We develop a model of innovation that enables us to trace the interplay among three key dimensions of the innovation process: (i) demand of and (ii) supply for innovation, and (iii) technological capabilities available to generate innovation in the forms of products, processes, and services. Building on triple helix research, we use entropy statistics to elaborate an indicator of mutual information among these dimensions that can provide indication of reduction of uncertainty. To do so, we focus on the medical context, where uncertainty poses significant challenges to the governance of innovation. We use the Medical Subject Headings (MeSH) of MEDLINE/PubMed to identify publications classified within the categories “Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E) and use these as knowledge representations of demand, supply, and technological capabilities, respectively. Three case-studies of medical research areas are used as representative 'entry perspectives' of the medical innovation process. These are: (i) human papilloma virus, (ii) RNA interference, and (iii) magnetic resonance imaging. We find statistically significant periods of synergy among demand, supply, and technological capabilities (C-D-E) that point to three-dimensional interactions as a fundamental perspective for the understanding and governance of the uncertainty associated with medical innovation. Among the pairwise configurations in these contexts, the demand-technological capabilities (C-E) provided the strongest link, followed by the supply-demand (D-C) and the supply-technological capabilities (D-E) channels.