has revealed certain issues, including high experimental intervariability observed in specific formulations and the settling of particles in the dead zone of the vessel. To address these concerns and gain a comprehensive understanding of the hydrodynamic conditions within the USP 2 apparatus, computational fluid dynamic simulations have been employed in this study. The base design employed in this study is the 900 mL USP 2 vessel along with a paddle stirrer at a 50 rpm rotational speed. Additionally, alternative stirrer designs, including the hydrofoil, pitched blade, and Rushton impeller, are investigated. A comparison is also made between a flat-bottom tank and the USP round-bottom vessel of the same volume and diameter. Furthermore, this work examines the impact of various parameters, such as clearance distance (distance between the bottom of the impeller and bottom of the vessel), number of impeller blades, impeller diameter, and impeller attachment angle. The volume-average shear rate (Stv), fluid velocity (Utv), and energy dissipation rates (ϵtv) represent the key properties evaluated in this study. Comparing the USP2 design and systems with the same stirrer but flat-bottom vessel reveals more homogeneous mixing compared to the USP2 design. Analyzing fluid flow streamlines in different designs demonstrates that hydrofoil stirrers generate more suspension or upward movement of fluid compared to paddle stirrers. Therefore, when impellers are of a similar size, hydrofoil designs generate higher fluid velocities in the coning area. Furthermore, the angle of blade attachment to the hub influences the fluid velocity in the coning area in a way that the 60° angle design generates more suspension than the 45° angle design. The findings indicate that the paddle stirrer design leads to a heterogeneous shear rate and velocity distributions within the vessel compared with the other designs, suggesting suboptimal performance. These insights provide valuable guidance for the development of improved in vitro dissolution testing devices, emphasizing the importance of optimized design considerations to minimize hydrodynamic variability, enhance dissolution characterization, and reduce variability in dissolution test results. Ultimately, such advancements hold potential for improving in vitro-in vivo correlations in drug development.

Material-Sparing Feasibility Screening for Hot Melt Extrusion

Hot melt extrusion (HME) offers a high-throughput process to manufacture amorphous solid dispersions. A variety of experimental and model-based approaches exist to predict API solubility in polymer melts, but these methods are typically aimed at determining the thermodynamic solubility and do not take into account kinetics of dissolution or the associated degradation of the API during thermal processing, both of which are critical considerations in generating a successful amorphous solid dispersion by HME. This work aims to develop a material-sparing approach for screening manufacturability of a given pharmaceutical API by HME using physically relevant time, temperature, and shear. Piroxicam, ritonavir, and phenytoin were used as model APIs with PVP VA64 as the dispersion polymer. We present a screening flowchart, aided by a simple custom device, that allows rapid formulation screening to predict both achievable API loadings and expected degradation from an HME process. This method has good correlation to processing with a micro compounder, a common HME screening industry standard, but only requires 200 mg of API or less.

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer

The authors present a steady-state-, particle-size-, and dose-dependent dissolution-permeation model that describes particle dissolution within the concentration boundary layer (CBL) adjacent to a semipermeable surface. It is critical to understand how particle size and dose affect the behavior of dissolving particles in the presence of a CBL adjacent to a semipermeable surface both in vivo and in vitro. Control of particle size is ubiquitous in the pharmaceutical industry; however, traditional pharmaceutical assumptions of particle dissolution typically ignore particle dissolution within the length scale of the CBL. The CBL does not physically prevent particles from traveling to the semipermeable surface (mucus, epithelial barrier, synthetic membrane, etc.), and particle dissolution can occur within the CBL thickness (δC) if the particle is sufficiently small (∼dparticle ≤ δC). The total flux (the time rate transport of molecules across the membrane surface per unit area) was chosen as a surrogate parameter for measuring the additional mass generated by particles dissolving within the donor CBL. Mass transfer experiments aimed to measure the total flux of drug using an ultrathin large-area membrane diffusion cell described by Sinko et al. with a silicone-based membrane ( Mol. Pharmaceutics 2020, 17, (7) 2319-2328, DOI: 10.1021/acs.molpharmaceut.0c00040). Suspensions of ibuprofen, a model weak-acid drug, with three different particle-size distributions with average particle diameters of 6.6, 37.4, and 240 μm at multiple doses corresponding to a range of suspension concentrations with dimensionless dose numbers of 2.94, 14.7, 147, and 588 were used to test the model. Experimentally measured total flux across the semipermeable membrane/CBL region agreed with the predictions from the proposed model, and at a range of relatively low suspension concentrations, dependent on the average particle size, there was a measurable effect on the flux due to the difference in δC that formed at the membrane surface. Additionally, the dose-dependent total flux across the membrane was up to 10% higher than the flux predicted by the standard Higuchi-Hiestand dissolution model where the effects of confinement were ignored as described by Wang et al. ( Mol. Pharmaceutics 2012, 9 (5), 1052-1066, DOI: 10.1021/mp2002818).

Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles

A quasi-steady-state model of the dissolution of a single prolate or oblate spheroidal particle has been developed based on the exact solution of the steady-state diffusion equation for mass transfer in an unconfined media. With appropriate treatment of bulk concentration, the model can predict the detailed dissolution process of a single particle in a container of finite size. The dimensionless governing equations suggest that the dissolution process is determined by three dimensionless control parameters, initial solid particle concentration, particle aspect ratio and the product of specific volume of solid particles and saturation concentration of the dissolved substance. Using this model, the dissolution processes of felodipine particles are analysed in a broad range of space of the three control parameters and some characteristics are identified. The effects of material properties indicated by the product of specific volume and saturation concentration are also analysed. The model and the analysis are applicable to the system of monodisperse spheroidal particles of the same shape.

Effect of fluid velocity and particle size on the hydrodynamic diffusion layer thickness

The aim of this study was to determine the thickness of the hydrodynamic diffusion layer (h_HDL) of three poor water-soluble compounds under laminar fluid flow using a single particle dissolution technique. The single particle dissolution experiments were performed in a flowing aqueous medium using four different fluid velocities (v), ranging from 46 to 103 mm/s. The particles used had an initial radius (r) of 18.8 to 52.3 μm. The determined h_HDL values were calculated from both dissolution experiments and computational fluid dynamics (CFD) simulation. In this study, single particle dissolution experiments gave, with one exception, h_HDL values in the range of 2.09 to 8.85 µm and corresponding simulations gave h_HDL values in the range of 2.53 to 4.38 µm. Hence, we found a semi-quantitative concordance between experimental and simulated determined h_HDL values. Also, a theoretical relation between the dependence of h_HDL on particle radius and flow velocity of the medium was established by a series of CFD simulations in a fluid velocity range of 10-100 mm/s and particle size (radius) range of 5-40 µm. The outcome suggests a power law relation of the form h_HDL∝r^3/5v^-2/5. In addition, the h_HDL seems to be independent of the solubility, while it has a diffusion coefficient dependence. In conclusion, the h_HDL values were determined under well-defined conditions; hence, this approach can be used to estimate the h_HDL under different conditions to increase the understanding of the mass transfer mechanisms during the dissolution process.

Modeling of Particle Dissolution Behavior Using a Geometrical Phase-Field Approach

Material dissolution is a critical attribute of many products in a wide variety of industries. The idealized view of dissolution through established prediction tools should be reconsidered because the number of new substances with low aqueous solubility is increasing. Due to this, a fundamental understanding of the dissolution process is desired. The aim of this study was to develop a tool to predict crystal dissolution performance based on experimentally measurable physical parameters. A numerical simulation, called the phase-field method, was used to simultaneously solve the time evolution of the phase and concentration fields of dissolving particles. This approach applies to diffusion-limited as well as surface reaction-limited systems. The numerical results were compared to analytical solutions, and the influence of particle shape and interparticle proximity on the dissolution process was numerically investigated. Dissolution behaviors of two different substances were modeled. A diffusion-limited model compound, xylitol, with a high aqueous solubility and a surface reaction-limited model compound, griseofulvin, with a low aqueous solubility were chosen. The results of the simulations demonstrated that phase-field modeling is a powerful approach for predicting the dissolution behaviors of pure crystalline substances.

