Open access peer-reviewed chapter

Biomechanics of Eye Globe and Methods of Its Study

Written By

Irina Bubnova

Submitted: 29 April 2018 Reviewed: 14 July 2018 Published: 05 November 2018

DOI: 10.5772/intechopen.80327

From the Edited Volume


Edited by Hadi Mohammadi

Chapter metrics overview

1,126 Chapter Downloads

View Full Metrics


Knowledge of biomechanical properties of eye globe is necessary both for correct selection of candidates for refractive surgery and right choice of operative intervention parameters. No less important, it is for corneal ectatic disease diagnostics and monitoring. Also it gives inestimable contribution for interpretation of intraocular pressure (IOP) indices especially in cases with irregular eye shape or after past corneal surgical procedures. Moreover, it allows studying injury mechanism by glaucoma process on optic nerve head fibers. Above it, scleral biomechanical properties research is necessary for the investigation of pathophysiologic factors of myopia manifestation and progression. This chapter is devoted to review of existed to date methods of study of eye fibrous tunic biomechanical properties. It describes mathematical, experimental, and clinical models provided evaluation of unsearchable by direct measurement parameters. It also observes effective technics of impact on both sclera and cornea with the aim of correction of its biomechanical condition.


  • corneal biomechanics
  • refractive surgery
  • keratokonus
  • IOP

1. Introduction

The cornea and the sclera are two conjugated quasi-spherical segments with unequal curvature radii; together they form corneoscleral (fibrous) tunic—the supporting structure of the eye capsule. Their mechanical properties play a crucial role of holding together the inner ocular structures. Despite them both being composed of connective tissue, they differ in physical (particularly, optical) and biomechanical properties [1].

The cornea is the anterior part of the fibrous tunic of the eyeball, and it takes up 1/6 of its length. Despite it being relatively thin, its main function is protection—assured by its high durability. But the cornea also participates in light ray refraction, making up an important part of the visual apparatus; as such, it is characterized by high optical homogeneity and complete transparence.

The cornea is an anisotropic, inhomogeneous structure; it mainly consists of highly specific connective tissue formed by parallel collagen fibrils that extend from one limb to another and act as load supporting elements [2].

The sclera takes up the other 5/6 of the eye length and represents the posterior part of the fibrous tunic of the eyeball. Scleral tunic is the main supporting structure of the eyeball; it consists of dense collagen fibers. In contrast to cornea, the sclera has high dispersive power due to its chaotically distributed fibrils and fibers, which prevents light from entering the eye cavity from the side. In natural conditions, in the living eye, scleral elements are constantly in a strain-stress state determined by intraocular pressure and mechanical properties of the scleral tissue, as well as by anisotropy and inhomogeneity of these properties [3].

Studying the biomechanical properties of the cornea is relevant for certain clinical needs associated with the appearance of new biomechanics examination methods, as well as the need to diagnose and monitor ectatic diseases of the cornea, to adequately select the parameters for keratorefractive surgeries, to correctly interpret the intraocular pressure (IOP) values, and, consequently, to appropriately assess IOP and monitor glaucomatous process.

In addition, conducting studies on the biomechanical properties of the sclera is a necessary step in the research of pathogenic factors relevant for occurrence and progression of myopia, as well as finding effective means and methods of influencing the sclera in order to correct its biomechanical state.

However, the lack of standardized terminology and uniform classification hurts the ability to compare research results and consequently hinders their introduction into the knowledge area of ophthalmology.


2. Classification of approaches to study the biomechanics of the eye

In accordance with different approaches, eye biomechanics can be divided into the following types:

  1. theoretical;

  2. physical (i.e., experimental); and

  3. clinical.

2.1.  Theoretical biomechanics of the eye

Theoretical biomechanics is a science that employs mathematical methodology and mathematical analysis. As applied to ophthalmology, it handles with specific physical constants characterizing elasticity, strength, and other mechanical parameters of the tissues (usually measured in vitro).

The main theoretical approach is mathematical modeling. The research may target separate structures of the eyeball and the tunic, or the eye in its entirety. It can also include modeling of physiological or pathological processes, changes induced by specific stimuli or effects of surgical treatment.

The results obtained from modeling can be used in experimental and clinical studies. In turn, all models are based on the figures acquired in experiments or from clinical diagnostic.

Disadvantages of the theoretical approach in studying eye biomechanics are associated with structural complexity of the eyeball, inhomogeneity, and variability of morphology of the ocular structures, and dependence on the technological advancement of experimental and clinical research methods.

2.2  Physical (experimental) biomechanics of the eye

Experimental biomechanics of the eye is based on studying individual tissues and the eyeball as a whole in vitro or by conducting animal experiments using physical methods. It is the most developed subdiscipline of biomechanics with many years of research history. Capabilities of the approach are limited by post-mortem changes in eye tissues, and anatomical and physiological differences between humans and animals. The main purpose of experimental studies is to find potentially useful methods of studying biomechanical properties of eye tissues in clinical environment and to acquire data for mathematical modeling. The main advantages of experimental researches are the absence of restrictions for employed methods and approaches, and the choice of which is only limited by technological and scientific advancement.

Methods of experimental biomechanics allow measurement of a big number of physical parameters of the cornea:

  • Young’s modulus (E),

  • Poisson’s ratio (μ),

  • Durability (σ),

  • Deformation capacity (Σ), etc.

However, they do not fully reflect the properties of fibrous tunic of the eye in vivo.

