Medical Engineering & Physics 36 (2014) 1115–1121
Contents lists available at ScienceDirect
Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Comparative study of corneal tangent elastic modulus measurement using corneal indentation device Match W.L. Ko, Leo K.K. Leung, David C.C. Lam ∗ Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong
a r t i c l e
i n f o
Article history: Received 28 December 2013 Received in revised form 9 May 2014 Accepted 8 June 2014 Keywords: Corneal biomechanical properties Glaucoma Tangent elastic modulus Stiffness Corneal indentation device
a b s t r a c t The aim of this study is to examine the corneal tangent modulus measurement repeatability and performance of the corneal indentation device (CID). Twenty enucleated porcine eyes were measured and the eyes were pressurized using saline solution-filled manometer to 15 and 30 mmHg. Corneal tangent moduli measured using the CID were compared with those measured using high precision universal testing machine (UTM). The within-subject standard deviation (Sw), repeatability (2.77 × Sw), coefficient of variation (CV) (Sw/overall mean), and intraclass correlation coefficient (ICC) were determined. The mean corneal tangent moduli measured using UTM and CID were 0.094 ± 0.030 and 0.094 ± 0.028 MPa at 15 mmHg, and 0.207 ± 0.056 and 0.207 ± 0.055 MPa at 30 mmHg, respectively, with a difference less than 0.13%. The 95% limit of agreement was between −0.009 and 0.009 MPa. The Sw, repeatability, CV and ICC of corneal tangent moduli measured by the CID were 0.006 MPa, 0.015 MPa, 4.3% and 0.993, respectively. The results showed that the corneal tangent moduli measured by the CID are repeatable and are in good agreement with the results measured by the high precision UTM. © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Intraocular pressure (IOP) is generally measured using Goldmann Applanation Tonometry (GAT) [1]. Studies [2–6] showed that inter-individual variations in the central corneal thickness (CCT) and variations in the corneal radius of curvature may lead to measurement errors up to 3.5 mmHg. Studies [7–13] showed that inter-individual variation in the corneal elasticity may also lead to significant errors in IOP measurement. Individual variations in corneal elasticity, which is currently ignored in tonometry, can come from race, sex, genetics and age [14–16]. The principal variation is associated with changes in stroma, which occupies over 90% of the corneal thickness. The stroma is not uniform. Stromal collagen fibrils undergo nonenzymatic cross-linking and the corneal stiffness may double with age [14–16]. Liu and Roberts [9] showed that corneal stiffness variation alone may lead to different IOP reading up to 17 mmHg. Mechanically, the cornea is a pressurized shell structure. Standard elastic modulus measurement methods for measuring
∗ Corresponding author at: Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, NT, Hong Kong. Tel.: +852 2358 7208; fax: +852 2358 1543. E-mail addresses: [email protected] (M.W.L. Ko), [email protected] (L.K.K. Leung), [email protected] (D.C.C. Lam). http://dx.doi.org/10.1016/j.medengphy.2014.06.003 1350-4533/© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
linear elastic shell stiffness are available, but they are unsuited for characterization of the cornea because the cornea’s mechanical behavior is nonlinear. Corneal mecahnical behavior is characterized by the load-specific corneal tangent modulus (instead of an elastic modulus). Corneal indentation method developed for the measurement of the corneal tangent modulus was validated and tested on porcine corneas ex vivo and rabbit corneas in vivo [13]. In an earlier study [13], the corneal tangent modulus was measured using a desktop universal testing machine (UTM), but the UTM is not designed for routine clinical use. A portable corneal indentation device (CID) for clinical use has been developed. In this study, the corneal tangent modulus measurement repeatability and performance of the CID on porcine eyes are studied and compared with the results measured using the UTM.
2. Materials and methods 2.1. Corneal indentation device (CID) The portable CID is designed for use on a slit-lamp (Fig. 1). The CID has a high precision load sensor (Bengbu Sensor System Engineering Company Ltd., Anhui, China) with a flat 2 mm cylindrical indenter mounted at the tip. The assembly is mounted onto a linear actuator (Haydon Kerk Motion Solutions, Inc., CT, USA) so that it can be moved forward on command to indent the cornea. Before
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Fig. 1. Prototype of the corneal indentation device.