Characterization of Membrane-Type Dissolution Profiles of Clinically Available Orally Inhaled Products Using a Weibull Fit and a Mechanistic Model

Dissolution rate impacts the absorption rate of poorly soluble inhaled drugs. In vitro dissolution tests that can capture the impact of changes in critical quality attributes of the drug product on in vivo dissolution are important for the development of products containing poorly soluble drugs, as well as modified release formulations. In this study, an extended mathematical model allowing for dissolution of polydisperse powders and subsequent diffusion of dissolved drug across a membrane is described. In vitro dissolution profiles of budesonide, fluticasone propionate, and beclomethasone dipropionate delivered from three commercial drug products were determined using a membrane-type Transwell dissolution test, which consists of a donor and an acceptor compartment separated by a membrane. Subsequently, the profiles were analyzed using the developed mechanistic model and a semi-empirical model based on the Weibull distribution. The two mathematical models provided the same rank order of the performance of the three drug products in terms of dissolution rates, but the rates were significantly different. The faster rate extracted from the mechanistic model is expected to reflect the true dissolution rate of the drug; the Weibull model provides an effective and slower rate that represents not only drug dissolution but also diffusion across the Transwell membrane. In conclusion, the developed extended model provides superior understanding of the dissolution mechanisms in membrane-type (Transwell) dissolution tests.

Exploring bulk volume, particle size and particle motion definitions to increase the predictive ability of in vitro dissolution simulations

The definition of the local dissolution environment is central to accurate particle dissolution simulation, and is determined by the apparatus and conditions used. In the flow-through apparatus dissolution occurs in the cell, often in a low velocity environment, with the reservoir considered the relevant volume for dissolution kinetics. Dissolution simulations were conducted using a reduced-order model based on the Ranz-Marshall correlation for mass transfer from spherical particles. Using ibuprofen as a model drug, the effect of defining a local volume to simulate dynamic bulk concentration conditions in the flow-through and paddle apparatus was assessed by comparing use of a near particle volume (NPV), extending a distance of one radius from the particle surface, with a flow-through apparatus cell volume or paddle apparatus vessel volume as the relevant instantaneous volume for dissolution. The instantaneous inlet concentration to NPV or cell volume is the reservoir/vessel concentration at that simulation time point, reflecting the continuous input to the cell of more dilute solution from the reservoir (closed system). Additionally, inputting particle size distribution (PSD) instead of a median particle size (MPS) and enabling or disabling particle motion were investigated, in two media (resulting in low and high solubility) and with two fluid velocity conditions in each apparatus. The NPV predicted effects of fluid velocity differences on dissolution in the high solubility medium in the flow-through apparatus, but had no effect on predictive ability in the paddle apparatus. In both apparatuses, simulations were reasonable for the high solubility environment but underpredicted dissolution in the low solubility environment. The PSD option and disabling particle motion increased the predictive ability of the simulations in low solubility media in the flow-through apparatus. The results highlight the necessity to incorporate the local dynamic dissolution conditions in the flow-through apparatus for accurate dissolution simulation, and the challenges of defining an effective particle size for dissolution simulation and of reflecting hydrodynamic complexity in simulating dissolution in the paddle apparatus.

Mechanistic Models for USP2 Dissolution Apparatus, Including Fluid Hydrodynamics and Sedimentation

Drug product dissolution is a key input to Physiologically Based Biopharmaceutics Models (PBBM) to be able to predict in vivo dissolution. The integration of product dissolution in PBBMs for immediate release drug products should be mechanistic, i.e. allow to capture the main determinants of the in vitro dissolution experiment, and extract product batch specific parameter(s). This work focussed on the Product Particle Size Distribution (P-PSD), which was previously shown to integrate the effect of dose, volume, solubility (pH), size and concentration of micelles in the calculation of a batch specific input to PBBMs, and proposed new hydrodynamic (HD) models, which integrate the effect of USP2 apparatus paddle rotation speed and medium viscosity on dissolution. In addition, new models are also proposed to estimate the quantitative impact of formulation and drug sedimentation or "coning" on dissolution. Model "HDC-1" predicts coning in the presence of formulation insoluble excipients and "HDC-2" predicts the sedimentation of the drug substance only. These models were parameterized and validated on 166 dissolution experiments and 18 different drugs. The validation showed that the HD model average fold errors (AFE) for dissolution rate prediction of immediate release formulations, is comprised between 0.85 and 1.15, and the absolute average fold errors (AAFE) are comprised between 1.08 and 1.28, which shows satisfactory predictive power. For experiments where coning was suspected, the HDC-1 model improved the precision of the prediction (defined as ratio of "AAFE-1"values) by 2.46 fold compared to HD model. The calculation of a P-PSD integrating the impact of USP2 paddle rotation, medium viscosity and coning, will improve the PBBM predictions, since these parameters could have an influence on in vitro dissolution, and could open the way to better prediction of the effect of prandial state on human exposure, by developing new in silico tools which could integrate variation of velocity profiles due to the chyme viscosity.

