“A dual-applanation physical model to improve accuracy in goldmann tonometry by accounting for corneal biomechanics”

Purpose We developed and analytically evaluated a novel physical-mathematical model aimed at quantifying and minimizing the systematic error ( ERR ) between true intraocular pressure ( IOPT ) and that measured by Goldmann applanation tonometry ( IOPG ), by incorporating patient-specific corneal biomechanical properties. Methods We constructed a model based on physical force balance, simulating the applanation of the cornea as a deformable elastic shell influenced by intraocular pressure and external forces. Four distinct forces were mathematically defined and computed: F1 – intraocular pressure acting on the posterior corneal surface; F2 – elastic resistance of the corneal tissue to flattening; F3 – adhesive force due to tear film surface tension; F4 – the net force applied by the examiner and recorded by the GAT device. The model integrates key anatomical and biomechanical parameterscentral corneal thickness, mean apical curvature radius, and corneal elastic modulus—to quantify ERR as a function of individual variability. These parameters are derived from two sequential applanation measurements ( IOPG 0 and IOPG 1 ), acquired through a custom-designed dual-zone applanation prism. Results Simulations demonstrated that ERR increases proportionally with central corneal thickness and elastic modulus, and decreases with increasing corneal curvature radius. For standard corneal values (thickness: 0.536 mm ; curvature: 7.15 mm ; elasticity: 0.16 MPa ), the model closely approximates IOPT . Deviations from these reference values result in systematic over- or underestimation of IOPG . Conclusion This analytical model provides a transparent, biomechanically grounded method for correcting GAT measurements and estimating true IOP with improved precision. It highlights the critical influence of patient-specific corneal properties and lays the foundation for personalized tonometry in clinical practice.