2.3.  Clinical biomechanics of the eye

Clinical biomechanics of the eye studies the influence of biomechanical properties of the fibrous tunic on the results of diagnostics, development, and treatment of various eye diseases. Clinical biomechanics operates on data obtained with specialized examination methods used in ophthalmology (in vivo) that characterize biomechanical properties of the fibrous tunic. Its research subject is strictly the eyeball as a whole, only allowing arbitrary delineation of the internal structures. This complicates the interpretation of data. However, in order to improve diagnostics and treatment of eye diseases, clinical methods for eye biomechanics need to have higher priority in research and development.

The following corneal parameters can be measured clinically:

  • Friedenwald’s rigidity coefficient;

  • Corneal hysteresis;

  • Corneal resistance factor;

  • Coefficient of elasticity;

  • Corneal deformation.

The biggest number of already existed studies are dedicated to investigation of biomechanical properties of the cornea, which is probably related to the specifics of corneal structure, or to its accessibility for examination.


3. Theoretical (mathematical) biomechanics

The originator of mathematical approach to study biomechanical properties of the cornea was F.A. Rachevsky. In 1930, in his theoretical study, he pointed “…for the first time at the paramount importance of the radius of the corneal curve and especially of its thickness for specific results of intraocular pressure tonometry.” Besides that, he proved mathematically that under effect of external and internal forces, tangentially directed stress occurs in the cornea, particularly during applanation tonometry [4].

At present, the research of corneal biomechanics is conducted in two main directions. Mathematical modeling is generally used for the calculation of parameters and prediction of results of keratorefractive surgeries [5, 6, 7, 8], as well as for the determination of possible procedural errors of applanation tonometry methods when biomechanical properties changed as the result of a surgery or a disease [9].

The main obstacle for proper mathematical modeling is anisotropy of the cornea. The majority of the proposed models does not consider it, which limits their application in practical ophthalmology [10, 11, 12].

According to Pinsky et al., the anisotropy of the cornea primarily depends on its structural features, that is, specific architectural organization of collagen fibers [13]. X-ray structural analysis revealed that collagen fibrils of the central area have orthogonal orientation predominantly in vertical and horizontal directions, while fibrils of the periphery have tangential orientation [14]. Pinsky et al. developed a mathematical model for corneal anisotropy mechanics that accounts for these findings [13]. Based on the finite element method, the model allows predicting biomechanical response of the cornea to tunnel cutting, radial keratotomy, and LASIK [15, 16, 17].

In order to determine the possible error margin of applanation tonometry methods, several mathematical models have been developed [18]. Liu et al. used mathematical modeling to study isolated effects of various biometric and biomechanical parameters of the cornea on Goldmann tonometry readings [19]. Kwon et al. developed a mathematical model demonstrating the need to take into account not only corneal thickness, but also its biomechanical properties when interpreting Goldmann tonometry readings [20].


4. Physical (experimental) biomechanics

4.1.  Normal (intact) cornea

Experimental studies based on extensiometry revealed distinguishing biomechanical anisotropy and heterogeneity of the cornea. Corneal material acquired with a radial cut has the best durability and margin of deformation capacity. Those parameters decrease with distance from the radial direction. Corneal material stretched tangentially shows approximately the same elastic properties along the corneal disc. The samples stretched radially appeared to have the highest rigidity. In the course of the study, Poisson’s ratio was determined for various parts of the cornea. This ratio characterizes the transverse deformation lateral to stretch direction, for radial direction, it was in the range of 0.445–0.450, and for tangential direction, it was in the range from 0.290 to 0.310 (middle periphery) and from 0.340 to 0.350 (perilimbal) [21, 22].

A variety of studies is dedicated to measuring the main elastic and strength properties of the cornea, but analysis of the data shows that isolated corneas exhibit big spread in the values—from 0.3 to 13.6 MPa. The phenomenon can be attributed to different experimental conditions and nonlinear nature of biomechanical properties of corneal material [23, 24, 25, 26]. Andreassen et al. studied the biomechanics of corneal discs with extensiometry; the discs were taken from patients with keratoconus after they underwent penetrating keratoplasty. The study revealed significant decrease of mechanical strength properties in pathologically altered corneas [27].

Soergel et al. used dynamic mechanical spectroscopy to evaluate viscoelastic properties of the cornea in experimental environment. They found that elastic and shearing deformation depend on the hydration, time elapsed after death, and temperature of the tissue [28].

Wang et al. calculated Young’s modulus by measuring the speed of ultrasound transmission through cadaver cornea and processing the data with Fourier analysis [29].

Like ultrasound spectroscopy, Brillouin microscopy can determine intrinsic viscoelastic properties decoupled from the structural information and applied pressure. In contrast, it can measure the local acoustic properties with much higher spatial resolution and sensitivity, and the measurement is performed optically without the need for acoustic transducers or physical contact with the cornea [30].

One of the techniques, holographic interferometry, is used to calculate Young’s modulus. The method is to some degree similar to videokeratography, that is, holographic technologies are used to examine the changes in corneal surface. A study conducted on an intact bull’s cornea showed Young’s modulus being two orders lower than when measured in an experiment with corneal tissue samples. The authors summarized that localization and hydration level plays the primary roles during measurement. This method, however, is limited in terms of practical use due to requiring maximum permissible laser emission in order for the resulting images to be high quality [31].

4.2.  Cornea after refractive surgery

Some studies showed significant increase of tangential elasticity of the cornea after it was incised with radial cuts (up to 46.5% with an incision depth of 0.6 mm), that is, in the direction of the lesser material rigidity [32]. In certain cases, the changes led to severe complications in the long-term postoperative period. Particularly, it manifested as a significant decrease of eyeball’s resistance to trauma with potential disruption of corneal cicatrices and loss of membranes [33].