Determination of Intrinsic Drug Dissolution and Solute Effective Transport Rate during Laminar Fluid Flow at Different Velocities

The objective of this study was to determine the intrinsic drug dissolution rate (IDR) and the solute effective transport rate of some drugs, using a single particle dissolution technique, satisfying qualified dissolution conditions. The IDR of three poorly water-soluble compounds was measured in milli-Q water using four different fluid velocities. The enveloped surface area of the particles was calculated from the projected area and the perimeter of the particle observed in the microscope. Furthermore, computational fluid dynamics (CFD) simulations were used to theoretically investigate the flow conditions and dissolution rate, comparing box shaped particles and spherical particles with similar dimensions and surface area as the particles used the experiments. In this study, the IDR measurement of the single particles was determined within 5–60 min using particles with an initial projected area diameter (Dp) between 37.5–104.6 µm. The micropipette-assisted microscopy technique showed a good reproducibility between individual measurements, and the CFD simulations indicated a laminar flow around the particles at all flow velocities, even though there were evident differences in local particle dissolution rates. In conclusion, the IDR and solute effective transport rate were determined under well-defined fluid flow conditions. This type of approach can be used as a complementary approach to traditional dissolution studies to gain in-depth insights into the dissolution process of drug particles.

The studies on wet chemical etching via in situ liquid cell TEM

Wet chemical etching is a widely used process to fabricate fascinating nanomaterials, such as nanoparticles with precisely controlled size and shape. Understanding the etching mechanism and kinetic evolution process is crucial for controlling wet chemical etching. The development of in situ liquid cell transmission electron microscopy (LCTEM) enables the study on wet chemical etching with high temporal and spatial resolutions. However, there still lack a detailed literature review on the wet chemical etching studies by in situ LCTEM. In this review, we summarize the studies on wet etching nanoparticles, one-dimensional nanomaterials and nanoribbons by in situ LCTEM, including etching rate, anisotropic etching, morphology evolution process, and etching mechanism. The challenges and opportunities of in situ LCTEM are also discussed.

Hierarchical Mass Transfer Analysis of Drug Particle Dissolution, Highlighting the Hydrodynamics, pH, Particle Size, and Buffer Effects for the Dissolution of Ionizable and Nonionizable Drugs in a Compendial Dissolution Vessel

Dissolution is a crucial process for the oral delivery of drug products. Before being absorbed through epithelial cell membranes to reach the systemic circulation, drugs must first dissolve in the human gastrointestinal (GI) tract. In vivo and in vitro dissolutions are complex because of their dependency upon the drug physicochemical properties, drug product, and GI physiological properties. However, an understanding of this process is critical for the development of robust drug products. To enhance our understanding of in vivo and in vitro dissolutions, a hierarchical mass transfer (HMT) model was developed that considers the drug properties, GI fluid properties, and fluid hydrodynamics. The key drug properties include intrinsic solubility, acid/base character, pK_a, particle size, and particle polydispersity. The GI fluid properties include bulk pH, buffer species concentration, fluid shear rate, and fluid convection. To corroborate the model, in vitro dissolution experiments were conducted in the United States Pharmacopeia (USP) 2 dissolution apparatus. A weakly acidic (ibuprofen), a weakly basic (haloperidol), and a nonionizable (felodipine) drug were used to study the effects of the acid/base character, pK_a, and intrinsic solubility on dissolution. 900 mL of 5 mM bicarbonate and phosphate buffers at pH 6.5 and 37 °C was used to study the impact of the buffer species on drug dissolution. To investigate the impacts of fluid shear rate and convection, the apparatus was operated at different impeller rotational speeds. Moreover, presieved ibuprofen particles with different average diameters were used to investigate the effect of particle size on drug dissolution. In vitro experiments demonstrate that the dissolution rates of both the ionizable compounds used in this study were slower in bicarbonate buffer than in phosphate buffer, with the same buffer concentration, because of the lower interfacial buffer capacity, a unique behavior of bicarbonate buffer. Therefore, using surrogates (i.e., 50 mM phosphate) for bicarbonate buffer for biorelevant in vitro dissolution testing may overestimate the in vivo dissolution rate for ionizable drugs. Model simulations demonstrated that, assuming a monodisperse particle size when modeling, dissolution may overestimate the dissolution rate for polydisperse particle size distributions. The hydrodynamic parameters (maximum shear rate and fluid velocity) under in vitro conditions in the USP 2 apparatus under different rotational speeds are orders of magnitude higher compared to the in vivo situation. The inconsistencies between the in vivo and in vitro drug dissolution hydrodynamic conditions may cause an overestimation of the dissolution rate under in vitro conditions. The in vitro dissolution data supported the accuracy of the HMT for drug dissolution. This is the first drug dissolution model that incorporates the effect of the bulk pH and buffer concentration on the interfacial drug particle solubility of ionizable compounds, combined with the medium hydrodynamics effect (diffusion, convection, shear, and confinement components), and drug particle size distribution.

