One of the key aspects of any e-health application is the quality management of urgent situations. Currently, these situations are accessible on a wide variety of embedded sensors. The heterogeneity of such sensors and the diversity of user's needs require management quality of service and adaptation to different critical situations (e.g. hypoglycemic diabetic coma). Since the last decade, a fair amount of research has been conducted in order to develop adaptation platforms. These platforms generally adapt services in order to comply with dynamic context evolution. However, we have noticed that current adaptation platforms do not fully exploit the semantic benefits for describing the heterogeneous contexts, the adaptation process. In this paper, we propose a model for specifying rich contexts containing explicit constraints expressions with qualitative and quantitative information. Our proposal has the great advantage to offer to users a global flexible adaptation infrastructure exploiting semantic information at multiple levels, i.e., from the design level to the run-time level. To demonstrate the utility of our approach, we propose the design of an ambient system applied to a diabetes case study.