Luminescent polariscopy revealed that after radial keratotomy, the main mechanical strain fell on the middle periphery of the cornea, particularly on the bottom of keratotomic incisions. An increase of intracameral pressure (analogue to intraocular pressure) raises the strain on peripheral part of the cornea and off-loads its central part, which can cause hypermetropic shift in refraction [34].

However, with the appearance and widespread implementation of excimer laser technologies for correction of refraction errors, such risks have greatly decreased. It can be attributed to different mechanisms of corneal refraction change, that is, its thinning in the central area.

Experimental studies on biomechanical properties of the cornea after excimer laser intervention indicate that thinning of the cornea in 6.0-mm optic zone for more than 15–20% results in significant changes of its mechanical properties. In terms of clinical relevance, the most meaningful change appears to be the significant (mean 20%) decrease of breaking load for experimental samples in comparison to the control samples. Additionally, changes in deformation properties of the cornea after laser ablation should also be taken into consideration, which manifested as lowered amount of movement the punch had to do before the cornea broke in experimental eyes in comparison to the control subjects in average by 10.72% [35].

However, the mechanical properties of the data obtained using an isolated cornea cannot objectively reflect the parameters of the tissues in natural environment. Adequate information on the biomechanical state of the cornea can only be obtained from a living eye.


5. Clinical biomechanics

5.1. Normal (intact) cornea

Clinical studies on the biomechanical properties of the relatively healthy cornea have been conducted since the middle of the twentieth century, but those methods remained widely unused due to various reasons.

In 1937, Friedenwald suggested that rigidity coefficient could be calculated based on a logarithmic dependence between IOP changes and eye volume employing differential tonometry with Schiotz tonometer [36]. Friedenwald depicted the relation between pressure and volume in a coordinate system. As was shown by further clinical studies, the proposed coefficient strongly depends on the corneal curvature and thickness, as well as on the IOP level [37]. According to research results, the parameter suggested by Friedenwald—the rigidity coefficient—was inaccurate in eyes with deviations in biomechanics (thickness and curvature) from the norm. It was also strongly influenced by IOP.

In 1936, S. F. Kalfa proposed a method of elastotonometry, that is, differential tonometry with four Maklakov tonometers weighing 5, 7.5, 10, and 15 g. Connecting the dots marked on a coordinate system forms an elastotonometric curve, which appears ascending line. The difference in mm Hg between the starting and ending points of the curve, that is, between IOP value obtained using 5.0 and 15.0 g tonometers, is called elasto-ascent. Essentially, Friedenwald’s rigidity coefficient and S. F. Kalfa’s elasto-ascent are different expressions of the same thing. In norm, the two figures are closely related, albeit not functionally [38].

There are a number of techniques described by their authors as potential intravital methods for examination of biomechanical properties of the cornea, but they have not been adopted into clinical practice: electronic speckle interferometry [39], dynamic cornea visualization [40], corneal applanation and indentation [41], ultrasound elastometry [42], and photoelasticity method [43].

As an alternative to holographic interferometry, a noncontact, nondisruptive method of electronic speckle interferometry was suggested; it is equally sensitive because it employs close wavelength for measurement. Advantages of the method include the absence of requirement of photographic hologram recording, which simplifies the procedure and enables real-time acquisition of corneal surface shift data using a television camera. The method is recommended for evaluation of changes in corneal biomechanics after excimer laser refractive surgery [39].

Grabner et al. proposed a method of dynamic visualization of the cornea. It involves applying dosed pressure to the central area of the cornea during videokeratography by means of a special indenter and subsequent analysis of the topographic pattern. As the result, high correlation between the bending curve and depression depth was found. The form of the curve was noted to be affected by central corneal thickness, intraocular pressure, and patient age. Moreover, bending curves were different in keratoconus patients, as well as in patients who had underwent keratorefractive surgeries [40].

Chang et al. studied biomechanical properties of the cornea in vivo using corneal applanation and indentation on rabbit and human eyes, regarding the cornea as a transversely isotropic material. The study showed normal Young’s modulus to vary from 1 to 5 MPa and transverse shift modulus from 10 to 30 KPa [41].

Some authors used photoelasticity method to evaluate mechanical stress in the cornea involving the measurement of its polarization and optical properties [43].

Scoping a large amount of clinical data, Edmund calculated Young’s modulus adhering to the hypothesis that the final form of cornea is the outcome of counteraction between tissue elasticity and intraocular pressure. The modulus values were significantly lower in keratoconus eyes when compared to norm. The study also showed significant difference between healthy and ectatic patients in relative distribution of stress in the central and peripheral areas of the cornea, which can help with the understanding of keratoconus pathogenesis. However, this method generally does not find much use in clinical practice [44].

The one method most widely used in present day clinical practice involves ocular response analyzer (ORA)—a device that analyses corneal biomechanical properties based on bi-directional corneal applanation by an air pulse [45]. The method’s authors proposed to evaluate biomechanical response of the cornea by quantifying the differential inward and outward corneal response to an air pulse and thus obtaining two parameters—corneal hysteresis (CH) and corneal resistance factor (CRF). Corneal hysteresis characterizes the viscoelastic properties of the cornea responsible for the partial absorption of the air pulse energy. Corneal resistance factor is a derived parameter with high correlation to central corneal thickness that reflects the elastic properties of the cornea.

