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Applanation pressure function in Goldmann tonometry and its correction

Śródka W.

Acta of Bioengineering and Biomechanics

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2013

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Vol. 15, no. 3

97--106

EN

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.

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Evaluating the material parameters of the human cornea in a numerical model

Śródka W.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 3

77-85

EN

The values of the biomechanical human eyeball model parameters reported in the literature are still being disputed. The primary motivation behind this work was to predict the material parameters of the cornea through numerical simulations and to assess the applicability of the ubiquitously accepted law of applanation tonometry – the Imbert–Fick equation. Methods: Numerical simulations of a few states of eyeball loading were run to determine the stroma material parameters. In the computations, the elasticity moduli of the material were related to the stress sign, instead of the orientation in space. Results: Stroma elasticity secant modulus E was predicted to be close to 0.3 MPa. The numerically simulated applanation tonometer readings for the cornea with the calibration dimensions were found to be lower by 11 mmHg then IOP = 48 mmHg. Conclusions: This discrepancy is the result of a strictly mechanical phenomenon taking place in the tensioned and simultaneously flattened corneal shell and is not related to the tonometer measuring accuracy. The observed deviation has not been amenable to any GAT corrections, contradicting the Imbert–Fick law. This means a new approach to the calculation of corrections for GAT readings is needed.

3

Goldmann applanation tonometry - not as good as gold

Śródka W.

Acta of Bioengineering and Biomechanics

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2010

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Vol. 12, no. 2

39-47

EN

A thesis that linear mechanics does not apply to the analysis of cornea load during Goldmann applanation tonometry measurement and that the concept of surface tension in the lacrimal fluid is an ineffective attempt at circumventing the associated problems is put forward. The fundamental problem emerging during numerically simulated measurement of pressure on the eyeball, whose dimensions are considered to be calibrated, stems from the fact that the flattening of the cornea at the nominal intraocular pressure leads to a critical state in which the shell loses stability. The consequences are far-reaching. The Goldmann tonometer performs well at low intraocular pressure, but above the nominal pressure its readings are always understated. The cause of the error is not the tonometer itself (its readings can be even very accurate). It is shell “solution” called Imbert–Fick law which is faulty.