Abstract
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.
Résumé
Un modèle bi-dimensionnel propre aux facteurs pertinents à la laryngoscopie difficile est analysé mathématiquement dans le but de determiner ses applications cliniques et ses limites. Le modèle décrit l’espace dans lequel le volume résiduel de la langue (la partie excédentaire de la langue antérieure à la lame du laymgoscope) peut être déplacé pour permettre la vision du larynx. On utilise quatre points: l’extrémité des incisives supérieures; un point situé dans les voies aériennes antérieures juste au-dessus du larynx; un point médian situé entre les condyles mandibulaires; et, finalement, le point médian de la symphyse. Le nombre F est défini par une formule développée à partir de leur relation spatiale. La diminution les valeurs du F signifie une laryngoscopie difficile probable. L’analyse étudie les effets de la translation des points individuels; la transposition des points individuels pour des valeurs données de F; la translation de paires de points adjacentes; la transformation d’un des trois points comme un triangle qui pivote sur chacun de ces sommets et finalement la translation individuelle de chacun des points. Le modèle se comporte très bien pendant ces manipulations. L’analyse des point isolés laisse supposer que la récession de la mâchoire et l’absence de protusion du mandibule ont un effet identique. La fermeture de la bouche sur le laryngoscope augmente les valeur du F. La prominence de la mâchoire nécessite un déplacmenet antérieur plus grand que le mouvement postérieur de la symphyse pour des valeurs equivalentes du F. Une rotation triangulaire particulière suggère un mécanisme de difficulté entièrement nouveau (le mandibule haul suspendu) lorsque les condyles occupent une position plus rostrale que la normale. Avec cette configuration, une mâchoire ordinairement normale se rétracte considérablement à l’ouverture. Des études supplémentaires sont nécessaires pour valider ce modèle. Une quantification des facteurs individuels particuliers à la laryngoscopie difficile deviendrait alors réalisable.
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Charters, P. Analysis of mathematical model for osseous factors in difficult intubation. Can J Anaesth 41, 594–602 (1994). https://doi.org/10.1007/BF03009999
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DOI: https://doi.org/10.1007/BF03009999