Biosensors and Bioelectronics 18 (2003) 381 Á/387
A study of piezoelectric and mechanical anisotropies of the human
A. Champa Jayasuriya a,*, Snehasish Ghosh a, Jerry I. Scheinbeim a, Virginia Lubkin b,
Greg Bennett b, Phillip Kramer b
Department of Chemical and Biochemical Engineering, Polymer Electroprocessing Laboratory, College of Engineering, Rutgers-The State University
of New Jersey, 98 Brett Road, Piscataway, NJ 08854-8058, USA
Aborn Laboratory, New York Eye and Ear Inﬁrmary, 310 East 14th Street, New York, NY 10003, USA
Received 19 July 2001; accepted 23 July 2002
The piezoelectric and dynamic mechanical properties of human cornea have been investigated as a function of drying time. As
expected, the piezoelectric coefficient, d31, and the Young’s modulus, Y , were found to be extremely sensitive to water content. d31
decreased with dehydration of the corneal tissue and Y increased with dehydration. While these results are significant, the discovery
of the unprecedented mechanical and electromechanical anisotropy exhibited by the cornea are the major findings of this study and
indicate that the collagen fibrils comprising the cornea are highly oriented. The piezoelectric responses of corneas observed in this
study are: diagonally cut samples starting at an average piezoelectric coefficient value of 2250 pC/N, followed by the vertically cut
samples, with an average starting value of about 600 pC/N and finally the horizontally cut samples with an average starting value of
about 200 pC/N.
# 2002 Elsevier Science B.V. All rights reserved.
Keywords: Cornea; Collagen; Piezoelectricity; Young’s modulus
1. Introduction procedures as well as the pathogenesis of certain corneal
A better understanding of the biomechanical proper- Both corneal and scleral tissue share many simila-
ties of the human cornea is certainly warranted based on rities. Both are primarily collagenous hydrogels consist-
the recent explosion in the numbers of refractive surgical ing of collagen fibrils; however, the scleral tissue is
procedures performed. Various procedures such as opaque while the cornea is transparent to visible light
radial keratotomy, photorefractive keratectomy, laser (Maurice, 1957). It was suggested that both the size and
in situ keratomileusis, and astigmatic keratotomy, rely some ordered distance between fibrils allowed for the
on the ‘average’ corneal structure to develop ‘normo- forward transmission or scattering of light. Others
grams’ which guide surgical planning. Disease states, suggest that corneal transparency is a function of the
such as keratoconus, result from surgically induced or refractive indices of the collagen fibrils and interfibril
congenital mechanisms, which cause unwanted corneal matricies (Smith, 1969). It is also believed that collagen
steeping and irregular astigmatism. Understanding cor- fibrils in scleral tissue are assumed to be of random size
neal elasticity and the corneal response to forces which and orientation and, therefore, cannot transmit light
deform it (intraocular pressure, variable atmospheric (Komai and Ushiki, 1991). While it is easy to accept the
pressure, extraocular pressure from lid disease, etc.), reasoning behind the inability of scleral tissue to
may offer insight to more predictable refractive surgical transmit light, it is less obvious that a full understanding
of cornea transparency exists. To contribute to the
understanding of corneal tissue and differences between
corneal and scleral tissue, we began an investigation into
* Corresponding author. Tel.: '/1-732-445-3660 the piezoelectric and mechanical properties of the
0956-5663/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 5 6 - 5 6 6 3 ( 0 2 ) 0 0 1 4 4 - 6
382 A.C. Jayasuriya et al. / Biosensors and Bioelectronics 18 (2003) 381 Á/387
cornea in hopes of observing any significant differences from them. Five human corneas were sectioned for
between the behavior of cornea and sclera. We also this purpose.
hoped to provide additional insights into the general 2) For the second set, the roughly circular corneas
structure/properties relationships of the cornea itself to were marked as the hour hand on the face of the
allow for further understanding of its transparent clock. The positions for 12 and 3 o’clock were
optical properties and its mechanical stiffness. determined by the location of the eye muscles and
Piezoelectricity in organic polymers (Fukada, 1974) marked with sutures at 12 and 3 o’clock. Rectan-
and in certain biological tissues (Shamos and Lavine, gular strips were then sectioned and labeled by
1967), such as collagen (Fukada and Yasuda, 1964; appointing 12 Á/6 o’clock sections as vertical; 3Á/9
Fukada et al., 1976; Christiansen and Silver, 1992; Pins o’clock sections as horizontal and diagonals as
and Silver, 1995) and bone (Fukada and Yasuda, 1957; either 01:30 Á/07:30 or 10:30 Á/05:30 (see Fig. 1).
