REVIEW
Concepts and misconceptions in corneal biomechanics Cynthia J. Roberts, PhD
This review looks at biomechanical concepts and misconceptions related to in vivo assessment of corneal biomechanical response via air-puff deformation, including both human donor corneas and the translation of similar concepts to clinical studies. The impact of corneal viscoelasticity on interpreting clinical data is discussed, as well as the differences between 2 clinical devices that produce air puffs with distinct temporal and magnitude profiles. Financial Disclosure: Dr. Roberts is a consultant to Oculus Optikger€ate GmbH and Ziemer Ophthalmic Systems AG and has received research funding from Carl Zeiss Meditec AG as well as travel funds from Sooft Italia. She has no financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2014; 40:862–869 Q 2014 ASCRS and ESCRS Online Video
Prior to 2005, the measurement of human cornea biomechanical properties was performed using cadaver tissue in a laboratory setting.1–3 Therefore, the introduction of the Ocular Response Analyzer (Reichert Technologies) in 2005 was extremely important, since it was the first time the cornea's biomechanical response to a perturbation could be measured clinically using an air puff to deform the cornea,4 as seen in Figure 1. Since that time, more than 250 papers have been published using this dynamic bidirectional applanation device, which is the generic term by which the device can be called for publication purposes. Appreciation for the role of corneal biomechanics in disease development and progression has grown, along with the possible role of corneal biomechanics in screening or predicting outcomes of various
Submitted: October 29, 2013. Final revision submitted: December 10, 2013. Accepted: December 14, 2013. From the Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA. Ashraf M. Mahmoud generated the Figures. Corresponding author: Cynthia J. Roberts, PhD, Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, 915 Olentangy River Road, Havener Eye Institute, Suite 5000, Columbus, Ohio 43212, USA. E-mail: [email protected].
862
Q 2014 ASCRS and ESCRS Published by Elsevier Inc.
procedures. Through the course of these investigations, a great deal about corneal biomechanical behavior has been learned. However, basic misconceptions that have clouded the interpretation of results have perpetuated, including the desire to biomechanically characterize the cornea with a single number that can answer clinical questions about the cornea's basic strength or weakness. Assessing the biomechanical response of living tissue is complex, and the desire to characterize the cornea with a single number is simplistic and ultimately unrealistic. A linearly elastic material can be characterized by a single elastic modulus, defined by the slope of the stress-strain plot, which describes how much a load (stress) will deform (strain) the material under specific conditions. The loading behavior and unloading behavior follow the same straight line. The higher the elastic modulus, the greater the slope and the stiffer the material; ie, greater force is required to deform a stiffer material. The cornea, however, is not a linear elastic material, and several important biomechanical concepts enhance its biomechanical complexity. First, the cornea is viscoelastic by nature, which means the behavior is different during loading and unloading, but also means the response to an applied force has a time-dependent component. This is one reason the evaluation of corneal biomechanical response in the laboratory has produced such a wide range of experimental values. The measured elastic modulus depends not only on the magnitude of the applied force, but also on the rate at 0886-3350/$ - see front matter http://dx.doi.org/10.1016/j.jcrs.2014.04.019
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
863
Figure 1. The cornea deforming under an air puff with an IR emitter on the left and a detector on the right, along with the corresponding air-pressure signal (blue) and IR applanation signal (red) that represents light collected by the detector with the geometry shown. As the cornea applanates, the light generates the first peak on the detector. The signal decreases as the cornea enters a state of concavity and peaks again in the outgoing direction as the cornea goes through applanation again, only in the outward direction. Peak 1 and 2 are the corresponding amplitudes of the 2 applanation spikes. The FWHM 1 and 2 are the full-width halfmaximum values of the 2 corresponding applanation peaks, and represent how fast the cornea traverses applanation in each direction. Time 1 and 2 represent the timing of each applanation event. Slope 1 and 2 are the slopes of the pressure curves bounded by the corresponding applanation peaks. P1 and P2 are the corresponding applanation pressures, and Pmax is the maximum pressure.
which it is applied. A faster strain rate produces a stiffer corneal response.5,6 Thus, the experimental conditions affect the resulting measurements. This basic concept translates from the laboratory to the in vivo condition. Clinically, the manner in which an air puff is applied to the cornea affects the corneal response. For example, the rate at which the air pressure increases and its maximum magnitude will affect the measured result. Clinical measurements illustrating this concept are given in Figure 2 and will be described later. A second important concept is that the stress-strain relationship of the cornea is nonlinear, during both the loading and unloading phases, with a nonconstant elastic modulus.7 The cornea can be thought of as a section of the outer wall of a pressurized vessel. The Laplace law states that wall tension is a function of
the internal pressure. For an eye, this implies that as intraocular pressure (IOP) increases, the wall tension will increase; ie, the cornea and sclera are stiffer at a higher IOP due to nonlinear properties, making IOP a confounding variable in the assessment of corneal biomechanics. The phenomenon has been explicitly reported using inflation tests in human donor eyes.7 This means that a fundamentally soft cornea at a higher IOP may exhibit stiffer behavior than a fundamentally stiffer cornea at a lower IOP. Biomechanical characterization of the cornea is thus, at the least, a 2dimensional (2-D) assessment of stiffness as a function of IOP. The relationship between elastic modules and IOP is also a function of age. The dynamic bidirectional applanator would not have been possible if the cornea were a purely elastic
Figure 2. Measured P1 and P2 values on the same individual with programmed airpressure curves using the dynamic bidirectional applanator. P1 is indicated with the first vertical line, and the corresponding P2 is indicated by the second vertical line. Note that P1 is robust and always occurs at the same pressure. However, P2 is a function of the maximum applied air pressure, which affects CH. The greater the maximum applied air pressure, the greater the CH.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
864
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
material. The device takes advantage of the viscoelasticity of the cornea to produce its metrics of biomechanical behavior. It is important to describe how it functions to understand how the viscoelastic nature of the cornea affects the measurements as well as the impact on data interpretation. The dynamic bidirectional applanator is similar to a noncontact tonometer in that it uses a collimated air jet to deform the cornea but differs from noncontact tonometers in other important ways. Most noncontact tonometers use an infrared (IR) detection system in which the IR emitter is aligned on 1 side of the cornea with an IR detector on the other side using known geometry. Prior to initiation of the air jet, the IR light broadly reflects from the corneal surface, so only a small amount of light is captured by the detector. As the cornea deforms under the applied air pressure, it quickly traverses a state of applanation, which causes the reflected light to align with the detector in a mirror-like fashion, creating an increase in captured light and a spike in the recorded infrared signal. The IR detection system and associated IR and air-pressure signals specifically associated with the dynamic bidirectional applanator are illustrated in Figure 1. Once the first applanation event is detected by the device, the piston producing the air jet receives a signal to shut down to allow the air pressure to dissipate and the cornea to recover its shape. However, the air pressure continues to rise after shutdown because of inertia in the piston, causing the cornea to continue deforming to a concave shape as the air pressure reaches a maximum (Pmax). As the pressure subsequently reduces and the cornea recovers in the outward direction, it rapidly passes through a second state of applanation before achieving the original convex shape. The pressure at which each applanation event occurs is different, with the second always less than the first in a valid measurement. If the cornea were purely elastic, these 2 pressure values would be the same. It is the difference between loading and unloading behavior due to corneal viscoelasticity that causes a reduction in the second applanation pressure. Four parameters are produced by the dynamic bidirectional applanator, based on the 2 pressure measurements at applanation, P1 in the inward direction and P2 in the outward direction. The difference between P1 and P2 is called corneal hysteresis (CH)4 and represents the viscoelastic response of the cornea to an applied force defined by a specific air-pressure curve. The average of P1 and P2 is called Goldmann-correlated IOP (IOPg). Through empirical investigation, 2 other parameters were defined: corneal resistance factor (CRF), which was designed to produce maximum correlation with central corneal thickness (CCT), and corneal-compensated IOP (IOPcc), which was designed
