(617b) A Thermodynamic Framework for Simultaneous Solvent and Coformer Selection, and Process Optimization of Continuous Cocrystallization Processes

Active pharmaceutical ingredients (APIs) are most commonly administrated as solid oral dosage forms due to various advantages they possess over other dosage forms (e.g., better stability). A typical solid dosage form consists of a single crystalline form of the API and excipients. However, modern drugs often suffer from a low aqueous solubility or slow dissolution rate, which may result in poor bioavailability. Since solubility is closely associated with the crystal structure of an API, one promising approach to overcome this limitation is to engineer crystal structures with an enhanced solubility. Cocrystallization can extend the range of crystalline forms available for a given API [1]. A pharmaceutical cocrystal usually comprises an API and a coformer at a fixed stoichiometric ratio in the crystal lattice. The API and coformer are both neutrally charged and exist as solids at room temperature. Consequently, the API and the coformer are bound by non-covalent interactions in the lattice and can immediately separate into their molecular forms upon dissolution. This property allows for modification of the dissolution behavior of an API by choosing a coformer appropriately. Solution crystallization is typically preferred [2] for cocrystallizatoin at the industrial scale. The existing decision variables of solution crystallization in combination with coformer selection create a rich decision space, which requires systematic methods for optimal design.

Solvent selection is important in solution crystallization processes due to the impact of solvents on aspects such as the final crystal quality and yield, production cost, waste generation, safety aspects, etc. The sheer number of potential solvent candidates (along with their blends) that are routinely used in the pharmaceutical industry and the need to consider different independent performance criteria often make solvent selection a challenging task. Mathematical optimization can be an effective tool in addressing the tradeoffs arising from conflicting demands. Early attempts on crystallization solvent selection based on mathematical optimization focus primarily on stand-alone batch crystallization units [3]. Simultaneous solvent and process optimization approaches for continuous crystallization processes were developed more recently [4] in order to capture the influence of process structures and operating conditions on the solvent selection decision [5]. Such systematic approaches have not yet been developed for cocrystallization processes.

While cocrystallization shares many similarities with traditional crystallization, there are a few important differences that make the solvent and process optimization for cocrystallization processes uniquely challenging. A cocrystallizing system can potentially form multiple solid phases, including the pure forms of the API, coformer, cocrystal, as well as a mixture of those solid phases. In order to selectively crystallize the desired cocrystal form, it is necessary to choose solvents (or solvent blends) and operating conditions (i.e., temperature, material flow rates and compositions) in such a way that the formation of the undesired solid-state forms is suppressed. Sufficient knowledge of the phase diagram is a key requirement to fulfill this goal [2]. Coformer selection is important when an API is known to cocrystallize with multiple coformers, because the phase behavior of a cocrystallizing system is dependent on the coformer type.

The objective of this work is to develop a thermodynamic framework to select solvents and coformers, and process operating conditions simultaneously for continuous cocrystallization processes. The coformer selection plays a critical role in tailoring the final product properties (e.g., the dissolution behavior). Thus, the aqueous solubility advantage of cocrystals, i.e., the factor by which the solubility of the pure API is enhanced, is predicted and included in the optimization problem formulation to balance product and process performance. The phase diagram is a requirement to identify solvents, coformers, and operating conditions to crystallize a cocrystal selectively. However, the phase behavior is dependent on the solvent and coformer type selected. The experimental determination of the phase diagrams of all possible solvent and coformer combinations is time- and resource-consuming. Thus, the perturbed-chain statistical associating fluid theory (PC-SAFT) [6] is used to predict thermodynamic properties, including phase behavior and solubility advantages, from a limited set of pure-component parameters. The PC-SAFT is a powerful thermodynamic tool that has been extensively used to model the phase behavior of pure components and mixtures, including those that are pharmaceutically relevant [7]. The PC-SAFT can also predict the phase behavior of cocrystallizing systems [2] from the melting properties of the pure solids and the solubility products of cocrystals.

Carbamazepine is the model system to illustrate the developed optimization framework. Carbamazepine is a Class II BCS drug whose bioavailability is limited by its low aqueous solubility and dissolution rate. Identification of coformers to improve the dissolution properties of carbamazepine has been an active area of research. A large number of coformers have been discovered for carbamazepine, and the solubility product values of these cocrystals are reported in the literature [8]. The PC-SAFT parameters of the coformers are obtained from solubility data from the literature and the UNIFAC activity coefficients when solubility data are not available. A solvent database comprising 38 polar solvents and 10 nonpolar solvents is adapted from our previous work [4].