Multiple studies have confirmed the usefulness of bi-directional corneal applanation for the evaluation of biomechanical properties of the cornea: they rise with the increase of the corneal thickness [46, 47]. Corneal hysteresis was in the average 10.8 ± 1.5 mm Hg and corneal resistance factor—11.0 ± 1.6 mm Hg. Statistically, a significant difference in the mean values of CH and CRF between groups of varying age was absent, with the exception of patients older than 60 years for whom the values were on lower. It is possible that the phenomenon reflects the changes in elastic properties of the cornea associated with age, but the authors also note the potential influence of other parameters (intraocular pressure and anterior-posterior axis length) that were disregarded in the study [48]. The comparison of CH and CRF in children and adults did not reveal any age-related differences [49].

Studying the diurnal variations in CH and CRF parameters revealed their hourly stability, while minor changes observed between the morning and evening measurements can be explained by diurnal IOP fluctuations [50]. CH and CRF correlated strongly with corneal thickness and to a lesser degree with an amount of astigmatism. No correlation was found with keratometry, age, gender, spherical equivalent, or IOPcc [51]. Moreover, ORA shows good repeatability of biomechanical and tonometry measurements [52].

Avetisov et al. studied the possibility of applying the dynamic pneumo-impression of the cornea approach to the existing corneal biomechanical properties analyzer (ORA). The fundamental principle was that at the curvature start point laying on the border of the impression area, the pneumatic jet is subject to the counter-force of IOP and corneal elasticity, in equal amounts. At the moment of maximum impression, the pneumatic jet is mainly countered by corneal elasticity—due to the maximum deformation of the cornea. As the result, a parameter named elasticity coefficient was calculated characterizing the elastic behavior of the cornea regardless of the IOP level [53].

The same principle was used in CorVis device (Oculus, Germany), in which corneal deformation responding to a pulse of air is monitored with high-speed Scheimpflug camera. The device can help to measure a whole range of parameters that characterize the particularities of corneal deformation during the impression process. It records the process between the initial and the second applanations involving the cornea recovering its initial form, captures the maximum indentation point, and measures IOP [54, 55].

5.2.  Keratoconic cornea

Intravital measurement of biomechanical properties of the cornea in keratoconus patients performed with dynamic bi-directional pneumo-applanation showed lower CH and CRF values than in healthy eyes. Apparent negative correlation between the CH and CRF parameters and the degree of keratoconus were also evident [56].

Additionally, CH was significantly higher than CRF in the keratoconus group. The authors suggested the CH decrease of less than 8 mm Hg in conjunction with positive CH-CRF difference to be considered a stronger sign of keratoconus than isolated decrease of CH. Glaucoma patients showed reverse tendency: CRF value was higher than CH [57].

Studying the parameters obtained with dynamic Scheimpflug analysis (Covis ST) showed the possibilities of the examination method for differential diagnostics of patients suspected of keratoconus or with early keratoconus from patients with normal cornea [58].

5.3  Cornea after refractive surgery

Intravital measurements of biomechanical properties of the cornea after excimer laser surgery performed using dynamic bi-directional pneumo-applanation also confirmed the loss of corneal strength. In patients who had underwent LASIK, examination showed decrease of IOP-related parameters such as corneal compensated IOP, as well as parameters reflecting the biomechanical properties. Along with that, significant correlation was observed between the amount of myopia correction and the deterioration of the biomechanical properties [59].

Another study analyzed the results of dynamic bi-directional pneumo-applanation of the cornea and assessed the correlation between CH decrease and ablation depth in three patient groups: after photorefractive keratectomy, after LASIK with mechanical corneal flap creation, and after LASIK with femtosecond flap creation. The authors found that the strongest correlation was present in femto-LASIK group, while in the two other groups, it was significantly lower [60].

Isolated creation of corneal flap was also found to cause minor changes in corneal refraction [61]. Roberts explained the phenomenon with a theory stating that after lamellar dissection, the corneal biomechanics change in such a way so that severed fibrils contract causing traction in the direction of limbus. With that, central corneal area deflates under the action of released fibrils inducing the so-called “hypermetropic” shift [62, 63].

In parallel, a comparison of changes in biomechanical properties of the cornea after superficial and intrastromal keratectomy was done using OCULUS Corvis (Germany) tonometer. Both types of keratectomy were found to cause statistically significant decrease of biomechanical parameters [64].

Despite the existing methods of measuring biomechanical properties of the cornea and the developed biomechanical models, the detection of ectasia after excimer laser vision correction varies from 0.04 to 0.6% of cases, but according to some researchers, the numbers may be an underestimation [65, 66].

Iatrogenic keratectasia is known to develop due to two factors: an ectatic corneal disease that was undiagnosed in the preoperative stage and excessive thinning of the cornea [67]. In the first case, early detection of keratoconus poses objective challenges [68, 69].

At the same time, even when keratoconus was timely diagnosed, the selection of candidates for keratorefractive surgeries is still difficult, and the evaluation of corneal biomechanics by means of dynamic bi-directional pneumo-applanation does not yield the necessary data.


6. Correction of corneal biomechanical properties

Presently, the most common method of correcting (strengthening) biomechanical properties of the cornea is corneal cross-linking [70].

The first specialists who in the 90s of the twentieth century created corneal cross-linking method for treating keratoconus were Wollensak, Spoerl, and Seiler [71]. They developed the protocol (“Dresden protocol”) for using this method of strengthening the cross-link bonds of collagen for treating progressive keratoconus involving riboflavin and ultraviolet A irradiation of the corneal stroma (UVA with a wavelength of 370 nm for peak absorption of riboflavin) [72].

Careful preclinical experimental validation showed that the combination of riboflavin and UVA leads to a significant improvement of biomechanical stability of the cornea (increase of elastic modulus approximately by 300%) and the formation of large collagen molecular aggregates, including the appearance of cross links—predominantly between the fibril surface molecules and also between proteoglycans in the interfibrillar space [73, 74, 75].