Netto and Zimmerman, 1975) has been extensively
investigated. Piezoelectric phenomena have been studied
extensively in bone. Mechanical energy can induce
electrical potentials of significant magnitude to theore-
tically exert a wide range of clinical effects. These
include potentially, control of cell mutation, enzyme
activation or suppression, and orientation of intra-and-
extra cellular macromolecules (Andrew, 1968).
Although some work has been done in determining
mechanical properties of collagen in general, no studies
have been done on the mechanical or electromechanical
properties of the cornea. However, a significant body of
literature does exist on both structural and microstruc-
tural studies of the cornea. Wide-angle X-ray diffraction
studies have been performed on collagen fibrils from
connective tissues to determine the orientation distribu-
tion function and preferred orientation of collagen
(Aspden and Hukins, 1979) as well as to measure the
angular distribution within the tissue (Aspden and
It was reported anisotropies in values of the piezo-
electric d-coefficient of human scleral collagen (Ghosh
et al., 1998) which depend on both the specific region of
the eye from which the sample is taken and the direction
the mechanical force is applied. In the current study we
present the discovery of the unprecedented piezoelectric
response exhibited by human cornea compared to sclera.
In addition, the data show that the piezoelectric
response differs significantly depending on the orienta-
tion of the corneal samples tested.
2. Materials and methods
2.1. Corneal samples
Human corneal samples were sectioned from eyes
obtained from the Eye-Bank for Sight Restoration, Inc.,
New York. The results presented here are from the
following two sets of samples.
1) In the first set studied, corneal samples were
sectioned into rectangular strips without any knowl-
edge of the orientation of the strips to find out the Fig. 1. Human cornea showing three different sections: vertical,
magnitude of the piezoelectric response obtained horizontal, and diagonal.
A.C. Jayasuriya et al. / Biosensors and Bioelectronics 18 (2003) 381 Á/387 383
Fourteen corneas were used for this part of the
study, seven were sectioned diagonally, four hor-
izontally and three vertically.
2.2. Measurement of the piezoelectric-coefﬁcient and
The piezoelectric d-coefficient of a material is defined
as the incremental change in electric polarization that
occurs as a result of an incremental change in mechan-
ical stress, s . Stress is defined as the force per unit area
applied to the material. For a linear elastic material, this
stress produces an elastic strain o , given by the relation
s0/Eo , where E , the elastic modulus, is also called the
Silver print conductive electrodes (GC Electronics, Fig. 2. Piezoelectric d -coefﬁcient versus time for ﬁrst set of ﬁve human
Rockford, IL) were painted on opposite surfaces of the corneas.
corneal strip and allowed to air dry. To compensate for
any dehydration that might occur in the corneal strip and falls somewhat asymptotically to roughly the same
during the painting and drying of the electrodes, these value after about 40 min. Interestingly enough, there
strips were rehydrated in saline for a 30-min period of was a surprisingly large amount of scatter from sample
time. The rehydrated samples were then placed between to sample. Cornea No. 3 had the highest starting value
the grips of the measuring device in the sample chamber. of d :/1600 pC/N (picoCoulombs per Newton); cornea
Care was taken not to let the samples dry out No. 2 around 1200 pC/N; cornea No. 1 about 700 pC/N;
significantly because experience indicates that unlike corneas No. 4 and 5 being the two lowest with a starting
scleral collagen (Pratzl and Daxer, 1993), corneal value of about 300 pC/N. All of the samples decrease to
collagen does not rehydrate if allowed to dry out a similar d -coefficient value of about 50 pC/N after 40
significantly. min. An interesting feature of the drying curve is that
The system used to measure the piezoelectric coeffi-
from an initial high value, the curves fall steeply at first
cient and Young’s modulus was a Rheolograph Solid† ,
and then level off to a plateau before finally making a
which was manufactured by Toyo Seiki Seisaku-Sho
second asymptotic decline to the final (dry) value of 50
Ltd., Japan. The piezoelectric response of the cornea,
pC/N. Whether this represents the suggested two-stage
both its magnitude and anisotropy are easily measured
drying process of the cornea remains to be determined
in a reproducible manner as this instrument was
(Roveri et al., 1979). Not only is there enormous scatter
designed to measure much smaller piezoelectric activity.