measurement, the patient’s eye is topically anesthetized with the head positioned and stabilized on the chinrest. Then, the indenter is aligned with the corneal apex, and on command from the operator, the actuator moves the indenter forward to indent the cornea. The indentation load–displacement curve is ascertained in less than 1 s and the corneal tangent modulus is determined from the curve. 2.2. Indenter and contact area In comparison with the GAT, CID characterizes the structural corneal property while the GAT characterizes the intraocular pressure. The GAT uses only the load at a single indentation depth corresponding to an applanation contact area of 7.35 mm2 . The CID measures corneal tangent modulus which is obtained from the slope of the indentation load–displacement curve. A variety of indenter sizes may be used for indentation. The effect of indenter contact area on the slope was examined. Indenters with diameters ranging from 1.7 to 5.1 mm were tested. Data showed that the slope of the load–displacement curves with larger indenter is steeper, but the slopes from indentation with different sizes become identical after they are normalized by the diameter of indenters. To minimize patient discomfort, a small 2-mm indenter that exerts a smaller load on the cornea is chosen in our tests. 2.3. Ex vivo experiments on porcine eyes Twenty porcine eyes were obtained from a local abattoir. The porcine eyes were kept moist at 4 ◦ C in an insulated bucket filled with refrigerants; and the experiments were conducted within 12 h after sacrifice. The central corneal thickness and corneal radius of curvature of the porcine eyes were measured using a
camera-mounted Leica M205C stereomicroscope (Leica Microsystems, Wetzlar, Germany). The eyes were mounted on a test jig and the anterior chamber was cannulated (Fig. 2). A needle connected to a saline-filled pressure-controlling manometer was inserted into the chamber to control the chamber pressure. The pressure in the test eyes was cycled 3 times between 5 and 50 mmHg by adjusting the bottle height of the manometer to condition the cornea, and set at 15 mmHg (normal eyes) and 30 mmHg (glaucomatous eyes) for testing. The intraocular pressure was measured using a pressure needle sensor inserted into the anterior chamber (OPP-M400, Opsens Inc., Canada) (Fig. 2), and the eyes were allowed to stabilize at the set IOP for over 10 min before experiments. After stabilization, the eyes were concentrically aligned with the indenter of the CID (Fig. 2). The indenter was then moved forward to touch the cornea until a small stable pre-load of less than 1 mN was registered. After the pre-load was stabilized, the indenter was actuated forward at 12 mm/s to indent the cornea to a set depth of 1 mm. After reaching the set depth, the motion was reversed at the same rate until the indenter was withdrawn from the corneal contact. With the high indentation rate, the indentation was completed in less than a quarter of a second, and the load–displacement curve ascertained was used for the calculation of the corneal tangent modulus. For comparison, the eyes were also indented using high precision UTM. The UTM (Alliance RT/5; MTS Corporation, Eden Prairie, MN, USA; rated to support 5 kN) is designed for testing with submicron precision and is substantially more rigid than the CID. An indenter with 2 mm (diameter) tip was mounted onto a 10 N load cell (MTS 100-090-795, MTS Corporation, Eden Prairie, MN, USA) and the assembly was screw-mounted onto the crosshead of the UTM testing frame (Fig. 3). For all eyes tested, testing was first
M.W.L. Ko et al. / Medical Engineering & Physics 36 (2014) 1115–1121
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Fig. 2. (a) Schematic experimental setup and (b) experimental setup for ex vivo measurement of corneal tangent modulus in porcine eyes using CID.
conducted using the CID, followed by testing on the UTM using the same procedure. 2.4. Corneal tangent modulus calculation The load–displacement (F–ı) data in the full indenter contact regime, i.e., when ı > ro2 /2R was used. For porcine eyes indentation with 2 mm diameter indenter, full contact threshold occurs when ı ∼ 0.1 mm. To ensure full contact, F–ı data for ı > 0.2 mm was used for analysis. The corneal tangent modulus EIOP at a set IOP was determined using,
E
IOP
=
a(R − t/2)
t2
where
Sin
IOP,fc
=
1 − 2
Sin
IOP,fc
(1)
indentation force acting on the corneal surface, ı is the indentation depth, is the Poisson’s ratio of the cornea ( ≈ 0.5, since the cornea consists principally of incompressible water [17]), R is the effective anterior corneal radius of curvature [18], t is the central corneal thickness and a is a geometry constant which can be determined from (Table 1) [19],
= ro
12(1 − 2 )
1/4
2
(R − t/2) t 2
(3)
where ro is the radius of the circular contact area between the flatpunch indenter and the cornea. R and t generally vary less than 5% over the normal physiological pressure range, and the R and t measured at a single pressure can be used in the calculation of EIOP for all pressures [20,21].
dF dı IOP,fc
(2)
where the corneal stiffness Sin |IOP,fc is the slope of tangent on the load–displacement curve in the full contact regime. F is the
2.5. Statistical analysis Statistical analyses were performed using SPSS version 20 (SPSS Inc, Chicago, IL, USA). Five consecutive measurements were
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Fig. 3. (a) Schematic experimental setup and (b) experimental setup for ex vivo measurement of corneal tangent modulus in porcine eyes using universal testing machine.
