The importance of corneal biomechanics in ophthalmology has fueled the drive to develop new devices for the clinical assessment of corneal biomechanical properties, as well as compensate for the influence of biomechanical properties on estimation of intraocular pressure (IOP).1 Historically, assessment of corneal stiffness has been accomplished via cutting strips of corneal tissue from post-mortem donors and applying a tensile load in the form of stretching the tissue to specific strains, defined as percent change in length, while plotting the stress at each level of strain.2–5 The slope of the stress–strain curve is defined as the tensile elastic modulus, with greater slope indicating a higher elastic modulus and a stiffer material. This can also be interpreted that a stiffer material has greater resistance to deformation because a higher stress is associated with a lower strain than in a softer material. The evaluation is more complicated in a cornea because it is viscoelastic in nature, which means that the stress–strain response is a function of the strain rate, or how quickly the tissue is stretched6 and exhibits a nonlinear stress–strain relationship such that higher levels of stress are associated with greater elastic modulus.6,7 The challenge in transferring biomechanical property assessment to the in vivo condition has been to determine a clinically acceptable approach to perturb a cornea that is preloaded by IOP and to manage eye motion. Because biomechanical properties are defined by the response to a perturbation or applied load, a clinically viable load must be determined. In addition, IOP is a confounding factor in assessment of corneal biomechanics because the cornea stiffens as IOP increases, making the two factors of stiffness and IOP inseparable.8
The first clinical device to be introduced capable of assessing biomechanics was the Ocular Response Analyzer (Reichert Technologies, Depew, NY),9 followed by the Corvis ST (Oculus Optikgeräte GmbH, Wetzlar, Germany).10 Both current clinical devices rely on an air puff to deform the cornea and assess biomechanical deformation response parameters. The Ocular Response Analyzer relies on an indirect assessment of deformation response and produces corneal hysteresis, which is widely recognized as a biomechanical parameter but is complicated to interpret due to the nature of the measurement. The Corvis ST uses ultra high-speed Scheimpflug imaging to directly assess deformation response. This allows visualization and analysis of a large set of biomechanical deformation response parameters. However, interpretation of the data produced is difficult due to the quantity of parameters and their interaction with both stiffness and IOP. Therefore, the purpose of the current study was to define two new stiffness parameters that are a function of IOP and investigate the relationship of various dynamic corneal response (DCR) parameters to these global indications of corneal stiffness in both normal patients and those diagnosed as having keratoconus.
Patients and Methods
Patients and Devices
A retrospective study was conducted with patients enrolled from two sites: the Instituto de Olhos Renato Ambrósio in Rio de Janeiro, Brazil, and the Vincieye Clinic in Milan, Italy. For each patient, a random eye was chosen for inclusion in the study. The combined dataset consisted of 180 eyes of 180 keratoconic patients (diagnosed by one author [RA or PV]) and 482 eyes of 482 normal patients. All patients received a complete ophthalmic examination that included the Corvis ST and Pentacam (Oculus Optikgeräte GmbH). The Corvis ST is a dynamic Scheimpflug analyzer that uses a consistent air puff to deform the cornea while an ultra high-speed camera (approximately 4,300 frames per second) using Scheimpflug geometry simultaneously captures a series of 140 images of a single, central, horizontal meridian of the cornea.
The inclusion criteria for the keratoconic population were the presence of bilateral clear topographic and tomographic keratoconus without any previous ocular surgeries, such as corneal collagen cross-linking or implanted intracorneal rings. Conversely, the inclusion criteria for the healthy patients were the presence of a Corvis ST examination in the database and a Belin/Ambrósio Enhanced Ectasia Index total deviation (BAD-D) from the Pentacam less than 1.6 standard deviations from normative values in both eyes. Exclusion criteria were any previous ocular surgery or disease, myopia greater than 10.00 diopters (D), and any concomitant or previous glaucoma or hypotonic therapies. The BAD-D cut-off of 1.6 standard deviations was used because it is described as the best performing screening parameter with values of 1.65 and 1.88 associated with a 95% and 97.5% confidence interval, respectively, with an acceptable false-negative rate of less than 1%.11 Only Corvis ST examinations with acceptable quality were included in the analysis, and Research Software (version 1.2b1302) was used. A manual, frame-by-frame analysis of each examination, made by an independent masked examiner, was performed to ensure quality of each acquisition. The main criterion was good edge detection over the whole deformation response, with the exclusion of alignment errors (x-direction). Similarly, blinking errors were omitted. Moreover, all examinations of the Vincieye Clinic were reevaluated by a masked anterior segment expert (RA) to confirm the diagnosis. Similarly, all of the examinations of the Instituto de Olhos Renato Ambrósio were reevaluated by a masked expert (PV). All measurements with the Corvis ST were taken by the same experienced technicians.
