Future healthcare systems and organisations demand huge computational resources, and the ability for the applications to interact and communicate with each other within and across organisational boundaries. Examples of healthcare applications include medical imaging and processing, electronic health records, epidemiology and other higher-level analysis of healthcare data. Grid Computing has the potential to provide solutions to many of the challenges in healthcare systems, including the deployment path and business models. This paper presents a quantitative, Markovian, performance model to evaluate the suitability of computational Grids for pervasive deployment of medical applications in healthcare organisations. For a range and mix of medical applications, we compute steady state probability distributions of the respective Markov models and analyse the system performance using the results. This study is a step forward to quantitatively demonstrate the potential of computational Grids for their use in healthcare organisations.