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A comparison of biomechanical properties between human and porcine cornea
Journal of Biomechanics 34 (2001) 533–537
Technical note
A comparison of biomechanical properties between human and porcine cornea Yanjun Zenga,*, Jian Yanga, Kun Huanga, Zhihui Leeb, Xiuyun Leec a
Biomechanical and Medical Information Institute, Beijing Polytechnic University, Beijing 100022, People’s Republic of China b Ophthalmology Department, Tong Ren Hospital, Beijing 100730, People’s Republic of China c Ophthalmology Department, Friendship Hospital, Beijing 100050, People’s Republic of China Accepted 8 November 2000
Abstract Due to the difficulty in obtaining human corneas, pig corneas are often substituted as models for cornea research. The purpose of this study is to find the similarities and differences in the biomechanical properties between human and porcine corneas. Uniaxial tests were conducted using an Instron apparatus to determine their tensile strength, stress–strain relationship, and stress-relaxation properties. The tensile strength and stress–strain relation were very similar but significant differences between the two tissues were observed in the stress-relaxation relationship. Under the same stretch ratio l ¼ 1:5, porcine cornea relaxed much more than human cornea. If tensile strength and the stress–strain relation are the only mechanical factors to be investigated, porcine cornea can be used as a substitute model for human cornea research. However, when stress relaxation is a factor, porcine corneas cannot be used as an appropriate model for human corneas in mechanical property studies. It is very difficult to get enough specimens of human cornea, so we did the experiments for stress–strain relationship at a specific value of strain rate (corresponding to the velocity of loading 10 mm/min), and for stress relaxation at a specific stretch ratio l ¼ 1:5. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Human cornea; Porcine cornea; Tensile strength; Stress–strain relationship; Stress relaxation
1. Introduction The cornea plays an important role in the refractive power of the eye. The shape of the cornea and its biomechanical properties are of great interest to both ophthalmologists and researchers. A number of studies on the mechanics of the cornea, both intact and cut into strips, have been published. Most notable are the works by Woo et al. (1972), Jue and Maurice (1986), Pinsky and Datye (1991) and Hjortdal and Jensen (1995). Because of the difficulty in obtaining human cornea specimens, it is useful to compare the biomechanical properties of human cornea with that of pigs, since people usually consider pigs to have eyes similar to human beings. The objective of the present study is to compare the biomechanical properties of *Corresponding author. Biomedical Engineering Center, Beijing Polytechnic University, Beijing, 100022, People’s Republic of China. Tel.: +86-10-67392172. E-mail address: [email protected] (Y. Zeng).
human corneas with those of pigs using the strip extensiometry method. The comparison is particularly important in the light of the need to acquire statistically significant material property data, which are extremely difficult to obtain from the normal human population.
2. Material and methods Due to the difficulty in obtaining intact human corneas, corneal material used in this experiment were the rings left over from corneal transplant operations from the Tong Ren Hospital in Beijing. As the donor’s corneas had been placed in optisol (a high-quality preservation medium) and stored below 48C for a few days before the transplant operation was performed, the ring-shaped remainders had become slightly swollen. In order to use the same protocol, the porcine corneas were also preserved in optisol before the experiment, and the central zone of the porcine corneas were also excised. According to our measurements, the intact porcine
0021-9290/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 0 ) 0 0 2 1 9 - 0
534
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
cornea and human cornea are very similar in size. In the experiment, the ring-shaped cornea was first cut into two-half-circles, and then the sclera was removed from the cornea with a pair of curved scissors. Uniaxial tests were conducted using an Instron apparatus as shown in Fig. 1. The thickness of the specimen was measured by an optical-magnifying scale. Since the cornea thickens towards its periphery, the thickness was calculated as the mean value of the inner and outer edges of the ring. The average thickness of both human cornea and porcine cornea was 1.0 mm. The typical specimens of human and porcine were approximately rectangle strips 2.5 mm in width which ranged in length from 12–16 mm. The experiment was performed at room temperature. An ultrasound moistener was used to keep the specimen
moist. Force and length data were collected automatically by the computer. The specimens are loaded and unloaded under a constant velocity of loading (10 mm/min) for three cycles. Biological tissues are known to possess strong stress–strain rate dependence. It is very difficult to get enough specimens of human cornea for different stress– strain rates, so the experiments have been completed for a specific value of strain rate (corresponding velocity of loading 10 mm/min) for the present. It was found that the hysteresis loop decreased between successive cycles and eventually disappeared. After three cycles, the specimen can be regarded as preconditioned. All specimens were preconditioned for the stress–strain relationship and stress-relaxation tests.