Demographic data, including age and sex, were also acquired. There were 93 women and 65 men in the normal group and 51 women and 107 men in the keratoconus group. In Brazil, the local institutional review board approved the study and determined that patient consent was not required. In Italy, the local institutional review board determined that approval was not required. However, patients provided informed consent to provide their data for research at the time they were seen in clinic. The study was conducted according to the tenets of the Declaration of Helsinki, as revised in 2000. All data were exported from the respective device at each site and transferred to The Ohio State University for further analysis after anonymization.
A description of the phases in the corneal deformation process and associated DCR parameters is given in Tables A–B and Figures A–C (available in the online version of this article).
Corneal Deformation Process and Dynamic Response Parameters
Dynamic Corneal Response Parameters and Associated Deformation Phase
The nine phases of corneal deformation response to an air puff are superimposed over the plots of apex deformation (blue) that includes whole eye motion (green) and pure corneal deflection (red), that is the difference between the other two.
Superimposed frames extracted from a single examination, showing (A) cornea in the predeformation phase (pseudocolored blue), at maximal corneal deflection (pseudocolored red), and at maximal whole eye movement (pseudocolored white); (B) cornea at maximum deflection (highest concavity) with illustration of displacement from predeformation anterior surface arc (blue line); and (C) correction for whole eye motion by aligning all corneal positions to that at predeformation. Note the example shown is from the cornea with the greatest magnitude of whole eye motion in the entire dataset for illustration of multiple phases, and therefore represents an extreme value. Note also that maximal whole eye motion occurred after corneal deflection had recovered completely.
Schematic diagram of three-point loading of a beam. Stiffness = Load/Displacement
Stiffness Parameter and IOP
Conceptually, stiffness describes the resistance to deformation. Therefore, with the goal to develop simple clinical parameters that would correlate with stiffness, two novel stiffness parameters were developed, defined as Resultant Pressure divided by displacement. The position of first applanation (A1) was the reference for calculating the load on the cornea, Resultant Pressure. Stiffness parameter A1 uses the displacement between the apex in the undeformed state and the deflection at A1 (A1DeflAmp). Stiffness parameter highest concavity (HC) uses the difference in A1 position and maximum deflection near highest concavity (DeflAmpMax) minus deflection amplitude at A1 (A1DeflAmp). Resultant Pressure was calculated as the air pressure impinging on the cornea at the time of applanation minus the IOP. To determine the air pressure on the cornea, the spatial and temporal profiles of the air puff were measured by hot wire anemometry in the xy and xz planes, shown in Figure DA (available in the online version of this article). A photocell sensor was installed at the outlet of the nozzle to synchronize measured velocity data and the pressure signal produced by the Corvis ST. Hot wire calibration was done with a 2.5-mm orifice to replicate the actual flow condition in the subsequent experiments. Data were acquired at a sampling rate of 20 kHz, from 0 to 16 mm from the nozzle in 2-mm increments in the axial direction and in 0.75-mm increments up to 3 mm on each side of the center line, for a total of 81 individual points, shown in Figure DB, with 40 individual puffs for each data point. The characterization of the air puff demonstrated that the velocity time history at a single location remained consistent for all 40 puffs that were measured, and the flow was also verified to be axisymmetric. This velocity was converted to a dynamic pressure using the ambient density.
(A) Experimental set-up for hot wire anemometry. (B) Locations for measurement of air puff velocity relative to nozzle.
For each clinical examination, pressure at first applanation (AP1) was used to align with the time-synchronized measured velocity and pressure signals, shown in Figure 1A. From this, the velocities at z positions of 10 and 12 mm from the nozzle were determined, corresponding to the phase-adjusted time of AP1. The z position of the corneal surface within the image window at A1 was exported from the Corvis ST and the total distance from the nozzle was calculated. This value was used to interpolate between the 10- and 12-mm positions on the centerline velocity distribution (Figure 1B). Prior to interpolation, each curve was fit with a polynomial in the region of A1, approximately 6 to 14 ms. The order of the polynomial was increased until a maximum R2 resulted, which was a cubic at 10 mm and 4th order at 12 mm, for an R2 of .9998. This interpolated velocity for each examination, along with the z position of the cornea at the time of inward applanation, was used to calculate the reduction of nozzle air pressure as it propagates in time and space, called the adjusted air pressure value (adjAP1) at the time and position of A1. An algorithm intended to produce an IOP estimate that compensates for the effects of central corneal thickness and age has been developed numerically using finite element analysis and validated both experimentally and clinically.12 This algorithm, modified with Corvis ST data to produce a biomechanically corrected IOP estimate (bIOP), was used to generate the IOP value in both stiffness parameter calculations, with the final equations:
(A) Measured velocity (red) and Corvis ST (Oculus Optikgeräte GmbH, Wetzlar, Germany) exported pressure signal (green), both time-synchronized by the photo cell signal (blue). (B) Centerline velocity distribution as a function of distance from the nozzle.
These values take into account both the intraocular pressure and pure corneal deflection, both of which have confounded earlier analyses of corneal deformation parameters.
