Biomechanical properties of the lens capsule: A review

journal of the mechanical behavior of biomedical materials 103 (2020) 103600

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Biomechanical properties of the lens capsule: A review K.S. Avetisov a, N.A. Bakhchieva a, S.E. Avetisov a, b, I.A. Novikov a, A.A. Frolova c, A. A. Akovantseva d, Yu.M. Efremov c, *, S.L. Kotova c, e, P.S. Timashev c, d, e a

Research Institute of Eye Diseases, 11 Rossolimo St., Moscow, 119021, Russia Sechenov University, 2 Bol’shaya Pirogovskaya St., Bldg.4, Moscow, 119991, Russia c Institute for Regenerative Medicine, Sechenov University, 8 Trubetskaya St., Moscow, 119991, Russia d Institute of Photon Technologies of Federal Scientific Research Centre “Crystallography and Photonics” of Russian Academy of Sciences, Moscow, Troitsk, Pionerskaya 2, Russia, 108840 e N.N. Semenov Institute of Chemical Physics, 4 Kosygin St., Moscow, 119991, Russia b

A R T I C L E I N F O

A B S T R A C T

Keywords: Lens capsule Mechanical tests Young’s modulus Atomic force microscopy Capsulotomy Cataract

The lens capsule, a thin specialized basement membrane that encloses the crystalline lens, is essential for both the structural and biomechanical integrity of the lens. Knowing the mechanical properties of the lens capsule is important for understanding its physiological functioning, role in accommodation, age-related changes, and for providing a better treatment of a cataract. In this review, we have described the techniques used for the lens capsule biomechanical testing on the macro- and microscale and summarized the current knowledge about its mechanical properties.

1. Introduction The lens capsule (LC) is a thin transparent membrane, which is � �c, 2017; enclosing the crystalline lens of the eye (Bassnett and Siki Danysh and Duncan, 2009; Wang and Pierscionek, 2018). It consists mainly of type IV collagen (up to 40% of the lens capsule’s dry weight) (Marshall et al., 1992), with its intercrossing network integrated within the laminin scaffold providing the LC’s strength and elasticity. Laminin shows side-specific distribution with abundance on the LC’s epithelial side (Halfter et al., 2013). Other components include entactin/nidogen, agrin, collagen XVIII, and some heparin sulfate proteoglycans (perlecan) (Danysh and Duncan, 2009). Overall, these are the same molecules that have been found in most other basement membranes. Anterior (facing aqueous humor), posterior (facing vitreous humor), and equatorial regions of the LC are generally distinguished based on the location and characteristic features (Fig. 1). At the inner anterior surface of the capsule, a single layer of lens epithelial cells exists which initiates the lens growth. In the equatorial region, there are epithelial cells differentiating into fiber cells, and close to the posterior portion of the lens, the adult lens fibers are presented. The thickness of the posterior LC (1–6 μm) is 3–5 times lower than that of the anterior LC (ALC) (Barra­ quer et al., 2006). The zonular attachment points are presented around the equatorial region of the LC. Many aspects of the LC structure and

function are extensively reviewed in (Danysh and Duncan, 2009; Krag and Andreassen, 2003). The capsule has several important biological functions, like providing an adequate environment for the lens cells (Blakely et al., 2000), storage and release of sequestered growth factors (Tholozan et al., 2007), and selective transportation of metabolites (Lee et al., 2006). However, its primary functions are related to the physical and mechanical roles it plays in maintaining the shape of the lens and in accommodation. Although there is no complete understanding of the accommodation process (concurring Helmholtz’s (Helmholtz, 1855), Schachar’s (Schachar, 1994) and other theories are reviewed in (Wang and Pierscionek, 2018)), the mechanical properties of the LC are undoubtfully important, because the LC transmits tensions from the relaxation and contraction of ciliary muscles to a compliant lens sub­ stance. From the mechanistic point of view, the lens capsule may be considered as a thin-walled capsule loaded from the inside and from the outside in a certain way. The elastic properties of the capsule are important for control of the lens shape during accommodation, specif­ ically, the relationship between the elastic properties of the capsule and those of its content, as well as interactions with the supporting appa­ ratus, muscular complex of the iris (sphincter and pupil dilator). The knowledge of the capsule thickness and mechanical properties provides a better understanding of the capsule’s role in accommodation and in

* Corresponding author. E-mail address: [email protected] (Yu.M. Efremov). https://doi.org/10.1016/j.jmbbm.2019.103600 Received 23 July 2019; Received in revised form 26 November 2019; Accepted 13 December 2019 Available online 14 December 2019 1751-6161/© 2019 Elsevier Ltd. All rights reserved.

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the onset of different vision impairments. This knowledge is equally important in relation to cataract surgery and implantation of artificial intraocular lenses (AIOL). Cataract surgery involves the removal of a circular segment of the ALC by means of manual or femtosecond laser capsulotomy. At initial stages, mechanical damages (such as tears) in the remaining ALC may compromise the surgical outcome (Reyes Lua et al., 2016; Roberts et al., 2013), while long-term properties of the LC will determine the insertion and stability of AIOLs. The capsule biome­ chanical properties and their assessment is the main topic of this review with a particular focus on the implications in clinical surgery and the novel experimental techniques. 2. Biomechanical testing of the lens capsule 2.1. Methods for assessment of the global mechanical parameters Traditional approaches to studying the LC biomechanical properties suggest stretching and deformation testing of sample fragments ob­ tained in the course of surgery from human and experimental animals (sometimes cadaver eyes), i.e., ex vivo studies (Fig. 2A–C, Fig. 3). The typical methods are pressure loading (Danielsen, 2004; Fisher, 1969; Pedrigi et al., 2007), stretching of the capsule opening after capsulotomy (removal of the part of the ALC) (Andreo et al., 1999; Assia et al., 1991; Morgan et al., 1996; Parel et al., 2006; Wood and Schelonka, 1999), and variations of the stress-strain analysis for LC specimens of different ge­ ometries (Auffarth et al., 2013; Avetisov et al., 2019; Krag et al., 1997a; Krag and Andreassen, 1996; Werner et al., 2010). In the pressure loading inflation test, first designed by Fisher (1969), a disc of LC is clamped in a hole between the two chambers filled with isotonic saline (Fig. 2A). The pressure between the two chambers is controlled in such a way that the applied pressure loading deforms the LC to a spherical cap. The Young’s modulus is determined from the applied pressure and the deformation of the capsular disc. The pressure loading was also performed by fluid injection via the needle inserted into the lens of an isolated eye; LC deformation was tracked by fluo­ rescent markers arranged on the exposed capsular surface (Pedrigi et al., 2007). Stretching tests were performed on ring-shaped LC specimens or openings generally in a uniaxial fashion (Fig. 2B–D). In a typical