Table 1 Determination of the coefficient a in Eq. (1) using the parameter given by Eq. (3). 0 0.433
0.1 0.431
0.2 0.425
0.4 0.408
obtained using the CID and UTM by a single operator and the repeatability was calculated. The within-subject standard deviation (Sw), repeatability (2.77 × Sw), coefficient of variation (CV) and intraclass correlation coefficient (ICC) were analyzed. An ICC above 0.75 indicates good measurement repeatability and most clinical application required an ICC value of at least 0.90 [22]. The agreement of corneal tangent modulus measured by UTM and CID was evaluated with Bland–Altman plot [23].
3. Results The mean central corneal thickness and radius of curvature of the 20 porcine corneas were 1.21 ± 0.15 mm and 8.25 ± 0.37 mm, respectively. The load–displacement curves indented at a pressure of 15 mmHg and 30 mmHg using CID and UTM on a porcine eye were shown in Fig. 4. The curves showed that the indentation load–displacement curves from the CID test were comparable to the curves from the UTM test. Both tests showed that the load–displacement in the full contact regime (ı > 0.2 mm) at low IOP was linear. At high IOP, the curves curved upward due to increased corneal bending at the indenter edge. To avoid inclusion of the edge bending error, the tangent of load–displacement curve at ı = 0.3 mm was used for calculation in this study. The mean corneal tangent moduli measured with CID and UTM were 0.094 ± 0.028 and 0.094 ± 0.030 MPa at 15 mmHg, and
0.6 0.386
0.8 0.362
1.0 0.337
1.2 0.311
1.4 0.286
0.15
UTM CID 0.1
Load (N)
a
IOP = 30 mmHg
0.05
IOP = 15 mmHg 0 0
0.2
0.4
0.6
0.8
1
Displacement (mm) Fig. 4. Corneal indentation load–displacement curves at 15 mmHg and 30 mmHg using UTM (solid line) and CID (dotted line).
0.207 ± 0.055 and 0.207 ± 0.056 MPa at 30 mmHg, respectively. The CID and UTM measurements had an average difference of 0.13% (95% CI: −0.81% to 1.08%) and it was statistically insignificant (p < 0.001).
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Table 2 Repeatability of UTM and CID. Overall mean (SD)
Sw
Repeatability
CV (%)
ICC
15 mmHg
30 mmHg
(95% CI)
(95% CI)
(95% CI)
(95% CI)
UTM
0.094 MPa (0.030)
0.207 MPa (0.056)
0.001 MPa (0.001–0.002)
0.004 MPa (0.003–0.005)
1.1 (0.8–1.3)
0.999 (0.999–1.000)
CID
0.094 MPa (0.028)
0.207 MPa (0.055)
0.006 MPa (0.005–0.006)
0.015 MPa (0.013–0.017)
4.3 (3.6–5.0)
0.993 (0.989–0.996)
0.3
0.4
Current study
0.35
Tangent modulus (MPa)
0.25
0.3
0.2
E
CID
(MPa)
0.25
0.15 0.1
Asejczyk-Widlicka Elsheikh
0.2
0.15
0.1
0.05 0.05 0
0 0
0.05
0.1 0.15
E
0.2 0.25
UTM
0.3 0.35
0.4
5
10
15
20
25
30
35
IOP (mmHg)
(MPa)
Fig. 5. Corneal tangent moduli measured by CID against those measured by UTM. (ECID = 0.9961 EUTM + 0.0006, R2 = 0.996 and dotted line represents the line of equality).
Fig. 7. Comparison of corneal tangent moduli measured in porcine eyes by ex vivo corneal indentation (as reported in this study) and inflation test [24,25].
4. Discussions UTM against CID
0.02
E Differences (MPa)
0.015 0.01
0.009
0.005 Mean = 0.000
0 -0.005 -0.01
-0.009
-0.015 -0.02
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 E Averages (MPa)
Fig. 6. Bland–Altman plot of the corneal tangent modulus measurements between the UTM and CID.
CID measurements were highly correlated with UTM measurements (p < 0.001, R2 = 0.996) (Fig. 5). The measurement error for each instrument (CID E–UTM E) at different Es was shown in the Bland–Altman plot in Fig. 6. The figure showed that the 95% limits of agreement were between −0.009 and 0.009 MPa. The Sw, repeatability, CV and ICC of corneal tangent modulus measurement were 0.001 MPa, 0.004 MPa, 1.1% and 0.999 for UTM, and 0.006 MPa, 0.015 MPa, 4.3% and 0.993 for CID, respectively (Table 2).