To determine the influence of stiffness on corneal deformation parameters, a series of regression analyses were performed with stiffness parameters A1 or HC as the independent variable and each deformation parameter as the dependent variable for both the normal and keratoconic groups. To compare deformation parameters between groups, a subset of 158 normal and 158 keratoconic patients were matched by bIOP, and t tests were performed on the corneal deformation parameters between groups. Using a Bonferroni correction for multiple t test comparisons, a P value of less than .0025 was considered significant. To investigate timing of the maximum difference in deformation of the corneal apex divided by the average deformation 2 mm from either side of the apex (DA Ratio) and the timing of maximum whole eye motion (WEMmax), two regression analyses were performed, including the time of DA Ratio vs A1 time and the time of WEMmax vs A2 time. In addition, to test the prediction that the difference in arclength between HC and the predeformation Arclength (HCdarclength) is a function of corneal deflection amplitude at HC (HCDeflAmp), a third regression analysis was performed between HCdarclength and HCDeflAmp.
Regression analysis of A1 time and DA Ratio time showed a significant positive linear relationship between the two for both normal and keratoconic patients (normal: R2 = .8164, P < .0001; keratoconic: R2 = .6749, P < .0001). The relationship between A2 time and the time of WEMmax is also a significantly positive linear relationship in both groups (normal: R2 = .0392, P < .0001; keratoconic: R2 = .0352, P = .0117). However, the R2 is substantially lower than the first comparison, meaning not only is there greater variability, but also a much weaker correlation between A2 time and the time of WEMmax. Finally, the relationship between HCDeflAmp and (a negative number) is significantly negative for normal eyes, meaning that higher HC deflection amplitude is associated with greater change in arclength (a larger magnitude negative value), which is expected. However, it is significantly positive for keratoconic eyes, which is opposite to that of normal eyes and unexpected (normal: R2 = .2627, P < .0001; keratoconic: R2 = .0307, P < .0185) (Figure 2A). This unexpected result led to a division of the keratoconic group into two subgroups for further analysis, with KC1 having less than 1 mm HCDeflAmp and KC2 with 1 mm or greater HCDeflAmp. The greater amplitude deflection is presumably associated with more advanced disease with less resistance to deformation. Only the KC2 subgroup with presumably more advanced disease maintained the significantly positive relationship (KC2: R2 = .0503, P < .0249). The KC1 subgroup behaved similarly to the normal group, with a significantly negative relationship (KC1: R2 = .0953, P < .0053) (Figure 2B).
Regression analyses of highest concavity delta arclength (HCdarclength) vs highest concavity deflection amplitude (HCDeflAmp). (A) Note the significant but opposite relationships of both normal (NL) and keratoconic (KC) groups. In normal eyes, as HCDeflAmp increases, the negative magnitude of delta arclength also increases. In other words, the greater the resistance to deformation (low HCDeflAmp), the less the arclength shortened. However, the keratoconic eyes had less shortening of the arclength, even with greater HCDeflAmp, likely due to pathology of the collagen fibers, limiting normal crimping with arclength shortening. (B) The keratoconic group is subdivided into KC1 with HCDeflAmp < 1 mm and KC2 with HCDeflAmp ≥ 1 mm. Note that KC1 has the same significantly negative relationship as normal eyes. Only the KC2 group with larger HC deflection amplitudes and therefore presumably more advanced disease, maintained the positive relationship.
Table 1 compares DCR parameters in the bIOP-matched subset of normal and keratoconic patients. Demographics of the two groups are listed in Table 2. Significant differences were found for all reported parameters except peak distance, which is the width of the concavity at HC, HCDeflArea, and WEMmax, with normal eyes exhibiting stiffer behavior, or less resistance to deformation, than keratoconic eyes for all other parameters. The normal group is stiffer with greater stiffness parameter A1 and stiffness parameter HC, thicker pachymetry, lower DA Ratio, later A1 times (requiring higher air pressure) with longer applanation lengths and slower velocities, lower deformation and deflection amplitudes, greater HC radius (flatter curvature) with lower Inverse Radius, and earlier A2 times.
Mean ± Standard Deviation in bIOP-Matched t test Comparison
Demographics of bIOP-Matched Groups
The results of the regression analyses are summarized in Tables C–D (available in the online version of this article) for stiffness parameters A1 and HC, respectively. Selected regression plots are shown in Figures 3–6. In both normal and keratoconic patients, both stiffness parameters were significantly positively correlated with second applanation length, first applanation time, HCRadius, pachymetry, and bIOP, as well as significantly negatively correlated with absolute magnitude of both applanation velocities, second applanation time, both DA and DA Ratio, HCDeflAmp, HCDeflArea, Peak Distance, and InvRadMax. Stiffness parameter A1 was significantly positively correlated with A1 Length and significantly negatively correlated with A1DeflAmp only in keratoconic eyes, and no relationship in either group with WEM. Stiffness parameter HC was significantly positively correlated with A1 Length in both groups, though weak, and both A1DeflAmp and WEM were correlated only in normal eyes. The relationship of WEM in keratoconic eyes was not significant for stiffness parameter HC. For HCdarclength, both stiffness parameters were significantly positively correlated in normal eyes and significantly negatively correlated in keratoconic eyes, although both relationships were weak.