to be similar before and after refractive surgery.A A summary of the equations is given below: CH Z a½P1 P2 CRF Z a½P1 0:7P2 þ d IOPg Z a½ðP1 þ P2Þ=2 þ c IOPcc Z b½P2 0:43P1 þ e where a, b, c, d, and e are calibration and regression constantsB and the expressions set off by brackets represent the generally accepted equations. However, without the constants, CRF would always be greater than CH, which is not the case clinically. Several important factors about these parameters should be remembered. First, all 4 are calculated based on the same 2 pressure measurements, P1 and P2. Therefore, only 2 can be considered completely independent; for example, IOPg (average of P1 and P2) and CH (difference between P1 and P2). The remaining values are highly correlated even though they describe different parameters. The IOPcc compensates for corneal properties in estimating IOP, producing a more accurate value in softer eyes.8 As previously described, corneal properties are a function of IOP.7 Therefore, it is not surprising that IOPcc and CH are highly correlated.9,10 The relationship is negative; that is, as IOPcc increases, CH decreases. The cornea and sclera are stiffer with a higher IOP, and CH decreases as the cornea's ability to dissipate energy decreases with greater wall tension. Second, both CH and CRF are viscoelastic parameters. In the literature, CH is sometimes described as viscoelasticity and CRF is incorrectly described as elasticity or stiffness. Neither of these is an appropriate description for CRF. It is a viscoelastic parameter, weighted by CCT and highly correlated with CH. The weighting by CCT increases the influence of the loading pressure, P1, in the equation for CRF, which increases the influence of elasticity, but it remains fundamentally a viscoelastic parameter due to the inclusion of the unloading applanation pressure, P2. Third, as a viscoelastic parameter, CH is a function of both elasticity and viscosity, so it is inappropriate to interpret CH as relating to stiffness or softness, terms that describe elastic properties. In addition, it has been shown theoretically that the same value of CH can be associated with different combinations of elasticity and viscosity.11 This theoretical model also demonstrates that at low viscosity, greater elastic modulus is associated with lower CH. In contrast, at higher viscosity, greater elastic modulus is associated with higher CH, demonstrating a complex interaction
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
to produce the measured result. Therefore, low CH should not be interpreted as a soft cornea, or a weak cornea, or a damaged cornea, as it is often described in the literature. These descriptions arose from some of the first corneas measured with the dynamic bidirectional applanator, which were keratoconic corneas with low CH4 and known to have low elastic modulus based on previous in vitro studies,12–14 as well as corneas after refractive surgery, which are thinner and softer.4,8 However, low CH can also be measured in a stiff cornea with higher IOP, as previously described. It has also been shown clinically10,15 and in donor corneas5 that CH decreases with age as the cornea is known to stiffen.16,17 Therefore, knowledge of CH alone does not imply that the cornea is either stiff or soft without additional information. For example, low CH is associated with glaucomatous damage,18 which cannot be interpreted as a stiff or a soft cornea without additional information. Further work is necessary to determine what component contributing to this viscoelastic parameter correlates to damage at the optic nerve. As mentioned previously, the maximum air pressure (Pmax) of the dynamic bidirectional applanation device is variable depending on the timing of the first applanation event. The earlier it occurs, the lower the Pmax. Two studies have been conducted to determine the influence of the characteristics of the air-pressure curve on measured CH.C,D In both studies, it was shown that the earlier the first applanation event occurred, which generated a lower maximum applied air pressure, the lower was the measured CH. The loading phase, in which the air pressure is increasing, is the same from examination to examination. However, the unloading phase, in which the cornea recovers its shape, is different depending on the timing of the first applanation event and Pmax. This is illustrated in Figure 2, with several different air-pressure curves for the same eye. Note that P1 is robust, occurring at the same point with each examination, but P2 occurs later with higher maximum applied air pressure, leading to a greater CH. Again, this phenomenon is due to the viscoelastic nature of the cornea. What influences P1 and how can the biomechanical data be interpreted in light of the device functionality? Most noncontact tonometers have only P1, so one can conclude that the strongest predictor of P1 should be IOP. Two factors influencing P1 have been reported, confirming IOP has a strong relationship and, to a less extent, CCT.19,20 Corneal stiffness was not evaluated. However, theory leads us to conclude that after IOP, corneal stiffness and, to a less extent, CCT would influence the timing and magnitude of P1.21 Thus, one can think of the CH produced by the dynamic bidirectional applanator as characteristic of an individual
865
cornea and IOP since it is tied to the P1 and Pmax of that eye. It is clear that this natural CH has clinical value due to the many reports in the literature, including its association with glaucomatous damage.18 However, it should not be mistaken for an elastic parameter, as in the quest to differentiate a soft keratoconic cornea from a stiffer normal cornea. Such an application might require a different parameter that is not viscoelastic. Since the timing of the first applanation event is influenced by IOP and corneal properties, and since the geometry of the corneal surface shape and IR detection system may affect the amount of light captured by the detector, detailed signal analysis can provide additional insight into corneal biomechanical characteristics. Figure 1 shows a schematic of the dynamic bidirectional applanation signal and the parameters that have been reported, along with their definitions. Each parameter carries a physical meaning associated with specific signal features. For example, the width of each IR peak (full width half maximum) corresponds to the speed at which the cornea moves through applanation. Greater width in a goodquality signal represents a cornea that is moving at a slower rate, since it takes longer to traverse applanation. Slower movement is associated with a stiffer cornea, since it takes greater force to deform a stiffer material and reach the same velocity.E The amplitude of the first IR peak (Peak 1) corresponds to the size of the area of applanation, with a larger area producing greater amplitude since more light is captured by the detector. It has been hypothesized that this may correspond to the stiffness of the cornea since a softer cornea with a lower elastic modulus would have greater deformation under the same load. Therefore, softer corneas would produce deep, narrow deformations, and stiffer corneas would produce wide, shallow deformations. There is clinical evidence to support this hypothesis,22 including the first report of signal analysis in 2008, which compared the signal features in a post-laser in situ keratomileusis (LASIK) ectatic eye and the fellow eye with a normal post-LASIK outcome.23 Both CH and CRF in the 2 eyes were similar, but the signals were distinct, as shown in Figure 3. The IR signal was dramatically damped in the ectatic eye, with lower peaks in the presumably softer cornea. The viscoelastic CH parameter did not clearly distinguish between the 2 corneas, with biomechanical decompensation in only 1 eye, likely because the elastic modulus and viscous damping were affected in a manner that produced similar CH. Other reports have shown the importance of Peak1 in qualitatively evaluating corneal stiffness, including correlating Peak 1 magnitude to severity of keratoconus,F screening forme fruste keratoconus,24,25 comparing
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
866
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
Figure 3. Dynamic bidirectional applanation signals from 2 contralateral eyes after LASIK. The eye on the left had a normal postoperative outcome, and the eye on the right developed ectasia. Note the presumed softer ectatic eye on the right has damped signals. (Figure adapted from reference 22.)
