Medical devices are becoming more interconnected and complex, and are increasingly supported by fragmented organizational systems, e.g. through different processes, committees, supporting staff and training regimes. Distributed Cognition has been proposed as a framework for understanding the design and use of medical devices. However, it is not clear that it has the analytic apparatus to support the investigation of such complexities. This paper proposes a framework that introduces concentric layers to DiCoT, a method that facilitates the application of Distributed Cognition theory. We use this to explore how an inpatient blood glucose meter is coupled with its context. The analysis is based on an observational study of clinicians using a newly introduced glucometer on an oncology ward over approximately 150h (11 days and 4 nights). Using the framework we describe the basic mechanics of the system, incremental design considerations, and larger design considerations. The DiCoT concentric layers (DiCoT-CL) framework shows promise for analyzing the design and use of medical devices, and how they are coupled with their context.