Regression Analysis Statistics Between Stiffness Parameter SP-A1 and Dynamic Corneal Response Parameters
Regression Analysis Statistics Between Stiffness Parameter SP-HC and Dynamic Corneal Response Parameters
Regression analysis of pachymetry vs (A) stiffness parameter applanation 1 (SP-A1) and (B) stiffness parameter highest concavity (SP-HC), both showing that thicker corneas tend to be stiffer in both normal (black) and keratoconic (red) eyes. Note that SP-A1 shows greater separation between keratoconic (KC) eyes and normal (NL) eyes.
Regression analysis of deformation amplitude ratio (DA Ratio) at 2 mm vs (A) stiffness parameter applanation 1 (SP-A1) and (B) stiffness parameter highest concavity (SP-HC), both showing that stiffer eyes with greater resistance to deformation have lower magnitude DA Ratio in both normal (black) and keratoconic (red) eyes. Note that SP-A1 shows greater separation between keratoconic (KC) eyes and normal (NL) eyes.
Regression analysis of maximum deflection amplitude (DeflAmpMax) vs (A) stiffness parameter applanation 1 (SP-A1) and (B) stiffness parameter highest concavity (SP-HC), both showing stiffer eyes have lower maximum corneal deflection in both normal (NL) (black) and keratoconic (KC) (red) eyes.
Regression analysis of highest concavity radius vs (A) stiffness parameter applanation 1 (SP-A1) and (B) stiffness parameter highest concavity (SP-HC), both showing stiffer eyes have greater radius of concave curvature or are flatter at highest concavity in both normal (NL) (black) and keratoconic (KC) (red) eyes.
Biomechanical response parameters can be interpreted relative to stiffness in terms of resistance to deformation. The stiffer the cornea, the greater the resistance to deformation, and therefore greater air pressure is required to initiate and maintain motion. The major confounding factor is IOP because both the cornea and sclera will stiffen as IOP increases.8 This is due to two factors in combination: LaPlace's Law, which states that as internal pressure increases, wall stress also increases, and the nonlinear properties of the cornea such that as stress increases, the elastic modulus, E, also increases. This leads to a complex corneal response to air puff–induced deformation in the intact globe. Certain response parameters will be dominated by IOP, whereas others will be dominated by corneal stiffness.13 However, the entire response will be integrated over all influencing factors. In the current study, the confounding influence of IOP was removed in the comparison of normal corneas to those with keratoconus by matching both groups on bIOP. With the consistency of the air puff pressure provided by the device under study validated during characterization, a direct comparison of the response parameters between the two groups can be performed with confidence in this matched subset. Additional interpretation of the influence of the stiffness parameters on the DCR parameters is given in Tables A–B and Figures A–C.
The differences between the two stiffness parameters include stronger correlations of both the HC deformation parameters and A2 parameters to stiffness parameter HC, than to stiffness parameter A1. However, stiffness parameter A1 has greater separation between normal and keratoconic groups, shown in Table 1 and Figures 3–6. Stiffness parameter A1 also has stronger correlations to both pachymetry and DA Ratio, which occurs near A1. Therefore, it might be expected that stiffness parameter A1 would be a stronger biomarker for corneal conditions, such as keratoconus, and this has been reported.14 It is expected that stiffness parameter HC might be a stronger biomarker for conditions that involve the sclera because a stiffer sclera can limit the magnitude of maximum corneal deformation.15 The relationships to A1DeflAmp are interesting in that with stiffness parameter HC, a positive correlation exists for the normal eyes, but no significant relationship exits in keratoconus. Conversely, there is no relationship in normal eyes in the regression of A1DeflAmp to stiffness parameter A1, but a significant negative correlation exists in keratoconic eyes. For stiffness parameter HC, this may be due to corneal geometry near the beginning of the pulse, so that the later applanation time in normal eyes will lead to greater air pressure and greater amplitude at applanation. However, in the comparison between the bIOP-matched groups, A1DeflAmp was lower in the normal eyes than keratoconic eyes. This may be due to greater curvature in keratoconus, which would impact early deflection amplitude, and can also explain the negative correlation in keratoconic eyes to stiffness parameter A1. The keratoconic eyes that are relatively stiffer (less severe disease) would presumably have lower curvature and thus less amplitude at A1.
