Computational fluid dynamics modeling of the paddle dissolution apparatus: agitation rate, mixing patterns, and fluid velocities

Effect of basket mesh size on the hydrodynamics of a partially filled (500 mL) USP rotating basket dissolution testing Apparatus 1

The USP Rotating Basket Dissolution Testing Apparatus 1 is listed in the USP as one of the tools to assess dissolution of oral solid dosage forms. Baskets of different mesh sizes can be used to differentiate between dissolution profiles of different formulations. Here, we used Particle Image Velocimetry (PIV) to study the hydrodynamics of the USP Apparatus 1 using baskets with different mesh openings (10-, 20- and 40-mesh) revolving at 100 rpm, when the vessel was filled with 500 mL. The velocity profiles throughout the liquid were found to vary significantly using baskets of different mesh sizes, typically increasing with increased size of the opening of the basket mesh, especially for axial and radial velocities. This, in turn, resulted in a significantly different flow rate through the basket, which can be expected to significantly impact the dissolution rate of the drug product. A comparison between the results of this work with those of a previous study with a 900-mL fill volume (Sirasitthichoke et al., Intern. J. Pharmaceutics, 2021, 607: 120976), shows that although the hydrodynamics in the USP Apparatus 1 changed with fill level in the vessel, the flow rate through the basket was not significantly affected. This implies that tablets dissolving in the two systems would experience similar tablet-liquid medium mass transfer coefficients, and therefore similar initial dissolution rates, but different dissolution profiles because of the difference in volume.

Particle Image Velocimetry (PIV) measurements of USP Apparatus 1 hydrodynamics with 500 mL fill volume

Changes to hydrodynamics arising from changes within dissolution testing systems, such as the fill volume level, can potentially cause variability in dissolution results. However, the literature on hydrodynamics in Apparatus 1 is quite limited and little information is available for vessels with different liquid volumes. Here, velocities in a USP Apparatus 1 vessel with a liquid fill volume of 500 mL, a common alternative to 900 mL, were experimentally measured using 2D-2C Particle Image Velocimetry (PIV) for different basket rotational speeds. Tangential velocities dominated the flow field, while axial and radial velocities were much lower and varied with location. The velocities distribution increased proportionately with the basket rotational speed almost everywhere in the vessel excepting for underneath the basket. A nearly horizontal radial liquid jet was found to originate close to the basket upper edge. Comparison of these results with those previously reported with 900-mL liquid volume (Sirasitthichoke et al., Intern. J. Pharmaceutics:X; 3 (2021) 100078) showed that the flow rate through the baskets was similar in both systems, implying that, at least initially, the amount of drug in solution would increase linearly with time. In other words, the flow rate through the baskets would be independent of the liquid volume. Velocity profiles were also found to be similar, except in the region above the basket, which was affected by the radial jet with an orientation significantly different between the 500-mL and the 900-mL systems.

Predictive Drug Release Modeling Across Dissolution Apparatuses I and II using Computational Fluid Dynamics

A modeling process is developed and validated with which active pharmaceutical ingredient (API) release is predicted across the United States Pharmacopeia (USP) dissolution apparatuses I and II based on limited experimental dissolution data (at minimum two dissolution profiles at different apparatus settings). The process accounts for formulation-specific drug release behavior and hydrodynamics in the apparatuses over the range of typical agitation rates and medium volumes. This modeling process involves measurement of experimental mass transfer coefficients via a conventional mass balance and the relationship of said mass transfer coefficients to hydrodynamics and apparatus setting via computational fluid dynamics (CFD). A novel 1-D model is hence established, which provided calibration data for a particular formulation, can model mass transfer coefficients and their corresponding drug release at apparatus configurations of interest. Based on validation against experimental data produced from five erosion-based formulations over a range of apparatus configurations, accuracy within 8 %LA (labelled amount of API) and an average root mean square deviation of 3 %LA is achieved. With this predictive capability, minimizing the number of dissolution experiments and the amount of chemical materials needed during method development appears feasible.

Simulating Tablet Dissolution Using Computational Fluid Dynamics and Experimental Modeling

The study of mass transfer is essential in the food digestion process, especially when gastric acid interacts with food and nutrients dissolve in the gastric system. In this study, a computational fluid dynamics (CFD) model was built based on an in vitro study, which investigated the mass transfer in a tablet dissolution process in a beaker and stirrer system. The predicted mass transfer coefficients from the simulation aligned well with the experimental values. The effect of the type and rotation speed of the stirrers was also investigated. Mass transfer from the tablet was found to be closely related to the tablet Reynolds number of the fluid (ranging from 0 to 938) and the shear stress (0 to 0.167 Pa) acting on the tablet. The relationship between the power number (0.0061 to 0.196) and the Reynolds number for the impeller (719 to 5715) was also derived for different stirrers.

