A Novel PBM for Nanomilling of Drugs in a Recirculating Wet Stirred Media Mill: Impacts of Batch Size, Flow Rate, and Back-Mixing.

We examined the evolution of fenofibrate (FNB, drug) particle size distribution (PSD) during the production of nanosuspensions via wet stirred media milling (WSMM) with a cell-based population balance model (PBM). Our objective was to elucidate the potential impacts of batch size, suspension volumetric flow rate, and imperfect mixing in a recirculating WSMM. Various specific breakage rate functions were fitted to experimental PSD data at baseline conditions assuming perfect mixing. Then, the best function was used to simulate the PSD evolution at various batch sizes and flow rates to validate the model. A novel function, which is a product of power-law and logistic functions, fitted the evolution the best, signifying the existence of a transition particle size commensurate with a grinding limit. Although larger batches yielded coarser and wider PSDs, the suspensions had identical PSDs when milled for the same effective milling time. The flow rate had an insignificant influence on the PSD. Furthermore, the imperfect mixing in the mill chamber was simulated by considering more than one cell and different back-mixing flow ratios. The effects were weak and restricted to the first few turnovers. These insights contribute to our understanding of recirculating WSMM, providing valuable guidance for process development.

Development of a Semi-Mechanistic Modeling Framework for Wet Bead Milling of Pharmaceutical Nanosuspensions.

This study aimed to develop a practical semi-mechanistic modeling framework to predict particle size evolution during wet bead milling of pharmaceutical nanosuspensions over a wide range of process conditions and milling scales. The model incorporates process parameters, formulation parameters, and equipment-specific parameters such as rotor speed, bead type, bead size, bead loading, active pharmaceutical ingredient (API) mass, temperature, API loading, maximum bead volume, blade diameter, distance between blade and wall, and an efficiency parameter. The characteristic particle size quantiles, i.e., x10, x50, and x90, were transformed to obtain a linear relationship with time, while the general functional form of the apparent breakage rate constant of this relationship was derived based on three models with different complexity levels. Model A, the most complex and general model, was derived directly from microhydrodynamics. Model B is a simpler model based on a power-law function of process parameters. Model C is the simplest model, which is the pre-calibrated version of Model B based on data collected from different mills across scales, formulations, and drug products. Being simple and computationally convenient, Model C is expected to reduce the amount of experimentation needed to develop and optimize the wet bead milling process and streamline scale-up and/or scale-out.

Do Mixtures of Beads with Different Sizes Improve Wet Stirred Media Milling of Drug Suspensions?

The impacts of bead sizes and bead mixtures on breakage kinetics, the number of milling cycles applied to prevent overheating, and power consumption during the nanomilling of drug (griseofulvin) suspensions were investigated from both an experimental and theoretical perspective. Narrowly sized zirconia beads with nominal sizes of 100, 200, and 400 µm and their half-and-half binary mixtures were used at 3000 and 4000 rpm with two bead loadings of 0.35 and 0.50. Particle size evolution was measured during the 3 h milling experiments using laser diffraction. An nth-order breakage model was fitted to the experimental median particle size evolution, and various microhydrodynamic parameters were calculated. In general, the beads and their mixtures with smaller median sizes achieved faster breakage. While the microhydrodynamic model explained the impacts of process parameters, it was limited in describing bead mixtures. For additional test runs performed, the kinetics model augmented with a decision tree model using process parameters outperformed that augmented with an elastic-net regression model using the microhydrodynamic parameters. The evaluation of the process merit scores suggests that the use of bead mixtures did not lead to notable process improvement; 100 µm beads generally outperformed bead mixtures and coarser beads in terms of fast breakage, low power consumption and heat generation, and low intermittent milling cycles.

Nanoseeded Desupersaturation and Dissolution Tests for Elucidating Supersaturation Maintenance in Amorphous Solid Dispersions.