HCdarclength showed a different relationship with stiffness between normal and keratoconic eyes, with a significantly positive relationship in normal eyes and significantly negative relationship in keratoconic eyes for both stiffness parameters A1 and HC. This can be interpreted that the stiffer the normal eye, the lower the negative change. In other words, with greater resistance to deformation, the arclength shortened less. This was confirmed in the regression between HCdarclength and HCDeflAmp (Figure 2) in normal eyes and in the KC1 subgroup with less advanced disease. As the cornea becomes concave, the arclength shortens with increased crimping of the collagen fibers. Therefore, the greater the amplitude of deflection, the shorter becomes the arclength, or in other words, the greater is the negative change in the HCdarclength in the less stiff normal eyes. However, in keratoconus, the relationship was the opposite, but only in the subgroup with greater HCDeflAmp and thus presumably more advanced disease, which seems paradoxical. One explanation to consider, however, is the biomechanical consequences of the pathology in the collagen fibers.16 Ultrastructural abnormalities have been identified in keratoconus, including disorganized collagen fibers17 with a loss of anchoring fibrils near Bowman's layer.18 It may be that the diseased collagen fibers are not able to crimp in the way that normal fibers do. This effect would be greater with more advanced disease. This is also consistent with the results of the bIOP-matched comparison, which showed a greater negative HCdarclength in normal eyes than in keratoconus, despite the greater stiffness and resistance to deformation in the normal eyes, combined with lower HCDeflAmp.
Two novel stiffness parameters have been introduced to allow interpretation of the corneal deformation parameters produced by a dynamic Scheimpflug analyzer, relating to how each parameter responds as corneal and scleral resistance to deformation is increased. Normal eyes show overall greater resistance to deformation than keratoconic eyes. Most DCR parameters investigated demonstrated a significant relationship to the novel stiffness parameters in normal and keratoconic eyes, based on both pure corneal deflection and deformation amplitude, which includes WEM. Keratoconic eyes also showed greater variability in the response parameters, likely due to variability of the disease process. Future research will focus on the clinical utility of the new stiffness parameters as potential biomarkers for pathology. It is reported that SP-A1 has greater clinical utility in corneal conditions,14 and it is predicted that SP-HC will have greater clinical utility in conditions involving the sclera, such as glaucoma.
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Mean ± Standard Deviation in bIOP-Matched t test Comparison
|Parameter||Normal (n = 158)||Keratoconus (n = 158)||P|
|Age||40 ± 16||35 ± 12||.0028|
|Pachymetry (µm)||542 ± 34||471 ± 36||< .0001|
|1st Applanation Length (A1 Length) (mm)||1.82 ± 0.08||1.72 ± 0.16||< .0001|
|1st Applanation Velocity (A1 Vel) (mm/ms)||0.16 ± 0.02||0.17 ± 0.03||< .0001|
|1st Applanation Time (A1 Time) (ms)||7.19 ± .28||7.00 ± 0.28||< .0001|
|A1 Deflection Amplitude (A1 DeflAmp) (mm)||0.09 ± 0.01||0.10 ± 0.02||< .0001|
|Deformation Amplitude Ratio (DA Ratio) (unitless)||4.37 ± 0.42||5.81 ± 1.38||< .0001|
|Deflection Amplitude Ratio (DeflA Ratio) (unitless)a||5.06 ± 0.65||7.16 ± 4.82||< .0001|
|Deformation Amplitude (DA) (mm)||1.09 ± 0.10||1.18 ± 0.12||< .0001|
|Highest Concavity Deflection Amplitude (HCDeflAmp) (mm)||0.91 ± 0.11||1.01 ± 0.13||< .0001|
|Highest Concavity Deflection Area (HCDeflArea) (mm2)||3.39 ± 0.55||3.54 ± 0.53||.013|
|Highest Concavity Delta Arclength (HCdarclength) (mm)||−0.14 ± 0.02||−0.12 ± 0.03||< .0001|
|Peak Distance (mm)||5.08 ± 0.26||5.05 ± 0.24||.226|
|Highest Concavity Radius of Concave Curvature (mm)||7.08 ± 0.79||5.62 ± 1.00||< .0001|
|Maximum Inverse Radius (InvRadMax) (1/mm)||0.168 ± 0.02||0.22 ± 0.04||< .0001|
|Maximum Whole Eye Motion (WEMmax) (mm)||0.29 ± 0.07||0.27 ± 0.06||.0065|
|2nd Applanation Length (A2 Length) (mm)||1.73 ± 0.31||1.53 ± 0.41||< .0001|
|2nd Applanation Velocity (A2 Vel) (mm/ms)||−0.40 ± 0.08||−0.47 ± 0.11||< .0001|
|2nd Applanation Time (A2 Time) (ms)||21.78 ± 0.37||21.96 ± 0.39||< .0001|
|Stiffness Parameter A1 (mm Hg/mm)||108.10 ± 20.52||68.67 ± 23.64||< .0001|
|Stiffness Parameter HC (mm Hg/mm)||12.09 ± 3.75||7.63 ± 3.27||< .0001|
Demographics of bIOP-Matched Groups
|OD (n = 86)||OS (n = 72)||Total (n = 158)||OD (n = 95)||OS (n = 63)||Total (n = 158)|
|Age||40.5 ± 17.1||38.8 ± 15.8||39.7 ± 16.5||35.4 ± 11.8||34.0 ± 12.3||34.8 ± 12.0|
|bIOP||14.1 ± 2.0||14.4 ± 2.0||14.2 ± 2.0||14.4 ± 2.0||14.5 ± 1.8||14.4 ± 1.9|
Corneal Deformation Process and Dynamic Response Parameters
