Article pubs.acs.org/Langmuir
Estimating the Mechanical Properties of Retinal Tissue Using Contact Angle Measurements of a Spreading Droplet Colin A. Grant,*,† Peter C. Twigg,† Michael D. Savage,‡ W. Hong Woon,§ Mark Wilson,∥ and Denis Greig‡ †
Advanced Materials Engineering RKT Centre, School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, United Kingdom ‡ School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom § Department of Ophthalmology, St James’ University Hospital, Leeds LS9 7TF, United Kingdom ∥ School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom ABSTRACT: When a drop of liquid is placed on the surface of a soft material, the surface deformation and the rate of spreading of the triple contact point is dependent on the mechanical properties of the substrate. This study seeks to use drop spreading behavior to infer the mechanical properties of soft biological materials. As an illustration of the value of this technique we have compared the spreading behavior of a liquid droplet on two viscoelastic, soft materials, namely, an elastomer and a low concentration agar gel. The ratio of the mechanical properties of these soft materials obtained in this way is confirmed by atomic force microscopy (AFM) nanoindentation. By comparing the spreading behavior of a liquid on the retina with that of the same liquid on each of two viscoelastic materials, we can then estimate the elastic moduli of the retina: an estimate that is extremely difficult to carry out using AFM.
1. INTRODUCTION The kinetics of a droplet of liquid spreading on an ideal rigid surface are controlled by the energy balance between capillary potential energy and the viscous dissipation within the liquid.1 Therefore, when a liquid droplet is placed on such a solid surface, the initial contact angle reaches a static equilibrium very quickly, satisfying the well-known Young’s equation (eq 1) γSV = γSL + γLV cos θ0
wetting ridges have been reported on highly viscoelastic polymeric surfaces following Wilhelmy plate experiments.4,5 When considering the energy balance of a liquid spreading on a soft surface, two distinct dissipation mechanisms must be taken account. These are the viscous dissipative component of the liquid due to flow and the viscoelastic dissipation occurring at the advancing wetting ridge (eq 2).3
(1)
where γSV, γSL, and γLV are the interfacial surface tensions that exist between the solid (S), liquid (L), and vapor (V) and θ0 is the equilibrium contact angle. However, if the surface is sufficiently deformable, a wetting ridge is formed, as shown in Figure 1a, due to the vertical component of the liquid/vapor surface tension.2 The height (h0) of such a deformation is estimated to be h0 ≈ γ sin θ0/G, where γ is the surface tension of the liquid and G is the shear modulus of the solid. The deformation, and its predicted profile, at the triple contact point of a liquid on such a soft surface has been experimentally observed by white light interferometry.3 Further, periodic © 2013 American Chemical Society
In this expression, η is the viscosity of the liquid, l is a logarithmic ratio involving cutoff distances to the dissipation zone of the droplet, U is the rate of spreading, ε is a small cutoff Received: February 19, 2013 Revised: March 24, 2013 Published: March 27, 2013 5080
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light sensitive neurons known as rods and cones. The fragility of the tissue makes it difficult to test the mechanical properties, although, tensile testing has been carried out. Chen and Weiland tested porcine retinal samples and suggested that blood vessels made a significant contribution to the tensile mechanical properties.17 Bulk elastic properties of porcine retina were reported not to vary under different applied strain rates, although different plastic behaviors were seen.18 Further tensile testing of retinas has been carried out in the superiorinferior and nasal-temporal directions in air and saline at room temperature and in saline at body temperature.19 All of these tests applied in-plane tensile stresses and do not describe the compressive mechanics in the anterior-posterior direction, which in turn may help to understand any tearing of the retina, such as in macular hole formation. In this study we hypothesize that soft materials of distinctly different mechanical properties should have different degrees of viscoelastic braking. We anticipate that this technique may be utilized to measure the shear modulus of very fragile biological tissues, which is experimentally difficult using standard AFM probes. We have therefore measured the mechanical properties of two homogeneous materials (an elastomer and agar gel) by AFM, correlated these data with contact angle spreading behavior, and then utilized the technique to obtain the shear modulus of the soft tissue.