The impact of residual drug crystals that are formed during the production and storage of amorphous solid dispersions (ASDs) has been studied using micron-sized seed crystals in solvent-shift (desupersaturation) and dissolution tests. This study examines the impacts of the seed size loading on the solution-mediated precipitation from griseofulvin ASDs. Nanoparticle crystals (nanoseeds) were used as a more realistic surrogate for residual crystals compared with conventional micron-sized seeds. ASDs of griseofulvin with Soluplus (Sol), Kollidon VA64 (VA64), and hydroxypropyl methyl cellulose (HPMC) were prepared by spray-drying. Nanoseeds produced by wet media milling were used in the dissolution and desupersaturation experiments. DLS, SEM, XRPD, and DSC were used for characterization. The results from the solvent-shift tests suggest that the drug nanoseeds led to a faster and higher extent of desupersaturation than the as-received micron-sized crystals and that the higher seed loading facilitated desupersaturation. Sol was the only effective nucleation inhibitor; the overall precipitation inhibition capability was ranked: Sol > HPMC > VA64. In the dissolution tests, only the Sol-based ASDs generated significant supersaturation, which decreased upon an increase in the nanoseed loading. This study has demonstrated the importance of using drug nanocrystals in lieu of conventional coarse crystals in desupersaturation and dissolution tests in ASD development.

Predicting the Temperature Evolution during Nanomilling of Drug Suspensions via a Semi-Theoretical Lumped-Parameter Model.

Although temperature can significantly affect the stability and degradation of drug nanosuspensions, temperature evolution during the production of drug nanoparticles via wet stirred media milling, also known as nanomilling, has not been studied extensively. This study aims to establish both descriptive and predictive capabilities of a semi-theoretical lumped parameter model (LPM) for temperature evolution. In the experiments, the mill was operated at various stirrer speeds, bead loadings, and bead sizes, while the temperature evolution at the mill outlet was recorded. The LPM was formulated and fitted to the experimental temperature profiles in the training runs, and its parameters, i.e., the apparent heat generation rate Qgen and the apparent overall heat transfer coefficient times surface area UA, were estimated. For the test runs, these parameters were predicted as a function of the process parameters via a power law (PL) model and machine learning (ML) model. The LPM augmented with the PL and ML models was used to predict the temperature evolution in the test runs. The LPM predictions were also compared with those of an enthalpy balance model (EBM) developed recently. The LPM had a fitting capability with a root-mean-squared error (RMSE) lower than 0.9 °C, and a prediction capability, when augmented with the PL and ML models, with an RMSE lower than 4.1 and 2.1 °C, respectively. Overall, the LPM augmented with the PL model had both good descriptive and predictive capability, whereas the one with the ML model had a comparable predictive capability. Despite being simple, with two parameters and obviating the need for sophisticated numerical techniques for its solution, the semi-theoretical LPM generally predicts the temperature evolution similarly or slightly better than the EBM. Hence, this study has provided a validated, simple model for pharmaceutical engineers to simulate the temperature evolution during the nanomilling process, which will help to set proper process controls for thermally labile drugs.

An Enthalpy-Balance Model for Timewise Evolution of Temperature during Wet Stirred Media Milling of Drug Suspensions.

PURPOSE: Nanosuspensions have been used for enhancing the bioavailability of poorly soluble drugs. This study explores the temperature evolution during their preparation in a wet stirred media mill using a coupled experimental-enthalpy balance approach. METHODS: Milling was performed at three levels of stirrer speed, bead loading, and bead sizes. Temperatures were recorded over time, then simulated using an enthalpy balance model by fitting the fraction of power converted to heat ξ. Moreover, initial and final power, ξ, and temperature profiles at 5 different test runs were predicted by power-law (PL) and machine learning (ML) approaches. RESULTS: Heat generation was higher at the higher stirrer speed and bead loading/size, which was explained by the higher power consumption. Despite its simplicity with a single fitting parameter ξ, the enthalpy balance model fitted the temperature evolution well with root mean squared error (RMSE) of 0.40-2.34°C. PL and ML approaches provided decent predictions of the temperature profiles in the test runs, with RMSE of 0.93-4.17 and 1.00-2.17°C, respectively. CONCLUSIONS: We established the impact of milling parameters on heat generation-power and demonstrated the simulation-prediction capability of an enthalpy balance model when coupled to the PL-ML approaches.

Analysis of heat generation during the production of drug nanosuspensions in a wet stirred media mill.