|The cornea deforms under the influence of the air puff in a complex manner while maintaining a constant state of force balance between the external air pressure, the internal intraocular pressure (IOP), and corneal resistance with nine distinct phases,1 as illustrated in Figure A. (1) Predeformation Phase: The cornea is fully loaded by the IOP and therefore the collagen fibers that make up its structure are under tension. (2) Ingoing Convex Phase: As the air puff impinges on the corneal surface, indentation begins to occur, and the arclength of the cornea shortens as the tension in the collagen fibers begins to reduce. Slow, linearly increasing motion of the whole eye in the backward direction is also initiated. (3) Ingoing Applanation, A1: At the time of first applanation, the force balance between the air puff pushing inward and the IOP pushing outward results in a flattened state of the central cornea, where the collagen fibers have reduced tension. (4) Ingoing Concave Phase: As the cornea passes through applanation, it becomes concave and the arclength continues to shorten.2 It is likely that the collagen fibers begin to buckle, or wrinkle with increased crimping just past applanation, and continue to crimp to a greater degree as the arclength continues to shorten. The cornea in a concave state is analogous to a rubber hemisphere that is turned inside-out. The outside is in compression (analogous to concave anterior corneal surface) and the inside is in tension (analogous to the posterior corneal surface). The anterior surface compression leads to increased crimping of the anterior collagen fibers, and is similar to what happens in the posterior layers of an edematous cornea,3 where the posterior lamellar layers are displaced toward the anterior chamber and the arclength of the posterior surface is shortened. Whole eye motion in the backward direction also continues in a slow, linearly increasing manner. Fluid in the aqueous chamber is displaced, causing the IOP to rise with increased scleral tension. (5) Oscillation Phase: Near the point where resistance to backward corneal deflection reaches a maximum, which is a function of scleral properties,4 the eye motion transitions from slow linear backward motion to more rapid, nonlinear backward motion. The air pressure continues to increase but further backward motion of the cornea is limited. This phase is where the highest concavity (HC) shape of the cornea occurs, as well as all maximum values for deformation, deflection, and HC parameters. (6) Outgoing Concave Phase: This phase begins as the air pressure reaches a maximum and begins to decrease. The central cornea begins to move relatively in the forward direction and the predicted crimping of the collagen fibers begins to reduce, as does the IOP. However, the whole eye motion continues to increase in the backward direction, even as the air pressure decreases. (7) Outgoing Applanation, A2: The cornea passes through applanation a second time in the outgoing direction, as the collagen fibers begin to regain tension and IOP returns to its predeformation level. This is also approximately the timing where whole eye motion in the backward direction is maximum, and forward motion begins. (8) Outgoing Convex State: The air pressure continues to decrease and the tension in the collagen fibers increases to its fully IOP-loaded state. Whole eye motion is in the forward direction with decreasing magnitude. (9) Post Corneal Deflection Phase: Whole eye motion continues to decrease in the forward direction until the eye fully recovers its initial state, which usually lasts beyond the recording window.|
|The Dynamic Corneal Response parameters (DCR parameters) provided by the Research Software are listed in Table B along with the phase in which they occur, and are illustrated in Figure B. Any parameter that uses the term deformation includes both cornea motion plus whole eye motion. Any parameter that uses the term deflection is compensated for whole eye motion and therefore represents cornea motion only. Applanation parameters in both ingoing and outgoing directions include length, velocity, and time. Deformation amplitude ratio (DA Ratio) is defined as the maximum ratio between central deformation and the average of deformation at 2 mm on either side of center (which is the apex or 1st Purkinje reflex), and deflection amplitude ratio (DeflA Ratio) is similar except whole eye motion is removed. Peak Distance is the width of the cornea at highest concavity, measured between the small bending curves on each side of the central bowl. Deflection Area is the area between the anterior surface of the cornea in the Predeformation Phase and that same surface at HC, without whole eye motion. HC Delta Arclength (HCdarclength) is the difference in the arclength of the anterior surface of the cornea in the Predeformation Phase and that at highest concavity. HC Radius is the radius of curvature at highest concavity and Inverse Radius Max is the maximum value for reciprocal of radius of curvature. Figure B shows the difference between the initial predeformation state before corneal deflection, maximum corneal deflection, and maximum whole eye motion after corneal deflection is recovered, and illustrates how whole eye motion can be removed to calculate corneal deflection parameters.|
