Analysis of the pressure-volume relationship for the eyeball loaded by a flat stamp on the basis of a two-segment elastic model

Moiseeva, I. N.; Stein, A.

doi:10.1134/s0015462811050012

Cited by 9 publications

(17 citation statements)

References 8 publications

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“…In [4], we proposed the maximally simple and general representation of the cornea by a twodimensional surface that does not resist bending. In the same study, we proposed to take into account the other eyeball tissues (sclera, etc.)…”

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Investigation of the pressure-volume relationship for the eyeball loaded by a thin rod

Moiseeva

Stein

2013

Fluid Dyn

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The static problem of loading the eyeball by a thin cylindrical cornea-deforming rod is solved for obtaining data on the mechanical properties of the eye in clinical examination. The analysis is carried out within the framework of a simple model which treats the cornea as a soft shell and takes into account the elastic properties of the sclera and tissues surrounding it by introducing an elastic constraint between the intraocular pressure and the scleral part of the intraocular volume. The dependence of the intraocular volume on the pressure and the load applied, as well as on the elastic characteristics of the system, is investigated. The problem of relationship between the intraocular pressure and the load at a constant volume is considered. It is shown that loading the same eye by thin rods and flat stamps of different weights makes it possible to find in clinical examination the individual elastic characteristics of the eyeball and the pressure in the unloaded eye.

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Investigation of the pressure-volume relationship for the eyeball loaded by a thin rod

Moiseeva

Stein

2013

Fluid Dyn

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“…At the same time, it does not coincide with Friedenwald rigidity also determined by Schiötz tonometry and differs from it in calculation method, dimension and distinct physical sense. On the other hand, coefficient γ M , determined using Maklakov tonometry with different weights appears to be significantly dependent on both structural rigidities E c and E s , but dependence on corneal rigidity is stronger [10,11]. These model calculations have formed a basis for the development of a method to determine relative contribution of changes in elastic properties of the cornea and the sclera to the biomechanical component of glaucomatous damage related to the state of the ocular corneoscleral shell.…”

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“…As stated above, γ S characterizes mainly the biomechanical status (rigidity) of the sclera [10,11].…”

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“…Then elastic rise coefficient γ M was calculated as the mean of two values γ M1 and γ M2 determined using the formulas: γ M1 =(p 2 -p 1 )/ (G 2 -G 1 ) and γ M2 =(p 3 -p 2 )/(G 3 -G 2 ). As mentioned above, γ M characterizes mainly the biomechanical status (rigidity) of the cornea [10,11].…”

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“…In the calculations [9][10][11] Elastic rise coefficients calculated according to different tonometer types for the same eye turn out to be different and are not expressed one through another, which is due to their different dependence on the two structural elastic parameters: rigidity of the cornea (E c ) and rigidity of the sclera (E s ) [10,11]. In particular, as our previous calculations show, elastic rise coefficient γ S determined using Schiötz tonometry data turned to depend little on corneal rigidity and, thus, can serve as a characteristic of scleral rigidity E s .…”

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Biomechanical Criteria for Estimating the Risk of Primary Open-Angle Glaucoma Progression

Iomdina¹,

Киселева²,

Moiseeva³

et al. 2016

Sovrem Tehnol Med

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The aim of the investigation was to identify new biomechanical parameters characterizing elastic properties of the ocular corneoscleral shell and to determine their significance for estimating the risk of primary open-angle glaucoma (POAG) progression.Materials and Methods. The study involved 41 patients (43 eyes) aged 55 to 72 (mean age 64.0±4.0 years) with non-operated POAG, including 20 eyes with stage I POAG and 23 eyes with stage II, as well as 15 patients of the same age group with no eye pathology (except for age-related cataract) who served as control. The examination included Maklakov elastic tonometry with three different weights, differential Schiötz tonometry using a GlauTest 60 tomograph (Russia), optic nerve imaging using HRT3 (Germany), and static Humphrey (Germany) perimetry. All patients were re-examined 18 months after the initial examination.Results. The biomechanical parameters were calculated based on mathematical modeling using elastic tonometry and differential tonometry data according to the method proposed by the authors. The value of a new parameter, elastic rise coefficient γ M , characterizing mainly the rigidity of the cornea and determined using Maklakov elastic tonometry data averaged 0.88±0.20 mm Hg/g in stage I POAG and 0.80±0.04 mm Hg/g in stage II, whereas the control group showed an average of 0.86±0.07 mm Hg/g. At the same time, we revealed increase in the other biomechanical parameter, elastic rise coefficient γ S , characterizing mainly the rigidity of the sclera and determined according to Schiötz elastic tonometry data. Its value amounted to 1.65±0.25 mm Hg/g for stage I POAG and 1.88±0.13 mm Hg/g for stage II, with the mean of 1.47±0.10 mm Hg/g in the control group. It was found that with the value К=γ S /γ M (an index showing the individual ratio of scleral and corneal rigidity) increasing above the threshold level clinical signs of glaucomatous process progression were observed.Conclusion. The results indicate growing imbalance between biomechanical parameters of the sclera (γ S ) and the cornea (γ M ) during POAG development. The ratio of these parameters (K=γ S /γ M ) can serve as a measure of risk in progression of glaucomatous process related to the change in the state of the ocular corneoscleral shell.

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A simple model for estimating the active reactions of embryonic tissues to a deforming mechanical force

Мансуров

Stein

Beloussov

2012

Biomech Model Mechanobiol

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Active reactions of embryonic tissues to mechanical forces play an important role in morphogenesis. To study these reactions, experimental models that enable to evaluate the applied forces and the deformations of the tissues are required. A model based upon the active intrusion of a living early gastrula Xenopus embryo into a tube half the embryo in diameter is described. The intrusion is initially triggered by a suction force of several dozen Pa but then continues in the absence of external driving force, stopping immediately after the entire embryo has penetrated into the tube. The process can be stopped by cytoskeletal drugs or by the damage of the part of the embryo still non-aspirated and is associated with the transversal contraction and meridional elongation of the non-aspirated part of the embryo surface and quasi-periodic longitudinal contractions/extensions of the cells within the part already aspirated. We suggest that this reaction is an active response to the embryo deformation and discuss its morphogenetic role. The problem of estimating the elastic modules of embryonic tissues is also discussed.

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Analysis of the pressure-volume relationship for the eyeball loaded by a flat stamp on the basis of a two-segment elastic model

Cited by 9 publications

References 8 publications

Investigation of the pressure-volume relationship for the eyeball loaded by a thin rod

Investigation of the pressure-volume relationship for the eyeball loaded by a thin rod

Biomechanical Criteria for Estimating the Risk of Primary Open-Angle Glaucoma Progression

A simple model for estimating the active reactions of embryonic tissues to a deforming mechanical force

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