Fig. 2. Techniques for the measurement of lens biomechanics, schematic rep­ resentation. (A) Inflation test. A disc of LC is clamped between two chambers filled with isotonic saline under controlled pressure; pressure loading is applied to deform the LC to a spherical cap (Fisher, 1969). (B) Stretching of the LC opening. Two probes are inserted to stretch the capsulotomy edges (Morgan et al., 1996). (C) Stretching test for isolated LC pieces. A ring-shaped LC specimen is stretched in a uniaxial fashion at a constant speed, while elongation and force are monitored (Krag et al., 1997a). (D) Mechanical stretching test of the anterior LC obtained after manual capsulotomy. The sample is folded on the wire loop, and free edges are held in pneumatic clamps of the testing device (marked with arrows are the directions of sample stretching). The red line marks the location of the incision remained after capsulotomy. Reprinted from (Avetisov et al., 2019) with permission. (E) Atomic force microscopy (AFM). The tip of a cantilever is impressed into the LC placed on a sample holder. The force of the contact interaction as a function of the indentation depth is registered.

Fig. 1. The lens structure, diagrammatic representation highlighting the location and regions of the lens capsule. 2

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Fig. 3. (A) Young’s modulus of the anterior LC versus age in years, data from (Fisher, 1969) and (Krag and Andreassen, 2003). (B) Graph of the load versus the extension for tearing test of a continuous curvilinear capsulorhexis (CCC) using the entire capsular bag of fresh human cadaver eye. The maximum load and extension during tearing were 0.44 N and 5.75 mm, respectively. Reprinted from (Werner et al., 2010) with permission from Elsevier, copyright 2010. (C) Force measurement of porcine ALC samples after femtosecond laser (top, rupture force between 97 mN and 123 mN) and manual (bottom, rupture force between 48 mN and 103 mN) capsulotomy during stretching using two retractors (F ¼ force; L ¼ length). Reprinted from (Auffarth et al., 2013) with permission from Elsevier, copyright 2013. (D) Diagrams “stress versus elongation” obtained from the mechanical testing of the human ALC samples after femtolaser (a) and manual (b) capsulotomy with the setup described in (Avetisov et al., 2019).

experiment, the stretching is performed at a constant speed, while elongation and force are monitored until the tissue is ruptured. In the case of openings, the complex LC geometry makes the calculation of the material parameters hardly possible, while for the LC pieces such ma­ terial parameters as Young’s modulus might be extracted. A nonlinear stress-strain response is typical for LC. Two regions (a bilinear response) were distinguished in (Krag et al., 1997a): an initial region with a low elastic modulus and a second, stiffer, region. The elastic moduli can be determined for each of the regions, or the entire curve can be described by an exponential equation. A third region may be observed, associated with the mechanical failure and tearing of the capsule. In our own study, to standardize the ALC samples after manual and laser capsulotomy in the course of mechanical testing, we hung the samples on a trapezoidal wire loop in such a way that the loop flexure corresponded to the sample diameter (Avetisov et al., 2019). When fixing the samples after manual capsulotomy, the incision at the capsule edge was located perpendicularly to the loop flexure (Fig. 2D). The upper end of the wire was fixed, the free edges of a sample were fixed in pneumatic grips of a tensile machine, and a uniaxial extension of the sample was performed up to the moment of rupture. We believe that such a procedure of mechanical testing allows receiving an averaged mechanical response from the four edges simultaneously, that both

solves the problem of inhomogeneity and increases the registered loads up to the favorable range of the registration device, as well as almost excludes the influence of an additional rupture resulting from manual capsulotomy. 2.2. Measurement of the local mechanical properties While the above methods may be classified as global or macroscopic, the recent instrumental development allows measurements of the capsule properties at a microscopic scale. In particular, a specific di­ rection in the estimation of the LC biomechanical properties is related to the application of nanoindentation (Simsek et al., 2017) and atomic force microscopy (AFM) (Binnig et al., 1986; Efremov et al., 2011; Francis et al., 2010; Gautier et al., 2015). AFM is used for investigations of the sample surface morphology with a high resolution (imaging), and also allows studying its mechanical properties. The technique is based upon the interaction of a sharpened tip (probe) located at the end of a cantilever with the sample surface due to attractive and repulsive forces of various nature which depend on the distance between the tip and the surface. Those forces cause the cantilever to deflect from its equilibrium position, with the deflection measured using a laser beam reflected from the upper cantilever surface and hitting a registering photodiode 3

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(Figs. 2E and 4). AFM images are obtained via scanning in the constant force regime, in which the tip repeats the surface relief during its line-by-line motion in respect to the surface. AFM images allow one to detect the presence of different objects on the surface (matrix compo­ nents, collagen fibers, cells), as well as to determine the roughness, i.e., the measure of the surface texture non-uniformity at the nanoscale. A considerable advantage of AFM is a possibility of conducting measure­ ments in fluid (e.g., in a buffer or a cell medium), i.e., in the close-to-native conditions. Mechanical properties are measured using AFM force spectroscopy mode (also referred to as nanoindentation) (Efremov et al., 2011; Gautier et al., 2015). In the course of an experi­ ment the tip (or, in certain cases, a microsphere attached to a cantilever instead of a sharp tip) plays a role of an indenter which is impressed into the material under study. During the indentation, the force of the con­ tact interaction between the indenter and the material is being regis­ tered. The dependencies of the force on the indentation depth are referred to as force curves. Based on force curves, a local Young’s modulus of a sample is calculated. For this purpose, experimental force curves are approximated with the physical models of contact interaction deduced for different indenter geometries. For example, the Hertz model describes indentation of a surface with a spherical indenter, while the Sneddon model describes a conical indenter (it is also used for pyramidal probes) (Efremov et al., 2011; Gautier et al., 2015). By performing indentation in a set of points uniformly distributed over the surface, the maps of local Young’s modulus distribution are acquired. Such maps