Figure 1. (a) Schematic diagram showing the deformation (h0) of a soft substrate at the triple contact point between solid (S), liquid (L), and vapor (V). Reprinted by permission from Nature Publishing Group: Letters to Nature, 379, pp 432−4, Carré, Gastel and Shanahan, copyright (1996). (b) Schematic of an AFM probe indenting a substrate.
2. MATERIALS AND METHODS
distance near the triple line below which the behavior of the solid is no longer linear elastic, while U0 and n are constants that are related to the rate-dependent viscoelastic properties of the solid.6,7 As the liquid spreads on a soft surface, the contact angle decreases over time as the radius of the droplet increases, provided there is no evaporation or absorption. Clearly, the wetting ridge at the triple contact line moves as the liquid droplet spreads, inducing a hysteretic strain/relaxation cycle on the surface.8 This viscoelastic dissipation within the substrate impedes the progressing liquid droplet, which now dominates the viscous dissipation effects within the spreading liquid droplet.9 The kinetic spreading of liquid droplets on soft surfaces, i.e., braking due viscoelastic dissipation, has been shown to be independent of liquid viscosity.10 The elastic modulus of materials covers a vast range of values from TPa to kPa, with a corresponding plethora of techniques available for characterization. Biologically soft materials lie at the extreme lower end of this range, with specialized instruments, such as atomic force microscopy (AFM), developed for this purpose.11−16 However, for the most fragile biological components at the lowest end of the known modular range even AFM can be extremely difficult to use, and in this paper we describe an alternative method for obtaining the value of the elastic modulus of a porcine retina. The technique, based on measuring the spread of a liquid droplet on the surface under investigation, is an adaptation of a method proposed by Shanahan and Carré.8 As is clear from Figure 1b the probe at the end of an AFM calibrated cantilever pressing against a sample surface will cause an indentation in a perpendicular direction to the solid surface, exactly opposite to the deformation caused at the triple contact point. It is therefore possible to combine measurements from the two deformations to gain an insight into the mechanical deformation of soft substrates. The retina is a complex multilayered structural tissue that coats the inside of the eye. The layers consist mainly of interconnecting neurons, and include in the outer layers the
2.1. Sample Preparation. The materials used in the spreading rate experiments were two homogeneous standard materials together with the porcine retina: (a) An ultrasoft thermoplastic elastomer, Versaflex CL2000X, supplied by The PolyOne Corporation, McHenry, IL, and Velox U.K., High Wycombe, with a known Young’s modulus of 100 kPa, recently confirmed using piezoelectric cantilevers.20 (b) Agar gels were made by dissolving agar powder (Sigma Aldrich, U.K.) in hot ultrapure water (resistivity ∼18 MΩ cm) at a concentration of 0.5% w/v. The hot solution is then pipetted onto a microscope slide and left in a sealed Petri dish for 1 h. Upon cooling, the gel sets and adheres to the glass slide and is approximately 2 mm thick. The elastic moduli of the gels were obtained by AFM nanoindentation. (c) Porcine eyes (n = 3) were obtained from a local slaughter house and dissected immediately. The vitreous humor was removed, and an approximately 10 mm square section of the ocular tissue was cut from the posterior pole of the eye. Each section was then placed into a Petri dish containing Hank’s balanced salt solution (Sigma Aldrich, U.K.), where the retina was gently peeled away from the sclera/choroid and slid on to a microscope slide. A gentle stream of nitrogen gas was blown over the retinal tissue to remove excess fluid and was then tested immediately. 2.2. Contact Angle Measurement and Liquid Spreading Theory. Contact angles were measured at room temperature (22 °C) using a CAM200 goniometer from KSV Instruments, Helsinki, Finland. Each separate microscope slide was placed in an enclosed chamber, attached to the goniometer sample stage, in order to reduce any evaporation. As the agar gel (0.5% w/v) and retina are predominantly made up of water and subsequently very hydrophilic, for this study we used olive oil (ρ = 900 kg/m3 and γ=32 mN/m) as our liquid droplet. Further, the olive oil is immiscible with water, which should restrict any porous absorption of the droplet into the gel. Droplets (5 μL) of the oil are dispensed by a Hamilton syringe onto each surface, and the contact angle and base length are captured using the instrument’s high speed camera over a period of 1 h. Ignoring the nondominant viscous effects due to the liquid, the spreading behavior of a liquid droplet on a soft elastomeric surface can be approximated by