LASIK and surface ablation,26 as well as the effect of creating a flap,27 and evaluating changes after corneal collagen crosslinking.28,29 Other customized parameters derived from signal analysis have been reported.30 With the additional biomechanical information that was evident in signal analysis of the dynamic bidirectional applanator, the manufacturer derived 42 parameters from the IR and air-pressure signals, including the original 4 parameters of CH, CRF, IOPcc, and IOPg. In cooperation with 4 investigators from 3 countries, a Keratoconus Match Index was developed, which was used to provide the probability that a particular waveform was consistent with keratoconus. Several reports use these new waveform metrics.31–33 More study is needed to identify the most clinically useful parameters. In the past 2 years, a new device designed to measure corneal deformation characteristics was introduceddthe Corvis ST (Oculus Optikger€ ate GmbH),34 called a dynamic Scheimpflug analyzer for the purpose of publication. This device is similar to the dynamic bidirectional applanator in that it uses an air puff to deform the cornea but is distinct in many ways. The dynamic Scheimpflug analyzer captures a single Scheimpflug image of the horizontal (0 degree) meridian of the cornea during deformation at greater than 4300 frames per second, producing about 140 images during 30 ms. Sample images are shown in Figure 4. From this real-time series of images, deformation characteristics can be extracted along with the potential to quantify corneal elastic parameters. The same basic biomechanical concepts apply to this device in that IOP will influence corneal biomechanical behavior. Therefore, in the overlapped images of Figure 5, both IOPcc (from the dynamic bidirectional applanator) and CCT were similar between the normal cornea (pseudocolored in blue) and the keratoconic cornea (pseudocolored in red). The overlapped videos show a comparison of the entire deformation process (Video 1, available at: http://jcrsjournal.org). Note that the maximum deformation amplitude in the keratoconic cornea is much greater than that in the normal cornea. This indicates that the normal cornea is stiffer
and thus deforms less, only because IOPcc is matched between the 2 eyes. Without this match, the difference could simply be a difference in IOP. In a study reported at the Association for Research in Vision and Ophthalmology meeting in 2011,E it was shown that IOP is the strongest predictor of deformation amplitude, followed by a corneal biomechanical parameter, and finally, CCT. The strong influence of IOP on corneal deformation was also verified in an ex vivo study using pig eyes.35 It is critical to note the differences in the characteristics of the air puffs between the 2 devices described. Unlike the dynamic bidirectional applanator, the dynamic Scheimpflug analyzer produces a consistent air puff with each examination. Therefore, although the same relative biomechanical relationships will
Figure 4. Scheimpflug images extracted from a series of 140 images of a cornea deforming under an air puff from the dynamic Scheimpflug analyzer.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
867
Figure 5. Overlapped images measured with dynamic Scheimpflug analyzer from a normal cornea (blue) and a keratoconic cornea (red), both with similar IOPcc from dynamic bidirectional applanation (13.3 mm Hg for normal cornea and 13.7 mm Hg for keratoconic cornea) and similar CCT. (Data from Renato Ambr osio Jr, MD, PhD, and processing by Ashraf M. Mahmoud.)
apply to both devices, including that a stiffer eye will deform later, move more slowly, and recover more quickly (all with consistent IOP), the magnitude of the specific parameters will likely be distinct in any comparisons between devices due to the differences in the air puff itself, in combination with the viscoelasticity of the cornea. In summary, a significant amount of biomechanical information regarding the natural CH of the eye and in vivo corneal viscoelastic response to an air puff has been learned since 2005. With the introduction of a new device using a distinctly different air-puff stimulus and new potential for analyzing specific deformation characteristics from real-time images, it is expected that new investigations will add complimentary information to our growing understanding of the important role of corneal biomechanics in many clinical applications. As these new studies move forward, it will be crucial to note the effect of IOP on corneal biomechanical assessment and broaden our expectations beyond a single biomechanical parameter to characterize an individual cornea's strength or weakness. Our goal can be modified to generate a 2-D assessment of stiffness as a function of IOP, as illustrated by the schematic diagram in Figure 6. The
weaker corneas will have lower stiffness at all values of IOP, corresponding to a region on this plot rather than a single point.
Figure 6. Schematic diagram of proposed 2-D assessment of corneal biomechanics showing stiffness as a function of IOP, with each curve representing a different hypothetical cornea. The lower curves represent softer corneas (yellow-red) and the upper curves represent stiffer corneas (green-blue). Note that a softer cornea at higher IOP will have greater apparent stiffness than a cornea that is fundamentally stiffer but with a lower IOP, indicated by the 2 black dots.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
868
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
REFERENCES 1. Schwartz NJ, Mackay RS, Sackman JL. A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of the intraocular pressure. Bull Math Biophys 1966; 28:585–643 2. Jue B, Maurice DM. The mechanical properties of rabbit and human cornea. J Biomech 1986; 19:847–853 3. Hoeltzel DA, Altman P, Buzard K. Choe K-i. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng 1992; 114:202–215. Available at: http://www.buzard.info/StripExtensiometry.pdf. Accessed January 9, 2014 4. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg 2005; 31:156–162 5. Elsheikh A, Wang D, Brown M, Rama P, Campanelli M, Pye D. Assessment of corneal biomechanical properties and their variation with age. Curr Eye Res 2007; 32:11–19 6. Elsheikh A, Wang D, Rama P, Campanelli M, Garway-Heath D. Experimental assessment of human corneal hysteresis. Curr Eye Res 2008; 33:205–213 7. Elsheikh A, Wang D, Pye D. Determination of the modulus of elasticity of the human cornea. J Refract Surg 2007; 23:808–818 8. Pepose JS, Feigenbaum SK, Qazi MA, Sanderson JP, Roberts CJ. Changes in corneal biomechancis and intraocular pressure following LASIK using static, dynamic and noncontact tonometry. Am J Ophthalmol 2007; 143:39–47 9. Alhamad TA, Meek KM. Comparison of factors that influence the measurement of corneal hysteresis in vivo and in vitro. Acta Ophthalmol 2011; 89:e443–e450. Available at: http://onlinelibrary. wiley.com/doi/10.1111/j.1755-3768.2011.02150.x/pdf. Accessed January 9, 2014 10. Roberts CJ, Reinstein DZ, Archer TJ, Mahmoud AM, Gobbe M, Lee L. Comparison of biomechanical response parameters using dynamic bidirectional applanation analysis between myopic and hyperopic eyes. J Cataract Refract Surg 2014; 40: 11. Glass DH, Roberts CJ, Litsky AS, Weber PA. A viscoelastic biomechanical model of the cornea describing the effect of viscosity and elasticity on hysteresis. Invest Ophthalmol Vis Sci 2008; 49:3919–3926. Available at: http://www.iovs.org/cgi/ reprint/49/9/3919. Accessed January 9, 2014 12. Foster CS, Yamamoto GK. Ocular rigidity in keratoconus. Am J Ophthalmol 1978; 86:802–806 13. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res 1980; 31:435–441 14. Nash IS, Greene PR, Foster CS. Comparison of mechanical properties of keratoconus and normal corneas. Exp Eye Res 1982; 35:413–424 15. Kamiya K, Shimizu K, Ohmoto F. Effect of aging on corneal biomechanical parameters using the Ocular Response Analyzer. J Refract Surg 2009; 25:888–893 16. Malik NS, Moss SJ, Ahmed N, Furth AJ, Wall RS, Meek KM. Ageing of the human corneal stroma: structural and biochemical changes. Biochem Biophys Acta 1992; 1138:222–228 17. Daxer A, Misof K, Grabner B, Ettl A, Fratzl P. Collagen fibrils in the human corneal stroma: structure and aging. Invest Ophthalmol Vis Sci 1998; 39:644–648. Available at: http://www.iovs.org/ cgi/reprint/39/3/644. Accessed January 9, 2014 18. Congdon NG, Broman AT, Bandeen-Roche K, Grover D, Quigley HA. Central corneal thickness and corneal hysteresis associated with glaucoma damage. Am J Ophthalmol 2006; 141:868–875 19. Kotecha A, Elsheikh A, Roberts CR, Zhu H, Garway-Heath DF. Corneal thickness-and age-related biomechanical properties of