Ex vivo methods to characterize the corneal mechanical properties are often destructive and/or invasive (see Appendix). In this study, a corneal indentation device designed for clinical measurement of corneal tangent modulus in vivo was built. The eyes tested were quasi-statically pressurized to 15 mmHg (normal eyes) and 30 mmHg (glaucomatous eyes). The corneal tangent moduli determined from the CID in porcine eyes (0.05–0.34 MPa) were similar to those reported by Elsheikh et al. (0.1–0.5 MPa) and AsejczykWidlicka et al. (0.05–0.24 MPa) using inflation tests [24,25] (Fig. 7). The average measurement difference between CID and UTM (the reference standard) results was less than 0.13% and the measurement agreement is good. The ICC of CID measurement was 0.993 from this study and is well above the minimum repeatability of 0.90 required for clinical device measurement [22]. The statistical performance of CID may also be compared with the GAT [1] as a cross-parametric reference. The reported CV and ICC for GAT are 9.7% and 0.79, respectively [26], which are below the performance of the CID (CV = 4.3%, ICC = 0.993). The difference in performance may be associated with the pulsation and eye movement in live human eyes, which are absent in porcine eyes. When these factors are included, the performances of the CID in clinical tests may become comparable to the repeatability level of GAT. Indentation on the cornea may induce IOP variation of 1–3 mmHg per 1 mm indentation. The influence of IOP fluctuation from indentation on the measurement of corneal tangent modulus is discussed in the Appendix of a companion paper by Leung et al. [18]. The paper showed that the influence is less than 3%, such that the influence can be regarded as negligible. However, further investigation is needed to determine the influence of IOP fluctuation from indentation on human. While the statistical performance of GAT IOP and CID corneal tangent modulus can be compared, it should be noted that corneal tangent modulus measured by CID is an elastic corneal structural
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property that is independent of the corneal thickness, radius of curvature and indenter size (see digital supplementary material in Leung et al. [18] for details), and is dependent on the stress in the cornea. Since IOP measured by GAT is dependent on corneal thickness, curvature and elasticity, individual variations are embedded in the GAT IOP. On the other hand, individual variations in thickness and in curvature are normalized out in the corneal tangent modulus. Thus, corneal tangent modulus is a property that is directly related to the stress in the cornea and is unclouded by the variations in corneal geometry. The unique character may allow the clinicians to use the corneal tangent modulus as an indicator of the mechanical state of the cornea and use it for the diagnosis and assessment of eye disorders alongside the primary indicator, IOP, which is an integrated parameter characterizing the general mechanical state of the eye. Funding None. Ethical approval Not required. Appendix. Ex Vivo corneal tissue testing methods Current understanding of the mechanical properties of the cornea is principally derived from ex vivo testing using strip extensiometry and inflation tests. In strip extensiometry [27–35], a strip of cornea tissue with a constant width is dissected from the cornea and attached to the grips of a loading machine and loaded in tension. The corneal tangent modulus is then determined from the tensile load-deformation curve. Corneal biomechanical properties can also be determined from inflation tests [14,20,21,24,25,35–38]. In inflation tests conducted by Elsheikh et al. [14,15,24,35], the porcine cornea with surrounding scleral rim was dissected and clamped onto a pressure chamber using mechanical clamps. The pressure was computer-controlled, and the corneal deformation was monitored using laser displacement sensor. The corneal modulus was then determined from the pressure-deformation data using a shell model. Others used whole eyeball (Asejczyk-Widlicka et al.) [25] wherein the corneal modulus was determined using from the deformation-pressure data using thin-walled pressure vessel models. Other than the strip extensiometry and inflation test, Ahearne et al. [39] used hemispherical indentation to characterize the mechanical properties of human and porcine corneas. A cornea specimen is clamped around its outer circumference using a specially designed holder. Analyses showed that the human and porcine corneas have similar mechanical properties but the porcine corneas were more compliant and the loading–unloading curves were more linear. These methods provide ex vivo approaches to characterize the corneal mechanical properties. Non-invasive methods including ultrasonic spectroscopy, supersonic shear imaging and holographic interferometry [40–42] are also available, but their determination from data are more sensitive to the analyses used and comparisons cannot be readily made without detailed analyses on the models and methods employed across different studies. Conflict of interests US provisional patent application (US 61/457,784) and international patent application (WO2012163080) on the described measurement method were applied.
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[14] 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;32:11–9. [15] Elsheikh A, Geraghty B, Rama P, Campanelli M, Meek KM. Characterization of age-related variation in corneal biomechanical properties. J R Soc Interface 2010;7:1475–85. [16] Saude T, Fletcher R. Ocular anatomy and physiology. UK: Blackwell Scientific; 2003. [17] Kampmeier J, Radt B, Birngruber R, Brinkmann R. Thermal and biomechanical parameters of porcine cornea. Cornea 2000;19:355–63. [18] Leung KK, Ko WL, Ye C, Lam DCC, Leung CK-S. Non-invasive measurement of scleral stiffness and tangent modulus in porcine eyes. Investigative ophthalmology & visual science 2014. IOVS-13-13674. [19] Young WC. Roark’s formulas for stress and strain. New York: McGraw-Hill Book Co.; 1989. [20] Pierscionek BK, Asejczyk-Widlicka M, Schachar RA. 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A comparison of the elastic properties of human choroid and sclera. Exp Eye Res 1988;47:429–36. [35] Elsheikh A, Anderson K. Comparative study of corneal strip extensometry and inflation tests. J R Soc Interface 2005;2:177–85.