Selection of In Vivo Predictive Dissolution Media Using Drug Substance and Physiological Properties

The rate and extent of drug dissolution in the gastrointestinal (GI) tract are highly dependent upon drug physicochemical properties and GI fluid properties. Biorelevant dissolution media (BDM), which aim to facilitate in vitro prediction of in vivo dissolution performance, have evolved with our understanding of GI physiology. However, BDM with a variety of properties and compositions are available, making the choice of dissolution medium challenging. In this tutorial, we describe a simple and quantitative methodology for selecting practical, yet physiologically relevant BDM representative of fasted humans for evaluating dissolution of immediate release formulations. Specifically, this methodology describes selection of pH, buffer species, and concentration and evaluates the importance of including bile salts and phospholipids in the BDM based upon drug substance log D, pK_a, and intrinsic solubility. The methodology is based upon a mechanistic understanding of how three main factors affect dissolution, including (1) drug ionization at gastrointestinal pH, (2) alteration of surface pH by charged drug species, and (3) drug solubilization in mixed lipidic aggregates comprising bile salts and phospholipids. Assessment of this methodology through testing and comparison with literature reports showed that the recommendations correctly identified when a biorelevant buffer capacity or the addition of bile salts and phospholipids to the medium would appreciably change the drug dissolution profile. This methodology can enable informed decisions about when a time, complexity, and/or cost-saving buffer is expected to lead to physiologically meaningful in vitro dissolution testing, versus when a more complex buffer would be required.

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.

Deconstructing the physical processes of digestion: reductionist approaches may provide greater understanding

I provide a broad overview of the physical factors that govern intestinal digestion i.e. the admixture of food particles in digesta with secreted enzymes and the subsequent mass transfer of liberated nutrients from the surfaces of particles to the gut wall, with a view to outlining the quantitative work that is required to determine the relative importance of these factors in the digestion of particular foods. I first discuss what is known of the mechanical forces generated by contraction of the walls of the various segments of the gut and the level of diffusive, and advective mixing that it generates within the lumen. I then discuss the particular physical effects that may limit the digestion of solid, physically and/or chemically homogenous and heterogeneous food particles, notably capillarity, porosity, poro-elastic flow and compaction and their likely effects on diffusive and convective mass transfer at particulate surfaces. Similarly, I discuss mucins and morphology on mass transfer of nutrients to the gut wall i.e. the mucosa.

A reaction limited in vivo dissolution model for the study of drug absorption: Towards a new paradigm for the biopharmaceutic classification of drugs

The aim of this work is to develop a gastrointestinal (GI) drug absorption model based on a reaction limited model of dissolution and consider its impact on the biopharmaceutic classification of drugs. Estimates for the fraction of dose absorbed as a function of dose, solubility, reaction/dissolution rate constant and the stoichiometry of drug-GI fluids reaction/dissolution were derived by numerical solution of the model equations. The undissolved drug dose and the reaction/dissolution rate constant drive the dissolution rate and determine the extent of absorption when high-constant drug permeability throughout the gastrointestinal tract is assumed. Dose is an important element of drug-GI fluids reaction/dissolution while solubility exclusively acts as an upper limit for drug concentrations in the lumen. The 3D plots of fraction of dose absorbed as a function of dose and reaction/dissolution rate constant for highly soluble and low soluble drugs for different "stoichiometries" (0.7, 1.0, 2.0) of the drug-reaction/dissolution with the GI fluids revealed that high extent of absorption was found assuming high drug- reaction/dissolution rate constant and high drug solubility. The model equations were used to simulate in vivo supersaturation and precipitation phenomena. The model developed provides the theoretical basis for the interpretation of the extent of drug's absorption on the basis of the parameters associated with the drug-GI fluids reaction/dissolution. A new paradigm emerges for the biopharmaceutic classification of drugs, namely, a model independent biopharmaceutic classification scheme of four drug categories based on either the fulfillment or not of the current dissolution criteria and the high or low % drug metabolism.