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
the cornea measured with the Ocular Response Analyzer. Invest Ophthalmol Vis Sci 2006; 47:5337–5347. Available at: http:// www.iovs.org/cgi/reprint/47/12/5337. Accessed January 9, 2014 Terai N, Raiskup F, Haustein M, Pillunat LE, Spoerl E. Identification of biomechanical properties of the cornea: the Ocular Response Analyzer. Curr Eye Res 2012; 37:553–562 Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement; quantitative analysis. J Cataract Refract Surg 2005; 31:146–155 Glass DH. Characterization of the Biomechanical Properties of the In Vivo Human Cornea [dissertation]. Columbus, OH, Ohio State University, 2008; Available at: https://etd.ohiolink.edu/ ap/0?0:APPLICATION_PROCESS%3DDOWNLOAD_ETD_ SUB_DOC_ACCNUM:::F1501_ID:osu1211920104%2Cinline. Accessed January 9, 2014 Kerautret J, Colin J, Touboul D, Roberts C. Biomechanical characteristics of the ectatic cornea. J Cataract Refract Surg 2008; 34:510–513 Schweitzer C, Roberts CJ, Mahmoud AM, Colin J, MauriceTison S, Kerautret J. Screening of forme fruste keratoconus with the Ocular Response Analyzer. Invest Ophthalmol Vis Sci 2010; 51:2403–2410. Available at: http://www.iovs.org/content/ 51/5/2403.full.pdf. Accessed January 9, 2014 nard A, Mahmoud AM, Gallois A, Colin J, Touboul D, Be Roberts CJ. Early biomechanical keratoconus pattern measured with an ocular response analyzer: curve analysis. J Cataract Refract Surg 2011; 37:2144–2150 Qazi MA, Sanderson JP, Mahmoud AM, Yoon EY, Roberts CJ, Pepose JS. Postoperative changes in intraocular pressure and corneal biomechanical metrics; laser in situ keratomileusis versus laser-assisted subepithelial keratectomy. J Cataract Refract Surg 2009; 35:1774–1788 lu G, Mahmoud AM, Roberts CJ. Kılıc‚ Uzbek A, Kamburog Change in biomechanical parameters after flap creation using the IntraLase femtosecond laser and subsequent excimer laser ablation. Curr Eye Res 2011; 36:614–619 E, Mahmoud AM, Trazza S, Hafezi F, Vinciguerra P, Albe Roberts CJ. Intra- and postoperative variation in ocular response analyzer parameters in keratoconic eyes after corneal cross-linking. J Refract Surg 2010; 26:669–676 Kılıc‚ A, Roberts CJ. Biomechanical and refractive results of transepithelial crosslinking treatment in keratoconic eyes. Int J Kertoconus Ectatic Corneal Dis 2012; 1(2):75–78. Available at: http:// www.jaypeejournals.com/eJournals/ShowText.aspx?IDZ3332& TypeZFREE&TYPZTOP&INZ_eJournals/images/JPLOGO. gif&IIDZ258&isPDFZYES. Accessed January 9, 2014 Hallahan KM, Roy AS, Ambrosio R Jr, Salomao M, Dupps WJ Jr. Discriminant value of custom Ocular Response Analyzer waveform derivatives in keratoconus. Ophthalmology 2013 Nov 26 [Epub ahead of print] Mikielewicz M, Kotliar K, Barraquer RI, Michael R. Air-pulse corneal applanation signal curve parameters for the characterisation of keratoconus. Br J Ophthalmol 2011; 95:793–798 Spoerl E, Terai N, Scholz F, Raiskup F, Pillunat LE. Detection of biomechanical changes after corneal cross-linking using Ocular Response Analyzer software. J Refract Surg 2011; 27:452–457 Lam AKC, Chen D, Tse J. The usefulness of waveform score from the ocular response analyzer. Optom Vis Sci 2010; 87:195–199. Available at: http://journals.lww.com/optvissci/ Fulltext/2010/03000/The_Usefulness_of_Waveform_Score_from_ the_Ocular.10.aspx. Accessed January 9, 2014 sio R Jr, Ramos I, Luz A, Correa Faria F, Steinmueller A, Ambro Krug M, Belin MW, Roberts CJ. Dynamic ultra-high-speed Scheimpflug imaging for assessing corneal biomechanical
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
properties. Rev Bras Oftalmol 2013; 72:99–102. Available at: http://www.scielo.br/pdf/rbof/v72n2/05.pdf. Accessed January 9, 2014 35. Kling S, Marcos S. Contributing factors to corneal deformation in air puff measurements. Invest Ophthalmol Vis Sci 2013; 54:5078–5085
OTHER CITED MATERIAL
A. Luce DA. Methodology for cornea compensated IOP and corneal resistance factor for the Reichert Ocular Response Analyzer. IOVS 2006; 47:ARVO E-Abstract 2266. Available at: http://abstracts.iovs.org//cgi/content/abstract/47/5/2266?sidZ 3427a143-0993-4537-a038-9896d5877b79. Accessed January 9, 2014 B. Reichert Technologies. Personal communication, May 2006. C. Rouse EJ, Roberts CJ, Mahmoud AM. The measurement of biomechanical parameters as a function of peak applied pressure in the Reichert Ocular Response Analyzer. IOVS 2007; 48:ARVO E-Abstract 1247. Available at: http://abstracts.iovs. org//cgi/content/abstract/48/5/1247?sidZ129416b7-6a47-4fecaf74-97dee0b9a1ae. Accessed January 9, 2014 D. Asaoka R, Kotecha A, White E, Garway-Heath DF. The effects of maximum air pulse pressure and intraocular pressure on corneal hysteresis measurements with the Reichert Ocular Response Analyzer. IOVS 2008; 49:ARVO E-Abstract 703. Available at: http://abstracts.iovs.org//cgi/content/abstract/49/
869
5/703?sidZ40cd0ea6-69e7-493a-87ba-42816c239142. Accessed January 9, 2014 E. Roberts CJ, Mahmoud AM, Ramos I, Caldas D, Siqueira da sio R Jr. Factors influencing corneal deformation Silva R, Ambro and estimation of intraocular pressure. IOVS 2011; 52:ARVO EAbstract 4384. Available at: http://abstracts.iovs.org//cgi/ content/abstract/52/6/4384?sidZ86e3462e-06d3-46fa-a25a6ddf31f7b7a2. Accessed January 9, 2014 F. Mahmoud AM, Twa MD, Qazi M, Pepose J, Roberts CJ. Comparison of biomechanical and topographic parameters in normal and pathologic corneas. IOVS 2007; 48:ARVO E-Abstract 1843. Available at: http://abstracts.iovs.org//cgi/content/abstract/48/5/ 1843?sidZffc278f0-2670-455b-8e48-d4147e08f778. Accessed January 9, 2014
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
First author: Cynthia J. Roberts, PhD Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA
Concepts and misconceptions in corneal biomechanics Cynthia J. Roberts, PhD
This review looks at biomechanical concepts and misconceptions related to in vivo assessment of corneal biomechanical response via air-puff deformation, including both human donor corneas and the translation of similar concepts to clinical studies. The impact of corneal viscoelasticity on interpreting clinical data is discussed, as well as the differences between 2 clinical devices that produce air puffs with distinct temporal and magnitude profiles. Financial Disclosure: Dr. Roberts is a consultant to Oculus Optikger€ate GmbH and Ziemer Ophthalmic Systems AG and has received research funding from Carl Zeiss Meditec AG as well as travel funds from Sooft Italia. She has no financial or proprietary interest in any material or method mentioned. J Cataract Refract Surg 2014; 40:862–869 Q 2014 ASCRS and ESCRS Online Video
Prior to 2005, the measurement of human cornea biomechanical properties was performed using cadaver tissue in a laboratory setting.1–3 Therefore, the introduction of the Ocular Response Analyzer (Reichert Technologies) in 2005 was extremely important, since it was the first time the cornea's biomechanical response to a perturbation could be measured clinically using an air puff to deform the cornea,4 as seen in Figure 1. Since that time, more than 250 papers have been published using this dynamic bidirectional applanation device, which is the generic term by which the device can be called for publication purposes. Appreciation for the role of corneal biomechanics in disease development and progression has grown, along with the possible role of corneal biomechanics in screening or predicting outcomes of various
Submitted: October 29, 2013. Final revision submitted: December 10, 2013. Accepted: December 14, 2013. From the Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA. Ashraf M. Mahmoud generated the Figures. Corresponding author: Cynthia J. Roberts, PhD, Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, 915 Olentangy River Road, Havener Eye Institute, Suite 5000, Columbus, Ohio 43212, USA. E-mail: [email protected].