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Contents lists available at ScienceDirect
Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Comparative study of corneal tangent elastic modulus measurement using corneal indentation device Match W.L. Ko, Leo K.K. Leung, David C.C. Lam ∗ Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong
a r t i c l e
i n f o
Article history: Received 28 December 2013 Received in revised form 9 May 2014 Accepted 8 June 2014 Keywords: Corneal biomechanical properties Glaucoma Tangent elastic modulus Stiffness Corneal indentation device
a b s t r a c t The aim of this study is to examine the corneal tangent modulus measurement repeatability and performance of the corneal indentation device (CID). Twenty enucleated porcine eyes were measured and the eyes were pressurized using saline solution-filled manometer to 15 and 30 mmHg. Corneal tangent moduli measured using the CID were compared with those measured using high precision universal testing machine (UTM). The within-subject standard deviation (Sw), repeatability (2.77 × Sw), coefficient of variation (CV) (Sw/overall mean), and intraclass correlation coefficient (ICC) were determined. The mean corneal tangent moduli measured using UTM and CID were 0.094 ± 0.030 and 0.094 ± 0.028 MPa at 15 mmHg, and 0.207 ± 0.056 and 0.207 ± 0.055 MPa at 30 mmHg, respectively, with a difference less than 0.13%. The 95% limit of agreement was between −0.009 and 0.009 MPa. The Sw, repeatability, CV and ICC of corneal tangent moduli measured by the CID were 0.006 MPa, 0.015 MPa, 4.3% and 0.993, respectively. The results showed that the corneal tangent moduli measured by the CID are repeatable and are in good agreement with the results measured by the high precision UTM. © 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Intraocular pressure (IOP) is generally measured using Goldmann Applanation Tonometry (GAT) [1]. Studies [2–6] showed that inter-individual variations in the central corneal thickness (CCT) and variations in the corneal radius of curvature may lead to measurement errors up to 3.5 mmHg. Studies [7–13] showed that inter-individual variation in the corneal elasticity may also lead to significant errors in IOP measurement. Individual variations in corneal elasticity, which is currently ignored in tonometry, can come from race, sex, genetics and age [14–16]. The principal variation is associated with changes in stroma, which occupies over 90% of the corneal thickness. The stroma is not uniform. Stromal collagen fibrils undergo nonenzymatic cross-linking and the corneal stiffness may double with age [14–16]. Liu and Roberts [9] showed that corneal stiffness variation alone may lead to different IOP reading up to 17 mmHg. Mechanically, the cornea is a pressurized shell structure. Standard elastic modulus measurement methods for measuring
∗ Corresponding author at: Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, NT, Hong Kong. Tel.: +852 2358 7208; fax: +852 2358 1543. E-mail addresses: [email protected] (M.W.L. Ko), [email protected] (L.K.K. Leung), [email protected] (D.C.C. Lam). http://dx.doi.org/10.1016/j.medengphy.2014.06.003 1350-4533/© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
linear elastic shell stiffness are available, but they are unsuited for characterization of the cornea because the cornea’s mechanical behavior is nonlinear. Corneal mecahnical behavior is characterized by the load-specific corneal tangent modulus (instead of an elastic modulus). Corneal indentation method developed for the measurement of the corneal tangent modulus was validated and tested on porcine corneas ex vivo and rabbit corneas in vivo [13]. In an earlier study [13], the corneal tangent modulus was measured using a desktop universal testing machine (UTM), but the UTM is not designed for routine clinical use. A portable corneal indentation device (CID) for clinical use has been developed. In this study, the corneal tangent modulus measurement repeatability and performance of the CID on porcine eyes are studied and compared with the results measured using the UTM.