Although heat is generated during the wet stirred media milling of drug suspensions, leading to notable temperature rise, a comprehensive analysis of heat generation does not exist. Hence, we investigated the impact of stirrer speed, bead loading, and bead size at three levels on the evolution of suspension temperature at the mill outlet during the milling of fenofibrate. The particle sizes and viscosities of the milled suspensions and power were measured. Our results suggest that stirrer speed had the most significant impact on the temperature increase, followed by bead loading and bead size. Both the time when the temperature reached 22 °C and the temperature at 5 min of milling were strongly correlated with the power. Assessing the impacts of the process parameters on the temperature rise, cycle time, power, and median particle size holistically, an optimal milling process was identified: 3000 rpm with 50% loading of 200 or 400 µm beads. A power number correlation was established to calculate power at any milling condition which determines the heat generation rate. Overall, this study indicated the importance of developing a good understanding of heat generation during nanomilling for development of a robust milling process especially for thermally labile drugs.

Kinetic and Microhydrodynamic Modeling of Fenofibrate Nanosuspension Production in a Wet Stirred Media Mill.

This study examined the impact of stirrer speed and bead material loading on fenofibrate particle breakage during wet stirred media milling (WSMM) via three kinetic models and a microhydrodynamic model. Evolution of median particle size was tracked via laser diffraction during WSMM operating at 3000-4000 rpm with 35-50% (v/v) concentration of polystyrene or zirconia beads. Additional experiments were performed at the center points of the above conditions, as well as outside the range of these conditions, in order to test the predictive capability of the models. First-order, nth-order, and warped-time kinetic models were fitted to the data. Main effects plots helped to visualize the influence of the milling variables on the breakage kinetics and microhydrodynamic parameters. A subset selection algorithm was used along with a multiple linear regression model (MLRM) to delineate how the breakage rate constant k was affected by the microhydrodynamic parameters. As a comparison, a purely empirical correlation for k was also developed in terms of the process/bead parameters. The nth-order model was found to be the best model to describe the temporal evolution; nearly second-order kinetics (n ≅ 2) was observed. When the process was operated at a higher stirrer speed and/or higher loading with zirconia beads as opposed to polystyrene beads, the breakage occurred faster. A statistically significant (p-value ≤ 0.01) MLRM of three microhydrodynamic parameters explained the variation in the breakage rate constant best (R2 ≥ 0.99). Not only do the models and the nth-order kinetic-microhydrodynamic correlation enable deeper process understanding toward developing a WSMM process with reduced cycle time, but they also provide good predictive capability, while outperforming the purely empirical correlation.

Use of Bead Mixtures as a Novel Process Optimization Approach to Nanomilling of Drug Suspensions.

PURPOSE: We aimed to evaluate the feasibility of cross-linked polystyrene (CPS)-yttrium-stabilized zirconia (YSZ) bead mixtures as a novel optimization approach for fast, effective production of drug nanosuspensions during wet stirred media milling (WSMM). METHODS: Aqueous suspensions of 10% fenofibrate (FNB, drug), 7.5% HPC-L, and 0.05% SDS were wet-milled at 3000-4000 rpm and 35%-50% volumetric loading of CPS:YSZ bead mixtures (CPS:YSZ 0:1-1:0 v:v). Laser diffraction, SEM, viscometry, DSC, and XRPD were used for characterization. An nth-order model described the breakage kinetics, while a microhydrodynamic model allowed us to gain insights into the impact of bead materials. RESULTS: CPS beads achieved the lowest specific power consumption, whereas YSZ beads led to the fastest breakage. Breakage followed second-order kinetics. Optimum conditions were identified as 3000 rpm and 50% loading of 0.5:0.5 v/v CPS:YSZ mixture from energy-cycle time-heat dissipation perspectives. The microhydrodynamic model suggests that YSZ beads experienced more energetic/forceful collisions with smaller contact area as compared with CPS beads owing to the higher density-elastic modulus of the former. CONCLUSIONS: We demonstrated the feasibility of CPS-YSZ bead mixtures and rationalized its optimal use in WSMM through their modulation of breakage kinetics, energy utilization, and heat dissipation.