Fig. 1. Photograph of INSTRON universal testing machine with the gripped tissue sample and schematic of the testing machine system. (a) Photograph of INSTRON universal testing machine. (b) Schematic of the testing machine system.
535
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
3. Results 3.1. Tensile strength The center cross-section of each specimen was measured, and then a load was applied to the specimen at a constant velocity of loading 10 mm/min until failure. Tensile strength was calculated as follows: sb ¼ Fb =A: The Lagrangian stress sb was used, which means stress was calculated from original unstrained cross-section of the specimen. Fb is the maximum load, and A is the area of the cross-section in the middle of the specimen. The tensile strength of the human and porcine corneas is shown in Table 1. The average human cornea tensile strength is 3.81 0.40 MPa, very similar to the experimental result of 3.8 MPa found by Hiroshi (1986).
a is a scale factor, and b represents the exponent of the nonlinear relationship between stress and strain. Our test shows that the data conform with the equation quite well. Fig. 2 shows fitting curves for mean values of 10 human and 10 porcine cornea specimens. For the stress–strain curves, they are similar, as the strains or stresses of human and porcine cornea only have slight differences under the same stress or strain. Table 2 shows the fitting parameters a and b (10 human cornea specimens and 10 porcine cornea specimens, respectively). There is no significant difference between these two kinds of specimens (P > 0:05, using t-test). Porcine corneas and human corneas present similar stress–strain patterns.
3.2. Stress–strain relationship Hoeltzel et al. (1992) tested strips of human cornea under small strain (e50:09), but we tested the strips of human and porcine cornea under different strain ranges. Hoeltzel used the following equation to describe stress– strain relationship of rabbit and human cornea ln s ¼ ln a þ b ln ðe em Þ; where s is the Lagrange stress, e ¼ 12ðl2 1Þ the Green strain was used for finite strain and l is the stretch ratio, em the slack strain (difference between zero strain and the smallest strain to initiate load bearing in the specimen) if De ¼ e em ;
then ln s ¼ ln a þ b ln De:
Table 2 The fitting parameter of the stress–strain
Table 1 The tensile strength of the human and porcine corneas
1 2 3 4 5 6 7 8 9 10 Mean S.D. a
Fig. 2. Stress–strain curves for mean values of 10 human and porcine cornea specimens.
Human
Human
Pig
3.30 3.43 3.94 4.03 4.03 4.45 3.26 4.26 3.61 3.81 3.81 0.40
3.96 3.54 3.58 3.88 3.96 4.00 3.54 3.30 3.52 3.69 3.70a 0.24
Not significant when compared with human group P > 0:17.
