Cellular Automata (CA) properties facilitate the detail required for the bottom-up approach to modelling and simulation of a broad range of physico-chemical reactions. In pharmaceutical applications, CA models use a combination of discrete-event rules based on probabilistic distributions and fundamental physical laws to predict the behaviour of active substances (drug molecules) and structural changes in Drug Dissolution Systems (DDS) over time. Several models of this type have been described so far in the scientific literature. Yet, practical applications are lacking in the context of large-scale, high-precision, high-fidelity simulations. The key obstacle to parallelisation of such models is not only the amount of data involved, but also the fact that many of these models incorporate agent-like behaviour within the CA framework in order to describe pharmaceutical components. This makes communication across process boundaries expensive. In this paper, we apply different parallelisation strategies to a large scale CA framework, used to model coated drug spheres. We use two parallel-computing application programming interfaces (APIs), namely OpenMP and MPI, to partition the simulation space. We analyse the applicability of each API to the problem individually, as well as in the hybrid solution. We examine speedup potential and overhead for local and global communication for simulation speed and solution scalability. For these types of problems, our results show that performance is much improved for appropriate combinations of parallelisation solutions.