862
Q 2014 ASCRS and ESCRS Published by Elsevier Inc.
procedures. Through the course of these investigations, a great deal about corneal biomechanical behavior has been learned. However, basic misconceptions that have clouded the interpretation of results have perpetuated, including the desire to biomechanically characterize the cornea with a single number that can answer clinical questions about the cornea's basic strength or weakness. Assessing the biomechanical response of living tissue is complex, and the desire to characterize the cornea with a single number is simplistic and ultimately unrealistic. A linearly elastic material can be characterized by a single elastic modulus, defined by the slope of the stress-strain plot, which describes how much a load (stress) will deform (strain) the material under specific conditions. The loading behavior and unloading behavior follow the same straight line. The higher the elastic modulus, the greater the slope and the stiffer the material; ie, greater force is required to deform a stiffer material. The cornea, however, is not a linear elastic material, and several important biomechanical concepts enhance its biomechanical complexity. First, the cornea is viscoelastic by nature, which means the behavior is different during loading and unloading, but also means the response to an applied force has a time-dependent component. This is one reason the evaluation of corneal biomechanical response in the laboratory has produced such a wide range of experimental values. The measured elastic modulus depends not only on the magnitude of the applied force, but also on the rate at 0886-3350/$ - see front matter http://dx.doi.org/10.1016/j.jcrs.2014.04.019
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
863
Figure 1. The cornea deforming under an air puff with an IR emitter on the left and a detector on the right, along with the corresponding air-pressure signal (blue) and IR applanation signal (red) that represents light collected by the detector with the geometry shown. As the cornea applanates, the light generates the first peak on the detector. The signal decreases as the cornea enters a state of concavity and peaks again in the outgoing direction as the cornea goes through applanation again, only in the outward direction. Peak 1 and 2 are the corresponding amplitudes of the 2 applanation spikes. The FWHM 1 and 2 are the full-width halfmaximum values of the 2 corresponding applanation peaks, and represent how fast the cornea traverses applanation in each direction. Time 1 and 2 represent the timing of each applanation event. Slope 1 and 2 are the slopes of the pressure curves bounded by the corresponding applanation peaks. P1 and P2 are the corresponding applanation pressures, and Pmax is the maximum pressure.
which it is applied. A faster strain rate produces a stiffer corneal response.5,6 Thus, the experimental conditions affect the resulting measurements. This basic concept translates from the laboratory to the in vivo condition. Clinically, the manner in which an air puff is applied to the cornea affects the corneal response. For example, the rate at which the air pressure increases and its maximum magnitude will affect the measured result. Clinical measurements illustrating this concept are given in Figure 2 and will be described later. A second important concept is that the stress-strain relationship of the cornea is nonlinear, during both the loading and unloading phases, with a nonconstant elastic modulus.7 The cornea can be thought of as a section of the outer wall of a pressurized vessel. The Laplace law states that wall tension is a function of
the internal pressure. For an eye, this implies that as intraocular pressure (IOP) increases, the wall tension will increase; ie, the cornea and sclera are stiffer at a higher IOP due to nonlinear properties, making IOP a confounding variable in the assessment of corneal biomechanics. The phenomenon has been explicitly reported using inflation tests in human donor eyes.7 This means that a fundamentally soft cornea at a higher IOP may exhibit stiffer behavior than a fundamentally stiffer cornea at a lower IOP. Biomechanical characterization of the cornea is thus, at the least, a 2dimensional (2-D) assessment of stiffness as a function of IOP. The relationship between elastic modules and IOP is also a function of age. The dynamic bidirectional applanator would not have been possible if the cornea were a purely elastic
Figure 2. Measured P1 and P2 values on the same individual with programmed airpressure curves using the dynamic bidirectional applanator. P1 is indicated with the first vertical line, and the corresponding P2 is indicated by the second vertical line. Note that P1 is robust and always occurs at the same pressure. However, P2 is a function of the maximum applied air pressure, which affects CH. The greater the maximum applied air pressure, the greater the CH.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
864
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
material. The device takes advantage of the viscoelasticity of the cornea to produce its metrics of biomechanical behavior. It is important to describe how it functions to understand how the viscoelastic nature of the cornea affects the measurements as well as the impact on data interpretation. The dynamic bidirectional applanator is similar to a noncontact tonometer in that it uses a collimated air jet to deform the cornea but differs from noncontact tonometers in other important ways. Most noncontact tonometers use an infrared (IR) detection system in which the IR emitter is aligned on 1 side of the cornea with an IR detector on the other side using known geometry. Prior to initiation of the air jet, the IR light broadly reflects from the corneal surface, so only a small amount of light is captured by the detector. As the cornea deforms under the applied air pressure, it quickly traverses a state of applanation, which causes the reflected light to align with the detector in a mirror-like fashion, creating an increase in captured light and a spike in the recorded infrared signal. The IR detection system and associated IR and air-pressure signals specifically associated with the dynamic bidirectional applanator are illustrated in Figure 1. Once the first applanation event is detected by the device, the piston producing the air jet receives a signal to shut down to allow the air pressure to dissipate and the cornea to recover its shape. However, the air pressure continues to rise after shutdown because of inertia in the piston, causing the cornea to continue deforming to a concave shape as the air pressure reaches a maximum (Pmax). As the pressure subsequently reduces and the cornea recovers in the outward direction, it rapidly passes through a second state of applanation before achieving the original convex shape. The pressure at which each applanation event occurs is different, with the second always less than the first in a valid measurement. If the cornea were purely elastic, these 2 pressure values would be the same. It is the difference between loading and unloading behavior due to corneal viscoelasticity that causes a reduction in the second applanation pressure. Four parameters are produced by the dynamic bidirectional applanator, based on the 2 pressure measurements at applanation, P1 in the inward direction and P2 in the outward direction. The difference between P1 and P2 is called corneal hysteresis (CH)4 and represents the viscoelastic response of the cornea to an applied force defined by a specific air-pressure curve. The average of P1 and P2 is called Goldmann-correlated IOP (IOPg). Through empirical investigation, 2 other parameters were defined: corneal resistance factor (CRF), which was designed to produce maximum correlation with central corneal thickness (CCT), and corneal-compensated IOP (IOPcc), which was designed
