Applanation pressure function in Goldmann tonometry and its correction

So far applanation tonometry has not worked out any theoretical basis for correcting the result of intraocular pressure measurement carried out on a cornea with noncalibration dimensions by means of the Goldmann tonometer. All the tables of instrument reading corrections for cornea thickness or cornea curvature radius are based exclusively on measurements. This paper represents an attempt at creating a mechanical description of corneal apex deformation in Goldmann applanation tonometry. The functional dependence between intraocular pressure and the pressure exerted on the corneal apex by the tonometer was determined from a biomechanical model. Numerical GAT simulations, in which this function was also interrelated with the cornea's curvature radius and thickness were run and a constitutive equation for applanation tonometry, i.e. a full analytical description of intraocular pressure as a function of the above variables, was derived on this basis. The correction factors were defined and an algorithm for correcting the measured pressure was formulated. The presented formalism puts the results of experimental tonometry in new light. Analytical correction factors need not to come exclusively from measurements. A geometric interdependence between them and their dependence on pressure have been revealed. The theoretical description of applanation tonometry contained in the constitutive equation consists of a pressure function developed for a cornea with calibration dimensions and a coefficient correcting this calibration function, dependent exclusively on the cornea's actual thickness and curvature radius. The calibration function is a generalization of the Imbert-Fick law.