In the following decades, the corneal cross-linking technique has seen widespread clinical application with indications for its usage expanding significantly. Effectiveness of the method for strengthening biomechanical properties was confirmed for the treatment of not only progressive keratoconus, but also pellucid marginal degeneration and iatrogenic ectasia caused by excimer laser surgery [76].

An important suggestion has been made recently for reinforcing the effect of corneal cross-linking—to combine the procedure with implantation of corneal segments [77, 78]. Comparative studies of different treatments—individually and in combination—showed the most pronounced effect to be from the combination therapy starting with the implantation of corneal segments and followed by cross-linking, and not in the reverse order. Such combination therapy also helps to achieve better results (weakening of manifest refraction and keratometric indicators) in cases with keratectasia after excimer laser surgery [79].

There is another method described in the literature as directed laser ablation; it involves biomechanical approach to ablation calculations. Vaporization of the tissue thus happens on the middle periphery, which contains certain relatively flat spots, and not in the central (thin) area. The rationale is that thinning of the area leads to steepening of the cornea subsequently flattening the unablated area, which has more optical power [80]. It should be noted that in clinical practice, this method requires very careful consideration and cautiousness due to insufficient studies on its after effects.

Furthermore, a multimodal approach involving implantation of intrastromal rings, CXL, and laser ablation in different configurations may provide not only stability of corneal topography, but also positive refraction result, thanks to the combination of all the methods’ advantages [81, 82, 83, 84, 85]. That said, the lack of established standards and clinical recommendations for combining different methods for the correction of corneal biomechanical properties may lead to various complications and unexpected aftermaths; it should be kept in mind when planning such treatment.


7. Conclusion

In summary, clinical relevance of studying biomechanics of the fibrous tunic is difficult to overestimate. The diversity of methods used for examination of biomechanical properties of the cornea means there is no single method that could fully satisfy the needs of practical ophthalmology. Further studies are necessary to develop simple, available, and sufficiently informative method for clinical assessment of ocular biomechanics. Moreover, the demand for techniques of correcting biomechanical properties keeps growing, and so this field of research has wide potential.


Conflict of interest

The author has no conflict of interest.