allow studying non-uniformity of a sample’s mechanical properties. However, sharp AFM probes may interact with the nanostructural fea­ tures of the fibrous network of the sample thus resulting in wide vari­ abilities of the extracted elastic moduli. AFM experiments were performed on both isolated pieces of the LC (Choi et al., 2012; Halfter et al., 2013; Haritoglou et al., 2013; Reyes Lua et al., 2016; Tsaousis et al., 2014; Ziebarth et al., 2011) (e.g., acquired by capsulorhexis) and on the surface of whole lenses (Sueiras et al., 2015; �lu et al., 2018). In the latter case, however, only the external surface is T¸a available (anterior side in the case of the ALC), while isolated pieces could be turned with the desired side facing up or mounted in a folded configuration with both sides exposed upward (Halfter et al., 2013; Reyes Lua et al., 2016). The sample must be firmly fixed on a surface for an AFM experiment, that might be achieved by mounting the whole lens in agarose gel in a way that only the bottom half of the lens is contained �lu et al., within the gel (Haritoglou et al., 2013; Sueiras et al., 2015; T¸a 2018). However, when the measurements are performed on a whole lens, the deformation and bending of a whole capsule under the AFM tip might occur and some complex response of the lens and capsule might be recorded instead of the capsule only (Ziebarth et al., 2011, 2007). To facilitate attachment of the LC pieces, the poly-lysine coated surfaces were used in some of the studies (Halfter et al., 2013; Reyes Lua et al., 2016). When the epithelial side of the ALC is studied by AFM, the epithelial cells were removed by incubation with detergents (e.g. Triton X-100) (Halfter et al., 2013; Reyes Lua et al., 2016) since, otherwise, the

Fig. 4. AFM investigations on the lens capsule. (A) The fibrous network at the surface of the human lens capsule, AFM height, and 3D images. The grayscale corresponds to 70 nm, the color scale corresponds to 120 nm, the scale bar is 2 μm. Reptinted from (Sueiras et al., 2015), CC BY-NC-ND 3.0, published by Molecular Vision. (B) A typical force curve obtained on the human anterior lens capsule. Reptinted from (Tsaousis et al., 2014) with permission from Springer Nature, copyright 2013. (C) The Young’s modulus values calculated from the AFM force curves obtained on the epithelial (Ep) and the vitreal (Vi) surfaces of the LC. The epithelial surface was about twice as stiff as the stromal surface. Adapted from (Halfter et al., 2013), CC BY, published by PLoS ONE. 4

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cells may hamper acquisition of the ALC’s own properties.

3.2. Biomechanical properties of the lens capsule and age

3. Biomechanical properties of the lens capsule and affecting factors

Several studies were aimed at the exploration of the age-related changes in the mechanical properties of the LC. At a high strain (Fisher, 1969), the age-related changes of the human LC manifested themselves as a decrease of the Young’s modulus (Fig. 3A), the maximum stress at fracture being 2.3 � 0.7 MPa. The average Young’s moduli of the rat ALC at low stresses and at fracture were 0.56 � 0.38 and 11.3 � 1.9 MPa, correspondingly, while the same parameters for LC of cats aging from 1 to 2 years were 0.82 � 0.29 and 7.74 � 1.38 MPa, correspondingly (Fisher and Hayes, 1979; Fisher and Wakely, 1976). In another study (Krag et al., 1997a), the annual age-related decrease of such biomechanical indices of the human LC as ultimate elongation, ultimate stress, and Young’s modulus was 0.5, 1.0 and 0.9%, respec­ tively. However, the elastic modulus at a low strain was found to in­ crease until the age of 35 years, after which no significant changes were observed (Fig. 3A) (Krag and Andreassen, 2003). The age-related alterations in the LC of primates were assessed using AFM (Ziebarth et al., 2011). The samples were ALC central fragments obtained ex vivo: 18 human samples (donor age 33–79 years), 9 samples from Cynomolgus monkey (age 5.9–8 years) and 8 samples from ba­ boons (age 2.8–10 years). The tests in the mentioned groups were con­ ducted within up to 12 (4.6 � 3.2), 2 (0.7 � 0.7), and 2 (1.1 � 0.4) days post-harvesting, respectively. The eyes were stored in a refrigerator at 4оС prior to the experiment. To eliminate a probable influence of the epithelium lining the interior surface of the capsule on the AFM results, it was removed by keeping samples in trypsin (0.1%) and EDTA (0.02%) solutions for 5 min. The Young’s modulus was calculated with the Sneddon model for a conical indenter. The Young’s moduli of a Cyn­ omolgus monkey’s and baboon’s ALC were 33.7 � 33.1 (9.19–117) and 33.3 � 16.7 (13.1–62.4) kPa, respectively. For human ALC the modulus was 28.7 � 6.7 (21.5–36.3) kPa for people younger than 45; 47.7 � 10.4 (31.1–62.0) kPa for the age range of 45–70 and 86.5 � 37.6 (39.6–131) kPa for those older than 70. In spite of the limitedness and non-uniformity of the material, the authors had come to the following basic conclusions: the absence of a relationship between the AFM results and the time passed from the donor death, the similar ALC elastic modulus in young people and in monkeys, the ALC elastic modulus in­ crease with age. It should be noted, that AFM applies small deformations and thus should be close to the low strain regime. Thus, the age-related stiffening for both the AFM data and low strain data of the uniaxial test appears to agree with each other (Krag and Andreassen, 2003). As was noted in the above section, the AFM imaging additionally revealed a decrease in the interfibrillar spacing and some functional parameters of the images with age (Sueiras et al., 2015; T¸� alu et al., 2018). The species-dependent and age-related variations in the biomechanical properties of the lens capsule are summarized in Table 1.