Printing of small molecular medicines from the vapor phase

There is growing need to develop efficient methods for early-stage drug discovery, continuous manufacturing of drug delivery vehicles, and ultra-precise dosing of high potency drugs. Here we demonstrate the use of solvent-free organic vapor jet printing to deposit nanostructured films of small molecular pharmaceutical ingredients, including caffeine, paracetamol, ibuprofen, tamoxifen, BAY 11-7082 and fluorescein, with accuracy on the scale of micrograms per square centimeter, onto glass, Tegaderm, Listerine tabs, and stainless steel microneedles. The printed films exhibit similar crystallographic order and chemistry as the original powders; controlled, order-of-magnitude enhancements of dissolution rate are observed relative to powder-form particles. In vitro treatment of breast and ovarian cancer cell cultures in aqueous media by tamoxifen and BAY 11-7082 films shows similar behavior to drugs pre-dissolved in dimethyl sulfoxide. The demonstrated precise printing of medicines as films, without the use of solvents, can accelerate drug screening and enable continuous manufacturing, while enhancing dosage accuracy.

Traditional approaches used in the pharmaceutical industry are not precise or versatile enough for customized medicine formulation and manufacture. Here the authors produce a method to form coatings, with accurate dosages, as well as a means of closely controlling dissolution kinetics.

Two-Stage Single-Compartment Models to Evaluate Dissolution in the Lower Intestine

The purpose was to propose two-stage single-compartment models for evaluating dissolution characteristics in distal ileum and ascending colon, under conditions simulating the bioavailability and bioequivalence studies in fasted and fed state by using the mini-paddle and the compendial flow-through apparatus (closed-loop mode). Immediate release products of two highly dosed active pharmaceutical ingredients (APIs), sulfasalazine and L-870,810, and one mesalamine colon targeting product were used for evaluating their usefulness. Change of medium composition simulating the conditions in distal ileum (SIFileum ) to a medium simulating the conditions in ascending colon in fasted state and in fed state was achieved by adding an appropriate solution in SIFileum . Data with immediate release products suggest that dissolution in lower intestine is substantially different than in upper intestine and is affected by regional pH differences > type/intensity of fluid convection > differences in concentration of other luminal components. Asacol® (400 mg/tab) was more sensitive to type/intensity of fluid convection. In all the cases, data were in line with available human data. Two-stage single-compartment models may be useful for the evaluation of dissolution in lower intestine. The impact of type/intensity of fluid convection and viscosity of media on luminal performance of other APIs and drug products requires further exploration.

Analysis of Diffusion-Controlled Dissolution from Polydisperse Collections of Drug Particles with an Assessed Mathematical Model

We introduce a "hierarchical" modeling strategy designed to be systematically extensible to increase the detail of dissolution predictions from polydisperse collections of drug particles and to be placed on firm mathematical and physical foundations with diffusion-dominated dissolution at its core to predict dissolution and the evolution of particle size distribution. We assess the model with experimental data and demonstrate higher accuracy by treating the polydisperse nature of dissolution. A level in the hierarchy is applied to study elements of diffusion-driven dissolution, in particular the role of particle-size distribution width with varying dose level and the influences of "confinement" on the process of dissolution. Confinement influences surface molecular flux, directly by the increase in bulk concentration and indirectly by the relative volume of particles to container. We find that the dissolution process can be broadly categorized within three "regimes" defined by the ratio of total concentration Ctot to solubility CS . Sink conditions apply in the first regime, when C tot /CS<∼0.1. When C tot /CS>∼5 (regime 3) dissolution is dominated by confinement and normalized saturation time follows a simple power law relationship. Regime 2 is characterized by a "saturation singularity" where dissolution is sensitive to both initial particle size distribution and confinement.