2. Materials and methods 2.1. Corneal indentation device (CID) The portable CID is designed for use on a slit-lamp (Fig. 1). The CID has a high precision load sensor (Bengbu Sensor System Engineering Company Ltd., Anhui, China) with a flat 2 mm cylindrical indenter mounted at the tip. The assembly is mounted onto a linear actuator (Haydon Kerk Motion Solutions, Inc., CT, USA) so that it can be moved forward on command to indent the cornea. Before
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M.W.L. Ko et al. / Medical Engineering & Physics 36 (2014) 1115–1121
Fig. 1. Prototype of the corneal indentation device.
measurement, the patient’s eye is topically anesthetized with the head positioned and stabilized on the chinrest. Then, the indenter is aligned with the corneal apex, and on command from the operator, the actuator moves the indenter forward to indent the cornea. The indentation load–displacement curve is ascertained in less than 1 s and the corneal tangent modulus is determined from the curve. 2.2. Indenter and contact area In comparison with the GAT, CID characterizes the structural corneal property while the GAT characterizes the intraocular pressure. The GAT uses only the load at a single indentation depth corresponding to an applanation contact area of 7.35 mm2 . The CID measures corneal tangent modulus which is obtained from the slope of the indentation load–displacement curve. A variety of indenter sizes may be used for indentation. The effect of indenter contact area on the slope was examined. Indenters with diameters ranging from 1.7 to 5.1 mm were tested. Data showed that the slope of the load–displacement curves with larger indenter is steeper, but the slopes from indentation with different sizes become identical after they are normalized by the diameter of indenters. To minimize patient discomfort, a small 2-mm indenter that exerts a smaller load on the cornea is chosen in our tests. 2.3. Ex vivo experiments on porcine eyes Twenty porcine eyes were obtained from a local abattoir. The porcine eyes were kept moist at 4 ◦ C in an insulated bucket filled with refrigerants; and the experiments were conducted within 12 h after sacrifice. The central corneal thickness and corneal radius of curvature of the porcine eyes were measured using a
camera-mounted Leica M205C stereomicroscope (Leica Microsystems, Wetzlar, Germany). The eyes were mounted on a test jig and the anterior chamber was cannulated (Fig. 2). A needle connected to a saline-filled pressure-controlling manometer was inserted into the chamber to control the chamber pressure. The pressure in the test eyes was cycled 3 times between 5 and 50 mmHg by adjusting the bottle height of the manometer to condition the cornea, and set at 15 mmHg (normal eyes) and 30 mmHg (glaucomatous eyes) for testing. The intraocular pressure was measured using a pressure needle sensor inserted into the anterior chamber (OPP-M400, Opsens Inc., Canada) (Fig. 2), and the eyes were allowed to stabilize at the set IOP for over 10 min before experiments. After stabilization, the eyes were concentrically aligned with the indenter of the CID (Fig. 2). The indenter was then moved forward to touch the cornea until a small stable pre-load of less than 1 mN was registered. After the pre-load was stabilized, the indenter was actuated forward at 12 mm/s to indent the cornea to a set depth of 1 mm. After reaching the set depth, the motion was reversed at the same rate until the indenter was withdrawn from the corneal contact. With the high indentation rate, the indentation was completed in less than a quarter of a second, and the load–displacement curve ascertained was used for the calculation of the corneal tangent modulus. For comparison, the eyes were also indented using high precision UTM. The UTM (Alliance RT/5; MTS Corporation, Eden Prairie, MN, USA; rated to support 5 kN) is designed for testing with submicron precision and is substantially more rigid than the CID. An indenter with 2 mm (diameter) tip was mounted onto a 10 N load cell (MTS 100-090-795, MTS Corporation, Eden Prairie, MN, USA) and the assembly was screw-mounted onto the crosshead of the UTM testing frame (Fig. 3). For all eyes tested, testing was first
M.W.L. Ko et al. / Medical Engineering & Physics 36 (2014) 1115–1121
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Fig. 2. (a) Schematic experimental setup and (b) experimental setup for ex vivo measurement of corneal tangent modulus in porcine eyes using CID.
conducted using the CID, followed by testing on the UTM using the same procedure. 2.4. Corneal tangent modulus calculation The load–displacement (F–ı) data in the full indenter contact regime, i.e., when ı > ro2 /2R was used. For porcine eyes indentation with 2 mm diameter indenter, full contact threshold occurs when ı ∼ 0.1 mm. To ensure full contact, F–ı data for ı > 0.2 mm was used for analysis. The corneal tangent modulus EIOP at a set IOP was determined using,
E
IOP
=
a(R − t/2)
t2
where
Sin
IOP,fc
=
1 − 2
Sin
IOP,fc
(1)
indentation force acting on the corneal surface, ı is the indentation depth, is the Poisson’s ratio of the cornea ( ≈ 0.5, since the cornea consists principally of incompressible water [17]), R is the effective anterior corneal radius of curvature [18], t is the central corneal thickness and a is a geometry constant which can be determined from (Table 1) [19],
= ro
12(1 − 2 )
1/4
2
(R − t/2) t 2
(3)
where ro is the radius of the circular contact area between the flatpunch indenter and the cornea. R and t generally vary less than 5% over the normal physiological pressure range, and the R and t measured at a single pressure can be used in the calculation of EIOP for all pressures [20,21].
dF dı IOP,fc
(2)
where the corneal stiffness Sin |IOP,fc is the slope of tangent on the load–displacement curve in the full contact regime. F is the
2.5. Statistical analysis Statistical analyses were performed using SPSS version 20 (SPSS Inc, Chicago, IL, USA). Five consecutive measurements were
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Fig. 3. (a) Schematic experimental setup and (b) experimental setup for ex vivo measurement of corneal tangent modulus in porcine eyes using universal testing machine.