1 2 3 4 5 6 7 8 9 10 Mean S.D. a
Pig
a
b
a
b
28.223 50.840 47.953 61.319 40.895 27.119 49.317 47.410 47.802 27.257 42.814 11.674
2.882 2.879 2.595 2.714 3.081 3.155 3.196 2.901 3.091 3.190 2.969 0.208
41.434 39.118 43.221 36.877 26.128 22.927 27.682 56.073 48.632 50.518 39.261a 11.039
3.196 2.883 3.087 3.158 2.669 2.927 3.058 3.138 2.781 2.799 2.970a 0.183
Not significant when compared with human group P > 0:09:
536
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
3.3. Stress relaxation
4. Discussion and conclusion
If the cornea tissue is suddenly loaded at a finite strain rate and then its length held constant, the stress decreased with time, exhibiting the stress-relaxation phenomenon. In this study, the elongation speed was 250 mm/min, and a stretch ratio l ¼ 1:5 was maintained for 1000 s. The relaxation data are normalized, that is, all the stress values are divided by the maximum stress. From the experimental data, the normalized relaxation GðtÞ curve is essentially a linear function of a log time within 1000 s (Fig. 3). Two parameters are adopted to describe the degree of relaxation: K is the slope of fitted GðtÞ-ln t line. P is the value of GðtÞ at the end of the stress-relaxation test (Table 3). A significant difference was observed in the two kinds of specimens (P50:01, using t-test). Porcine cornea relaxes more rapidly than human cornea.
The results show that porcine cornea is similar to human cornea only in tensile strength and the form of the stress–strain curve. The stress-relaxation properties of porcine corneas differ significantly from that of human corneas. Therefore, if tensile strength and stress– strain are the only mechanical factors to be considered, porcine cornea can be used as a satisfactory model in human cornea research. However, when stress relaxation is a factor to be considered, the biomechanical properties of the two corneas are quite different. In conclusion, porcine cornea cannot be used as an appropriate model for human cornea in research, where viscoelastic behavior needs to be considered. The samples which we used were taken from different parts of the cornea periphery. Some people may consider that the structure of the cornea varies greatly in different parts of its periphery. There is no doubt that the degree of cross-linking, the angles of fibers, the density of glycoproteins, and other features differ in different parts of the periphery used in these experiments. But the experimental results are not discrete, therefore the structural difference does not have basic influence on the biomechanical properties of the cornea reported here. Before transplanting, the human corneal tissues have been stored in optisol. In order to compare, the porcine corneal tissues have also been stored in optisol. Although the properties of corneal tissues stored in optisol may be affected by hydration, our approach is in keeping with clinical practice. The tensile strength of human cornea from our results coincided with Hiroshi’s (1986) experimental results, which indicates that strip tissue taken from the periphery of the cornea can be used in tensile strength experiments.
Fig. 3. Typical normalized stress-relaxation curves of human and porcine cornea.
Acknowledgements Table 3 The parameter of stress relaxation Human
1 2 3 4 5 6 7 8 9 Mean S.D. a
We gratefully acknowledge the National Natural Science Foundation of China for the research grants that made this work possible.
Pig
Pð100Þ
KðÞ
Pð100Þ
KðÞ
86.7 84.4 85.6 86.5 87.8 85.3 82.6 85.2 86.7 85.6 1.5
0.0138 0.0171 0.0155 0.0170 0.0140 0.0197 0.0191 0.0189 0.0134 0.0165 0.0024
59.5 66.5 67.9 65.8 67.2 67.2 65.3 59.3 63.1 64.6a 3.3
0.0558 0.0525 0.0511 0.0535 0.0521 0.0504 0.0498 0.0712 0.0611 0.0553a 0.0069
Compared with human group p50:01.
References Hiroshi, Y. 1986. The Strength and Aging of Human Body. Qing Hai People Publishing House, pp. 169–170. Hjortdal, J., Jensen, P.K., 1995. In vitro measurement of corneal strain, thickness and curvature using digital image processing. Acta Ophthalmologica 73, 5–11. Hoeltzel, D.A., Altman, P., Buzard, K., Choe, K., 1992. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. Journal of Biomechanical Engineering 114, 202–215.
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537 Jue, B., Maurice, D.M., 1986. The mechanical properties of the rabbit and human cornea. Journal of Biomechanics 19, 847–853. Pinsky, P.M., Datye, D.V., 1991. A microstructurally-based finite element model of the incised human cornea. Journal of Biomechanics 24, 907–922.
537
Woo, S.Y., Kobayashi, A.S., Lawrence, C., Schlegel, W.A., 1972. Nonlinear material properties of intact cornea and sclera. Experimental Eye Research 14, 29–39.