  1. 1. Iomdina EN, Bauer SM, Kotliar KE. Eye Biomechanics: Theoretical Aspects and Clinical Applications. Moscow: Real Time; 2015. p. 208
  2. 2. DelMonte DW, Kim T. Anatomy and physiology of the cornea. Journal of Cataract & Refractive Surgery. 2011;37(3):588-598
  3. 3. Egorova E, Borsenok S, Bessarabov A, Miligert A, Sevostyanov M, Baikin A. Biomechanical properties of sclera in groups of patients with different refraction. Ophthalmosurgery. 2015;4:65-69
  4. 4. Avetisov SE, Bubnova IA, Antonov AA. Corneal biomechanics: Clinical importance, evaluation, possibilities of sistemization of examination approaches. Vestnik Oftalmologii. 2010;126(6):3-7
  5. 5. Lanchares E, Calvo B, Cristóbal JA, Doblaré M. Finite element simulation of arcuates for astigmatism correction. Journal of Biomechanics. 2008;41(4):797-805. DOI: 10.1016/j.jbiomech.2007.11.010
  6. 6. Roy AS, Dupps WJ. Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes. Journal of Biomechanical Engineering. 2011;133(1):011002
  7. 7. Achiron A, Gur Z, Aviv U, Hilely A, Mimouni M, Karmona L, et al. Predicting refractive surgery outcome: Machine learning approach with big data. Journal of Refractive Surgery. 2017;33(9):592-597. DOI: 10.3928/1081597X-20170616-03
  8. 8. Bao F, Wang J, Cao S, Liao N, Shu B, Zhao Y, et al. Development and clinical verification of numerical simulation for laser in situ keratomileusis. Journal of the Mechanical Behavior of Biomedical Materials. 2018;83:126-134. DOI: 10.1016/j.jmbbm.2018.04.016
  9. 9. Bauer SM, Venatovskaya LA, Voronkova EB, Smirnov AL. The three-dimensional problem of the axisymmetric deformation of an orthotropic spherical layer. Vestnik St Petersburg University: Mathematics. 2016;49(3):277-283
  10. 10. Pandolfi A, Manganiello F. A model for the human cornea: Constitutive formulation and numerical analysis. Biomechanics and Modeling in Mechanobiology. 2006;5(4):237-246. DOI: 10.1007/s10237-005-0014-x
  11. 11. Bauer S, Venatovskaya L, Franus D, Fedotova L. Estimation of changes in the stress-strain state of an eye shell and intraocular pressure readings after refractive correction of hyperopia. Russian Journal of Biomechanics/Rossijski Zurnal Biomehaniki. 2015;19(2):136-143
  12. 12. Bryant MR, McDonnell PJ. Constitutive laws for biomechanical modeling of refractive surgery. Journal of Biomechanical Engineering. 1996;118(4):473-481
  13. 13. Pinsky PM, van der Heide D, Chernyak D. Computational modeling of mechanical anisotropy in the cornea and sclera. Journal of Cataract & Refractive Surgery. 2005;31(1):136-145. DOI: 10.1016/j.jcrs.2004.10.048
  14. 14. Meek KM, Newton RH. Organization of collagen fibrils in the corneal stroma in relation to mechanical properties and surgical practice. Journal of Refractive Surgery. 1999;15(6):695-699
  15. 15. Roy AS, Dupps WJ. Effects of altered corneal stiffness on native and postoperative LASIK corneal biomechanical behavior: A whole-eye finite element analysis. Journal of Refractive Surgery. 2009;25(10):875-887
  16. 16. Kling S, Marcos S. Finite-element modeling of intrastromal ring segment implantation into a hyperelastic cornea. Investigative Ophthalmology & Visual Science. 2013;54(1):881-889
  17. 17. Choi K-S, Soo S, Chung F-L. A virtual training simulator for learning cataract surgery with phacoemulsification. Computers in Biology and Medicine. 2009;39(11):1020-1031
  18. 18. Elsheikh A, Wang D, Kotecha A, Brown M, Garway-Heath D. Evaluation of Goldmann applanation tonometry using a nonlinear finite element ocular model. Annals of Biomedical Engineering. 2006;34(10):1628-1640
  19. 19. Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement: Quantitative analysis. Journal of Cataract & Refractive Surgery. 2005;31(1):146-155. DOI: 10.1016/j.jcrs.2004.09.031
  20. 20. Kwon TH, Ghaboussi J, Pecknold DA, Hashash YM. Role of corneal biomechanical properties in applanation tonometry measurements. Journal of Refractive Surgery. 2010;26(7):512-519
  21. 21. Elsheikh A, Anderson K. Comparative study of corneal strip extensometry and inflation tests. Journal of the Royal Society Interface. 2005;2(3):177-185
  22. 22. Avetisov SE, Mamikonyan VR, Zavalishin NN, Nenukov AK. Experimental study of mechanical properties of cornea and sclera. Ophthalmic Journal. 1988;4:233-237
  23. 23. Elsheikh A, Brown M, Alhasso D, Rama P, Campanelli M, Garway-Heath D. Experimental assessment of corneal anisotropy. Journal of Refractive Surgery. 2008;24(2):178-187
  24. 24. Shin TJ, Vito RP, Johnson LW, McCarey BE. The distribution of strain in the human cornea. Journal of Biomechanics. 1997;30(5):497-503
  25. 25. Zeng Y, Yang J, Huang K, Lee Z, Lee X. A comparison of biomechanical properties between human and porcine cornea. Journal of Biomechanics. 2001;34(4):533-537
  26. 26. Woo S-Y, Kobayashi A, Schlegel W, Lawrence C. Nonlinear material properties of intact cornea and sclera. Experimental Eye Research. 1972;14(1):29-39
  27. 27. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Experimental Eye Research. 1980;31(4):435-441
  28. 28. Soergel F, Jean B, Seiler T, Bende T, Mücke S, Pechhold W, et al. Dynamic mechanical spectroscopy of the cornea for measurement of its viscoelastic properties in vitro. German Journal of Ophthalmology. 1995;4(3):151-156
  29. 29. Wang H, Prendiville PL, McDonnell PJ, Chang WV. An ultrasonic technique for the measurement of the elastic moduli of human cornea. Journal of Biomechanics. 1996;29(12):1633-1636
  30. 30. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Investigative Ophthalmology & Visual Science. 2012;53(1):185-190
  31. 31. Kasprzak H, FÖrster W. Measurement of elastic modulus of the bovine cornea by means of holographic interferometry. Part 1. Method and experiment. Optometry and Vision Science. 1993;70(7):535-544
