Categorical Medicine: a mathematical embedding of clinical medicine with applications to headache medicine.
The practice of clinical medicine, diagnosing and treating patients appear to be very different from proving mathematical theorems. Since the 1950s, category theory has been introduced as a potentially unifying theory for disparate disciplines in mathematics. Our project investigates whether it is possible to convert disease classification and iatrogenic interventions, and therefore clinical medicine, axiomatically through the application of category theory. Here we propose two ways of unifying these two seemingly disparate areas of research by interpreting clinical medicine as a mathematical category. Our models allow the practice of medicine to be interpreted from an algebraic topological fashion, thereby opening up the possibility of modeling disease phenotypes/classifications and clinical decision making as topological spaces. We also show that medication intervention and disease classification are inherently linked. We applied the above model to headache medicine as a practical example of the approach. We anticipate that our formulations can be applied to any classifiable arenas of medicine, serving as a theoretical starting point for more sophisticated modeling of clinical medicine mathematically and therefore computationally.