Impact of Select Geometric and Operational Parameters on Hydrodynamics in Dissolution Apparatus 2 (Paddle Apparatus): A Design of Experiments Analysis Based on Computational Fluid Dynamics Simulations

Purpose

A Design of Experiments (DOE) analysis driven by Computational Fluid Dynamics (CFD) simulations was used to evaluate individual and two-factor interaction effects of varying select geometric and operational parameters on the hydrodynamics in dissolution apparatus 2 (paddle apparatus).

Methods

Simulations were run with meshing controls and solution strategies retained from a mesh-independent validated baseline model. Distance between vessel and impeller bottom surfaces, impeller offset, vessel radius and impeller rotation speed were considered as input parameters. The velocity magnitudes at four locations near the vessel bottom surface were considered as output parameters. Response surfaces and Pareto charts were generated to understand individual and two-factor interaction effects of input parameters on the output parameters.

Results

Impeller offset has a dominating influence of a linear and quadratic nature on the output parameters and affects overall hydrodynamics. Changes to other input parameters have limited influence on velocity magnitudes at locations closest to the vessel axis and on overall hydrodynamics. However, these parameters have important influences of varying degrees on velocity magnitudes at locations away from the vessel axis.

Conclusions

The hydrodynamics in Apparatus 2 is influenced differently by different parameters and their combinations. Impeller offset has a stronger influence when compared to parameters that do not alter apparatus symmetry.

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.

Influence of basket mesh size on the hydrodynamics in the USP rotating basket dissolution testing Apparatus 1

The USP Apparatus 1 (rotating basket), typically used to assess drug product reproducibility and evaluate oral solid dosage forms performance, consists of a cylindrical glass vessel with a hemispherical bottom and a wire basket rotating at constant speed. Baskets with different wire openings can be used in alternative to the standard mesh opening (40-mesh) in order to discriminate between drug formulations during early stage of drug product development. Any changes introduced by different basket geometries can potentially and significantly impact the system hydrodynamics and cause variability of results, thus affecting product quality. In this work, Particle Image Velocimetry (PIV) was used to experimentally quantify the velocity distribution in the USP rotating basket Apparatus 1 using baskets of different mesh sizes (10-, 20-, and 40-mesh size) under the typical operating conditions described in dissolution testing procedures. Similar flow patterns were observed in all cases. However, the radial and axial velocities in the USP Apparatus 1 generally increased with increasingly larger openings of the basket mesh. Increasing the basket agitation speed also resulted in an overall increase in the velocities, especially below in the innermost core region below the basket, where drug fragments typically reside. More importantly, the flow entering and leaving the baskets was quantified from the velocity profiles in the immediate vicinity of the baskets. It was found that the flow increased significantly with increasingly larger mesh openings, which can, in turn, promote faster dissolution of the oral solid dosage forms, thus affecting drug dissolution profiles. Hence, the selection of the basket mesh size must be carefully considered during drug product development.

Studying Drug Release through Polymeric Controlled Release Formulations in United States Pharmacopoeia 2 Apparatus Using Multiphysics Simulation and Experiments

In vitro dissolution of oral drug formulations is often studied using the United States Pharmacopoeia (USP) apparatus. Although a well-stirred vessel or a perfect sink assumption is often employed in the modeling of in vitro dissolution in USP apparatus, such a limit is usually not realized in actual experimental conditions. The interplay of hydrodynamics in the vessel and the swelling and erosion of dosage forms often results in substantial deviations from the dissolution behavior obtained under perfect sink approximation. We develop a multiphysics model of drug release from controlled release tablets of polymeric excipients with active pharmaceutical ingredients (APIs). Simulations are performed in COMSOL for the USP 2 (paddle) apparatus and the effects of stirring speed, drug loading, erosion rate, and polymer swelling and erosion are analyzed in detail. We demonstrate that the drug release phenomena can be conveniently interpreted using the Weibull equation to fit the simulation results. This is further confirmed using drug release experiments performed on mechanically compressed tablets of naproxen sodium as the API with poly-methyl-methacrylate-co-methacrylic acid as the excipient. We show that the API-to-polymer ratio may be varied to obtain different regimes of controlled release.

