A Mathematical Model of the Goldmann Applanation Tonometry

Abstract The aim of this study is to present mathematical formulas describing all forces involved in Goldmann applanation tonometry to calculate the measurement error of the true intraocular pressure as a function of the surface tension of the tear film, the corneal modulus of elasticity, the corneal thickness and the average apical corneal radius of curvature.The portion of the indented cornea has been modeled as a shell having a uniform thickness. To assess corneal behavior during applanation tonometry, the physical equations of the deformation of a symmetrical shell due to an applanating force as well as the surface tension of the tear film and intraocular pressure have been used.Formulas to calculate the true intraocular pressure, the pulling force of the tear film on the tonometer cone and the measurement error with the Goldmann applanation tonometer are provided. These mathematical models can be used to estimate the true intraocular pressure of each single patient by correcting the pressure measured with Goldmann applanation tonometry with enhanced accuracy.