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A membrane, or P system, is a biologically inspired computational modelling paradigm that simulates both the structure and dynamical processes of a cellular mechanism. The computational power of a membrane system is derived from the non-deterministic nature and the inherent parallelism of these structures and processes. Recently a number of researchers have tried to utilise this powerful computational paradigm to solve complex problems. Currently, parallelisation in practical implementations of this paradigm use a SIMD (Single Instruction Multiple Data) type approach, normally focusing on a specific aspect of the P system structure and applying this to the rest of the system in a parallel manner; in a few cases the rule selection algorithm has been parallelised for this purpose, the rules themselves being applied in a traditional sequential manner. In this paper we propose that a MIMD (Multiple Instruction Multiple Data) architecture is a closer representation of the biological membrane/P system structure and allows a degree of parallelism that is not possible using SIMD type approaches. We identify the elements of the membrane system that can be parallelised and also demonstrate how these elements can be parallelised using a MIMD approach. We examine how the XMOS XS1 Simulator, which has an architecture suited to MIMD, can be used to implement a Numerical P system. Furthermore we suggest that the temporal aspects of cellular aging may be simulated by a simple extension to the standard P system model.