log[cos θ0 − cos θ(t )]≈n log U +[log(γ /G)] + constant 5081
(3)
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where U is the spreading rate, γ the surface tension, G the shear modulus of the surface, θ0 the equilibrium contact angle, and n a constant.8,10,21,22 Equation 3 can be written in the linear form, y = n log U + c, where it has been shown that the gradient n should lie between 0.5 and 0.6.6−8,10 This value of n links together wetting and adhesion phenomena.22,23 Common surfaces used for investigating the viscoelastic braking phenomenon by contact angle goniometry include elastomers3,6−10,24,25 and polymers.22,26 When considering the spreading behavior from two different materials, the vertical distance between them on a y versus log U graph will be the difference between the [log(γ/G)] terms. 2.3. AFM Nanoindentation. All AFM scans and force measurements were made using an MFP-3D scanner (Asylum Research, Santa Barbara, CA). Silicon nitride cantilever tips (Applied Nanostructures, Santa Clara, CA) with a tip radius of 15 nm and spring constant of ∼0.3 N/m were used and were calibrated using the thermal tuning method.27 Indentations and spring constant calibration were carried out under pure water to restrict any dehydration of the agar sample and to limit adhesion when testing the elastomeric sample. A large number of indentations (n = 800) was made on the elastomer and agar gel surface, in a series of 10 × 10 arrays, with 1 μm separation between indentations. The maximum force was adjusted so that the maximum indentation on the agar gel and elastomer surface was ∼500 nm. This corresponded to a maximum load of 5 and 35 nN for the agar gel and elastomer, respectively, with a constant AFM tip velocity of 2 μm/s. This array was then repeated at eight different locations over each surface. Force plots are then fitted to the conical Hertzian based contact theory where, as shown in eq 4, the applied force, F, is related to the elastic modulus, E, by
F=
2⎡ E ⎤ 2 ⎢ ⎥h tan α π ⎣ 1 − ν2 ⎦
(4)
In this expression ν is Poisson’s ratio (ν = 0.4 for elastomer20 and ν = 0.5 for the agar gel16), h is the indentation depth, and α is the half cone angle of the AFM probe. For this we use the manufacturer’s nominal value of 36°, which had been previously independently confirmed by scanning a standard calibration sample.
3. RESULTS AND DISCUSSION 3.1. AFM Nanoindentation. Typical force versus indentation plots for the agar and elastomeric surfaces are shown in Figure 2a,b, with their corresponding curves fitted to the data using elastic theory. Each theoretical fit to the experimental data is excellent. Figure 2c shows the distribution of the modulus results from the agar and elastomeric surfaces. Here, the mean and standard deviation of the moduli for agar was 26.4 ± 5.2 kPa. This is in excellent agreement with our recent publication, where we demonstrated a variation of modulus in agar gels with concentration and deuteration, resulting in a corresponding modulus of 28.7 ± 8.9 kPa.16 As mentioned previously, the modulus for the CL2000X elastomer is wellknown and recently reported as 100 kPa,20 which is again in excellent agreement with our AFM nanoindentation results (105.8 ± 6.7 kPa). The elastic modulus via AFM nanoindentation of agar gels of differing concentrations does vary considerably.28−30 Variations in the modulus of agar/agarose in the literature will vary due to the variety of agar sources used as well as gelation conditions and water content. The shear modulus (G) can be estimated using elastic theory where E = 2G(1+ν). The Poisson ratio is 0.5 for agar gel (i.e., incompressible) and 0.4 for the elastomer, and so the resulting shear moduli would be 8.8 ± 1.73 kPa and 37.8 ± 2.4 kPa for the agar and elastomeric surfaces, respectively. The ratio of shear moduli (Gelast/Gagar) as measured by AFM nanoindentation is 4.29, which will be used later.
