Simulation and Optimization: A New Direction in Supercritical Technology Based Nanomedicine

Abstract

In recent years, nanomedicines prepared using supercritical technology have garnered widespread research attention due to their inherent attributes, including structural stability, high bioavailability, and commendable safety profiles. The preparation of these nanomedicines relies upon drug solubility and mixing efficiency within supercritical fluids (SCFs). Solubility is closely intertwined with operational parameters such as temperature and pressure while mixing efficiency is influenced not only by operational conditions but also by the shape and dimensions of the nozzle. Due to the special conditions of supercriticality, these parameters are difficult to measure directly, thus presenting significant challenges for the preparation and optimization of nanomedicines. Mathematical models can, to a certain extent, prognosticate solubility, while simulation models can visualize mixing efficiency during experimental procedures, offering novel avenues for advancing supercritical nanomedicines. Consequently, within the framework of this endeavor, we embark on an extensive review encompassing the application of mathematical models, artificial intelligence (AI) methodologies, and computational fluid dynamics (CFD) techniques within the medical domain of supercritical technology. We undertake the synthesis and discourse of methodologies for calculating drug solubility in SCFs, as well as the influence of operational conditions and experimental apparatus upon the outcomes of nanomedicine preparation using supercritical technology. Through this comprehensive review, we elucidate the implementation procedures and commonly employed models of diverse methodologies, juxtaposing the merits and demerits of these models. Furthermore, we assert the dependability of employing models to compute drug solubility in SCFs and simulate the experimental processes, with the capability to serve as valuable tools for aiding and optimizing experiments, as well as providing guidance in the selection of appropriate operational conditions. This, in turn, fosters innovative avenues for the development of supercritical pharmaceuticals.

Keywords: computational fluid dynamics; machine learning; model; particles; supercritical fluids.

Scheme 1

Empirical models, EoS models, and AI models can be employed to predict the solubility of drugs in SCCO₂. Simultaneously, CFD models can visualize the processes of SCF technology, enhancing the mixing efficiency in experiments, and thereby aiding in the preparation of small-sized drug particles. Copied with permission [19]. Copyright 2023, Elsevier B.V. Copied with permission [20]. Copyright 2022, Elsevier B.V. Copied with permission [21]. Copyright 2023, Nature. Copied with permission [22]. Copyright 2018, Elsevier B.V.

Figure 1

Metoprolol solubility, y(mol·mol⁻¹), at different conditions. Copied with permission [24]. Copyright 2023, Elsevier B.V.

Figure 2

Comparison of experimental Febuxostat solubility, y(mol·mol⁻¹), in SCCO₂ (points) and calculated ones (line): (i) Chrastil, AARD% = 15.738, (ii) Bartle, AARD% = 17.540, (iii) Sung and Shim, AARD% = 15.506, (iv) Hozhabr, AARD% = 16.314, (v) Adachi and Lu, AARD% = 13.304 and (vi) Keshmiri, AARD% = 10.630, models at different conditions. Copied with permission [28]. Copyright 2022, Elsevier B.V.

Figure 3

Comparison of experimental (points) and calculated (line) solubility of Chloroquine, y(mol·mol⁻¹), in SCCO₂, (left column) along with the related parity plot (right column), based on (a1,a2) PR-EoS and (b1,b2) SRK-EoS models. Copied with permission [20]. Copyright 2022, Elsevier B.V.

Figure 4

Experimental solubility of flurbiprofen, y₂(mol·mol⁻¹), in SCCO₂, at 313.15 K, and correlation results obtained with the four different mixing rules: (a) PR EoS and (b) PTV EoS. mrPR (···); vdW2 (—); MR (- · · -); vdW1 (- - -). Copied with permission [52]. Copyright 2006, Elsevier B.V.

Figure 5

(i) 3D demonstration of inputs, outputs; Y: solubility; X₂: temperature; X₁: pressure. (ii) Decision tree sample architecture. (iii) Actual versus predicted values/Y: solubility (a) DT Model, RMSE: 4.96 × 10⁻⁶, R²: 0.836. (b) ADA-DT Model, RMSE: 2.34 × 10⁻⁶, R²:0.921. (c) Nu-SVR Model, RMSE: 5.26 × 10⁻⁶, R²: 0.813. Copied with permission [21]. Copyright 2023, Nature.

Figure 6

Scheme of simulating SCF technology by ANSYS Fluent.

Figure 7

(i) Profiles for the mean diameter of the microparticles calculated for different cases (a–c). (ii) Profiles for the population density for different cases (a–c). (iii) Profile for the velocity of the microparticles calculated for case in (a). Copied with permission [90]. Copyright 2018, Elsevier B.V.

Figure 7

(i) Profiles for the mean diameter of the microparticles calculated for different cases (a–c). (ii) Profiles for the population density for different cases (a–c). (iii) Profile for the velocity of the microparticles calculated for case in (a). Copied with permission [90]. Copyright 2018, Elsevier B.V.

Figure 8

(i) Different shapes of nozzles: (a) Geometries of T-mixer and cross-mixer nozzles. (b) Contour of turbulence intensity in mixing zone of cross nozzle and T-nozzle. (ii) SEM images of Curcuma mangga micronized particles under various operating conditions using (a) T-nozzle and (b) cross nozzle. Copied with permission [92]. Copyright 2020, Elsevier B.V.

Figure 9

(a) Theoretical driving force represented at constant pressure (P₂) at different crystallization vessel temperatures (T₂) and corresponding equilibrium solubility of NIF in SCCO₂. Pressures (P₂) of the three surface plots correspond from the bottom to the top to 5, 7, and 9 MPa, respectively. (b) SEM images of processed drug at operating conditions compared to raw NIF (magnification 2000×; scale bar = 30 µm). Copied with permission [102]. Copyright 2023, Elsevier B.V.

Figure 9

(a) Theoretical driving force represented at constant pressure (P₂) at different crystallization vessel temperatures (T₂) and corresponding equilibrium solubility of NIF in SCCO₂. Pressures (P₂) of the three surface plots correspond from the bottom to the top to 5, 7, and 9 MPa, respectively. (b) SEM images of processed drug at operating conditions compared to raw NIF (magnification 2000×; scale bar = 30 µm). Copied with permission [102]. Copyright 2023, Elsevier B.V.