A challenge of current innovation in healthcare processes is to improve the time to treatment. This paper addresses the benefits of telematic services and mobile & wireless devices such as vital sign sensors and head mounted cameras for healthcare processes. It explores the telematic requirements for a distributed healthcare environment of body area networks of the mobile devices which are connected by wireless (public) networks (e.g. GPRS and UMTS) to healthcare centres. Our main contribution is the development of enterprise models, which are expressed in terms of the unified modelling language, for the purpose of identification and justification of the telematic system requirements. The developed enterprise models separate organizational modelling concerns such as the separation of medical roles from the agents acting in these roles. This separation enables roles to be dispatched virtually to a point of care without transporting along with all the agents, but it requires support of a telematic system to bridge the distance gap. We validate the proposed models against a trauma team scenario and consequently obtain the telematic system requirements which enable improved time to treatment for emergency services.