3.1. Species-dependent variations in the biomechanical properties of the lens capsule In a series of the first experimental studies (Fisher, 1969; Fisher and Hayes, 1979; Fisher and Wakely, 1976), the LC biomechanical charac­ teristics were measured for humans and experimental animals(Fisher and Wakely, 1976). The mechanical behavior of the LC was compared with that of a rubber membrane of a similar thickness, and they appeared to differ substantially: the rubber membrane exhibited a decrease of the Young’s modulus with extension, while the LC exhibited an increase. The deformation of the LC prior to fracture was only 25%, while for the rubber membrane it was by several orders of magnitude higher (750%). In comparative studies of the biomechanical character­ istics of the corneal Descemet membrane and ALC of bovine, porcine, rat and human cadaver eyes, the Descemet membrane in animal samples appeared less deformable than LC, while in human samples both struc­ tures had similar mechanical properties (Danielsen, 2004). The analysis of the stretching process of a labeled human LC using a 2D videosystem showed anisotropy in the peripheral regions of the LC and a higher stiffness in the annular direction (Pedrigi et al., 2007). When analyzing the mechanical data from animal models, one should take into account the differences between the LC of humans and other mammals. For example, the porcine LC is approximately 4 times thicker and substantially more elastic than the human LC, its Young’s modulus fluctuates in the range of 10.0–31.5 MPa vs. 0.7–2.3 MPa for humans (Fisher, 1969; Fisher and Hayes, 1979; Fisher and Wakely, 1976; Krag and Andreassen, 1996). To a certain extent, the minimiza­ tion of those differences’ effect on the results of biomechanical studies may be solved via using young (6–12 months of age) animals (Andreo et al., 1999; Krag and Andreassen, 1996). As noted in the previous section, AFM can be used to assess both the topography and mechanical properties of a sample (Fig. 4) that is especially advantageous since the topography reflects the specifics of the sample’s structure which may be directly related to its mechanical properties. Species-dependent differences were detected by AFM in the LC overall structure and surface roughness: the surface of the porcine LC was the smoothest, while the human and cynomolgus monkey capsules were significantly rougher (Sueiras et al., 2015). The AFM images depicted a highly ordered fibrous structure at the surface of the LC in all the three species (Fig. 4A), the interfibrillar spacing was highest in the human and monkey LCs and decreased linearly as a function of age. The AFM images also revealed a fractal nature of the LC surface, and some functional parameters demonstrated significant change with age (T¸� alu et al., 2018). AFM allowed studying the mechanics of both sides of the LC, epithelial and vitreal. The epithelial side was found to be about two times stiffer in agreement with the properties of other basal membranes (Halfter et al., 2013). Using AFM, Ziebarth et al. investigated elasticity of 18 freshly enucleated lenses of Cynomolgus monkeys (Ziebarth et al., 2007). A studied sample represented a complex of the lens-zonular liga­ ments-ciliary body-sclera obtained after removal of the cornea, iris, sclera and vitreous body. The average Young’s modulus calculated using the Sneddon model was 1720 � 880 Pa (the entire range was 409–3210 Pa). These results are comparable with the earlier presented data ob­ tained as a result of dynamic mechanical tests of young people’s lenses, but mush lower than the results obtained on the isolated LC pieces, which might be associated the global deformation of the lens and the bending deformation of the capsule (Ziebarth et al., 2011).

3.3. Biomechanical properties of the lens capsule in relation to clinical surgery A whole direction in the studies of the LC biomechanical properties is stipulated by the clinical importance of this anatomical structure in the modern lens surgery (phaco surgery). In low-invasive phaco surgery, the annular ALC dissection in the central region (anterior capsulotomy or anterior continuous curvilinear capsulorhexis) is one of the basic tech­ nical elements. When performed correctly, it largely provides adequately conducted procedures at the subsequent stages of the surgery (fragmentation of the nucleus, aspiration of the lens masses and im­ plantation of the intraocular lens). From the viewpoint of the capsulo­ rhexis adaptation to the subsequent intracapsular manipulation, a crucial index is the biomechanical “strength” of the ALC edge. In the clinical practice, along with the traditional (manual) capsulotomy, socalled energetic techniques are also used (bipolar radiofrequency endodiathermy and femtolaser). The technique of manual capsulotomy is based on the procedures well-known in surgery – dissection and 5

