The primary aim of the HPC/Exascale Centre of Excellence in Personalised Medicine (PerMedCoE) is to develop a robust and sustainable roadmap for adopting upcoming European HPC/Exascale technologies in this field. To do so, PerMedCoE is optimizing key software tools in computational biology to enhance their computational capabilities. Through this effort, the PerMedCoE initiative seeks to empower the research community to harness supercomputing resources effectively, enabling the transformation of complex biomedical data analysis into actionable models of cellular functions with medical significance. PerMedCoE roadmap is divided into four steps: 1) optimising core applications for mathematical modelling and cell-level simulations to the new pre-exascale platforms; 2) integrating personalised medicine into the new European HPC/Exascale ecosystem, by offering access to HPC/Exascale-adapted and optimised software; 3) running a comprehensive set of biomedical use cases; & 4) building the basis for the sustainability of PerMedCoE by coordinating personalised medicine initiatives and HPC communities, and reaching out to industrial and academic end-users, with use cases, training, expertise, and best practices. In this context, the combination of simulations and HPC computing is expected to have a great impact on society, health and business. In addition, the European healthcare systems are under great economic and social pressure, demanding better, faster and cheaper solutions. These challenges represent a unique opportunity for cellular simulations, which offer sophisticated tools to accelerate diagnostics and personalise treatments for patients. In doing so, they uphold the basic principle of personalised medicine: saving invaluable time and resources for healthcare systems and, more importantly, alleviating patient suffering.