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On the Validity of the Imbert-Fick Law: Mathematical Modelling of Eye Pressure Measurement
Gonzalez Castro, Gabriela Fitt, A.D. Sweeney, John
Gonzalez Castro, Gabriela
Fitt, A.D.
Sweeney, John
Publication Date
2016-03-23
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© 2016 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
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Accepted for publication
2016-03-20
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Abstract
Ophthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular
pressure (IOP) measurements. It measures the force required to press a flat disc against
the cornea to produce a flattened circular region of known area. The IOP is deduced from this
force using the Imbert-Fick principle. However, there is scant analytical justification for this
analysis. We present a mathematical model of tonometry to investigate the relationship between
the pressure derived by tonometry and the IOP. An elementary equilibrium analysis suggests that
there is no physical basis for traditional tonometric analysis. Tonometry is modelled using a hollow
spherical shell of solid material enclosing an elastic liquid core, with the shell in tension and
the core under pressure. The shell is pressed against a rigid flat plane. The solution is found using
finite element analysis. The shell material is anisotropic. Values for its elastic constants are obtained
from literature except where data are unavailable, when reasonable limits are explored.
The results show that the force measured by the Goldmann tonometer depends on the elastic constant
values. The relationship between the IOP and the tonometer readings is complex, showing
potentially high levels of inaccuracy that depend on IOP.
Version
published version paper
Citation
Gonzalez Castro G, Fitt AD and Sweeney J (2016) On the Validity of the Imbert-Fick Law: Mathematical Modelling of Eye
Pressure Measurement. World Journal of Mechanics. 6: 35-51.
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