from sample to sample in piezoelectric d-coefficient
A dynamic stress, s0/5 N peak to peak, was applied to
apparent from Fig. 2, but the drying curve for cornea
each strip at a frequency of 104 Hz (default value) and
the piezoelectric d -coefficient as well the elastic modulus No. 3 is much steeper compared to that of the other
were continuously monitored as the sample dried out corneas. Also, even at the end of 40 min, the samples
with time. still show a response that is higher than the piezoelectric
response obtained from synthetic piezoelectric polymers
(Winsor et al., 1996; Furukawa, 1989; Mei et al., 1993).
3. Results and discussion Further, measurements of the elastic modulus showed a
similarly wide scatter of values. The scattered values in
3.1. Human cornea piezoelectric response and Young’s modulus led to the
suspicion that the corneas may, in fact, not be direc-
Since this study began with the assumption that tionally isotropic.
human cornea was mechanically isotropic in nature, This prompted a second investigation of the human
we proceeded to measure the piezoelectric d -coefficient corneas. In the second set of corneas studied, each of the
and Young’s modulus without paying any particular corneas was directionally specified (see Section 2) in Fig.
attention to the direction in which corneal samples were 1. Fig. 3a represents the piezoelectric d-coefficient as a
cut from the cornea. function of drying time for four human corneas cut
Fig. 2 shows the piezoelectric d -coefficient as a horizontally. Even for similar horizontal sections there
function of drying time obtained from five human is a fair amount of scatter from cornea to cornea.
corneas. The qualitative behavior is similar for all Cornea No. 8 starts at the lowest value of :/100 pC/N;
samples studied. The response starts at a high value cornea No. 7 starts at :/200 pC/N, while corneas No. 6
384 A.C. Jayasuriya et al. / Biosensors and Bioelectronics 18 (2003) 381 Á/387
Fig. 3. (a) Piezoelectric d -coefﬁcient versus time for horizontally cut corneal sections. (b) Piezoelectric d -coefﬁcient versus time for vertically cut
corneal sections. (c) Piezoelectric d -coefﬁcient versus time for diagonally cut corneal samples. (d) Piezoelectric d -coefﬁcient versus time for
horizontal, vertical and diagonal corneal sections averaged over seven human corneas.
and 9 start at :/275 pC/N. The difference between large amount of scatter in the initial values of the d-
corneas No. 6 and 8 is almost 300%. The drying coefficients. Corneas No. 14, 15 and 16 all start at values
behavior is also different. Corneas No. 7, 8 and 9 all around 1400 pC/N. Corneas 17 and 18 starts at around
dry out to the same final piezoelectric d -coefficient value 2000 pC/N while corneas No. 13 and 19 have initial
of around 30 pC/N. Cornea No. 6 follows a very values between 3500 and 4000 pC/N. All of the
different drying pattern and is still decreasing with a diagonally cut corneas show similar drying behavior
value of :/125 pC/N at the end of the drying time. and asymptote to around 100 pC/N except for cornea
Fig. 3b shows the drying behavior for the three No. 19 which is still decreasing with a value of 1000 pC/
corneal samples sectioned vertically. Their initial piezo- N at the end of the measurement time.