|Stiffness Parameters and Dynamic Corneal Response Parameters|
|Stiffness describes the resistance to deformation. Therefore, with a high corneal stiffness it becomes difficult to deform the cornea in general. In the specific case of tonometry, greater force is required to applanate the cornea, causing an overestimation of IOP.5 The stiffness of the cornea, similar to that of any other mechanical structure, is influenced by two main factors: the tomography (including the thickness and the curvature) and the material behavior. Earlier work on sources of error in IOP measurement concentrated on the corneal thickness because it was easy to measure and it had a dominant influence on stiffness. Later, the significant effect of the corneal material behavior on the stiffness was reported6, and hence IOP measurement. However, due to the difficulties in measuring corneal material properties in vivo, this work did not lead to quantifiable estimations of the effect of material behavior. The objective of the stiffness parameters presented in this study is to overcome this obstacle and present overall stiffness measures based on Corvis ST output. A cornea deformed into a concave state can be considered analogous to three-point bending of a beam, illustrated in Figure C. In this one-dimensional case, stiffness is defined as the applied load divided by displacement. The cornea is far more complex than a simple beam in air, since there is pressurized fluid behind the cornea; there are no strict fixation points; and the cornea is more than a single dimension. However, in the case of air puff deformation by the Corvis ST, a one-dimensional deflection of the cornea can be considered, with calculation of the load at applanation where IOP can be determined. After applanation, the air pressure continues to increase, causing backward corneal deflection with an increase in IOP as fluid is displaced. Therefore, the stiffness parameter is defined as the load on the cornea at applanation, divided by displacement.|
|Both the IOP-matched comparison between normal and keratoconic eyes, together with the series of regression analyses of both groups, allow dynamic corneal responses to be interpreted in terms of how they vary with stiffness, with recognition that greater IOP leads to higher stiffness. For example, it is clear from the regression analyses that peak distance is shorter for stiffer eyes. This is due to the spatial profile of the fully developed air pressure pulse at highest concavity depth. At the edges of the pulse, the pressure is high enough to deform a soft cornea, but not high enough to deform a stiff cornea, leading to a shorter peak distance. However, Peak Distance is not significantly different in the IOP-matched comparison between normal and keratoconic eyes. This leads to the conclusion that it is highly influenced by IOP, and that the stiffness of the eyes with shorter peak distance is driven by their higher IOP. In general, stiffer behavior is characterized by later first applanation times, longer applanation lengths, lower applanation velocities, lower DA, lower DA Ratio, lower HCDeflAmp, lower HCDeflArea, greater HCRadius (flatter), lesser InvRadMax, and earlier second applanation times. This means that stiff eyes with greater resistance to deformation require higher air pressure, so they deform later in the pulse as the air pressure increases, and recover earlier as the air pressure drops, all with lower amplitude deflections and deformations, leading to flatter concave curvatures. Lower DA Ratio reflects less difference between the center and 2 mm from the center, which is also consistent with greater resistance to deformation. Although eyes with thicker corneas and higher IOP also tend to be stiffer, the range of pachymetry at a particular level of either stiffness parameter can be over 100 µm, as seen in Figure 3. This demonstrates the importance of evaluating stiffness in individual eyes.|
Ambrósio R Jr, Ramos I, Luz A, etal. Dynamic ultra-high-speed Scheimpflug imaging for assessing corneal biomechanical properties. Rev Bras Oftalmol. 2013;72:99–102.
Roberts CJ, Mahmoud AM, Liu J, etal. Conservation of arclength in keratoconic and normal corneas with air puff induced deformation. Invest Ophth Vis Sci. 2012;53:ARVO E-Abstract 6893.