to be similar before and after refractive surgery.A A summary of the equations is given below: CH Z a½P1 P2 CRF Z a½P1 0:7P2 þ d IOPg Z a½ðP1 þ P2Þ=2 þ c IOPcc Z b½P2 0:43P1 þ e where a, b, c, d, and e are calibration and regression constantsB and the expressions set off by brackets represent the generally accepted equations. However, without the constants, CRF would always be greater than CH, which is not the case clinically. Several important factors about these parameters should be remembered. First, all 4 are calculated based on the same 2 pressure measurements, P1 and P2. Therefore, only 2 can be considered completely independent; for example, IOPg (average of P1 and P2) and CH (difference between P1 and P2). The remaining values are highly correlated even though they describe different parameters. The IOPcc compensates for corneal properties in estimating IOP, producing a more accurate value in softer eyes.8 As previously described, corneal properties are a function of IOP.7 Therefore, it is not surprising that IOPcc and CH are highly correlated.9,10 The relationship is negative; that is, as IOPcc increases, CH decreases. The cornea and sclera are stiffer with a higher IOP, and CH decreases as the cornea's ability to dissipate energy decreases with greater wall tension. Second, both CH and CRF are viscoelastic parameters. In the literature, CH is sometimes described as viscoelasticity and CRF is incorrectly described as elasticity or stiffness. Neither of these is an appropriate description for CRF. It is a viscoelastic parameter, weighted by CCT and highly correlated with CH. The weighting by CCT increases the influence of the loading pressure, P1, in the equation for CRF, which increases the influence of elasticity, but it remains fundamentally a viscoelastic parameter due to the inclusion of the unloading applanation pressure, P2. Third, as a viscoelastic parameter, CH is a function of both elasticity and viscosity, so it is inappropriate to interpret CH as relating to stiffness or softness, terms that describe elastic properties. In addition, it has been shown theoretically that the same value of CH can be associated with different combinations of elasticity and viscosity.11 This theoretical model also demonstrates that at low viscosity, greater elastic modulus is associated with lower CH. In contrast, at higher viscosity, greater elastic modulus is associated with higher CH, demonstrating a complex interaction
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
to produce the measured result. Therefore, low CH should not be interpreted as a soft cornea, or a weak cornea, or a damaged cornea, as it is often described in the literature. These descriptions arose from some of the first corneas measured with the dynamic bidirectional applanator, which were keratoconic corneas with low CH4 and known to have low elastic modulus based on previous in vitro studies,12–14 as well as corneas after refractive surgery, which are thinner and softer.4,8 However, low CH can also be measured in a stiff cornea with higher IOP, as previously described. It has also been shown clinically10,15 and in donor corneas5 that CH decreases with age as the cornea is known to stiffen.16,17 Therefore, knowledge of CH alone does not imply that the cornea is either stiff or soft without additional information. For example, low CH is associated with glaucomatous damage,18 which cannot be interpreted as a stiff or a soft cornea without additional information. Further work is necessary to determine what component contributing to this viscoelastic parameter correlates to damage at the optic nerve. As mentioned previously, the maximum air pressure (Pmax) of the dynamic bidirectional applanation device is variable depending on the timing of the first applanation event. The earlier it occurs, the lower the Pmax. Two studies have been conducted to determine the influence of the characteristics of the air-pressure curve on measured CH.C,D In both studies, it was shown that the earlier the first applanation event occurred, which generated a lower maximum applied air pressure, the lower was the measured CH. The loading phase, in which the air pressure is increasing, is the same from examination to examination. However, the unloading phase, in which the cornea recovers its shape, is different depending on the timing of the first applanation event and Pmax. This is illustrated in Figure 2, with several different air-pressure curves for the same eye. Note that P1 is robust, occurring at the same point with each examination, but P2 occurs later with higher maximum applied air pressure, leading to a greater CH. Again, this phenomenon is due to the viscoelastic nature of the cornea. What influences P1 and how can the biomechanical data be interpreted in light of the device functionality? Most noncontact tonometers have only P1, so one can conclude that the strongest predictor of P1 should be IOP. Two factors influencing P1 have been reported, confirming IOP has a strong relationship and, to a less extent, CCT.19,20 Corneal stiffness was not evaluated. However, theory leads us to conclude that after IOP, corneal stiffness and, to a less extent, CCT would influence the timing and magnitude of P1.21 Thus, one can think of the CH produced by the dynamic bidirectional applanator as characteristic of an individual
865
cornea and IOP since it is tied to the P1 and Pmax of that eye. It is clear that this natural CH has clinical value due to the many reports in the literature, including its association with glaucomatous damage.18 However, it should not be mistaken for an elastic parameter, as in the quest to differentiate a soft keratoconic cornea from a stiffer normal cornea. Such an application might require a different parameter that is not viscoelastic. Since the timing of the first applanation event is influenced by IOP and corneal properties, and since the geometry of the corneal surface shape and IR detection system may affect the amount of light captured by the detector, detailed signal analysis can provide additional insight into corneal biomechanical characteristics. Figure 1 shows a schematic of the dynamic bidirectional applanation signal and the parameters that have been reported, along with their definitions. Each parameter carries a physical meaning associated with specific signal features. For example, the width of each IR peak (full width half maximum) corresponds to the speed at which the cornea moves through applanation. Greater width in a goodquality signal represents a cornea that is moving at a slower rate, since it takes longer to traverse applanation. Slower movement is associated with a stiffer cornea, since it takes greater force to deform a stiffer material and reach the same velocity.E The amplitude of the first IR peak (Peak 1) corresponds to the size of the area of applanation, with a larger area producing greater amplitude since more light is captured by the detector. It has been hypothesized that this may correspond to the stiffness of the cornea since a softer cornea with a lower elastic modulus would have greater deformation under the same load. Therefore, softer corneas would produce deep, narrow deformations, and stiffer corneas would produce wide, shallow deformations. There is clinical evidence to support this hypothesis,22 including the first report of signal analysis in 2008, which compared the signal features in a post-laser in situ keratomileusis (LASIK) ectatic eye and the fellow eye with a normal post-LASIK outcome.23 Both CH and CRF in the 2 eyes were similar, but the signals were distinct, as shown in Figure 3. The IR signal was dramatically damped in the ectatic eye, with lower peaks in the presumably softer cornea. The viscoelastic CH parameter did not clearly distinguish between the 2 corneas, with biomechanical decompensation in only 1 eye, likely because the elastic modulus and viscous damping were affected in a manner that produced similar CH. Other reports have shown the importance of Peak1 in qualitatively evaluating corneal stiffness, including correlating Peak 1 magnitude to severity of keratoconus,F screening forme fruste keratoconus,24,25 comparing
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
866
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
Figure 3. Dynamic bidirectional applanation signals from 2 contralateral eyes after LASIK. The eye on the left had a normal postoperative outcome, and the eye on the right developed ectasia. Note the presumed softer ectatic eye on the right has damped signals. (Figure adapted from reference 22.)
