Abstract text (incl. figure legends and references)
Introduction: Trying combinations of medications in headaches is often inevitable in clinical practice. However, switching multiple medications concurrently may expose patients to unwanted side effects and introduce confusion in determining efficacies of individual medications. This concern raises the question: Is there a way of systematically trying all possible "pick two" combinations of abortive/preventives while adjusting only one medication at a time? Methods: We take as inputs non-interacting lists of abortive medications based on DrugBank from Kayter and Zhang's "Non-interacting, Non-opioid, and Non-barbiturate Containing Acute Medication Combinations in Headache". We generate a mathematical graph using the following definitions: 1) Nodes are all "pick two" medication combinations. 2) An edge exists between two nodes if there is only 1 drug difference between two nodes. We then look for a "Hamiltonian path" for this graph using brute force strategy. (A Hamiltonian path is a way of visiting each nodes in a graph only once by traversing through edges.) A graph is generated using the same definition for "pick two" prevention medications using non-interacting data from Dave et al (AHS Scientific 2022). Results: Hamiltonian path exists for prevention/abortive medications. Table 1 and 2 shows the Hamiltonian path for "pick two" abortives as well as preventive, respectively. (These table results are simplified by condensing some similar medication classes.) Every element in each table differs from the next by only 1 medication. Notice that the last element in the prevention list forms an edge with the first element, therefore forming a cycle. Detailed versions of hamiltonian paths for individual medications will be presented in the meeting. Conclusion: It is possible to try all possible non-interacting "pick two" medication combinations by adjusting only one medication at a time. This project is also the first known use of Hamiltonian path in medicine.