Table 1 Determination of the coefficient a in Eq. (1) using the parameter given by Eq. (3). 0 0.433
0.1 0.431
0.2 0.425
0.4 0.408
obtained using the CID and UTM by a single operator and the repeatability was calculated. The within-subject standard deviation (Sw), repeatability (2.77 × Sw), coefficient of variation (CV) and intraclass correlation coefficient (ICC) were analyzed. An ICC above 0.75 indicates good measurement repeatability and most clinical application required an ICC value of at least 0.90 [22]. The agreement of corneal tangent modulus measured by UTM and CID was evaluated with Bland–Altman plot [23].
3. Results The mean central corneal thickness and radius of curvature of the 20 porcine corneas were 1.21 ± 0.15 mm and 8.25 ± 0.37 mm, respectively. The load–displacement curves indented at a pressure of 15 mmHg and 30 mmHg using CID and UTM on a porcine eye were shown in Fig. 4. The curves showed that the indentation load–displacement curves from the CID test were comparable to the curves from the UTM test. Both tests showed that the load–displacement in the full contact regime (ı > 0.2 mm) at low IOP was linear. At high IOP, the curves curved upward due to increased corneal bending at the indenter edge. To avoid inclusion of the edge bending error, the tangent of load–displacement curve at ı = 0.3 mm was used for calculation in this study. The mean corneal tangent moduli measured with CID and UTM were 0.094 ± 0.028 and 0.094 ± 0.030 MPa at 15 mmHg, and
0.6 0.386
0.8 0.362
1.0 0.337
1.2 0.311
1.4 0.286
0.15
UTM CID 0.1
Load (N)
a
IOP = 30 mmHg
0.05
IOP = 15 mmHg 0 0
0.2
0.4
0.6
0.8
1
Displacement (mm) Fig. 4. Corneal indentation load–displacement curves at 15 mmHg and 30 mmHg using UTM (solid line) and CID (dotted line).
0.207 ± 0.055 and 0.207 ± 0.056 MPa at 30 mmHg, respectively. The CID and UTM measurements had an average difference of 0.13% (95% CI: −0.81% to 1.08%) and it was statistically insignificant (p < 0.001).
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Table 2 Repeatability of UTM and CID. Overall mean (SD)
Sw
Repeatability
CV (%)
ICC
15 mmHg
30 mmHg
(95% CI)
(95% CI)
(95% CI)
(95% CI)
UTM
0.094 MPa (0.030)
0.207 MPa (0.056)
0.001 MPa (0.001–0.002)
0.004 MPa (0.003–0.005)
1.1 (0.8–1.3)
0.999 (0.999–1.000)
CID
0.094 MPa (0.028)
0.207 MPa (0.055)
0.006 MPa (0.005–0.006)
0.015 MPa (0.013–0.017)
4.3 (3.6–5.0)
0.993 (0.989–0.996)
0.3
0.4
Current study
0.35
Tangent modulus (MPa)
0.25
0.3
0.2
E
CID
(MPa)
0.25
0.15 0.1
Asejczyk-Widlicka Elsheikh
0.2
0.15
0.1
0.05 0.05 0
0 0
0.05
0.1 0.15
E
0.2 0.25
UTM
0.3 0.35
0.4
5
10
15
20
25
30
35
IOP (mmHg)
(MPa)
Fig. 5. Corneal tangent moduli measured by CID against those measured by UTM. (ECID = 0.9961 EUTM + 0.0006, R2 = 0.996 and dotted line represents the line of equality).
Fig. 7. Comparison of corneal tangent moduli measured in porcine eyes by ex vivo corneal indentation (as reported in this study) and inflation test [24,25].
4. Discussions UTM against CID
0.02
E Differences (MPa)
0.015 0.01
0.009
0.005 Mean = 0.000
0 -0.005 -0.01
-0.009
-0.015 -0.02
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 E Averages (MPa)
Fig. 6. Bland–Altman plot of the corneal tangent modulus measurements between the UTM and CID.