Hydrodynamic Effects on Drug Dissolution and Deaggregation in the Small Intestine-A Study with Felodipine as a Model Drug

The aim of this study was to understand and predict the influence of hydrodynamic effects in the small intestine on dissolution of primary and aggregated drug particles. Dissolution tests of suspensions with a low-solubility drug, felodipine, were performed in a Couette cell under hydrodynamic test conditions corresponding to the fed small intestine. Dissolution was also performed in the USP II apparatus at two paddle speeds of 25 and 200 rpm and at different surfactant concentrations below critical micelle concentration. The experimental dissolution rates were compared with theoretical calculations. The different levels of shear stress in the in vitro tests did not influence the dissolution of primary or aggregated particles and experimental dissolution rates corresponded very well to calculations. The dissolution rate for the aggregated drug particles increased after addition of surfactant because of deaggregation, but there were still no effect of hydrodynamics. In conclusion, hydrodynamics do not influence dissolution and deaggregation of micronized drug particles in the small intestine of this model drug. Surface tension has a strong effect on the deaggregation and subsequent dissolution. Addition of surfactants at in vivo relevant surface tension levels is thus critical for in vivo predictive in vitro dissolution testing.

A multiscale three-zone reactive mixing model for engineering a scale separation in enzymatic hydrolysis of cellulose

This multiscale three-zone reactive mixing model provides a theoretical framework for engineering a scale separation in batch enzymatic hydrolysis of cellulose to strategize significant leaps in glucose yields. Formulated using the Liapunov-Schmidt method of the classical bifurcation theory, our model explores the multiscale spatiotemporal dynamics between the fundamental processes of macromixing (convection) and micromixing (diffusion) of the enzymes (Endoglucanase, Exoglucanase, β-glucasidase) and reducing sugars, adsorption and desorption of enzymes on the solid cellulosic substrates, and the product-inhibited liquid and solid phase enzymatic reactions that depolymerize microcrystalline cellulose (Avicel). The model is validated for a range of substrate loadings (2-5%) using our experimental results for the two asymptotic cases of no mixing and continuous mixing, as well as for the macro/micro scale-separated optimal mixing strategy that increases the glucose yield by up to 26% by macromixing completely for an initial period followed by micromixing for the remaining duration of the hydrolysis.

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.

Identification of key factors affecting the oral absorption of salts of lipophilic weak acids: a case example

Objectives

Evaluate the ability of biorelevant media to adequately predict solubility in human gastrointestinal aspirates collected in the fasted state for the sodium salt of a highly dosed, Biopharmaceutics Classification System II (BCS II) compound with weakly acidic properties (L-870,810, pKa 7.3, HA (5-(1,1-dioxothiazinan-2-yl)-N-((4-fluorophenyl)methyl)-8-hydroxy-1,6-naphthyridine-7-carboxamide)). Identify key luminal processes that dictate the behaviour of sodium salt of HA (NaA), after single-dose administrations of high (relatively to solubility limit) doses corresponding to 400 and 800 mg of HA in the fasted state.

Methods

Aspirates from stomach and upper small intestine were collected from eight healthy fasted adults, after administration of 240 ml of water. Solubilities of NaA and HA were measured in aspirated samples and biorelevant media. Dissolution experiments of NaA granules were performed in biorelevant media. Prediction of oral pharmacokinetics was evaluated in silico using Stella software.

Key findings

Equilibrium solubility of NaA in fluids aspirated from the upper gastrointestinal tract is more transient than of HA. Solubility in upper gastrointestinal lumen was adequately estimated by data in biorelevant media. Supersaturation, followed by precipitation, which did not fully revert to the equilibrium solubility of HA, was observed during the dissolution of NaA granules in biorelevant media. Physiologically based pharmacokinetic modelling indicated that while intragastric processes had no significant impact on absorption kinetics, dissolution kinetics, kinetic solubility, radial transport rates and, for the 800-mg dose, precipitation kinetics in the small intestine had the greatest impact on absorption profiles.

Conclusions

Adequate prediction of the average plasma profile, after administration of NaA, required consideration of region-dependent dissolution rates and/or solubilisation.

Application of mathematical modeling in sustained release delivery systems

INTRODUCTION

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems.

AREAS COVERED

The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered.

EXPERT OPINION

Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Analytical technologies for real-time drug dissolution and precipitation testing on a small scale

Objectives

This review focuses on real-time analytics of drug dissolution and precipitation testing on a comparatively small scale.