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stress at fracture was 5.2 times lower, while the rigidity was 2.8 times lower. When testing porcine eyes, the dependence of the LC edge me­ chanical properties on the capsulotomy technique was less pronounced and not uniform. No changes in elasticity were found, and the average ultimate stress and rigidity after diathermic capsulotomy were lower only by 1.7 and 1.8 times, respectively, as compared to the manual technique, that is probably explained by a significantly thicker (by 2.5–3 times) porcine ALC. The biomechanical properties of the ALC edge remaining after manual and femtosecond laser capsulotomy are important during and after the surgery (Al Harthi et al., 2014; Avetisov et al., 2016; Bala et al., 2014; Mastropasqua et al., 2013; Ostovic et al., 2013; Reyes Lua et al., 2016; Schultz et al., 2015). When studying the ALC edge after a femtosecond laser by electron microscopy, one can see numerous microheterogeneities (ruptures) resulting from laser pulses, which become more pronounced with the laser power gain. The profile of the free capsule edge after performing a manual capsulorhexis appears more uniform along the entire perimeter and only at a high magnification one can see single incisions, depressions and small “nicks”. Independently of the capsulotomy technique, a de-epithelization region appears along the free ALC edge, expressed to a various degree. In a series of comparative studies on the ALC edge biomechanics after manual and femtosecond laser capsulotomy, a porcine lens capsule was used as a model. Using porcine eyes, Friedman et al. mimicked ultra­ sound phacoemulsification after manual and femtosecond laser capsu­ lotomy (Friedman et al., 2011). After removal of the cornea and iris, the capsular bag was filled with gelatin, and the LC edges were stretched using retractors immersed into the capsular opening with the rate of 0.25 mm/s. The force required for the rupture was registered with piezo dynamometers. The LC edge after the femtosecond laser action appeared significantly stiffer (in some cases, by almost 2 times) than that after the manual technique. In another similar study (Auffarth et al., 2013), ALC samples after manual and femtosecond laser capsulotomy were immersed in hyaluronic acid, and the capsule edges were stretched using two retractors (mobile and fixed) with the rate of 36 mm/s. The average values of the force registered at rupture and the extension coefficient after laser capsulotomy appeared higher by 35 and 16%, respectively, than those after a manual removal (Fig. 3C). The results obtained in the above studies were possibly influenced by the application of gelatin and hyaluronic acid in the course of mechanical testing. “Wetting” of the capsule edge with such viscous substances may, to some extent, increase its mechanical strength, while microheterogeneities at the capsule edge after femtosecond laser capsulotomy essentially expand the general area of the capsule edge’s surface, as compared to the manual technique. �ndor et al. The results of an opposite character were obtained by Sa (2014), who performed a comparative study of mechanical properties of annular ALC samples, cut out after manual and femtosecond laser cap­ sulotomy on porcine eyes. The testing was conducted using a universal tensile testing machine by means of two metallic pins placed into the post-capsulotomy opening, one of which was immobile and the other one moved at the rate of 10 mm/min up to the moment of rupture. The average force registered at rupture appeared significantly higher after manual capsulorhexis (155 mN vs. 119 mN), while the increase of the average coefficient of extension in those cases was less pronounced (150% vs. 148%). In their subsequent study, using the same technique, the authors performed an estimation of the ALC mechanical properties after femtosecond capsulotomy depending on the laser pulse power (2, 5 and 10 nJ, or arbitrary low, moderate and high, respectively) (S� andor et al., 2015). The edges of post-capsulotomy openings formed in the regime of high energy appeared significantly weaker mechanically than those obtained when using low and moderate laser radiation power: the force registered at rupture was on the average 108, 119 and 118 mN, respectively. A similar dependence was obtained for the coefficient of extension (144, 148, and 148%, respectively). The authors explain these findings by a substantial boost of the photothermal and photodestructive effects with the raise of the laser power above 5 nJ.

Table 1 Species-dependent and age-related variations in mechanical properties of the lens capsule. The data are presented as mean � SD, characteristic range, or characteristic value. Method

Mechanical parameter

Species

Value

Inflation test/ pressure loading

Young’s modulus

human

6–8 MPa, age 0–1 years ( Fisher, 1969) 5–6 MPa, age 25 years ( Fisher, 1969) 3–4 MPa, age 50 years ( Fisher, 1969) 2.40 � 0.27 MPa, age 58–96 years (Danielsen, 2004) 0.82 � 0.29 MPa at low stress (Fisher and Wakely, 1976) 7.74 � 1.38 MPa at rupture (Fisher and Wakely, 1976) 0.56 � 0.38 MPa at low stress (Fisher and Hayes, 1979) 11.3 � 1.9 MPa at rupture ( Fisher and Hayes, 1979) 0.54 � 0.03 MPa ( Danielsen, 2004) 1.20 � 0.08 MPa ( Danielsen, 2004) 1.26 � 0.06 MPa ( Danielsen, 2004) 0.4, age 0–1 years (Krag et al., 1997a; Krag and Andreassen, 2003) 1.2, age 25 years (Krag et al., 1997a; Krag and Andreassen, 2003) 1.5, age 50 years (Krag et al., 1997a; Krag and Andreassen, 2003) 1.07 � 0.11 N/m, age 71 � 4 years (Pedrigi et al., 2009) 28.7 � 6.7 kPa, age <45 years (Ziebarth et al., 2011) 47.7 � 10.4 kPa, age 45–70 years (Ziebarth et al., 2011) 86.5 � 37.6 kPa, age >70 years (Ziebarth et al., 2011) 120 kPa, age 19–84 years, epithelial side (Halfter et al., 2013) 40 kPa, age 19–84 years, vitreal side (Halfter et al., 2013) 200–400 kPa, age 75 � 4 years (Tsaousis et al., 2014) 1.72 � 0.882 kPa (Ziebarth et al., 2007) 33.7 � 33.1 kPa (Ziebarth et al., 2011) 33.3 � 16.7 kPa (Ziebarth et al., 2011)

cat

rat

cow sow Uniaxial stretching test

Young’s modulus

human

Uniaxial stretching test AFM

Stiffness, N/m

human

Young’s modulus, kPa

human

cynomolgus monkey hamadryas

rupture of a tissue. The separation of biological tissues with a femto­ second near-infrared laser occurs due to the formation of minuscule gas bubbles which subsequently coalesce resulting in the tissue rupture. Short femtosecond pulses minimize release of the thermal energy. The main advantage of a femtosecond laser application is a possibility of performing anterior capsulotomy prior to dissection of the eyeball fibrous shell. According to a comparative study (Krag et al., 1997b), the me­ chanical properties of the ALC edge of human cadaver eyes after diathermic capsulotomy appeared essentially worse than those after the manual technique: on the average, the elasticity was lower by 1.8 times; 6