  32. 32. Avetisov SE, Fyodorov AA, Vvedenskyi AS, Nenukov AK. Experimental study of radial keratotomy influence on corneal mechanical properties. Ophthalmic Journal. 1990;1:54-58
  33. 33. Forstot SL, Damiano RE. Trauma after radial keratotomy. Ophthalmology. 1988;95(6):833-835
  34. 34. Avetisov S, Bubnova I, Novikov I, Antonov A, Siplivyi V. Experimental study on the mechanical strain of corneal collagen. Journal of Biomechanics. 2013;46(10):1648-1654. DOI: 10.1016/j.jbiomech.2013.04.008
  35. 35. Avetisov SE, Voronin GV. Experimental study of corneal mechanical properties after eximer laser ablation. RMJ Clinical Ophthalmology. 2001;3:83-86
  36. 36. Friedenwald JS, Moses R. Modern refinements in tonometry. Documenta Ophthalmologica. 1950;4(1):335-362
  37. 37. Moses RA. Theory of the Schiotz tonometer and its empirical calibration. Transactions of the American Ophthalmological Society. 1971;69:494
  38. 38. Avetisov SE, Bubnova IA, Antonov AA. Once more about the diagnostic capacities of elastic tonometry. Vestnik Oftalmologii. 2008;124(5):19-21
  39. 39. Jaycock PD, Lobo L, Ibrahim J, Tyrer J, Marshall J. Interferometric technique to measure biomechanical changes in the cornea induced by refractive surgery. Journal of Cataract & Refractive Surgery. 2005;31(1):175-184
  40. 40. Grabner G, Eilmsteiner R, Steindl C, Ruckhofer J, Mattioli R, Husinsky W. Dynamic corneal imaging. Journal of Cataract & Refractive Surgery. 2005;31(1):163-174
  41. 41. Chang S, Hjortdal J, Maurice D, Pinsky P. Corneal Deformation by Indentation and Applanation Forces. Investigative Ophthalmology & Visual Science. Philadelphia, PA: Lippincott-Raven Publ; 1993. p. 19106
  42. 42. Dupps WJ, Netto MV, Herekar S. Surface wave elastometry of the cornea in porcine and human donor eyes. Journal of Refractive Surgery. 2007;23(1):66-75
  43. 43. Volokov V, Juravlev A, Malyshev L, Saulgosis U, Nekrasov U, Pavilainen V. Current state and prospects of application of the method of photoelasticity in ophthalmology. Journal of Ophthalmology. 1990;8:479-482
  44. 44. Edmund C. Corneal topography and elasticity in normal and keratoconic eyes. A methodological study concerning the pathogenesis of keratoconus. Acta Ophthalmologica. Supplement. 1989;193:1-36
  45. 45. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. Journal of Cataract & Refractive Surgery. 2005;31(1):156-162. DOI: 10.1016/j.jcrs.2004.10.044
  46. 46. Medeiros FA, Weinreb RN. Evaluation of the influence of corneal biomechanical properties on intraocular pressure measurements using the ocular response analyzer. Journal of Glaucoma. 2006;15(5):364-370
  47. 47. Annette H, Kristina L, Bernd S, Mark-Oliver F, Wolfgang W. Effect of central corneal thickness and corneal hysteresis on tonometry as measured by dynamic contour tonometry, ocular response analyzer, and Goldmann tonometry in glaucomatous eyes. Journal of Glaucoma. 2008;17(5):361-365
  48. 48. Kotecha A, Elsheikh A, Roberts CR, Zhu H, Garway-Heath DF. Corneal thickness-and age-related biomechanical properties of the cornea measured with the ocular response analyzer. Investigative Ophthalmology & Visual Science. 2006;47(12):5337-5347
  49. 49. Kirwan C, O’keefe M, Lanigan B. Corneal hysteresis and intraocular pressure measurement in children using the reichert ocular response analyzer. American Journal of Ophthalmology. 2006;142(6):990-992
  50. 50. Gonzalez-Meijome JM, QueirOS A, Jorge J, DIAz-Rey A, Parafita MA. Intraoffice variability of corneal biomechanical parameters and intraocular pressure (IOP). Optometry and Vision Science. 2008;85(6):457-462
  51. 51. Montard R, Kopito R, Touzeau O, Allouch C, Letaief I, Borderie V, et al. Ocular response analyzer: Feasibility study and correlation with normal eyes. Journal Français d'Ophtalmologie. 2007;30(10):978-984
  52. 52. Moreno-Montanés J, Maldonado MJ, García N, Mendiluce L, García-Gómez PJ, Seguí-Gómez M. Reproducibility and clinical relevance of the ocular response analyzer in nonoperated eyes: Corneal biomechanical and tonometric implications. Investigative Ophthalmology & Visual Science. 2008;49(3):968-974
  53. 53. Avetisov SE, Novikov IA, Bubnova IA, Antonov AA, Siplivyi VI. Determination of corneal elasticity coefficient using the ORA database. Journal of Refractive Surgery. 2010;26(7):520-524
  54. 54. Reznicek L, Muth D, Kampik A, Neubauer AS, Hirneiss C. Evaluation of a novel Scheimpflug-based non-contact tonometer in healthy subjects and patients with ocular hypertension and glaucoma. British Journal of Ophthalmology. 2013;97(11):1410-1414
  55. 55. Asaoka R, Nakakura S, Tabuchi H, Murata H, Nakao Y, Ihara N, et al. The relationship between Corvis ST tonometry measured corneal parameters and intraocular pressure, corneal thickness and corneal curvature. PLoS One. 2015;10(10):e0140385
  56. 56. Fontes BM, Ambrósio R, Velarde GC, Nosé W. Ocular response analyzer measurements in keratoconus with normal central corneal thickness compared with matched normal control eyes. Journal of Refractive Surgery. 2011;27(3):209-215
  57. 57. Touboul D, Roberts C, Kérautret J, Garra C, Maurice-Tison S, Saubusse E, et al. Correlations between corneal hysteresis, intraocular pressure, and corneal central pachymetry. Journal of Cataract & Refractive Surgery. 2008;34(4):616-622
  58. 58. Francis M, Pahuja N, Shroff R, Gowda R, Matalia H, Shetty R, et al. Waveform analysis of deformation amplitude and deflection amplitude in normal, suspect, and keratoconic eyes. Journal of Cataract & Refractive Surgery. 2017;43(10):1271-1280
  59. 59. Pedersen IB, Bak-Nielsen S, Vestergaard AH, Ivarsen A, Hjortdal J. Corneal biomechanical properties after LASIK, ReLEx flex, and ReLEx smile by Scheimpflug-based dynamic tonometry. Graefe's Archive for Clinical and Experimental Ophthalmology. 2014;252(8):1329-1335
