Matrix and Graphical Representation of the Primary Headache Syndromes in the International Classification of Headache Disorders (ICHD3): A Basis for Automated Diagnosis and Analysis of Criteria.

Structured AbstractO_ST_ABSObjectiveC_ST_ABSWe represent primary headaches of the ICHD3 in matrix form and show that this representation allows for automated diagnosis as well as additional insights into headache classification. MethodsEach diagnosis in the ICHD3 is defined by a list of characteristics; combinations of characteristics form phenotypes. Multiple phenotypes may fit a given diagnosis. We first translated all characteristics for primary headache diagnoses in the ICHD3 into true/false statements. We generated a matrix of valid ICHD3 diagnosis as follows: O_LIEach row of the matrix represents a phenotype. C_LIO_LIEach column of the matrix represents a characteristic. C_LIO_LIIf any phenotype contains a characteristic, then that element is encoded as 1. Otherwise, it is encoded as 0. C_LI From this matrix, we calculated its bipartite projection and Markov cluster. We also row reduced to derive the basis vectors that span the space of all headache phenotypes. ResultsChronic migraine diagnoses as well as the characteristics "greater than 15 days per month" and "more than 3 months" have the strongest associations based on bipartite projection. Markov clustering yields 64 clusters. These clusters can be organized by ICHD3 diagnoses and demonstrates the level of fragmentation of individual diagnosis in the classification: Migraine is composed of 1 cluster, for example, whereas paroxysmal hemicrania can be broken down into 9 clusters. Finally, row reduction of our matrix yields 63 basis vectors, implying that all headache diagnoses in the ICHD3 can be represented as linear combinations of 63 characteristics. These 63 characteristics corresponds to the following: duration, frequency, aura characteristics, size/location, laterality, clearly remembered onset, TAC features, total number of episodes, severity, nausea/vomiting, photophobia, pulsating, alleviation by triptans, and association with awakening, sexual activity, physical activity, temperature, compression or traction, coughing. ConclusionOur result demonstrates that ICHD3 is a mathematical entity and that headache diagnoses exist in a 63-dimensional vector space. This mathematical embodiment of classification allows us to conduct 1) large scale systematic investigations of relationships between headache and phenotypes, 2) generate a graphical representation of characteristics and phenotypes and 3) improves diagnostic accuracy and efficiency.