A single-stage continuous crystallization process is considered. The API and the coformer are separately fed and fully dissolved in the same solvent. The cocrystal forms inside the crystallizer and is separated from the mother liquor using a filter. The optimization problem consists of a process model based on material and energy balances, thermodynamic property calculations from the PC-SAFT, and feasibility constraints. The coformer, solvent, and the composition of the inlet streams and flow rates are the decision variables. The objective function addresses both the process performance by favoring a reduced solvent and energy consumption and a higher yield, and the product performance by favoring a high aqueous solubility advantage. Both single-objective and multi-objective optimization formulations are investigated. The resulting optimization problem is an MINLP problem due to the discrete nature of the solvent and coformer selection and the continuous nature of operating conditions. It is likely impractical to solve a problem of this scale using MINLP solvers due to the high nonlinearity arising from the PC-SAFT equations. Therefore, an MINLP relaxation strategy is developed. First, the coformer and solvent PC-SAFT parameters are relaxed, whereby the MINLP problem is converted to a computationally tractable NLP problem. The resulting optimal (hypothetical) coformer parameters are mapped onto the coformer database to identify the optimal real coformer parameters. The rest of the strategy is similar to the continuous mapping method described in [5]. The relaxed solvent parameters and operating conditions are optimized with fixed coformer parameters. The resulting optimal (hypothetical) solvent parameters are mapped onto the solvent database, and optimal real solvent parameters are identified. Finally, another NLP problem is solved to optimize the operating conditions with both the coformer and solvent parameters fixed.

The results show that the developed optimization framework is computationally feasible and more efficient than brute-force search. The following coformer and solvent combinations give the best overall performance in this case study: oxalic acid-benzyl alcohol, nicotinamide-benzyl alcohol, and succinic acid-DMSO. The proposed optimization framework allows for the simultaneous identification of optimal solvents, coformers, and process operating conditions while taking into account the complex tradeoffs related to cocrystallization process efficiency and cocrystal product functionality. The proposed approach has the potential to reduce the experimental burden associated with early API process development via rapid identification of attractive combinations of solvents, coformers, and operating conditions, which can serve as an attractive starting point for experimental verification.

This work was supported by the Research Grant Council of Hong Kong under Grant No. 16214418.

References

[1] N. Shan and M. J. Zaworotko, “The role of cocrystals in pharmaceutical science,” Drug Discov. Today, vol. 13, no. 9–10, pp. 440–446, May 2008.

[2] L. Lange and G. Sadowski, “Thermodynamic Modeling for Efficient Cocrystal Formation,” Cryst. Growth Des., vol. 15, no. 9, pp. 4406–4416, Sep. 2015.

[3] A. T. Karunanithi, L. E. K. Achenie, and R. Gani, “A computer-aided molecular design framework for crystallization solvent design,” Chem. Eng. Sci., vol. 61, no. 4, pp. 1247–1260, Feb. 2006.

[4] J. Wang and R. Lakerveld, “Integrated solvent and process design for continuous crystallization and solvent recycling using PC-SAFT,” AIChE J., vol. 64, no. 4, pp. 1205–1216, Apr. 2018.

[5] A. Bardow, K. Steur, and J. Gross, “Continuous-Molecular Targeting for Integrated Solvent and Process Design,” Ind. Eng. Chem. Res., vol. 49, no. 6, pp. 2834–2840, Mar. 2010.

[6] J. Gross and G. Sadowski, “Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules,” Ind. Eng. Chem. Res., vol. 40, no. 4, pp. 1244–1260, 2001.

[7] F. Ruether and G. Sadowski, “Modeling the Solubility of Pharmaceuticals in Pure Solvents and Solvent Mixtures for Drug Process Design,” J. Pharm. Sci., vol. 98, no. 11, pp. 4205–4215, Nov. 2009.

[8] D. J. Good and N. Rodríguez-Hornedo, “Solubility advantage of pharmaceutical cocrystals,” Cryst. Growth Des., vol. 9, no. 5, 2009.