  60. 60. Hamilton DR, Johnson RD, Lee N, Bourla N. Differences in the corneal biomechanical effects of surface ablation compared with laser in situ keratomileusis using a microkeratome or femtosecond laser. Journal of Cataract & Refractive Surgery. 2008;34(12):2049-2056
  61. 61. Güell JL, Velasco F, Roberts C, Sisquella MT, Mahmoud A. Corneal flap thickness and topography changes induced by flap creation during laser in situ keratomileusis. Journal of Cataract & Refractive Surgery. 2005;31(1):115-119. DOI: 10.1016/j.jcrs.2004.09.045
  62. 62. Potgieter FJ, Roberts C, Cox IG, Mahmoud AM, Herderick EE, Roetz M, et al. Prediction of flap response. Journal of Cataract & Refractive Surgery. 2005;31(1):106-114
  63. 63. Roberts C. Biomechanical customization: The next generation of laser refractive surgery. Journal of Cataract & Refractive Surgery. 2005;31(1):2-5
  64. 64. Hassan Z, Modis L, Szalai E, Berta A, Nemeth G. Examination of ocular biomechanics with a new Scheimpflug technology after corneal refractive surgery. Contact Lens & Anterior Eye. 2014;37(5):337-341. DOI: 10.1016/j.clae.2014.05.001
  65. 65. Vahdati A, Seven I, Mysore N, Randleman JB, Dupps WJ. Computational biomechanical analysis of asymmetric ectasia risk in unilateral post-LASIK ectasia. Journal of Refractive Surgery. 2016;32(12) :811-820. DOI: 10.3928/1081597X-20160929-01
  66. 66. Santhiago MR, Giacomin NT, Smadja D, Bechara SJ. Ectasia risk factors in refractive surgery. Clinical Ophthalmology (Auckland, NZ). 2016;10:713. DOI: 10.2147/OPTH.S51313
  67. 67. Pallikaris IG, Kymionis GD, Astyrakakis NI. Corneal ectasia induced by laser in situ keratomileusis. Journal of Cataract & Refractive Surgery. 2001;27(11):1796-1802
  68. 68. Comaish IF, Lawless MA. Progressive post-LASIK keratectasia: Biomechanical instability or chronic disease process? Journal of Cataract & Refractive Surgery. 2002;28(12):2206-2213
  69. 69. Dupps WJ. Biomechanical modeling of corneal ectasia. Journal of Refractive Surgery. 2007;23(1):186-190
  70. 70. Roberts CJ, Dupps WJ. Biomechanics of corneal ectasia and biomechanical treatments. Journal of Cataract & Refractive Surgery. 2014;40(6):991-998. DOI: 10.1016/j.jcrs.2014.04.013
  71. 71. Spoerl E, Seiler T. Techniques for stiffening the cornea. Journal of Refractive Surgery. 1999;15(6):711-713
  72. 72. Spoerl E, Mrochen M, Sliney D, Trokel S, Seiler T. Safety of UVA-riboflavin cross-linking of the cornea. Cornea. 2007;26(4):385-389
  73. 73. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin–ultraviolet-A-induced cross-linking. Journal of Cataract & Refractive Surgery. 2003;29(9):1780-1785
  74. 74. Kohlhaas M, Spoerl E, Schilde T, Unger G, Wittig C, Pillunat LE. Biomechanical evidence of the distribution of cross-links in corneastreated with riboflavin and ultraviolet A light. Journal of  Cataract & Refractive Surgery. 2006;32(2):279-283
  75. 75. Seiler T, Hafezi F. Corneal cross-linking-induced stromal demarcation line. Cornea. 2006;25(9):1057-1059
  76. 76. Hersh PS, Greenstein SA, Fry KL. Corneal collagen crosslinking for keratoconus and corneal ectasia: One-year results. Journal of Cataract & Refractive Surgery. 2011;37(1):149-160. DOI: 10.1016/j.jcrs.2010.07.030
  77. 77. Dauwe C, Touboul D, Roberts CJ, Mahmoud AM, Kérautret J, Fournier P, et al. Biomechanical and morphological corneal response to placement of intrastromal corneal ring segments for keratoconus. Journal of Cataract & Refractive Surgery. 2009;35(10):1761-1767. DOI: 10.1016/j.jcrs.2009.05.033
  78. 78. Kılıç A, Kamburoglu G, Akıncı A.Riboflavin injection into the corneal channel for combined collagen crosslinking and intrastromal corneal ring segment implantation. Journal of Cataract & Refractive Surgery. 2012;38(5):878-883
  79. 79. Coskunseven E, Jankov MR II, Hafezi F, Atun S, Arslan E, Kymionis GD. Effect of treatment sequence in combined intrastromal corneal rings and corneal collagen crosslinking for keratoconus. Journal of Cataract & Refractive Surgery. 2009;35(12):2084-2091
  80. 80. Cennamo G, Intravaja A, Boccuzzi D, Marotta G, Cennamo G. Treatment of keratoconus by topography-guided customized photorefractive keratectomy: Two-year follow-up study. Journal of Refractive Surgery. 2008;24(2):145-149
  81. 81. Stojanovic A, Zhang J, Chen X, Nitter TA, Chen S, Wang Q. Topography-guided transepithelial surface ablation followed by corneal collagen cross-linking performed in a single combined procedure. Journal of Refractive Surgery. 2010;26(2):145-152. DOI: 10.3928/1081597X-20100121-10
  82. 82. Krueger RR, Kanellopoulos AJ. Stability of simultaneous topography-guided photorefractive keratectomy and riboflavin/UVA cross-linking for progressive keratoconus. Journal of Refractive Surgery. 2010;26(10):S827-SS32. DOI: 10.3928/1081597X-20100921-11
  83. 83. Kamburoglu G, Ertan A. Intacs implantation with sequential collagen cross-linking treatment in postoperative LASIK ectasia. Journal of Refractive Surgery. 2008;24(7):S726-S7S9
  84. 84. Kanellopoulos AJ. Comparison of sequential vs same-day simultaneous collagen cross-linking and topography-guided PRK for treatment of keratoconus. Journal of Refractive Surgery. 2009;25(9):S812-S8S8. DOI: 10.3928/1081597X-20090813-10
  85. 85. Kymionis GD, Kontadakis GA, Kounis GA, Portaliou DM, Karavitaki AE, Magarakis M, et al. Simultaneous topography-guided PRK followed by corneal collagen cross-linking for keratoconus. Journal of Refractive Surgery. 2009;25(9):S807-SS11. DOI: 10.3928/1081597X-20090813-09

Written By

Irina Bubnova

Submitted: 29 April 2018 Reviewed: 14 July 2018 Published: 05 November 2018