The ultimate goal of this research is to develop a package of simulation tools which will be used in the design of delivery systems for pharmaceuticals. Current widespread models of tablet dissolution are not designed to investigate the effects of changes to the tablet micro-structure. The simulations herein focus on systems of compacted particles, paying particular attention to such factors as particle size, active particle distribution and porosity. Using this model, an algorithm has been designed which determines effective tablet parameters which will achieve a desired output.
An initial representation of the tablet is built or input into the workspace. This is essentially a 3-D model on a fixed Cartesian grid, implemented as a series of matrices storing cell based effective constants and values representing particle size, concentration, shape as well as information regarding the excipients. The dissolution of the tablet is considered for the case of said tablet completely submerged in a fluid. The tablet fluid interaction is calculated using a series of equations, each one modeling a particular process. The surface of the tablet is modeled using a level set method to track the moving boundary. This allows for a smooth representation of the interface existing between nodes, and is integral to the proper application of boundary conditions on the other equations. The penetration of solvent into the tablet is governed by a modified version of Fick's second law, the diffusion equation. This equation models how the surrounding fluid enters the tablet, thus controlling the actual amount of active particulate which is currently dissolving. Particle dissolution is considered to occur only in areas of the tablet where solvent is present. As the particles dissolve, the drug concentration of the solute increases. The diffusion of active drug in solution is then modeled using the same Fick's law equation as the solvent penetration. The drug is considered released as the solute diffuses through the tablet fluid interface. Most calculations are performed using a finite differencing technique. This model serves as the basis for the tablet design algorithm. The design algorithm iteratively simulates the dissolution of tablets within a given set of parameter ranges in an attempt to define a set of parameters which will produce a desired release profile. Both the release profile and tablet design constraints are input by the user, but all subsequent tablet design is performed by the algorithm.
The model is able to produce curves representing the release of active drug into the fluid as well as track the concentration of solvent and volume of active particles inside the tablet. The tablet design algorithm is tested against physical dissolution profiles with reasonable agreement in tablet composition.
The current model provides an excellent basis for future extensions. The current framework is able to properly characterize a number of processes and is easily expandable to more. Even if a perfect representation of the true physical processes is unattainable, valuable insight into the importance of micro-scale factors on the overall dissolution of a tablet can still be determined.