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Taking into account the known fact of human ALC thickening in the direction from the center to periphery (according to Barraquer et al., from 13.5 to 16 μm) (Barraquer et al., 2006), Packer et al. analyzed a possible dependence of the ALC mechanical properties on the capsu­ lotomy diameter (Packer et al., 2015). The diameter of the manual capsulotomy opening was 5.0 mm, and that of femtosecond laser cap­ sulotomy opening fluctuated from 4.0 to 5.5 mm. Two plastic retractors with the diameter of 2 mm were placed into the capsulotomy opening (as judging from the technique description, the lens substance was not removed), one of which remained immobile, and the other one was moved with the rate of 62 μm/s by a step motor, stretching the capsule edge. The stress at rupture and extension capability of the ALC edge were found to depend on the initial diameter of femtosecond laser capsulotomy. At a diameter of capsulotomy equal or exceeding 5.0 mm, the elasticity and extensibility of the capsule edge after femtosecond laser capsulotomy is higher than that after manual capsulotomy with the same diameter. An increase of the femtosecond laser capsulotomy diameter from 4.0 to 5.0 mm essentially improves mechanical properties of the capsule edge. In another series of studies, human cadaver eyes were used as a model for the estimation of the ALC biomechanical properties. Pedrigi et al. conducted comparative studies of ALC samples obtained ex vivo from previously non-operated eyes and from eyes after an earlier per­ formed cataract surgery (Pedrigi et al., 2009). Two adjacent annular samples were cut out from the capsule: an arbitrarily central one and a peripheral one, with the width of 1.5 and 1.0 mm, respectively. In previously operated eyes, the inner diameter of the central ring coin­ cided with the capsulotomy border, while in intact eyes it was approx­ imately 4.5 mm. In the course of uniaxial mechanical testing, the loading force and extension of the capsule were assessed simultaneously. As a result, a significant (almost fourfold) increase of the stiffness was found for the samples obtained from operated eyes and corresponding to the capsule edge in comparison with the similar parameters of intact eyes. In peripheral samples, this difference in stiffness was small and statistically insignificant. The revealed stiffness increase was probably associated with the post-surgical ALC alterations in the capsulotomy region which manifest itself clinically through thickening and contraction of the capsule edge and immunohistochemically through the increase in the fibronectin level, as well as of collagen types I, III, V and VI (Shigemitsu et al., 1999). Werner et al. had analyzed the fracture strength of the ALC edge ex vivo after manual circular capsulotomy (Werner et al., 2010). Two re­ tractors of the testing machine were placed through the opening in the capsulotomy region with the diameter of 5–5.5 mm into the capsular bag with the lens substance removed, and the retractors were moved in the opposite directions with the rate of 7.0 mm/min up to the rupture. The average force required to break the capsule edge was 390 mN, and the extension was 5.85 mm (Fig. 3B). Using a similar technique, Thompson et al. compared the strength of the ALC capsule edge with the diameter of 5.0–5.5 mm after manual and femtosecond laser capsulotomy (Thompson et al., 2016). No significant difference was found in the strength of the capsule edge between the two techniques. It is not impossible that the postmortem changes of the tissues may have influenced the significance of the results obtained in the mechan­ ical studies of human eyes. At the same time, the modern techniques of phacoemulsification surgery allow obtaining ALC samples intrasurgically as a result of capsulotomy. Such samples represent a conve­ nient material for the experimental studies with more methods available than in the case of capsulotomy openings. However, the technique for the preparation of the central capsule fragment for tensile measurements is quite important, taking into account that it might affect the capsu­ lotomy edges and might require additional features such as the addi­ tional incision of the sample edge after manual capsulotomy. In the study by Chan et al. the ALC samples explanted after femto­ second laser–assisted cataract surgery were fixed between two grips of

the tensile machine at a distance of 1.5 mm and subjected to stretching (Chan et al., 2017). The average rupture force (measured in grams) for the capsule after the manual and laser technique was 2.3 and 2.0 g, respectively, however, the difference was statistically insignificant, and only in five cases appeared notable. It is not exactly clear from the description of the technique presented in the study, how the difference in the configuration of “manual” and “laser” samples was eliminated in the course of the mechanical testing and to what extent the obtained results reflected the mechanical properties of the capsule edge itself. That is why, evidently, when discussing the validity of this model of mechanical studies, the authors deliver a possibly disputable suggestion: “although the in vivo capsulotomy is subject to circumferential forces from instruments, this can be seen as a longitudinal stretch when small segments are tested, such as between clamps” (cited from (Chan et al., 2017)). In our own experimental study, the standardized ALC samples after manual and laser capsulotomy were analyzed using the setup described in Fig. 2D (Avetisov et al., 2019). A uniaxial extension of the sample was conducted with the rate of 2 mm/min up to the moment of rupture. After manual capsulotomy, the indices of the ultimate tensile stress and strain at fracture appeared to be essentially higher than those after femto­ second laser capsulotomy (Fig. 3D). The special dyes are often used in the surgery of mature and congenital cataracts to improve visualization and facilitate manipula­ tions with ALC. Using AFM, Haritoglou et al. estimated the changes of the ALC mechanical properties after its staining with brilliant blue, indocyanine green, and trypan blue (Haritoglou et al., 2013). 15 ALC samples were studied directly after the intraoperative harvesting. Each of the samples was divided into 7 V-shaped parts: 3 of them were stained with the above dyes for 1 min, 3 underwent an additional post-staining illumination with a standard light source mimicking the illumination of a surgical microscope, 1 sample remained intact as a control. After staining with brilliant blue, indocyanine green and trypan blue, a sta­ tistically significant increase of the Young’s moduli was noted, by 1.61 � 0.15; 1.63 � 0.22 and 1.23 � 0.11 times, respectively. The additional illumination resulted in a further increase in the Young’s modulus by approximately 1.2 times. However, two technical features of the study complicate the obtained data’s transfer to the clinic: in the real practice the time of the ALC interaction with a dye, as a rule, does not exceed 15–20 s, while the duration of illumination is essentially longer. Authors of another study (Simsek et al., 2017) did not detect any effects of intracameral trypan blue application on capsule elasticity and stiffness using the nanoindentation technique. In the same study, a decreased stiffness was found for the ALCs of patients with pseudoexfoliation syndrome. In a rather sophisticatedly designed study (Choi et al., 2012), the morphological and biomechanical characteristics of intraoperative central ALC samples were investigated. Each of eight ALC fragments was divided into two equal parts and placed into a balanced saline: one part in an intact state, the other part – after a treatment with a 2% povidone-iodine solution for the removal of epithelial cells from the interior side of the capsule. Then, each of the samples was again divided into two parts for the studies in a hydrated and dehydrated state. Using AFM, the Young’s moduli were measured at the interior and exterior ALC sides. Light and scanning electron microscopy did not reveal epithelial cells at the interior ALC side both in hydrated and dehydrated conditions after the treatment with povidone-iodine. The interior side was significantly less rough (by 354 nm), than that in the untreated samples. The exterior ALC surface after the treatment, on the contrary, appeared rougher (by 382 nm). In the absence of epithelial cells, the Young’s moduli measured both at the exterior and interior LC sides appeared higher by � 70 kPa, than those of the intact ALC. Indepen­ dently of the sample preparation technique, the Young’s modulus of the anterior LC surface was higher than that of the posterior LC surface by 144 kPa. The question about a possible influence of povidone-iodine on the ALC elasticity remains open. 7

