Analysis of mathematical model for osseous factors in difficult intubation

A two-dimensional model of the factors relevant to difficult laryngoscopy was analysed mathematically to determine clinical implications and limitations. The model describes the space into which the “inevitable residual volume” of the tongue (that part remaining anterior to the blade at laryngoscopy) can be displaced to permit a view of the larynx. Four points are used: the tip of the upper incisors; a point on the anterior airway just above the larynx; the mid-point between the mandibular condyles and the internal mid-point of the symphysis. The number, F, was defined by a formula developed from their spacial relationships. Decreasing F values imply an increasing likelihood of difficult laryngoscopy. The analysis investigated the effects of: translation of individual points; plotting individual point positions for specified F-values; translating adjacent pairs of points; treating any three points as a triangle which rotates about each of its apices; and lastly, translating three points independently. During manipulations the model behaved well mathematically. Single point analysis implied that jaw recession and a non-protruding mandible were comparable in effect. Closing the mouth around the laryngoscope blade maximised F-values. Prominence of the maxilla required greater forward displacement than backward movement of the symphysis for equivalent F-value change. One particular triangular rotation suggested an entirely novel mechanism for difficulty (the “hi-slung mandible”) where the condyles are positioned more rostral than normal. An otherwise normal jaw with this configuration recedes markedly on opening. Further studies are required to validate the model. Accurate quantification of individual factors in difficult laryngoscopy may then be feasible.