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Metzler K, Mahmoud AM, Liu J, Roberts CJ. Deformation response of paired donor corneas to an air puff: intact whole globe vs mounted corneoscleral rim. J Cataract Refract Surg. 2014;40:888–896
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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.
Dynamic Corneal Response Parameters and Associated Deformation Phase
|1st Applanation Length (A1 Length)||A1|
|1st Applanation Velocity (A1 Vel)||A1|
|1st Applanation Time (A1 Time)||A1|
|1st Applanantion Deflection Amplitude (A1 DeflAmp)||A1|
|Deformation Amplitude Ratio (DA Ratio) at 2 mm||Near A1|
|Deflection Amplitude Ratio (DefA Ratio) at 2 mm||Near A1|
|Stiffness Parameter A1||Ingoing Convex Phase and A1|
|Stiffness Parameter HC||A1 and Oscillation Phase|
|Deformation Amplitude (DA)||Oscillation Phase|
|Highest Concavity Deflection Amplitude (HCDeflAmp)||Oscillation Phase|
|Highest Concavity Deflection Area (HCDeflArea)||PreDef and Oscillation Phase|
|Highest Concavity Delta Arclength (HCdarclength)||PreDef and Oscillation Phase|
|Peak Distance (Wing, Width or Wdist in literature)||Oscillation Phase|
|Highest Concavity Radius (HC Radius)||Oscillation Phase|
|Maximum Inverse Radius (InvRadMax)||Oscillation Phase|
|Maximum Whole Eye Movement (WEMmax)||Near A2|
|2nd applanation length (A2 Length)||A2|
|2nd applanation velocity (A2 Vel)||A2|
|2nd applanation time (A2 Time)||A2|
Regression Analysis Statistics Between Stiffness Parameter SP-A1 and Dynamic Corneal Response Parameters
|Parameter||Normal (n = 482)||Keratoconus (n = 180)||Slope (Normal, Keratoconus)|
|Pachymetry (µm)||R2 = 0.2213; P < .0001||R2 = 0.2266; P < .0001||+, +|
|1st Applanation Length (A1 Length) (mm)||P = .81||R2 = 0.0434; P = .006||0, +|
|1st Applanation Velocity (A1 Vel) (mm/ms)||R2 = 0.3312; P < .0001||R2 = 0.1586; P < .0001||−, −|
|1st Applanation Time (A1 Time) (ms)||R2 = 0.4270; P < .0001||R2 = 0.3771; P < .0001||+, +|
|A1 Deflection Amplitude (A1 DeflAmp) (mm)||P = .98||R2 = 0.1347; P < .0001||0, −|
|Deformation Amplitude Ratio (DA Ratio) (unitless)||R2 = 0.2914; P < .0001||R2 = 0.3179; P < .0001||−, −|
|Deformation Amplitude (DA) (mm)||R2 = 0.3253; P < .0001||R2 = 0.4833; P < .0001||−, −|
|Highest Concavity Deflection Amplitude (HCDeflAmp) (mm)||R2 = 0.3331; P < .0001||R2 = 0.4973; P < .0001||−, −|
|Highest Concavity Deflection Area (HCDeflArea (mm2)||R2 = 0.2982; P < .0001||R2 = 0.3618; P < .0001||−, −|
|Highest Concavity Delta Arclength (HCdarclength) (mm)||R2 = 0.0294; P = .0002||R2 = 0.0561; P = .0017||+, −|
|Peak Distance (mm)||R2 = 0.2771; P < .0001||R2 = 0.1952; P < .0001||−, −|
|Highest Concavity Radius (mm)||R2 = 0.0767; P < .0001||R2 = 0.2802; P < .0001||+, +|
|Maximum Inverse Radius (InvRadMax) (1/mm)||R2 = 0.1206; P < .0001||R2 =0.3319; P < .0001||−, −|
|Maximum Whole Eye Movement (WEMmax) (mm)||P = .09||P = .36||0, 0|
|2nd Applanation Length (A2 Length) (mm)||R2 = 0.0530; P < .0001||R2 = 0.0683; P = .0005||+, +|
|2nd Applanation Velocity (A2 Vel) (mm/ms)||R2 = 0.3082; P < .0001||R2 = 0.3142; P < .0001||+, +|
|2nd Applanation Time (A2 Time) (ms)||R2 = 0.2631; P < .0001||R2 =0.1852; P < .0001||−, −|
Regression Analysis Statistics Between Stiffness Parameter SP-HC and Dynamic Corneal Response Parameters
|Parameter||Normal (n = 482)||Keratoconus (n = 180)||Slope (Keratoconus, Normal)|
|Pachymetry (µm)||R2 = 0.2070; P < .0001||R2 = 0.1760; P < .0001||+, +|
|1st Applanation Length (A1 Length) (mm)||R2 = 0.0210; P = .002||R2 = 0.0522; P = .003||+, +|
|1st Applanation (A1 Vel) (mm/ms)||R2 = 0.2685; P < .0001||R2 = 0.0554; P = 0.002||−, −|
|1st Applanation Time (A1 Time) (ms)||R2 = 0.6280; P < .0001||R2 = 0.5726; P < .0001||+, +|
|A1 Deflection Amplitude (A1 DeflAmp) (mm)||R2 = 0.2103; P < .0001||P = .84||+, 0|
|Deformation Amplitude Ratio (DA Ratio) (unitless)||R2 = 0.2398; P < .0001||R2 = 0.2357; P < .0001||−, −|
|Deformation Amplitude (DA) (mm)||R2 = 0.5112; P < .0001||R2 = 0.5268; P < .0001||−, −|
|Highest Concavity Deflection Amplitude (HCDeflAmp) (mm)||R2 = 0.6184; P < .0001||R2 = 0.5654; P < .0001||−, −|
|Highest Concavity Deflection Area (HCDeflArea) (mm2)||R2 = 0.5610; P < .0001||R2 = 0.4771; P < .0001||−, −|
|Highest Concavity Delta Arclength (HCdarclength) (mm)||R2 = 0.0620; P < .0001||R2 = 0.0243; P = .041||+, −|
|Peak Distance (mm)||R2 = 0.6320; P < .0001||R2 = 0.3899; P < .0001||−, −|
|Highest Concavity Radius (mm)||R2 = 0.1095; P < .0001||R2 = 0.2084; P < .0001||+, +|
|Maximum Inverse Radius (InvRadMax) (1/mm)||R2 = 0.0923; P < .0001||R2 = 0.2213; P < .0001||−, −|
|Maximum Whole Eye Movement (WEMmax) (mm)||R2 = 0.0334; P < .0001||P = .46||+, 0|
|2nd Applanation Length (A2 Length) (mm)||R2 = 0.0936; P < .0001||R2 = 0.0596; P = .001||+, +|
|2nd Applanation Velocity (A2 Vel) (mm/ms)||R2 = 0.5028; P < .0001||R2 = 0.3197; P < .0001||+, +|
|2nd Applanation Time (A2 Time) (ms)||R2 = 0.3248; P < .0001||R2 = 0.2911; P < .0001||−, −|