### Description

Bellhouse and Dore developed an equation for predicting the probability of a difficult endotracheal intubation. They studied a variety of cephalometric measurements taken using lateral radiographs of the head and neck.

Factors associated with difficult intubation when taken together:

(1) reduced atlanto-occipital extension

(2) reduced mandibular space

(3) increased antero-posterior thickness of the tongue

Measurements:

(1) angle in degrees between the following two lines with the neck maximally extended and the mouth open:

(1a) a line running along the occlusal surface of the maxillary teeth to the most anterior aspect of the body of the first cervical vertebra (lower anterior edge in the midline)

(1b) a line running from the most anterior aspect of the body of the first cervical vertebra to antero-inferior border of the body of the sixth cervical vertebra

(2) length of the perpendicular from the lower genial tubercle of the mandible (on lower edge of anterior surface in the midline) to the "line of vision", a line drawn from the upper incisor teeth to the corniculate cartilage (at the posterior aryepiglottic fold on the supero-posterior aspect of the larynx

(3) antero-posterior thickness of the tongue: distance in cm from the front edge of the tongue to the posterior edge

f =

= (-64.44) + (0.4925 * (angle in degrees)) + (17.43 * ((length of perpendicular in cm) / (antero-posterior thickness of the tongue in cm)))

probability of difficult intubation =

= 1 / (1 + EXP(f))

where:

• The form in the paper for the probability equation is 1 / ((1 + EXP)^f). However, in an accompanying example the only form of the equation giving the correct answer is that used.

• Most probability equations are in the form 1 / (1 + EXP((-1) * X)). My guess is that the (-1) is incorporated into the f equation.