Enhancement of mass transfer from particles by local shear‐rate and correlations with application to drug 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.

Estimation of the concentration boundary layer adjacent to a flat surface using computational fluid dynamics

Dissolution-permeation (D/P) experiments are widely used during preclinical development due to producing results with better predictability than traditional monophasic experiments. However, it is difficult to compare absorption across in vitro setups given the propensity to only report apparent permeability. We therefore developed an approach to predict the concentration boundary layer for any D/P device by using computational fluid dynamics (CFD). The Navier-Stokes and continuity equation in 2D were solved numerically in MATLAB and by finite element methods in COMSOL v6.1 to predict the momentum [Formula: see text] and concentration ηg boundary layer for a flow over a flat plate, i.e. the classical Blasius boundary layer flow. A MATLAB algorithm was developed to calculate the edge of either boundary layer. The methodology to determine the concentration boundary layer based on Blasius's analysis provided an accurate estimate for both [Formula: see text] and ηg, resulting in, [Formula: see text] , at high Schmidt numbers (Sc ∼ 1000) within 14 % of the Blasius solution and 6.6 % of the accepted Schmidt number correlation ( [Formula: see text] ). The methodology based on the Blasius analysis of the concentration boundary layer using velocity and concentration profiles computed using CFD presented herein will enable characterization/analysis of complex D/P apparatuses used in preclinical development, where an analytical solution may not be available.

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).

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.

Computational Modeling of Drug Dissolution in the Human Stomach

A computational model of drug dissolution in the human stomach is developed to investigate the interaction between gastric flow and orally administrated drug in the form of a solid tablet. The stomach model is derived from the anatomical imaging data and the motion and dissolution of the drug in the stomach are modeled via fluid-structure interaction combined with mass transport simulations. The effects of gastric motility and the associated fluid dynamics on the dissolution characteristics are investigated. Two different pill densities are considered to study the effects of the gastric flow as well as the gravitational force on the motion of the pill. The average mass transfer coefficient and the spatial distributions of the dissolved drug concentration are analyzed in detail. The results show that the retropulsive jet and recirculating flow in the antrum generated by the antral contraction wave play an important role in the motion of the pill as well as the transport and mixing of the dissolved drug concentration. It is also found that the gastric flow can increase the dissolution mass flux, especially when there is substantial relative motion between the gastric flow and the pill.

Insights into the Release Mechanisms of ITZ:HPMCAS Amorphous Solid Dispersions: The Role of Drug-Rich Colloids

Understanding the dissolution mechanisms of amorphous solid dispersions (ASDs) and being able to link enhanced drug exposure with process parameters are key when formulating poorly soluble compounds. Thus, in this study, ASDs composed by itraconazole (ITZ) and hydroxypropylmethylcellulose acetate succinate (HPMCAS) were formulated with different polymer grades and drug loads (DLs) and processed by spray drying with different atomization ratios and outlet temperatures. Their in vitro performance and the ability to form drug-rich colloids were then evaluated by a physiologically relevant dissolution method. In gastric media, drug release followed a diffusion-controlled mechanism and drug-rich colloids were not formed since the solubility of the amorphous API at pH 1.6 was not exceeded. After changing to intestinal media, the API followed a polymer dissolution-controlled release, where the polymer rapidly dissolved, promoting the immediate release of API and thus leading to liquid-liquid phase separation (LLPS) and consequent formation of drug-rich colloids. However, the release of API and polymer was not congruent, so API surface enrichment occurred, which limited the further dissolution of the polymer, leading to a drug-controlled release. ASDs formulated with M-grade showed the highest ability to maintain supersaturation and the lowest tendency for AAPS due to its good balance between acetyl and succinoyl groups, and thus strong interactions with both the hydrophobic drug and the aqueous dissolution medium. The ability to form colloids increased for low DL (15%) and high specific surface area due to the high amount of polymer released until the occurrence of API surface enrichment. Even though congruent release was not observed, all ASDs formed drug-rich colloids that were stable in the solution until the end of the dissolution study (4 h), maintaining the same size distribution (ca. 300 nm). Drug-rich colloids can, in vivo, act as a drug reservoir replenishing the drug while it permeates. Designing ASDs that are prone to form colloids can overcome the solubility constraints of Biopharmaceutics Classification System (BCS) II and IV drugs, posing as a reliable formulation strategy.

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.

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.