The goal of the HPC/Exascale Centre of Excellence in Personalised Medicine (PerMedCoE) is to provide an efficient and sustainable entry point to the HPC/Exascale-upgraded methodology to translate omics analyses into actionable models of cellular functions of medical relevance. It will accomplish so by 1) optimising four core applications for cell-level simulations to the new pre-exascale platforms; 2) integrating PerMed into the new European HPC/Exascale ecosystem, by offering access to HPC/Exascale-adapted and optimised software; 3) running a comprehensive set of PerMed use cases; & 4) building the basis for the sustainability of the PerMedCoE by coordinating PerMed and HPC communities, and reaching out to industrial and academic end-users, with use cases, training, expertise, and best practices. The combination of simulations and HPC computing are expected to have a great impact on society, health and business. The European healthcare systems are under great economic and social pressure, demanding better, faster and cheaper solutions. Cell-based simulations can contribute to speeding up the process of identifying diagnostic and finding patient-tailored treatments, fulfilling the promise of PerMed to save precious time and money for the healthcare systems and, more importantly, patient suffering.