Technical note
A comparison of biomechanical properties between human and porcine cornea Yanjun Zenga,*, Jian Yanga, Kun Huanga, Zhihui Leeb, Xiuyun Leec a
Biomechanical and Medical Information Institute, Beijing Polytechnic University, Beijing 100022, People’s Republic of China b Ophthalmology Department, Tong Ren Hospital, Beijing 100730, People’s Republic of China c Ophthalmology Department, Friendship Hospital, Beijing 100050, People’s Republic of China Accepted 8 November 2000
Abstract Due to the difficulty in obtaining human corneas, pig corneas are often substituted as models for cornea research. The purpose of this study is to find the similarities and differences in the biomechanical properties between human and porcine corneas. Uniaxial tests were conducted using an Instron apparatus to determine their tensile strength, stress–strain relationship, and stress-relaxation properties. The tensile strength and stress–strain relation were very similar but significant differences between the two tissues were observed in the stress-relaxation relationship. Under the same stretch ratio l ¼ 1:5, porcine cornea relaxed much more than human cornea. If tensile strength and the stress–strain relation are the only mechanical factors to be investigated, porcine cornea can be used as a substitute model for human cornea research. However, when stress relaxation is a factor, porcine corneas cannot be used as an appropriate model for human corneas in mechanical property studies. It is very difficult to get enough specimens of human cornea, so we did the experiments for stress–strain relationship at a specific value of strain rate (corresponding to the velocity of loading 10 mm/min), and for stress relaxation at a specific stretch ratio l ¼ 1:5. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Human cornea; Porcine cornea; Tensile strength; Stress–strain relationship; Stress relaxation
1. Introduction The cornea plays an important role in the refractive power of the eye. The shape of the cornea and its biomechanical properties are of great interest to both ophthalmologists and researchers. A number of studies on the mechanics of the cornea, both intact and cut into strips, have been published. Most notable are the works by Woo et al. (1972), Jue and Maurice (1986), Pinsky and Datye (1991) and Hjortdal and Jensen (1995). Because of the difficulty in obtaining human cornea specimens, it is useful to compare the biomechanical properties of human cornea with that of pigs, since people usually consider pigs to have eyes similar to human beings. The objective of the present study is to compare the biomechanical properties of *Corresponding author. Biomedical Engineering Center, Beijing Polytechnic University, Beijing, 100022, People’s Republic of China. Tel.: +86-10-67392172. E-mail address: [email protected] (Y. Zeng).
human corneas with those of pigs using the strip extensiometry method. The comparison is particularly important in the light of the need to acquire statistically significant material property data, which are extremely difficult to obtain from the normal human population.
2. Material and methods Due to the difficulty in obtaining intact human corneas, corneal material used in this experiment were the rings left over from corneal transplant operations from the Tong Ren Hospital in Beijing. As the donor’s corneas had been placed in optisol (a high-quality preservation medium) and stored below 48C for a few days before the transplant operation was performed, the ring-shaped remainders had become slightly swollen. In order to use the same protocol, the porcine corneas were also preserved in optisol before the experiment, and the central zone of the porcine corneas were also excised. According to our measurements, the intact porcine
0021-9290/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 0 0 ) 0 0 2 1 9 - 0
534
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
cornea and human cornea are very similar in size. In the experiment, the ring-shaped cornea was first cut into two-half-circles, and then the sclera was removed from the cornea with a pair of curved scissors. Uniaxial tests were conducted using an Instron apparatus as shown in Fig. 1. The thickness of the specimen was measured by an optical-magnifying scale. Since the cornea thickens towards its periphery, the thickness was calculated as the mean value of the inner and outer edges of the ring. The average thickness of both human cornea and porcine cornea was 1.0 mm. The typical specimens of human and porcine were approximately rectangle strips 2.5 mm in width which ranged in length from 12–16 mm. The experiment was performed at room temperature. An ultrasound moistener was used to keep the specimen
moist. Force and length data were collected automatically by the computer. The specimens are loaded and unloaded under a constant velocity of loading (10 mm/min) for three cycles. Biological tissues are known to possess strong stress–strain rate dependence. It is very difficult to get enough specimens of human cornea for different stress– strain rates, so the experiments have been completed for a specific value of strain rate (corresponding velocity of loading 10 mm/min) for the present. It was found that the hysteresis loop decreased between successive cycles and eventually disappeared. After three cycles, the specimen can be regarded as preconditioned. All specimens were preconditioned for the stress–strain relationship and stress-relaxation tests.
