A similarity function to evaluate the orthodontic condition in patients with cleft lip and palate

The objective of this work is the modeling of a similarity function adapted to the medical environment using the logical-combinatorial approach of pattern recognition theory, and its application to compare the orthodontic conditions of patients with cleft-primary palate and/or cleft-secondary palate congenital malformations. The variables in domains with no a priori algebraic or topological structure are objects whose similarity or difference is evaluated by comparison criteria functions. The range of these functions is an ordered set normalized into the unit interval, and they are designed to allow differentiation and non-uniform treatment of the object-variables. The analogy between objects is formalized as a similarity function that stresses the relations among the comparison criteria and evaluates the partial descriptions (partial similarity/difference) or total descriptions (total similarity/difference) of the objects. For the orthodontic problem we defined a set of 12 variables featuring the unilateral/bilateral fissures, the conditions of maxilla, premaxilla, mandible and patient's bite. The comparison criteria (logical for malocclusion, fuzzy for maxillary collapse unilateral/anteroposterior and for overbite, and Boolean for protrusive/retrusive premaxilla conditions) were assigned a relevance factor based on the orthodontist accumulated knowledge and experience. The modeling of the similarity function and its effectiveness in comparing orthodontic conditions in patients are illustrated by the study of four clinical cases with different clefts. The results through similarity are close to the expected ones. Moreover evaluated at different moments it allows to assess the effect of treatment in a single patient, hence providing valuable auxiliary criteria for medical decision making as to the patient's rehabilitation. We include the potential extension of the methodology to other medical disciplines such as speech therapy and reconstructive surgery.