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Journal of the Mechanical Behavior of Biomedical Materials 103 (2020) 103600

In the study by Reyes Lua et al. (Reyes Lua et al., 2016), the structure and mechanical stability of the human ALC edge were evaluated after manual and femtosecond laser capsulotomy (34 and 18 samples, correspondingly, obtained intraoperatively from donors aged from 58 to 87 years). To remove cell elements from the interior capsule surface, all the samples were washed with 2% Triton X-100 solution for 5 min. Under light and scanning electron microscope, the ALC samples’ edge appeared smooth and V-shaped after manual capsulotomy, while after femtosecond laser capsulotomy it was jagged, with depressions of 5.48 � 2.27 μm on the average. The mechanical stability of the ALC edge was estimated with AFM using the finite element analysis and a 3D model of AFM images. The manual continuous capsulotomy was found to provide a higher stability of the capsule edge towards mechanical stresses and less propensity to radial ruptures, correspondingly, as compared to femtosecond laser capsulotomy. A computerized 3D modeling showed that after manual capsulotomy the stress is distributed uniformly along the entire smooth capsule edge, while in the jagged edge after femto­ second laser capsulotomy, foci of high stress arise that makes the capsule more inclined to ruptures. From the viewpoint of transferring the data obtained in this study into clinical practice, the need for the ALC sam­ ples’ treatment for the removal of cell elements appears doubtful. On the one hand, the “natural” border cell-lacking regions near the ALC edge have certain differences for manual and femtosecond laser capsulotomy: in the former case this region is of width comparable with the diameter of an epitheliocyte itself (11.9 � 3.8 μm on the average), in the latter case it increases with the laser radiation power (from 15.9 � 3.7 to 35.6 � 14.8 μm at the power of 5200 and 7000 nJ, respectively) (Avetisov et al., 2016). Mechanical parameters of the lens capsule in relation to clinical surgery are summarized in Table 2.

Table 2 Mechanical parameters of the lens capsule in relation to clinical surgery. The data are presented as mean � SD, characteristic range, or characteristic value. Method

Mechanical parameter

Species

Capsulotomy technique

Value

Stretching of the capsule opening

rupture force

human

CCC

134 � 36 mN ( Krag et al., 1997b) 150 � 60 mN ( Morgan et al., 1996) 26.3 � 20.3 mN, central region ( Parel et al., 2006) 50.8 � 20.5 mN, peripheral region ( Parel et al., 2006) 390 � 160 mN ( Werner et al., 2010) 29.1 � 23.1 mN ( Thompson et al., 2016) 26 � 8 mN (Krag et al., 1997b) 20 � 10 mN ( Morgan et al., 1996) 73.3 � 24.9 mN ( Thompson et al., 2016) 26.1 � 6.8 mN ( Thompson et al., 2016) 65 � 21 mN ( Friedman et al., 2011) 73 � 22 mN ( Auffarth et al., 2013) 119.1 � 39.9 mN, diameter 5 mm ( Packer et al., 2015) median 155; IQR: 129–201 mN ( S� andor et al., 2015) 152 � 21 mN, 3 mJ pulse energy ( Friedman et al., 2011) 121 � 16 mN, 6 mJ pulse energy ( Friedman et al., 2011) 113 � 23 mN, 10 mJ pulse energy ( Friedman et al., 2011) 113 � 12 mN ( Auffarth et al., 2013) 95.6 � 15.7 mN, diameter 4 mm ( Packer et al., 2015) 173.7 � 47.3 mN, diameter 5 mm ( Packer et al., 2015) 186.1 � 52.3 mN, diameter 5.5 mm ( Packer et al., 2015) median: 119; IQR: 108–128 mN (

RFC

PPC FLC pig

CCC

3.4. Nonlinearity and viscoelasticity of the lens capsule As with most biological soft tissues, the non-linear stress-strain response is an important characteristic of the LC. The region of low deformation provides the elastic modulus at low strain (<10%) and assumed to have the most significance in relation to accommodation (Krag and Andreassen, 2003). The following region of large, often non-physiological deformation, provides the modulus at high strains, ultimate strain, and ultimate stress (Fisher, 1969). These parameters might be more relevant for the surgery. It is thought that the collagen IV network’s polygonal structure might be responsible for the non-linearity through a geometric effect associated with an initial alignment of the collagen filaments in the direction of loading (Burd, 2009). Although the deformations applied by AFM are small and a low strain regime is expected, the non-linearity could be observed here as well. In a small study (including four ALC fragments obtained intra­ operatively, with the average patient’s age of 75.25 � 4.03 years) the influence of the cantilever force (2; 5; 10; 20 30 nN) on a sample was investigated in the course of the sample’s elasticity measurement (Tsaousis et al., 2014). In order to evaluate the reproducibility of results, five sequential measurements were conducted for each force level. The Young’s modulus value was found to depend on the load level (Fig. 4B). The most uniform results were obtained at a load force of 10 and 20 nN (the variation coefficients being 12.4 and 11.7%, correspondingly). As a majority of biological tissues (Fung, 1993; Verdier et al., 2009), the LC shows a pronounced viscoelastic behavior. Such a behavior is manifested as a time-dependent (thus, also rate-dependent) mechanical response. In a viscoelastic material, an energy loss occurs during the deformation due to rearrangements within the matrix network and the viscous flow of water through it. The typical manifestations of visco­ elasticity are a hysteresis loop during the loading-unloading cycle (Fig. 5A), and stress relaxation or the creep after application of a step strain or stress, respectively (Fig. 5B). The stress-relaxation behavior of the ALCs was found to be consistent with age (Krag and Andreassen, 2003), it proceeded exponentially with time, and the mean relaxation after 20 s of 10% constant applied strain was �12%. Another important