Experimental determination of the velocity distribution in USP Apparatus 1 (basket apparatus) using Particle Image Velocimetry (PIV)

The USP Apparatus 1 (basket apparatus) is commonly used to evaluate the dissolution performance of oral solid dosage forms. The hydrodynamics generated by the basket contributes, in general, to the dissolution rate and hence the dissolution results. Here, the hydrodynamics of Apparatus 1 was quantified in a vessel filled with 900-mL de-ionized water at room temperature by determining, via Particle Image Velocimetry (PIV), the velocity profiles on a vertical central plane and on 11 horizontal planes at different elevations at three different basket agitation speeds. The flow field was dominated by the tangential velocity component and was approximately symmetrical in all cases. Despite all precautions taken, small flow asymmetries were observed in the axial and radial directions. This appears to be an unavoidable characteristic of the flow in Apparatus 1. The magnitudes of the axial and radial velocity components varied with location but were always low. A small jet was seen emanating radially near the top edge of the basket. Velocities typically scaled well with increasing agitation speed in most regions of the vessel except for a region directly below the basket. The results of this work provide a major insight into the flow field inside the USP Apparatus 1.

Simulation of Unit Operations in Formulation Development of Tablets Using Computational Fluid Dynamics

Tablets are the most customarily used solid oral unit dosage form for its better patient compliance. Preparation of these tablets include granulation, granule drying, die filling, and tablet coating as few unit operations and evaluation tests like dissolution test and disintegration test. These are the most crucial segments influencing the quality of the tablet. Critical analysis of the impact of factors like flow pattern, temperature, velocity, and other properties of fluid affecting the unit operations is obligatory to enhance their efficiency. Computational fluid dynamics (CFD), a combined mathematical and numerical approach, is used to analyze the process parameters of fluid affecting the abovementioned processes during tablet formulation. The equations governing the laws of conservation of energy, mass, and momentum are solved numerically utilizing CFD software for better understanding of the role of fluids within the tablet processing steps. This review not only focuses on discrete explanations on how CFD is utilized in formulation and evaluation of tablet but it is also a compilation of multiple research works performed on each unit operation by applying CFD.

Small volume method for drug release screening using ultrasonic agitation

Drug release testing plays a major role along all parts of the dosage form development and manufacturing process. However, official methods to perform this type of testing are often resource intensive and require highly specialized facilities. Affordable and accessible methods for studying drug release behavior are currently lacking. This work presents a small volume approach to solid dissolution and drug release testing of solid dosage forms using ultrasonic agitation. Cavitation and acoustic streaming were generated by a microprobe horn delivering a 40 kHz acoustic signal into a 50 mL test vessel. These two phenomena resulted in breakdown of and release of drug from tablet samples. Prednisone Performance Verification Tablets were used as model tablets to study the effect of system parameters on the drug release process. The effects of these parameters on the acousto-hydrodynamic environment were studied using streak photography and hydrophone measurements. Drug release behavior showed a slow/fast threshold transition separated by a highly variable regime as a function of the system parameters. Observations from drug release experiments and results from acoust-hydrodynamic characterization experiments suggested that this transition is dominated by acoustic streaming. This method represents a screening method to probe relative differences in dosage form composition and acts as a complimentary approach to official testing methods. The small volume format of this test has potential applications in the study of drug release properties from low-dose and novel solid dosage forms as well as reduced cost and increased accessibility of release testing for post-manufacturing tablet quality screening, a current need in low- and middle-income countries.

Computational fluid dynamics (CFD) studies of a miniaturized dissolution system

Dissolution testing is an important tool that has applications ranging from fundamental studies of drug-release mechanisms to quality control of the final product. The rate of release of the drug from the delivery system is known to be affected by hydrodynamics. In this study we used computational fluid dynamics to simulate and investigate the hydrodynamics in a novel miniaturized dissolution method for parenteral formulations. The dissolution method is based on a rotating disc system and uses a rotating sample reservoir which is separated from the remaining dissolution medium by a nylon screen. Sample reservoirs of two sizes were investigated (SR6 and SR8) and the hydrodynamic studies were performed at rotation rates of 100, 200 and 400rpm. The overall fluid flow was similar for all investigated cases, with a lateral upward spiraling motion and central downward motion in the form of a vortex to and through the screen. The simulations indicated that the exchange of dissolution medium between the sample reservoir and the remaining release medium was rapid for typical screens, for which almost complete mixing would be expected to occur within less than one minute at 400rpm. The local hydrodynamic conditions in the sample reservoirs depended on their size; SR8 appeared to be relatively more affected than SR6 by the resistance to liquid flow resulting from the screen.

