As a fundamentally resource-intensive endeavour, healthcare innovation can benefit from a problem-based approach. This kind of methodology needs to define the problem by applying a range of well-established techniques, such as ethnographic research, market analysis, and stakeholder exploration. However, no in-depth investigation has taken place on how these techniques interact and relate to one another. As such, an overarching methodology is needed in order to represent, critically assess, and evolve problem-driven, or needled , innovation approaches. Graph theory provides a useful way by which this can be done. This paper exemplifies how different elements of a problem-first approach to innovation can be graphically represented within a system, in order to provide insights into the processes that support real-world impact for new technologies. By providing a more refined description of the needled innovation methodology, it is hoped that these models can drive a more evidence-based and empirical mindset within the field to ultimately drive valuable innovations with increased efficiency.