The feasibility analysis of calculating proptosis by simple Pythagorean theorem

We propose a new method to analyze the feasibility of calculating proptosis on the basis of simple Pythagorean theorem.

This is a non-inferiority trial, and the registration number is ChiCTR1900026490. The absolute value of proptosis of two eyes of patients without eye injury or diseases visiting our clinic from December 2017 to June 2019 was measured by computed tomography, Hertel exophthalmometer, and by simple Pythagorean theorem. With the application of MedCalc software version 19.0.4, the differences between these methods in two eyes were showed by Bland and Altman plot.

A 95% limit of agreement between computed tomography and Hertel exophthalmometer is -0.7 to 0.62 mm in right eye proptosis. A total of 4.44% (4/90) points were outside 95% limit of agreement. Similarly, the same method was used to compare the proptosis between computed tomography and other ways. We also compared the proptosis measured by homolateral and heterolateral simple Pythagorean theorem method in order to find out the consistence between them. The points in all Bland and Altman plots were lower than 5%, which means that the results of comparison between any two methods had a good consistency in the measurement of proptosis of both eyes.

Pythagorean theorem can be applied to evaluate proptosis and has a good consistency comparing with computed tomography and the Hertel exophthalmometer. The method can be used for measuring proptosis of unilateral orbital, maxillofacial trauma, and dysplasia accurately. It is practical in clinical use of proptosis assessment because of its accuracy, reliability, and simplicity.