electric d -coefficient starting values are similar and lie Fig. 3d shows the averaged piezoelectric d-coefficient
between 600 and 800 pC/N. Although all three samples as a function of drying time for the differently oriented
decrease over time to around 40 pC/N, their drying sections together. The difference in their respective
pattern is very different as is evident from Fig. 3b. response is evident: the diagonally cut samples starting
Cornea No. 12 appears to show clear evidence of a two at an average piezoelectric coefficient value of 2250 pC/
stage drying process. Fig. 3c represents the piezoelectric N, followed by the vertically cut samples, with an
behavior with drying time for the seven corneal samples average starting value of about 600 pC/N and finally
sectioned diagonally. All of the starting values of the horizontally cut samples with an average starting
piezoelectric d -coefficient obtained from these diagonal value of about 200 pC/N. Not only are the d-coefficient
sections are astonishingly high. Once again there is a values of the diagonal sections considerable, but they
A.C. Jayasuriya et al. / Biosensors and Bioelectronics 18 (2003) 381 Á/387 385
are an order of magnitude greater than the response time for the horizontally cut samples. Corneas No. 6
from the horizontally cut sections and more than three and 9 which exhibit the highest initial piezoelectric d-
times that of the vertically cut sections. These represent coefficient values (see Fig. 3a) have the lowest initial
significant electromechanical anisotropies in the cornea. value of Young’s modulus: about 2 MPa. Cornea No. 7
In addition, if one considers that the highest piezo- has a 4 MPa Young’s modulus as the starting value and
electric response known for synthetic polymers e.g. cornea No. 8 has the highest initial value of Young’s
P(VDF-TrFE) copolymers (Furukawa, 1989) at room modulus at 5 MPa. The nature of the drying curves is,
temperature and nylon (Mei et al., 1993) at higher however, very different. Corneas No. 6 and 9 show a
temperatures are on the order of 30Á/50 pC/N, one can linear slowly increasing trend. However, the curve for
truly appreciate the magnitude of this response. cornea No. 8 increases almost linearly from 5 to 6 MPa
The nature of the drying curves of the diagonally cut for about 35 min and then starts rising sharply to 8
sections is also different from both the vertically cut and MPa. Cornea No. 7 shows a sharper climb in general
horizontally cut sections. The diagonally cut samples from 4 to 7 MPa for 30 min and an even steeper climb to
dry out to a final average d-coefficient value of :/275 almost 12 MPa by 40 min.
pC while the other two sections dry out an average value Fig. 4b shows the drying behavior of the Young’s
of :/100 pC/N, although at sufficiently long drying modulus for the vertically cut samples. All three samples
times, all three sets of values may converge. Fig. 4a start at an initial value of :/1.3 MPa. Corneas No. 10
presents the Young’s modulus as a function of drying and 11 show a very similar linear increase to about 2.5
Fig. 4. (a) Young’s modulus versus time for horizontally cut corneal sections. (b) Young’s modulus versus time for vertically cut corneal sections. (c)
Young’s modulus versus time for diagonally cut corneal sections. (d) Young’s modulus versus time for horizontal, vertical and diagonally cut corneal
sections averaged over seven human corneas.
386 A.C. Jayasuriya et al. / Biosensors and Bioelectronics 18 (2003) 381 Á/387
MPa for the first 30 min and continue to gradually when subjected to a mechanical stress, we anticipated
increase. However, cornea No. 12, which had the lowest that for any particular corneal section, the lowest
initial piezoelectric d -coefficient (see Fig. 3b), shows a piezoelectric response would be generated by the section
much steeper initial rate of increase and then increases that exhibits the lowest response to mechanical stress,
to a final value of :/7 MPa after 40 min. i.e. the one with the highest Young’s modulus. In other
Fig. 4c represents Young’s modulus as a function of words, the direction in which the cornea is stiffest will
drying time for the diagonally cut corneal samples. generate the lowest piezoelectric response.
There is a large amount of scatter in the initial and final Also human corneas exhibit significant mechanical
values of Young’s modulus for all the samples. Cornea anisotropy with a starting values of Young’s modulus
No. 13 has the lowest initial value starting at 0.05 MPa for horizontally cut samples with 3 MPa, a vertically cut
while cornea No. 14 has the highest initial value of 0.75 samples with 1 MPa and a diagonally cut samples with
MPa. The final values are between 0.6 MPa for cornea 0.3 MPa. This difference in the value of Young’s
No. 17 and 1.5 MPa for cornea No. 15. The nature of Modulus suggests a higher degree of fiber orientation
the drying curves is qualitatively similar for most along specific directions of the cornea. One may
samples. Only cornea No. 13 shows a very rapid and speculate that the highest modulus direction has the
steep increase in Young’s modulus with time. greatest number of collagen fibrils oriented in that
Fig. 4d shows the averaged Young’s modulus with direction while the lowest modulus direction has the
drying time for the three differently oriented sections. least number of collagen fibrils oriented in that direc-
The response shown in Fig. 4d is the reverse of the tion.
averaged response of the piezoelectric d -coefficients
shown in Fig. 3d. The average Young’s modulus of
the horizontally cut samples, with the smallest piezo-
electric response, has the highest initial value of :/3
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