Most existing Grid technology has been foremost designed with performance and scalability in mind. When using Grid infrastructure for medical applications, privacy and security considerations become paramount. This leads to a re-thinking of implementation and deployment aspects of common components of the current Grid architecture. This paper describes the impact of privacy and security considerations on the Grid infrastructure design, and enumerates trust aspects which must underpin the design of Grid technology to support medical applications. We propose a novel security framework for securely handling privacy sensitive information on the Grid.