2016
DOI: 10.4236/wjm.2016.63005
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On the Validity of the Imbert-Fick Law: Mathematical Modelling of Eye Pressure Measurement

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 … Show more

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Cited by 6 publications
(6 citation statements)
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“…In addition, according to the concept of stress-relaxation and the fact that G ∞ of L65, L60, and R decreased in subsequent turn ( Figure 9 ), we knew that, during a long time, the transient stresses in the strips of the ablated corneas were larger than those in corneal strips without surgery. On the other hand, the formula in [ 32 ], σ c + 2 σ t rt / a 2 = ( r / a ) 2 p , gives the relationship of real IOP and its measurement value. In the formula, σ c is the compressive contact stress, that is, the IOP measurement value, and a , r , t , p , and σ t are the radius of the flattened area on the cornea by σ c , corneal radius, corneal thickness, real IOP, and tensile stress, respectively.…”
Section: Discussionmentioning
confidence: 99%
“…In addition, according to the concept of stress-relaxation and the fact that G ∞ of L65, L60, and R decreased in subsequent turn ( Figure 9 ), we knew that, during a long time, the transient stresses in the strips of the ablated corneas were larger than those in corneal strips without surgery. On the other hand, the formula in [ 32 ], σ c + 2 σ t rt / a 2 = ( r / a ) 2 p , gives the relationship of real IOP and its measurement value. In the formula, σ c is the compressive contact stress, that is, the IOP measurement value, and a , r , t , p , and σ t are the radius of the flattened area on the cornea by σ c , corneal radius, corneal thickness, real IOP, and tensile stress, respectively.…”
Section: Discussionmentioning
confidence: 99%
“…The eyeball can be regarded as a sphere filled with liquid and surrounded by a wall. The pressure inside therefore equal to the counter pressure which flattens the membrane (Castro et al 2016). Thus, the estimation of the IOP follows the equation:…”
Section: Goldmann Applanation Tonometrymentioning
confidence: 99%
“…Empirical studies suggest a correction factor for applanation IOP readings of 0.19 to 1 mm Hg per 10-µm deviation from the average CCT [5]. Therefore, in individuals with thick corneas, the IOP measurement by using GAT may show falsely high readings and low readings for thin corneas [6]. A device called a tonometer is used to measure IOP.…”
Section: Introductionmentioning
confidence: 99%
“…A device called a tonometer is used to measure IOP. The instrument considered to be the "gold standard" by the ophthalmic community, and the focus of this study, is the Goldmann Applanation Tonometer ("GAT") [6]. The normal range of the intraocular pressure in human is 10 -20 mm Hg.…”
Section: Introductionmentioning
confidence: 99%
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