Fig. 1. Photograph of INSTRON universal testing machine with the gripped tissue sample and schematic of the testing machine system. (a) Photograph of INSTRON universal testing machine. (b) Schematic of the testing machine system.
535
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
3. Results 3.1. Tensile strength The center cross-section of each specimen was measured, and then a load was applied to the specimen at a constant velocity of loading 10 mm/min until failure. Tensile strength was calculated as follows: sb ¼ Fb =A: The Lagrangian stress sb was used, which means stress was calculated from original unstrained cross-section of the specimen. Fb is the maximum load, and A is the area of the cross-section in the middle of the specimen. The tensile strength of the human and porcine corneas is shown in Table 1. The average human cornea tensile strength is 3.81 0.40 MPa, very similar to the experimental result of 3.8 MPa found by Hiroshi (1986).
a is a scale factor, and b represents the exponent of the nonlinear relationship between stress and strain. Our test shows that the data conform with the equation quite well. Fig. 2 shows fitting curves for mean values of 10 human and 10 porcine cornea specimens. For the stress–strain curves, they are similar, as the strains or stresses of human and porcine cornea only have slight differences under the same stress or strain. Table 2 shows the fitting parameters a and b (10 human cornea specimens and 10 porcine cornea specimens, respectively). There is no significant difference between these two kinds of specimens (P > 0:05, using t-test). Porcine corneas and human corneas present similar stress–strain patterns.
3.2. Stress–strain relationship Hoeltzel et al. (1992) tested strips of human cornea under small strain (e50:09), but we tested the strips of human and porcine cornea under different strain ranges. Hoeltzel used the following equation to describe stress– strain relationship of rabbit and human cornea ln s ¼ ln a þ b ln ðe em Þ; where s is the Lagrange stress, e ¼ 12ðl2 1Þ the Green strain was used for finite strain and l is the stretch ratio, em the slack strain (difference between zero strain and the smallest strain to initiate load bearing in the specimen) if De ¼ e em ;
then ln s ¼ ln a þ b ln De:
Table 2 The fitting parameter of the stress–strain
Table 1 The tensile strength of the human and porcine corneas
1 2 3 4 5 6 7 8 9 10 Mean S.D. a
Fig. 2. Stress–strain curves for mean values of 10 human and porcine cornea specimens.
Human
Human
Pig
3.30 3.43 3.94 4.03 4.03 4.45 3.26 4.26 3.61 3.81 3.81 0.40
3.96 3.54 3.58 3.88 3.96 4.00 3.54 3.30 3.52 3.69 3.70a 0.24
Not significant when compared with human group P > 0:17.
1 2 3 4 5 6 7 8 9 10 Mean S.D. a
Pig
a
b
a
b
28.223 50.840 47.953 61.319 40.895 27.119 49.317 47.410 47.802 27.257 42.814 11.674
2.882 2.879 2.595 2.714 3.081 3.155 3.196 2.901 3.091 3.190 2.969 0.208
41.434 39.118 43.221 36.877 26.128 22.927 27.682 56.073 48.632 50.518 39.261a 11.039
3.196 2.883 3.087 3.158 2.669 2.927 3.058 3.138 2.781 2.799 2.970a 0.183
Not significant when compared with human group P > 0:09:
536
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537
3.3. Stress relaxation
4. Discussion and conclusion
If the cornea tissue is suddenly loaded at a finite strain rate and then its length held constant, the stress decreased with time, exhibiting the stress-relaxation phenomenon. In this study, the elongation speed was 250 mm/min, and a stretch ratio l ¼ 1:5 was maintained for 1000 s. The relaxation data are normalized, that is, all the stress values are divided by the maximum stress. From the experimental data, the normalized relaxation GðtÞ curve is essentially a linear function of a log time within 1000 s (Fig. 3). Two parameters are adopted to describe the degree of relaxation: K is the slope of fitted GðtÞ-ln t line. P is the value of GðtÞ at the end of the stress-relaxation test (Table 3). A significant difference was observed in the two kinds of specimens (P50:01, using t-test). Porcine cornea relaxes more rapidly than human cornea.
