(198e) A Dissolution model for in Vitro Cocrystal Dissolution with Surface and Bulk Precipitation

Low aqueous solubility is a major source of clinical inefficiency of modern drugs, which is associated with around 40% of the small-molecule drugs on the market and 90% of those under development.[1], [2] Cocrystallization of such orally administered, small-molecule drugs with high-soluble, pharmaceutically acceptable coformers is a promising means of mitigating poor aqueous solubility. In a cocrystal, both the drug and the coformer(s) are neutrally charged and exist at a fixed stoichiometric ratio in the cocrystal lattice, bound to each other non-covalently. The relatively weaker bonding between the drug and the coformer typically allows the cocrystal to dissociate rapidly into its molecular form upon contact with an aqueous medium.[3] This can result in a supersaturated solution of the drug, which favors faster gastrointestinal absorption. However, precipitation of the stable drug form can occur, which may neutralize the solubility advantage of the cocrystal. The precipitation of the stable drug can take place both in the bulk solution and at the cocrystal surface.[4] The latter is typically enhanced by the high drug concentration at the cocrystal surface and heterogeneous nucleation. Excessive surface precipitation is undesirable, as it can prevent the cocrystal from generating any supersaturation.[5] The existing methods to optimize the dissolution-supersaturation-precipitation (DSP) behavior of cocrystals primarily revolve around selecting additives such as surfactants,[6] polymers,[7] and excess coformer [8] to stabilize supersaturated solutions.

Optimization of the cocrystal dissolution behavior can be supported by models that can describe and predict the in vitro DSP behavior of cocrystals.[9] These models can potentially reduce the trial-and-error-based experimentation during formulation development.[10] A dynamic model for cocrystal dissolution should describe three kinetic phenomena: cocrystal dissolution, bulk precipitation, and surface precipitation. Cao and coworkers [11] developed a model to describe cocrystal dissolution under sink conditions, where drug precipitation is negligible. Common approaches to model bulk drug precipitation include first-order precipitation kinetics,[12] the classical nucleation theory (CNT),[13] and population balance models.[14] First-order precipitation models are commonly employed in commercial physiologically-based pharmacokinetic (PBPK) modeling software.[15] However, precipitation models based on the CNT or population balances were shown to give better descriptions of the experimental bulk precipitation data compared to first-order models,[13], [14] likely owing to the empirical nature of the latter. To our best knowledge, precipitation models explicitly accounting for surface precipitation do not yet exist. However, the impact of surface precipitation on the cocrystal DSP behavior can be significant,[5] which makes accounting for surface precipitation critical when developing dynamic models to describe cocrystal dissolution.

The objective of this work is to develop a predictive dynamic model accounting for cocrystal dissolution and precipitation of the drug to describe the dose-dependent cocrystal DSP behavior in vitro. Drug precipitation is modeled based on population balances in which nucleation and growth are described by power law relations. In order to account for surface and bulk precipitation separately, the dissolution medium is compartmentalized into two regions, i.e., the surface region and the bulk region, and three crystal populations are considered to coexist, i.e., the cocrystal, drug crystals in the surface region, and drug crystals in the bulk region. The model performance is evaluated from in vitro drug concentration-time profiles obtained from dissolution experiments conducted with the carbamazepine-succinic acid model cocrystal.

The surface region is the vicinity of the cocrystal phase, which is characterized by a relatively high drug concentration due to mass transfer limitations. It is assumed that the onset of surface precipitation is instantaneous due to this high drug concentration and the potential for heterogeneous nucleation. As the surface crystals grow, they consume a part of the cocrystal mass, slowing down the drug release to the bulk region. It is further assumed that the volume of the surface region is related to the diffusion boundary layer thickness, and, therefore, the surface region gradually disappears as the cocrystal dissolves. As the surface region shrinks, surface crystals gradually transfer to the bulk region. We assume the growth of these transferring crystals to be the main precipitation mechanism in the bulk region. The surface and bulk regions are assumed to be two well-mixed crystallizers when constructing population balances. The resulting PDEs are converted into ODEs by applying the method of moments.[16] The Noyes-Whiteney dissolution model is adopted to model cocrystal dissolution.[17] The solution to the resulting set of ODEs provides the concentration-time profile of the drug. For comparison, a cocrystal dissolution model is constructed considering cocrystal dissolution and bulk precipitation only, without explicitly accounting for surface precipitation.

Dissolution experiments are conducted for five different carbamazepine-succinic acid cocrystal powder doses ranging from 15 to 50 mg of carbamazepine at pH 2.5, which resembles the stomach pH. The dissolution and precipitation kinetic parameters are estimated by fitting the developed models with the experimental drug concentration data. To verify the predictive capabilities of the model, only part of the experimental data is utilized for model parameter estimation, while the rest is used for validation. Finally, the developed model with the estimated parameters is combined with numerical optimization to illustrate the application of the model to identify an optimal cocrystal dose, particle size, and the initially dissolved coformer concentration to maximize the area under the curve (AUC) of the concentration-time profile.

The results show that the model is capable of correctly capturing all the major experimental trends of the concentration profiles resulting from cocrystal dissolution, including the increase of the initial dissolution rate and the bulk precipitation rate with the dose and the dominant effect of surface precipitation at low doses. Furthermore, the model can be used to make predictions outside the dataset used for parameter estimation in good agreement with the experimental data. Explicitly accounting for surface precipitation in the model is essential, particularly for low doses, where the impact of surface precipitation on concentration profiles becomes dominant. The optimal cocrystal dose is identified, which shows good quantitative agreement with experimental observations. These optimization results show how the model can be used to find an optimal dose that is sufficiently high to generate substantial supersaturation but does not cause rapid precipitation, which would mitigate the solubility enhancement. It is further seen from the optimization results that a small cocrystal mean particle size and a moderate amount of coformer in the dissolution medium contribute favorably to the AUC. Overall, our model shows good potential as a new tool to aid formulation development for cocrystal drugs by reducing the overall experimental burden. Extending and further validating the model to predict the dissolved coformer concentration and cocrystal dissolution in various physiological conditions are of interest for future work.

Acknowledgment

This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, People’s Republic of China (Project No. 16308122).

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