CID measurements were highly correlated with UTM measurements (p < 0.001, R2 = 0.996) (Fig. 5). The measurement error for each instrument (CID E–UTM E) at different Es was shown in the Bland–Altman plot in Fig. 6. The figure showed that the 95% limits of agreement were between −0.009 and 0.009 MPa. The Sw, repeatability, CV and ICC of corneal tangent modulus measurement were 0.001 MPa, 0.004 MPa, 1.1% and 0.999 for UTM, and 0.006 MPa, 0.015 MPa, 4.3% and 0.993 for CID, respectively (Table 2).
Ex vivo methods to characterize the corneal mechanical properties are often destructive and/or invasive (see Appendix). In this study, a corneal indentation device designed for clinical measurement of corneal tangent modulus in vivo was built. The eyes tested were quasi-statically pressurized to 15 mmHg (normal eyes) and 30 mmHg (glaucomatous eyes). The corneal tangent moduli determined from the CID in porcine eyes (0.05–0.34 MPa) were similar to those reported by Elsheikh et al. (0.1–0.5 MPa) and AsejczykWidlicka et al. (0.05–0.24 MPa) using inflation tests [24,25] (Fig. 7). The average measurement difference between CID and UTM (the reference standard) results was less than 0.13% and the measurement agreement is good. The ICC of CID measurement was 0.993 from this study and is well above the minimum repeatability of 0.90 required for clinical device measurement [22]. The statistical performance of CID may also be compared with the GAT [1] as a cross-parametric reference. The reported CV and ICC for GAT are 9.7% and 0.79, respectively [26], which are below the performance of the CID (CV = 4.3%, ICC = 0.993). The difference in performance may be associated with the pulsation and eye movement in live human eyes, which are absent in porcine eyes. When these factors are included, the performances of the CID in clinical tests may become comparable to the repeatability level of GAT. Indentation on the cornea may induce IOP variation of 1–3 mmHg per 1 mm indentation. The influence of IOP fluctuation from indentation on the measurement of corneal tangent modulus is discussed in the Appendix of a companion paper by Leung et al. [18]. The paper showed that the influence is less than 3%, such that the influence can be regarded as negligible. However, further investigation is needed to determine the influence of IOP fluctuation from indentation on human. While the statistical performance of GAT IOP and CID corneal tangent modulus can be compared, it should be noted that corneal tangent modulus measured by CID is an elastic corneal structural
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property that is independent of the corneal thickness, radius of curvature and indenter size (see digital supplementary material in Leung et al. [18] for details), and is dependent on the stress in the cornea. Since IOP measured by GAT is dependent on corneal thickness, curvature and elasticity, individual variations are embedded in the GAT IOP. On the other hand, individual variations in thickness and in curvature are normalized out in the corneal tangent modulus. Thus, corneal tangent modulus is a property that is directly related to the stress in the cornea and is unclouded by the variations in corneal geometry. The unique character may allow the clinicians to use the corneal tangent modulus as an indicator of the mechanical state of the cornea and use it for the diagnosis and assessment of eye disorders alongside the primary indicator, IOP, which is an integrated parameter characterizing the general mechanical state of the eye. Funding None. Ethical approval Not required. Appendix. Ex Vivo corneal tissue testing methods Current understanding of the mechanical properties of the cornea is principally derived from ex vivo testing using strip extensiometry and inflation tests. In strip extensiometry [27–35], a strip of cornea tissue with a constant width is dissected from the cornea and attached to the grips of a loading machine and loaded in tension. The corneal tangent modulus is then determined from the tensile load-deformation curve. Corneal biomechanical properties can also be determined from inflation tests [14,20,21,24,25,35–38]. In inflation tests conducted by Elsheikh et al. [14,15,24,35], the porcine cornea with surrounding scleral rim was dissected and clamped onto a pressure chamber using mechanical clamps. The pressure was computer-controlled, and the corneal deformation was monitored using laser displacement sensor. The corneal modulus was then determined from the pressure-deformation data using a shell model. Others used whole eyeball (Asejczyk-Widlicka et al.) [25] wherein the corneal modulus was determined using from the deformation-pressure data using thin-walled pressure vessel models. Other than the strip extensiometry and inflation test, Ahearne et al. [39] used hemispherical indentation to characterize the mechanical properties of human and porcine corneas. A cornea specimen is clamped around its outer circumference using a specially designed holder. Analyses showed that the human and porcine corneas have similar mechanical properties but the porcine corneas were more compliant and the loading–unloading curves were more linear. These methods provide ex vivo approaches to characterize the corneal mechanical properties. Non-invasive methods including ultrasonic spectroscopy, supersonic shear imaging and holographic interferometry [40–42] are also available, but their determination from data are more sensitive to the analyses used and comparisons cannot be readily made without detailed analyses on the models and methods employed across different studies. Conflict of interests US provisional patent application (US 61/457,784) and international patent application (WO2012163080) on the described measurement method were applied.
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