The results show that porcine cornea is similar to human cornea only in tensile strength and the form of the stress–strain curve. The stress-relaxation properties of porcine corneas differ significantly from that of human corneas. Therefore, if tensile strength and stress– strain are the only mechanical factors to be considered, porcine cornea can be used as a satisfactory model in human cornea research. However, when stress relaxation is a factor to be considered, the biomechanical properties of the two corneas are quite different. In conclusion, porcine cornea cannot be used as an appropriate model for human cornea in research, where viscoelastic behavior needs to be considered. The samples which we used were taken from different parts of the cornea periphery. Some people may consider that the structure of the cornea varies greatly in different parts of its periphery. There is no doubt that the degree of cross-linking, the angles of fibers, the density of glycoproteins, and other features differ in different parts of the periphery used in these experiments. But the experimental results are not discrete, therefore the structural difference does not have basic influence on the biomechanical properties of the cornea reported here. Before transplanting, the human corneal tissues have been stored in optisol. In order to compare, the porcine corneal tissues have also been stored in optisol. Although the properties of corneal tissues stored in optisol may be affected by hydration, our approach is in keeping with clinical practice. The tensile strength of human cornea from our results coincided with Hiroshi’s (1986) experimental results, which indicates that strip tissue taken from the periphery of the cornea can be used in tensile strength experiments.
Fig. 3. Typical normalized stress-relaxation curves of human and porcine cornea.
Acknowledgements Table 3 The parameter of stress relaxation Human
1 2 3 4 5 6 7 8 9 Mean S.D. a
We gratefully acknowledge the National Natural Science Foundation of China for the research grants that made this work possible.
Pig
Pð100Þ
KðÞ
Pð100Þ
KðÞ
86.7 84.4 85.6 86.5 87.8 85.3 82.6 85.2 86.7 85.6 1.5
0.0138 0.0171 0.0155 0.0170 0.0140 0.0197 0.0191 0.0189 0.0134 0.0165 0.0024
59.5 66.5 67.9 65.8 67.2 67.2 65.3 59.3 63.1 64.6a 3.3
0.0558 0.0525 0.0511 0.0535 0.0521 0.0504 0.0498 0.0712 0.0611 0.0553a 0.0069
Compared with human group p50:01.
References Hiroshi, Y. 1986. The Strength and Aging of Human Body. Qing Hai People Publishing House, pp. 169–170. Hjortdal, J., Jensen, P.K., 1995. In vitro measurement of corneal strain, thickness and curvature using digital image processing. Acta Ophthalmologica 73, 5–11. Hoeltzel, D.A., Altman, P., Buzard, K., Choe, K., 1992. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. Journal of Biomechanical Engineering 114, 202–215.
Y. Zeng et al. / Journal of Biomechanics 34 (2001) 533–537 Jue, B., Maurice, D.M., 1986. The mechanical properties of the rabbit and human cornea. Journal of Biomechanics 19, 847–853. Pinsky, P.M., Datye, D.V., 1991. A microstructurally-based finite element model of the incised human cornea. Journal of Biomechanics 24, 907–922.
537
Woo, S.Y., Kobayashi, A.S., Lawrence, C., Schlegel, W.A., 1972. Nonlinear material properties of intact cornea and sclera. Experimental Eye Research 14, 29–39.