Key findings

Miniaturisation of test equipment is an important trend in pharmaceutics, and several small-scale experiments have been reported for drug dissolution and precipitation testing. Such tests typically employ analytics in real-time. Fibre optic ultraviolet (UV) analytics has become a well-established method in this field. Novel imaging techniques are emerging that use visible or UV light; also promising is Fourier transform infrared imaging based on attenuated total reflection. More information than just a rate constant is obtained from these methods. The early phase of a dissolution process can be assessed and drug precipitation may eventually be observed. Some real-time techniques are particularly well suited to studying drug precipitation during formulation dispersion; for example, turbidity, focused beam reflectance measurement and Raman spectroscopy.

Summary

Small-scale dissolution tests equipped with real-time analytics have become important to screen drug candidates as well as to study prototype formulations in early development. Future approaches are likely to combine different analytical techniques including imaging. Miniaturisation started with mini-vessels or small vials and future assays of dissolution research will probably more often reach the level of parallel well plates and microfluidic channels.

The Biopharmaceutics Classification System: subclasses for in vivo predictive dissolution (IPD) methodology and IVIVC

The Biopharmaceutics Classification System (BCS) has found widespread utility in drug discovery, product development and drug product regulatory sciences. The classification scheme captures the two most significant factors influencing oral drug absorption; solubility and intestinal permeability and it has proven to be a very useful and a widely accepted starting point for drug product development and drug product regulation. The mechanistic base of the BCS approach has, no doubt, contributed to its wide spread acceptance and utility. Nevertheless, underneath the simplicity of BCS are many detailed complexities, both in vitro and in vivo which must be evaluated and investigated for any given drug and drug product. In this manuscript we propose a simple extension of the BCS classes to include sub-specification of acid (a), base (b) and neutral (c) for classes II and IV. Sub-classification for Classes I and III (high solubility drugs as currently defined) is generally not needed except perhaps in border line solubility cases. It is well known that the , pKa physical property of a drug (API) has a significant impact on the aqueous solubility dissolution of drug from the drug product both in vitro and in vivo for BCS Class II and IV acids and bases, and is the basis, we propose for a sub-classification extension of the original BCS classification. This BCS sub-classification is particularly important for in vivo predictive dissolution methodology development due to the complex and variable in vivo environment in the gastrointestinal tract, with its changing pH, buffer capacity, luminal volume, surfactant luminal conditions, permeability profile along the gastrointestinal tract and variable transit and fasted and fed states. We believe this sub-classification is a step toward developing a more science-based mechanistic in vivo predictive dissolution (IPD) methodology. Such a dissolution methodology can be used by development scientists to assess the likelihood of a formulation and dosage form functioning as desired in humans, can be optimized along with parallel human pharmacokinetic studies to set a dissolution methodology for Quality by Design (QbD) and in vitro-in vivo correlations (IVIVC) and ultimately can be used as a basis for a dissolution standard that will ensure continued in vivo product performance.

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.

Dissolution studies of poorly soluble drug nanosuspensions in non-sink conditions

Sink conditions used in dissolution tests lead to rapid dissolution rates for nanosuspensions, causing difficulties in discriminating dissolution profiles between different formulations. Here, non-sink conditions were studied for the dissolution testing of poorly water-soluble drug nanosuspensions. A mathematical model for polydispersed particles was established to clarify dissolution mechanisms. The dissolution of nanosuspensions with either a monomodal or bimodal size distribution was simulated. In the experimental part, three different particle sizes of indomethacin nanosuspensions were prepared by the wet milling technique. The effects of the dissolution medium pH and agitation speed on dissolution rate were investigated. The dissolution profiles in sink and non-sink conditions were obtained by changing the ratio of sample amount to the saturation solubility. The results of the simulations and experiments indicated that when the sample amount was increased to the saturation solubility of drug, the slowest dissolution rate and the best discriminating dissolution profiles were obtained. Using sink conditions or too high amount of the sample will increase the dissolution rate and weaken the discrimination between dissolution profiles. Furthermore, the low solubility by choosing a proper pH of the dissolution medium was helpful in getting discriminating dissolution profiles, whereas the agitation speed appeared to have little influence on the dissolution profiles. This discriminatory method is simple to perform and can be potentially used in any nanoproduct development and quality control studies.

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.