The effect of the nature of organic acids and the hydrodynamic conditions on the dissolution of Pb particles

Rapid stabilization of pH values while Pb dissolution by three organic acids continues to progress.

Preformulation studies of mucoadhesive tablets for carbamazepine sublingual administration

The purpose of this research work was the realization of a bi-layered mucoadhesive dosage form intended for carbamazepine sublingual administration and planned in order to obtain a unidirectional drug release and diffusion only across buccal mucosa avoiding the liberation in the buccal environment. Bi-layered tablets were constituted by an impermeable ethyl cellulose backing layer and a mucoadhesive layer. The latter was composed by a blend of a semisynthetic polymer, as hydroxyethyl cellulose or hydroxypropyl methylcellulose, and a synthetic polymer as, Carbopol(®), physically mixed in different ratios. The active ingredient carbamazepine was homogeneously dispersed in the mucoadhesive layer. The prepared formulations were carefully characterized by thickness, friability, swelling index, matrix erosion, ex vivo and in vivo mucoadhesive force and time, moreover patient acceptability was evaluated as well. Tablets constituted by Carbopol(®):hydroxypropyl methylcellulose (25%:75%) and Carbopol(®):hydroxyethyl cellulose (75%:25%) showed the best properties and for this reason were submitted to in vitro release studies. Both tablet groups gave good results in terms of ex vivo and in vivo bioadhesive force and time giving a sustained release.

An investigation into the influence of experimental conditions on in vitro drug release from immediate-release tablets of levothyroxine sodium and its relation to oral bioavailability

The aim of this study was to investigate the influence of experimental conditions on levothyroxine sodium release from two immediate-release tablet formulations which narrowly passed the standard requirements for bioequivalence studies. The in vivo study was conducted as randomised, single-dose, two-way cross-over pharmacokinetic study in 24 healthy subjects. The in vitro study was performed using various dissolution media, and obtained dissolution profiles were compared using the similarity factor value. Drug solubility in different media was also determined. The in vivo results showed narrowly passing bioequivalence. Considering that levothyroxine sodium is classified as Class III drug according to the Biopharmaceutics Classification System, drug bioavailability will be less sensitive to the variation in its dissolution characteristics and it can be assumed that the differences observed in vitro in some of investigated media probably do not have significant influence on the absorption process, as long as rapid and complete dissolution exists. The study results indicate that the current regulatory criteria for the value of similarity factor in comparative dissolution testing, as well as request for very rapid dissolution (more than 85% of drug dissolved in 15 min), are very restricted for immediate-release dosage forms containing highly soluble drug substance and need further investigation. The obtained results also add to the existing debate on the appropriateness of the current bioequivalence standards for levothyroxine sodium products.

The science of USP 1 and 2 dissolution: present challenges and future relevance

Since its inception, the dissolution test has come under increasing levels of scrutiny regarding its relevance, especially to the correlation of results to levels of drug in blood. The technique is discussed, limited to solid oral dosage forms, beginning with the scientific origins of the dissolution test, followed by a discussion of the roles of dissolution in product development, consistent batch manufacture (QC release), and stability testing. The ultimate role of dissolution testing, "to have the results correlated to in vivo results or in vivo in vitro correlation," is reviewed. The recent debate on mechanical calibration versus performance testing using USP calibrator tablets is presented, followed by a discussion of variability and hydrodynamics of USP Apparatus 1 and Apparatus 2. Finally, the future of dissolution testing is discussed in terms of new initiatives in the industry such as quality by design (QbD), process analytical technology (PAT), and design of experiments (DOE).

Experimental and computational determination of blend time in USP Dissolution Testing Apparatus II

Blend time, the time to achieve a predefined level of homogeneity of a tracer in a mixing vessel, is an important parameter to evaluate the mixing efficiency of mixing devices. In this work, the blend time required to homogenize the liquid content of a USP Dissolution Testing Apparatus II under a number of operating conditions was obtained using two different experimental methods (tracer detection via colorimetric and conductivity measurements), a computational approach (computational fluid dynamics (CFD)), and a semi-theoretical analysis of the phenomenon. Under the standard geometric and operating conditions in which the USP Apparatus II is typically used (N = 50 rpm) the experimental blend time to achieve a 92.74% uniformity level was found to be between 27.5 and 33.3 s, depending on the location of the injection point and monitoring point for the tracer. These values were in close agreement with those obtained from CFD simulations. Changing the impeller vertical position (+/-2 mm) had only a limited effect. The CFD predictions also indicated that blend time is inversely proportional to the agitation speed. This conclusion is in agreement with previous reports and equations for blend time in mixing vessels. The blend times obtained in this work appear to be some two orders of magnitude smaller than the time usually required for appreciable tablet dissolution during the typical dissolution test, implying that the liquid contents of the USP Apparatus II can be considered to be relatively well mixed during the typical dissolution test.