Figure 2. Force versus indentation plots on (a) agar gel and (b) CL2000X elastomer with their corresponding fitting to the elastic conical indentation equation. (c) Distribution of modulus results from AFM nanoindentation for agar gel (blue dash line) and elastomers (solid red line); n = 800 indentations for each surface.
3.2. Spreading Behavior of Reference Materials. Figure 3a,b shows two high speed camera images illustrating the spreading of an oil droplet on the agar surface over a period of 1 h. Using the liquid droplet theory of spreading (eq 3), Figure 3c shows a scatter plot of three experimental repeats of tests on the reference surfaces (agar gel and elastomer). The recorded gradients of the fitted lines are n = 0.49 and 0.50 for the agar gel and elastomer, respectively. This demonstrates that the viscoelastic braking phenomenon (i.e., gradient n = 0.5−0.6) is present on elastomeric surfaces,6−9,21,22,24 and can also be found on agar gel substrates. If the dominating effect of liquid spreading was via the liquid rather than the solid (i.e., viscous dissipation), then the slope of such a line would be unity.21 Carré and Shanahan demonstrated that a vertical shift in these linear fittings of log(cos θ0 − cos θ(t)) versus log(U) is related to the shear modulus and surface tension (γ) of the droplet.8 In Figure 3c the values of the maximum and minimum vertical gaps between the agar and elastomer data, as indicated by the blue dash lines, are 0.64 and 0.61. That is, from eq 3 these give the range of values of log[(γ/G)agar/(γ/G)elast], which for a common liquid reduces to log[Gelast/Gagar]. A vertical shift 5082
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Figure 4. Spreading behavior of the oil droplet on the retinal surface (gradient n = 0.52) with (a) agar gel and (b) Versaflex CL2000X elastomer. Figure 3. Camera shots of oil droplet on agar gel surface at time (a) t = 0 and (b) t = 1 h. (c) Variation of log[cos θ0 − cos θ(t)] with the logarithm of the spreading rate (U) of 5 μL of oil for agar gel (red circles) and elastomer (black squares).
Table 1. Values of Vertical Shift of Dynamic Contact Angle Spreading Leading to the Shear Modulus Ratioa
of between 0.61 and 0.64 at the two extremes of the linear fitted lines therefore gives a shear modulus ratio [Gelast/Gagar] in the range 4.07−4.37, with the shear modulus of the elastomer between 4.07 and 4.37 times greater than that of the agar gel. Using AFM nanoindentation our estimate of the shear modulus ratio between the two homogeneous materials was [Gelast/Gagar] = 4.29, in excellent agreement with the viscoelastic braking theory using eq 3. 3.3. Shear Modulus of the Retina. In the same way as the spreading behavior of an oil droplet on two homogeneous reference surfaces can be used to make estimates of the shear modulus ratio, one can obtain the shear modulus of an unknown soft material by measuring and comparing its spreading behavior with a material of known shear modulus. Experimentally, examining the cellular and fragile nature of large mammalian retina using AFM nanoindentation is very difficult due to problems obtaining adherence of the retinal tissue to a solid substrate. However the spreading behavior of suitable fluids on the soft retinal material is an ideal solution to the problem, and Figure 4a,b shows the spreading behavior of an oil droplet on the retina together with an agar gel and elastomer. The gradient of the linear retinal data is n = 0.53, confirming that viscoelastic braking phenomenon due to a wetting ridge at the triple point of the droplet is the dominant mechanism. Table 1 shows that, by taking the inverse log of the vertical shift and using the known shear modulus of the elastomer/agar gel from AFM nanoindentation, an estimated range for the shear modulus of porcine retina can now be calculated. Our estimates using AFM values for agar gel (Gagar = 8.8 kPa) gave a
agar−retina
vertical shift
elastomer− retina
0.38− 0.42 1.01− 1.04
inverse log (G1/ Gretina)
retinal shear modulus range (kPa)
2.40−2.63
3.35−3.67
10.23−10.96
3.45−3.69
a
The shear modulus ratio then can be used to estimate the shear modulus of retina using the AFM nanoindentation values.
