Graphical processing unit (GPU) acceleration for numerical solution of population balance models using high resolution finite volume algorithm

Prediction of directional solidification in freeze casting of biomaterial scaffolds using physics-informed neural networks

Freeze casting, a manufacturing technique widely applied in biomedical fields for fabricating biomaterial scaffolds, poses challenges for predicting directional solidification due to its highly nonlinear behavior and complex interplay of process parameters. Conventional numerical methods, such as computational fluid dynamics (CFD), require adequate and accurate boundary condition knowledge, limiting their utility in real-world transient solidification applications due to technical limitations. In this study, we address this challenge by developing a physics-informed neural networks (PINNs) model to predict directional solidification in freeze-casting processes. The PINNs model integrates physical constraints with neural network predictions, requiring significantly fewer predetermined boundary conditions compared to CFD. Through a comparison with CFD simulations, the PINNs model demonstrates comparable accuracy in predicting temperature distribution and solidification patterns. This promising model achieves such a performance with only 5000 data points in space and time, equivalent to 250,000 timesteps, showcasing its ability to predict solidification dynamics with high accuracy. The study's major contributions lie in providing insights into solidification patterns during freeze-casting scaffold fabrication, facilitating the design of biomaterial scaffolds with finely tuned microstructures essential for various tissue engineering applications. Furthermore, the reduced computational demands of the PINNs model offer potential cost and time savings in scaffold fabrication, promising advancements in biomedical engineering research and development.

Development of a Digital Twin for the Prediction and Control of Supersaturation during Batch Cooling Crystallization

Fine chemicals produced via batch crystallization with properties dependent on the crystal size distribution require precise control of supersaturation, which drives the evolution of crystal size over time. Model predictive control (MPC) of supersaturation using a mechanistic model to represent the behavior of a crystallization process requires less experimental time and resources compared with fully empirical model-based control methods. Experimental characterization of the hexamine-ethanol crystallization system was performed in order to collect the parameters required to build a one-dimensional (1D) population balance model (PBM) in gPROMS FormulatedProducts software (Siemens-PSE Ltd.). Analysis of the metastable zone width (MSZW) and a series of seeded batch cooling crystallizations informed the suitable process conditions selected for supersaturation control experiments. The gPROMS model was integrated with the control software PharmaMV (Perceptive Engineering Ltd.) to create a digital twin of the crystallizer. Simulated batch crystallizations were used to train two statistical MPC blocks, allowing for in silico supersaturation control simulations to develop an effective control strategy. In the supersaturation set-point range of 0.012-0.036, the digital twin displayed excellent performance that would require minimal controller tuning to steady out any instabilities. The MPC strategy was implemented on a physical 500 mL crystallizer, with the simulated solution concentration replaced by in situ measurements from calibrated attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy. Physical supersaturation control performance was slightly more unstable than the in silico tests, which is consistent with expected disturbances to the heat transfer, which were not specifically modeled in simulations. Overall, the level of supersaturation control in a real crystallizer was found to be accurate and precise enough to consider future adaptations to the MPC strategy for more advanced control objectives, such as the crystal size.

Effect of Mold Geometry on Pore Size in Freeze-Cast Chitosan-Alginate Scaffolds for Tissue Engineering

Freeze-casting is a popular method to produce biomaterial scaffolds with highly porous structures. The pore structure of freeze-cast biomaterial scaffolds is influenced by processing parameters but has mostly been controlled experimentally. A mathematical model integrating Computational Fluid Dynamics with Population Balance Model was developed to predict average pore size (APS) of 3D porous chitosan-alginate scaffolds and to assess the influence of the geometrical parameters of mold on scaffold pore structure. The model predicted the crystallization pattern and APS for scaffolds cast in different diameter molds and filled to different heights. The predictions demonstrated that the temperature gradient and solidification pattern affect ice crystal nucleation and growth, subsequently influencing APS homogeneity. The predicted APS compared favorably with APS measurements from a corresponding experimental dataset, validating the model. Sensitivity analysis was performed to assess the response of the APS to the three geometrical parameters of the mold: well radius; solution fill height; and spacing between wells. The pore size was most sensitive to the distance between the wells and least sensitive to solution height. This validated model demonstrates a method for optimizing the APS of freeze-cast biomaterial scaffolds that could be applied to other compositions or applications.