FLC

(continued on next page)

8

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Journal of the Mechanical Behavior of Biomedical Materials 103 (2020) 103600

Table 2 (continued ) Method

Table 2 (continued ) Mechanical parameter

Maximum stretch

Species

Capsulotomy technique

rabbit

CCC

human

CCC

pig

CCC

vitrectorhexis COC FLC

Uniaxial stretching test

rupture force

rabbit

CCC

human

CCC

FLC

AFM

Young’s modulus

human

CCC

Value

Method

S� andor et al., 2015) 19.8 � 15.2 mN, central region ( Parel et al., 2006) 13.5 � 9.5 mN, peripheral region ( Parel et al., 2006) 50 � 18%, central region (Parel et al., 2006) 69 � 17%, peripheral region ( Parel et al., 2006) 5.85 � 1.17 mm ( Werner et al., 2010) 57, range 47–69% (Andreo et al., 1999) 47.7 � 9.9% ( Wood and Schelonka, 1999) 35 � 4% (Auffarth et al., 2013) 35, range 24–47% (Andreo et al., 1999) 46.7 � 8.3% ( Wood and Schelonka, 1999) 60 � 10% ( Auffarth et al., 2013) 38 � 13%, central region (Parel et al., 2006) 30 � 7%, peripheral region ( Parel et al., 2006) median 136; full range 37–660 mN (Avetisov et al., 2019) median 55; full range 48–91 mN ( Avetisov et al., 2019) 485.80 � 44.95 kPa, anterior side ( Choi et al., 2012) 342.60 � 43.80 kPa, posterior side (Choi et al., 2012) 416.20 � 31 kPa, cataract, anterior side (Choi et al., 2012) 272.60 � 91.30 kPa, cataract, posterior side ( Choi et al., 2012) 207 kPa ( Haritoglou et al., 2013) 334 kPa, stained with BB ( Haritoglou et al., 2013) 423 kPa, BB þ illumination ( Haritoglou et al., 2013) 337 kPa, stained with ICG (

Nanoindentation

Mechanical parameter

Young’s modulus

Species

human

Capsulotomy technique

CCC

Value Haritoglou et al., 2013) 416 kPa, ICG þ illumination ( Haritoglou et al., 2013) 254 kPa, stained with TB ( Haritoglou et al., 2013) 289 kPa, TB þ illumination ( Haritoglou et al., 2013) 7.53 � 1.07 GPa, senile cataract ( Simsek et al., 2017) 6.01 � 1.25 GPa, pseudoexfoliation syndrome (Simsek et al., 2017) 8.12 � 0.98 GPa, dye-enhanced surgery, trypan blue (Simsek et al., 2017)

CCC - continuous circular capsulorhexis; COC - can-opener capsulotomy; RFC radiofrequency diathermy capsulotomy; PPC - precision pulse capsulotomy; BB brilliant blue; ICG - indocyanine green; TB - trypan blue; FLC - femtosecond laser capsulotomy; IQR - interquartile range.

experimental consideration is the rate-dependence of the measured elastic modulus and stiffness: a viscoelastic material has a larger elastic modulus when loaded at a high rate compared to a slow rate (Efremov et al., 2019). Overall, the viscoelasticity of the LC remains poorly analyzed and completely uncharacterized on the microscale. Some cataract surgical techniques, such as viscoexpression of the lens nucleus, take advantage of the LC viscoelasticity: the nucleus expression is performed slowly using a viscoelastic material instead of water, and relaxation and creep of the capsulorhexis edge lead to decrease in the resistance against the nucleus expression (Thim et al., 1993). The lens as a whole structure also displays a viscoelastic behavior (Glasser and Campbell, 1999; Sharma et al., 2014), more pronounced than that of the LC and continuing over several time scales (Sharma et al., 2014). The future description of the LC mechanical behavior might benefit from the novel concepts, like poroelasticity (Malandrino and Moeen­ darbary, 2017). The theory of poroelasticity studies the behavior of a porous biopolymer matrix containing a liquid phase (water). Like viscoelasticity, it also describes a time-dependent material behavior and has been successfully used to characterize a range of tissues. The theory predicts differences in the material response at different spatial scales and might account for the material nonlinearities. 4. Conclusions In conclusion, the following should be noted. Application of human and experimental animals’ ALC samples obtained ex vivo as experi­ mental models does not exclude a potential effect of both postmortem changes and anatomical peculiarities of an animal capsule on the study results. The central human ALC fragment harvested in the course of microinvasive phaco surgery is currently one of the best experimental models for quantitative measurements, yet further improvements in models that mimic in vivo situation to the highest extent are required. The variability of the absolute values characterizing the ALC mechanical properties (rupture force, maximum stretch, Young’s modulus) obtained 9

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Journal of the Mechanical Behavior of Biomedical Materials 103 (2020) 103600

Fig. 5. Viscoelasticity of the lens capsule. (A) Hysteresis in the loading-unloading cycle (hatched area) represents energy dissipation in the human ALC. (B) Stress relaxation tests performed on the human ALC at 10% and 40% strains. Normalized stress decays with time exponentially (or as a sum of several exponential decays). Reprinted from (Krag and Andreassen, 2003) with permission from Elsevier, copyright 2003.

to date may be related to a number of factors that might be separated in two groups. The first group includes the factors related to the intrinsic ALC mechanical properties, including nonlinearity, viscoelasticity, and heterogeneity. These properties require advanced mechanical models and an optimal set of parameters for characterization, which is not generally achievable in a single experiment. The second group includes the factors related to the experiment design: sample preparation, spe­ cifics of mechanical testing, the way of the mechanical data represen­ tation. Overall, the need for the standardization of the used methods and parameters is warranted in the area. However, in spite of the experi­ mental differences, the past studies have registered such specifics of the ALC biomechanics as age-related changes and effects of different surgery techniques.

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