range for shear modulus of 3.35−3.67 kPa. Likewise, using AFM values for the elastomer (Gelast = 37.8 kPa) gave a range of values for retinal shear modulus of 3.45−3.69 kPa. These estimates are in excellent agreement with each other giving selfconsistent values for the shear modulus of the porcine retina, when compared to the spreading behavior of the elastomer or agar gel. A direct comparison of other modular values is difficult due to the limited literature on the mechanics of similar retinal tissue in the same orthotropic direction. Chen and Weiland found that the tensile modulus of a strip of porcine retina with no visible blood vessels was 11 kPa.17 Translating this to a shear modulus using E = 2G(1 + ν) would give 3.6 kPa, which is in good agreement with our results. Franze et al. used large polystyrene beads to indent a guinea pig retinal tissue sample, giving a range of apparent modulus of 0.9−1.8 kPa for different discrete anatomical locations.31 The modulus results showed a plateau of modulus values, approximately 1.5−1.6 kPa, at a distance of ∼2.5 mm from the optic nerve. These results are the same order of magnitude as the results presented here, with the differences explained by the retinal tissue coming from other species with varying retinal orientations and measured by diverse experimental techniques. It should be noted that the deformation at the triple point of a spreading droplet would 5083
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(12) Grant, C. A.; Brockwell, D. J.; Radford, S. E.; Thomson, N. H. Tuning the Elastic Modulus of Hydrated Collagen Fibrils. Biophys. J. 2009, 97 (11), 2985−2992. (13) Grant, C. A.; McKendry, J. E.; Evans, S. D. Temperature Dependent Stiffness and Visco-Elastic Behaviour of Lipid Coated Microbubbles Using Atomic Force Microscopy. Soft Matter 2012, 8 (5), 1321−1326. (14) Grant, C. A.; Thomson, N. H.; Savage, M. D.; Woon, H. W.; Greig, D. Surface Characterisation and Biomechanical Analysis of the Sclera by Atomic Force Microscopy. J. Mech. Behav. Biomed. Mater. 2011, 4 (4), 535−540. (15) Grant, C. A.; Twigg, P. C. Pseudo-Static and Dynamic NanoMechanics of the Tunica Adventitia in Elastic Arteries using Atomic Force Microscopy. ACS Nano 2013, 7 (1), 456−464. (16) Grant, C. A.; Twigg, P. C.; Savage, M. D.; Woon, W. H.; Greig, D. Mechanical Investigations on Agar Gels Using Atomic Force Microscopy: Effect of Deuteration. Macromol. Mater. Eng. 2012, 297 (3), 214−18. (17) Chen, K.; Weiland, J. D. Anisotropic and Inhomogeneous Mechanical Characteristics of the Retina. J. Biomech. 2010, 43 (7), 1417−1421. (18) Wollensak, G.; Spoerl, E. Biomechanical Characteristics of Retina. Retina 2004, 24 (6), 967−970. (19) Chen, K.; Rowley, A. P.; Weiland, J. D. Elastic Properties of Porcine Ocular Posterior Soft Tissues. J. Biomed. Mater. Res., Part A 2009, 93A (2), 634−645. (20) Markidou, A.; Shih, W. Y.; Shih, W.-H. Soft-Materials Elastic and Shear Moduli Measurement Using Piezoelectric Cantilevers. Rev. Sci. Instrum. 2005, 76 (6), 064302. (21) Carré, A.; Shanahan, M. E. R. Effect of Cross-Linking on the Dewetting of an Elastomeric Surface. J. Colloid Interface Sci. 1997, 191 (1), 141−145. (22) Tomasetti, E.; Rouxhet, P. G.; Legras, R. Viscoelastic Behavior of Polymer Surface during Wetting and Dewetting Processes. Langmuir 1998, 14 (12), 3435−3439. (23) Maugis, D.; Barquins, M. Fracture Mechanics and the Adherence of Viscoelastic Bodies. J. Phys. D: Appl. Phys. 1978, 11 (14), 1989. (24) Voué, M.; Rioboo, R.; Bauthier, C.; Conti, J.; Charlot, M.; De Coninck, J. Dissipation and Moving Contact Lines on Non-Rigid Substrates. J. Eur. Ceram. Soc. 2003, 23 (15), 2769−2775. (25) Extrand, C. W.; Kumagai, Y. Contact Angles and Hysteresis on Soft Surfaces. J. Colloid Interface Sci. 1996, 184 (1), 191−200. (26) Yuk, S. H.; Jhon, M. S. Contact Angles on Deformable Solids. J. Colloid Interface Sci. 1986, 110 (1), 252−257. (27) Hutter, J. L.; Bechhoefer, J. Calibration of Atomic-Force Microscope Tips. Rev. Sci. Instrum. 1993, 64 (7), 1868−1873. (28) Nitta, T.; Endo, Y.; Haga, H.; Kawabata, K. Microdomain Structure of Agar Gels Observed by Mechanical-Scanning Probe Microscopy. J. Electron Microsc. 2003, 52, 277−281. (29) Salerno, M.; Dante, S.; Patra, N.; Diaspro, A. AFM Measurement of the Stiffness of Layers of Agarose Gel Patterned with Polylysine. Microsc. Res. Tech. 2010, 73 (10), 982−990. (30) Stolz, M.; Raiteri, R.; Daniels, A. U.; VanLandingham, M. R.; Baschong, W.; Aebi, U. Dynamic Elastic Modulus of Porcine Articular Cartilage Determined at Two Different Levels of Tissue Organization by Indentation-Type Atomic Force Microscopy. Biophys. J. 2004, 86 (5), 3269−3283. (31) Franze, K.; Francke, M.; Gunter, K.; Christ, A. F.; Korber, N.; Reichenbach, A.; Guck, J. Spatial Mapping of the Mechanical Properties of the Living Retina using Scanning Force Microscopy. Soft Matter 2011, 7 (7), 3147−3154.
form into a sharp point, similar to a sharp AFM probe, rather than a large spherical indenting probe.
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CONCLUSIONS In this work, it has been demonstrated that the viscoelastic braking effect of a spreading liquid oil droplet on two reference surfaces is related to the shear moduli of each surface. In particular, a soft, compliant surface will be deformed by the action of the vertical component of the surface tension of the droplet. This surface deformation is in the opposite direction to the indentation from a sharp AFM probe. We have proposed that it is therefore possible to combine the dynamic, spreading contact angle measurement with AFM nanoindentation, in order to gain surface mechanical data on biological soft matter. Each of the reference surface moduli was characterized using AFM nanoindentation, agreeing with previous data. Following validation of the viscoelastic braking effect on these standard surfaces, we applied these data to contact angle spreading on retinal surfaces, enabling us to use this novel technique to obtain reasonable estimates of the shear modulus of retinal samples.
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AUTHOR INFORMATION
Corresponding Author
*Phone: (0)1274 235808. Fax: (0)1274 234525. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This project was funded by the Medical Research Council (U.K.), Project G0802583. We are also grateful to the PolyOne Corporation, 833 Ridgeview Drive, McHenry, IL60050, and to Velox UK, High Wycombe, for the samples of Versaflex CL2000X.
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REFERENCES
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