Hydrodynamic Investigation of USP Dissolution Test Apparatus II

The USP Apparatus II is the device commonly used to conduct dissolution testing in the pharmaceutical industry. Despite its widespread use, dissolution testing remains susceptible to significant error and test failures, and limited information is available on the hydrodynamics of this apparatus. In this work, laser-Doppler velocimetry (LDV) and computational fluid dynamics (CFD) were used, respectively, to experimentally map and computationally predict the velocity distribution inside a standard USP Apparatus II under the typical operating conditions mandated by the dissolution test procedure. The flow in the apparatus is strongly dominated by the tangential component of the velocity. Secondary flows consist of an upper and lower recirculation loop in the vertical plane, above and below the impeller, respectively. A low recirculation zone was observed in the lower part of the hemispherical vessel bottom where the tablet dissolution process takes place. The radial and axial velocities in the region just below the impeller were found to be very small. This is the most critical region of the apparatus since the dissolving tablet will likely be at this location during the dissolution test. The velocities in this region change significantly over short distances along the vessel bottom. This implies that small variations in the location of the tablet on the vessel bottom caused by the randomness of the tablet descent through the liquid are likely to result in significantly different velocities and velocity gradients near the tablet. This is likely to introduce variability in the test.

Towards a universal dissolution medium for carbamazepine

The aim of this study was to develop a dissolution medium for assessment of various carbamazepine (CBZ) formulations with different strengths. The design of a system inhibiting transformation of the anhydrous CBZ (CBZ A) to the dihydrate form (CBZ D), with minimum surface-active properties and suitable sink was investigated. The effect of pH, different concentrations of sodium lauryl sulphate (SLS), polyvinylpyrrolidone (PVP), and methyl cellulose (MC) on dissolution rate, solubility, dissolution solubility, and polymorphic transformation of CBZ was assessed. Solution-mediated transformation of CBZ A into CBZ D was monitored using optical microscopy, Fourier transform infrared spectroscopy and differential scanning calorimetry. Results showed that different strengths (100, 200, 400 mg) of the same CBZ tablet formulation exhibited different dissolution patterns, in 1% SLS (USP system). Such differences were reduced in 0.5% SLS solution which provided sufficient sink for up to 200 mg CBZ. It was also shown that solubility of CBZ A could not be detected in the media under study (water, SGF, SIF, and SLS solutions) due to its rapid transformation into CBZ D. The use of 3% PVP solution protected CBZ A from conversion for 75 min, while 0.01% MC completely inhibited the transformation up to 24 h. Therefore, a medium consisting of 0.5% SLS and 0.01% MC was selected. The medium provided: a) protection against transformation of CBZ A to CBZ D, b) increased solubility of CBZ A (204 mg % compared to 128 mg % of CBZ D in 0.5% SLS), c) suitable sink for up to 400 mg CBZ and d) overlapping dissolution profiles of various strengths of the same CBZ formulation. The suggested system may be a step in the way of solving CBZ dissolution problems that forced the USP to specify two similar dissolution tests with two different limits for conventional 200 mg CBZ tablets.

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.

Evaluation of hydrodynamics in the basket dissolution apparatus using computational fluid dynamics—Dissolution rate implications

The aim of this work was to simulate the fluid flow in the basket dissolution apparatus using computational fluid dynamics (CFD) and to use the resulting velocity data (in combination with velocity data from simulated flow fields of the paddle dissolution apparatus) to relate velocities in the vicinity of a dissolving surface to dissolution rate. A further objective of the work was to compare fluid velocities between the basket and paddle dissolution apparatuses. CFD simulations of the basket apparatus were carried out using Fluent software. Flow field solutions were compared with results from flow visualisation techniques and with published ultrasound-pulse-echo velocity data. Velocity data from the flow field solution revealed velocities within the basket to be of the same order as those at the base of the paddle apparatus at the same rotation speed, supporting equivalent dissolution rate data from these locations. Dissolution rates were obtained for compacts of benzoic acid dissolved in 0.1 M HCl at 37 degrees C in the basket apparatus at 50 rpm. The relationship between maximum velocity in the vicinity of a dissolving surface and dissolution rate data from both the paddle and basket apparatuses was in good agreement with theoretical predictions. Analysis of the dissolution rates suggests a significant contribution from free convection in regions of low velocity at the base of the vessel of the basket apparatus.