LASIK and surface ablation,26 as well as the effect of creating a flap,27 and evaluating changes after corneal collagen crosslinking.28,29 Other customized parameters derived from signal analysis have been reported.30 With the additional biomechanical information that was evident in signal analysis of the dynamic bidirectional applanator, the manufacturer derived 42 parameters from the IR and air-pressure signals, including the original 4 parameters of CH, CRF, IOPcc, and IOPg. In cooperation with 4 investigators from 3 countries, a Keratoconus Match Index was developed, which was used to provide the probability that a particular waveform was consistent with keratoconus. Several reports use these new waveform metrics.31–33 More study is needed to identify the most clinically useful parameters. In the past 2 years, a new device designed to measure corneal deformation characteristics was introduceddthe Corvis ST (Oculus Optikger€ ate GmbH),34 called a dynamic Scheimpflug analyzer for the purpose of publication. This device is similar to the dynamic bidirectional applanator in that it uses an air puff to deform the cornea but is distinct in many ways. The dynamic Scheimpflug analyzer captures a single Scheimpflug image of the horizontal (0 degree) meridian of the cornea during deformation at greater than 4300 frames per second, producing about 140 images during 30 ms. Sample images are shown in Figure 4. From this real-time series of images, deformation characteristics can be extracted along with the potential to quantify corneal elastic parameters. The same basic biomechanical concepts apply to this device in that IOP will influence corneal biomechanical behavior. Therefore, in the overlapped images of Figure 5, both IOPcc (from the dynamic bidirectional applanator) and CCT were similar between the normal cornea (pseudocolored in blue) and the keratoconic cornea (pseudocolored in red). The overlapped videos show a comparison of the entire deformation process (Video 1, available at: http://jcrsjournal.org). Note that the maximum deformation amplitude in the keratoconic cornea is much greater than that in the normal cornea. This indicates that the normal cornea is stiffer
and thus deforms less, only because IOPcc is matched between the 2 eyes. Without this match, the difference could simply be a difference in IOP. In a study reported at the Association for Research in Vision and Ophthalmology meeting in 2011,E it was shown that IOP is the strongest predictor of deformation amplitude, followed by a corneal biomechanical parameter, and finally, CCT. The strong influence of IOP on corneal deformation was also verified in an ex vivo study using pig eyes.35 It is critical to note the differences in the characteristics of the air puffs between the 2 devices described. Unlike the dynamic bidirectional applanator, the dynamic Scheimpflug analyzer produces a consistent air puff with each examination. Therefore, although the same relative biomechanical relationships will
Figure 4. Scheimpflug images extracted from a series of 140 images of a cornea deforming under an air puff from the dynamic Scheimpflug analyzer.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
867
Figure 5. Overlapped images measured with dynamic Scheimpflug analyzer from a normal cornea (blue) and a keratoconic cornea (red), both with similar IOPcc from dynamic bidirectional applanation (13.3 mm Hg for normal cornea and 13.7 mm Hg for keratoconic cornea) and similar CCT. (Data from Renato Ambr osio Jr, MD, PhD, and processing by Ashraf M. Mahmoud.)
apply to both devices, including that a stiffer eye will deform later, move more slowly, and recover more quickly (all with consistent IOP), the magnitude of the specific parameters will likely be distinct in any comparisons between devices due to the differences in the air puff itself, in combination with the viscoelasticity of the cornea. In summary, a significant amount of biomechanical information regarding the natural CH of the eye and in vivo corneal viscoelastic response to an air puff has been learned since 2005. With the introduction of a new device using a distinctly different air-puff stimulus and new potential for analyzing specific deformation characteristics from real-time images, it is expected that new investigations will add complimentary information to our growing understanding of the important role of corneal biomechanics in many clinical applications. As these new studies move forward, it will be crucial to note the effect of IOP on corneal biomechanical assessment and broaden our expectations beyond a single biomechanical parameter to characterize an individual cornea's strength or weakness. Our goal can be modified to generate a 2-D assessment of stiffness as a function of IOP, as illustrated by the schematic diagram in Figure 6. The
weaker corneas will have lower stiffness at all values of IOP, corresponding to a region on this plot rather than a single point.
Figure 6. Schematic diagram of proposed 2-D assessment of corneal biomechanics showing stiffness as a function of IOP, with each curve representing a different hypothetical cornea. The lower curves represent softer corneas (yellow-red) and the upper curves represent stiffer corneas (green-blue). Note that a softer cornea at higher IOP will have greater apparent stiffness than a cornea that is fundamentally stiffer but with a lower IOP, indicated by the 2 black dots.
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
868
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
REFERENCES 1. Schwartz NJ, Mackay RS, Sackman JL. A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of the intraocular pressure. Bull Math Biophys 1966; 28:585–643 2. Jue B, Maurice DM. The mechanical properties of rabbit and human cornea. J Biomech 1986; 19:847–853 3. Hoeltzel DA, Altman P, Buzard K. Choe K-i. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng 1992; 114:202–215. Available at: http://www.buzard.info/StripExtensiometry.pdf. Accessed January 9, 2014 4. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg 2005; 31:156–162 5. Elsheikh A, Wang D, Brown M, Rama P, Campanelli M, Pye D. Assessment of corneal biomechanical properties and their variation with age. Curr Eye Res 2007; 32:11–19 6. Elsheikh A, Wang D, Rama P, Campanelli M, Garway-Heath D. Experimental assessment of human corneal hysteresis. Curr Eye Res 2008; 33:205–213 7. Elsheikh A, Wang D, Pye D. Determination of the modulus of elasticity of the human cornea. J Refract Surg 2007; 23:808–818 8. Pepose JS, Feigenbaum SK, Qazi MA, Sanderson JP, Roberts CJ. Changes in corneal biomechancis and intraocular pressure following LASIK using static, dynamic and noncontact tonometry. Am J Ophthalmol 2007; 143:39–47 9. Alhamad TA, Meek KM. Comparison of factors that influence the measurement of corneal hysteresis in vivo and in vitro. Acta Ophthalmol 2011; 89:e443–e450. Available at: http://onlinelibrary. wiley.com/doi/10.1111/j.1755-3768.2011.02150.x/pdf. Accessed January 9, 2014 10. Roberts CJ, Reinstein DZ, Archer TJ, Mahmoud AM, Gobbe M, Lee L. Comparison of biomechanical response parameters using dynamic bidirectional applanation analysis between myopic and hyperopic eyes. J Cataract Refract Surg 2014; 40: 11. Glass DH, Roberts CJ, Litsky AS, Weber PA. A viscoelastic biomechanical model of the cornea describing the effect of viscosity and elasticity on hysteresis. Invest Ophthalmol Vis Sci 2008; 49:3919–3926. Available at: http://www.iovs.org/cgi/ reprint/49/9/3919. Accessed January 9, 2014 12. Foster CS, Yamamoto GK. Ocular rigidity in keratoconus. Am J Ophthalmol 1978; 86:802–806 13. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res 1980; 31:435–441 14. Nash IS, Greene PR, Foster CS. Comparison of mechanical properties of keratoconus and normal corneas. Exp Eye Res 1982; 35:413–424 15. Kamiya K, Shimizu K, Ohmoto F. Effect of aging on corneal biomechanical parameters using the Ocular Response Analyzer. J Refract Surg 2009; 25:888–893 16. Malik NS, Moss SJ, Ahmed N, Furth AJ, Wall RS, Meek KM. Ageing of the human corneal stroma: structural and biochemical changes. Biochem Biophys Acta 1992; 1138:222–228 17. Daxer A, Misof K, Grabner B, Ettl A, Fratzl P. Collagen fibrils in the human corneal stroma: structure and aging. Invest Ophthalmol Vis Sci 1998; 39:644–648. Available at: http://www.iovs.org/ cgi/reprint/39/3/644. Accessed January 9, 2014 18. Congdon NG, Broman AT, Bandeen-Roche K, Grover D, Quigley HA. Central corneal thickness and corneal hysteresis associated with glaucoma damage. Am J Ophthalmol 2006; 141:868–875 19. Kotecha A, Elsheikh A, Roberts CR, Zhu H, Garway-Heath DF. Corneal thickness-and age-related biomechanical properties of
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
the cornea measured with the Ocular Response Analyzer. Invest Ophthalmol Vis Sci 2006; 47:5337–5347. Available at: http:// www.iovs.org/cgi/reprint/47/12/5337. Accessed January 9, 2014 Terai N, Raiskup F, Haustein M, Pillunat LE, Spoerl E. Identification of biomechanical properties of the cornea: the Ocular Response Analyzer. Curr Eye Res 2012; 37:553–562 Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement; quantitative analysis. J Cataract Refract Surg 2005; 31:146–155 Glass DH. Characterization of the Biomechanical Properties of the In Vivo Human Cornea [dissertation]. Columbus, OH, Ohio State University, 2008; Available at: https://etd.ohiolink.edu/ ap/0?0:APPLICATION_PROCESS%3DDOWNLOAD_ETD_ SUB_DOC_ACCNUM:::F1501_ID:osu1211920104%2Cinline. Accessed January 9, 2014 Kerautret J, Colin J, Touboul D, Roberts C. Biomechanical characteristics of the ectatic cornea. J Cataract Refract Surg 2008; 34:510–513 Schweitzer C, Roberts CJ, Mahmoud AM, Colin J, MauriceTison S, Kerautret J. Screening of forme fruste keratoconus with the Ocular Response Analyzer. Invest Ophthalmol Vis Sci 2010; 51:2403–2410. Available at: http://www.iovs.org/content/ 51/5/2403.full.pdf. Accessed January 9, 2014 nard A, Mahmoud AM, Gallois A, Colin J, Touboul D, Be Roberts CJ. Early biomechanical keratoconus pattern measured with an ocular response analyzer: curve analysis. J Cataract Refract Surg 2011; 37:2144–2150 Qazi MA, Sanderson JP, Mahmoud AM, Yoon EY, Roberts CJ, Pepose JS. Postoperative changes in intraocular pressure and corneal biomechanical metrics; laser in situ keratomileusis versus laser-assisted subepithelial keratectomy. J Cataract Refract Surg 2009; 35:1774–1788 lu G, Mahmoud AM, Roberts CJ. Kılıc‚ Uzbek A, Kamburog Change in biomechanical parameters after flap creation using the IntraLase femtosecond laser and subsequent excimer laser ablation. Curr Eye Res 2011; 36:614–619 E, Mahmoud AM, Trazza S, Hafezi F, Vinciguerra P, Albe Roberts CJ. Intra- and postoperative variation in ocular response analyzer parameters in keratoconic eyes after corneal cross-linking. J Refract Surg 2010; 26:669–676 Kılıc‚ A, Roberts CJ. Biomechanical and refractive results of transepithelial crosslinking treatment in keratoconic eyes. Int J Kertoconus Ectatic Corneal Dis 2012; 1(2):75–78. Available at: http:// www.jaypeejournals.com/eJournals/ShowText.aspx?IDZ3332& TypeZFREE&TYPZTOP&INZ_eJournals/images/JPLOGO. gif&IIDZ258&isPDFZYES. Accessed January 9, 2014 Hallahan KM, Roy AS, Ambrosio R Jr, Salomao M, Dupps WJ Jr. Discriminant value of custom Ocular Response Analyzer waveform derivatives in keratoconus. Ophthalmology 2013 Nov 26 [Epub ahead of print] Mikielewicz M, Kotliar K, Barraquer RI, Michael R. Air-pulse corneal applanation signal curve parameters for the characterisation of keratoconus. Br J Ophthalmol 2011; 95:793–798 Spoerl E, Terai N, Scholz F, Raiskup F, Pillunat LE. Detection of biomechanical changes after corneal cross-linking using Ocular Response Analyzer software. J Refract Surg 2011; 27:452–457 Lam AKC, Chen D, Tse J. The usefulness of waveform score from the ocular response analyzer. Optom Vis Sci 2010; 87:195–199. Available at: http://journals.lww.com/optvissci/ Fulltext/2010/03000/The_Usefulness_of_Waveform_Score_from_ the_Ocular.10.aspx. Accessed January 9, 2014 sio R Jr, Ramos I, Luz A, Correa Faria F, Steinmueller A, Ambro Krug M, Belin MW, Roberts CJ. Dynamic ultra-high-speed Scheimpflug imaging for assessing corneal biomechanical
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
CORNEAL BIOMECHANICS: CONCEPTS AND MISCONCEPTIONS
properties. Rev Bras Oftalmol 2013; 72:99–102. Available at: http://www.scielo.br/pdf/rbof/v72n2/05.pdf. Accessed January 9, 2014 35. Kling S, Marcos S. Contributing factors to corneal deformation in air puff measurements. Invest Ophthalmol Vis Sci 2013; 54:5078–5085
OTHER CITED MATERIAL
A. Luce DA. Methodology for cornea compensated IOP and corneal resistance factor for the Reichert Ocular Response Analyzer. IOVS 2006; 47:ARVO E-Abstract 2266. Available at: http://abstracts.iovs.org//cgi/content/abstract/47/5/2266?sidZ 3427a143-0993-4537-a038-9896d5877b79. Accessed January 9, 2014 B. Reichert Technologies. Personal communication, May 2006. C. Rouse EJ, Roberts CJ, Mahmoud AM. The measurement of biomechanical parameters as a function of peak applied pressure in the Reichert Ocular Response Analyzer. IOVS 2007; 48:ARVO E-Abstract 1247. Available at: http://abstracts.iovs. org//cgi/content/abstract/48/5/1247?sidZ129416b7-6a47-4fecaf74-97dee0b9a1ae. Accessed January 9, 2014 D. Asaoka R, Kotecha A, White E, Garway-Heath DF. The effects of maximum air pulse pressure and intraocular pressure on corneal hysteresis measurements with the Reichert Ocular Response Analyzer. IOVS 2008; 49:ARVO E-Abstract 703. Available at: http://abstracts.iovs.org//cgi/content/abstract/49/
869
5/703?sidZ40cd0ea6-69e7-493a-87ba-42816c239142. Accessed January 9, 2014 E. Roberts CJ, Mahmoud AM, Ramos I, Caldas D, Siqueira da sio R Jr. Factors influencing corneal deformation Silva R, Ambro and estimation of intraocular pressure. IOVS 2011; 52:ARVO EAbstract 4384. Available at: http://abstracts.iovs.org//cgi/ content/abstract/52/6/4384?sidZ86e3462e-06d3-46fa-a25a6ddf31f7b7a2. Accessed January 9, 2014 F. Mahmoud AM, Twa MD, Qazi M, Pepose J, Roberts CJ. Comparison of biomechanical and topographic parameters in normal and pathologic corneas. IOVS 2007; 48:ARVO E-Abstract 1843. Available at: http://abstracts.iovs.org//cgi/content/abstract/48/5/ 1843?sidZffc278f0-2670-455b-8e48-d4147e08f778. Accessed January 9, 2014
J CATARACT REFRACT SURG - VOL 40, JUNE 2014
First author: Cynthia J. Roberts, PhD Department of Ophthalmology and Visual Science, Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA
