Ординатура / Офтальмология / Английские материалы / Biomaterials and regenerative medicine in ophthalmology_Chirila_2010

13.17 Model predictions for poly(acrylic acid) refractive index.

dissolution as a result of crosslinks. Ionic hydrogels respond to changes in pH, ionic strength, and temperature. Their interactions are changed by use of good or poor solvents. Hydrogels have strong orientation-dependent interactions

(hydrogen bonds), which influence swelling equilibrium. Inhomogeneities in hydrogels can arise from crosslinking inefficiency. Imperfections are caused by pre-existing order, network defects, or phase separation.

Flory equilibrium swelling theory states that the polymer absorbs solvent until chemical potentials in the gel phase and in the free solution are equal. Gels swell when solvent penetrates the polymer mesh. Swelling equilibrium occurs when the net osmotic pressure equals zero and when cohesive energy density and solubility of solvent equal those of the polymer. Polymer chains are stretched when the gel is swollen. Swelling properties depend upon polymer functionality, crosslink density, ionic content, and solvent characteristics (Flory and Rehner, 1943). Peppas and Lucht modified the

Flory–Rehner equation to describe swelling behavior for non-Gaussian networks crosslinked in solution (Peppas and Lucht, 1984).

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Overlay plot

2.00

RI : 1.336

13.18 Model predictions for poly(acrylic acid) target values.

Table 13.6 Microindentation of 7.5% poly(acrylic acid) hydrogels

13.19 Poly(acrylic acid) toxicity in RPE cells.

Mc is the molecular weight between crosslinks, Mn is the number-averaged molecular weight, and x1 is the Flory–Huggins polymer–solvent interaction parameter. The relaxed state of the polymer is the condition immediately after initial polymerization. The gel contains some water in the relaxed state because it was polymerized in solution.

According to Peppas and Brannon-Peppas (1990), N can be calculated as follows:

where Mr is the molecular weight of the polymer repeating unit. The copolymers synthesized in this project are tetrafunctional and follow the phantom network model. They are highly swollen gels and not all the chains may interact with each other. The polymers were treated as highly crosslinked non-Gaussian networks, so the Peppas-Lucht equation was utilized.

The degree of swelling decreases with initial monomer concentration because of the decreased likelihood of cyclization during reaction, increased entanglements, and decreased mesh size. Swelling increases as a result of higher molecular weights between crosslinks, porosity, conversion, and fewer defects. The degree of swelling decreases with hydrophobicity because of hydrophobic physical interactions and the change in the c1 parameter. As a result, the gel density increases and the modulus increases. The modulus is

364 Biomaterials and regenerative medicine in ophthalmology

higher in a collapsed state than in a swollen state due to physical crosslinks (Bajpai et al., 2004).

Copolymerization with hydrophilic monomers increases water sorption and swelling. Addition of hydrophobic copolymeric groups will decrease the degree of swelling. Ions repel each other, which leads to swelling. Hydrophilicity decreases interfacial tension which also leads to swelling. Swelling decreases with increased crosslink density. This also causes increased homogeneity and decreased solvent diffusivity. The effective crosslink density can be increased by entanglements. At high crosslink densities, some gels can have two phases: an unswollen core and an outer swollen shell (Bajpai et al., 2004).

As previously mentioned, equilibrium swelling occurs when the net osmotic pressure is zero. The equilibrium swelling ratio, Q, is the swollen volume, Vs, divided by the dry volume of the polymer, Vd.

The volumes V can be calculated by dividing the mass W by the density r.

In the present study, the crosslink density is the reciprocal of the thiol content. It can be compared to the theoretical value of the crosslink density, which is calculated as

Hydrogels swell rather than dissolve in solution. A good solvent (x1 < 0.5) is one in which repulsion between polymer chains occurs, resulting in swelling. A poor solvent (c1 > 0.5) results in interchain attractive forces and shrinking behavior. The energy of swelling behavior is described by Flory–Rehner (Flory and Rehner, 1943) equations below based on Gibbs free energy (dG) of mixtures. At equilibrium swelling, dG is minimized and the osmotic pressure (p) terms sum to zero. This is represented mathematically by the equations below, in which dμ1 is chemical potential and n1 is moles.

Equations [13.9] to [13.11] show that the swelling osmotic pressure is a result of the contribution of four terms: the mixing effects between the polymer and solvent, the elastic component due to the contraction of polymer chains, the effects of ions, and the electrolytic effects. The PAA synthesized in this project was synthesized at neutral pH in the sodium salt form, and no electric potential was applied, so the electrolyte term can be discarded. The mixture and elastic potentials are given by Equations [13.12] and [13.13], respectively.

[1 + (1/N)(ν2s /ν2r )1/3]2

In Equations [13.12] and [13.13], R is the gas constant, T is the temperature, f is the polymer functionality, and the other terms are as defined previously.

For swelling in physiological salt solutions, an additional osmotic pressure term must be added. Following the Donnan ion exclusion theory, the ionic effects can be calculated as:

where I is the salt concentration in DPBS, f is the fraction of ionized polymer, Ka is the acid dissociation constant of the polymer, and pH is that of the

solvent. For PAA swollen in DPBS, the parameters are I = 0.101 mol/L, f = 1, Ka = 5.5 ∞ 10–5, and pH = 7.4 (Jabbari et al., 2007). To determine

the osmotic pressure exerted by the hydrogel, the elastic, mixing, and ionic osmotic terms in Equations [13.12] to [13.14] are summed, resulting in Equation 13.15.

The Flory–Huggins interaction parameter used in the swelling equations was calculated using known swelling parameters, and Equation [13.15] was used

Equilibrium swelling

The hydrogels formed at 7.5% initial monomer concentration were swollen in DPBS, pH 7 water, or pH 4 water. The swelling solution was changed every 24 hours for 1 week. By 7 days, the hydrogels had reached equilibrium, as determined by constant mass between consecutive weighings.

13.4.3 Results and discussion

AAB4N3 hydrogels synthesized at 7.5% concentration were swollen in

DPBS, pH 7 water, or pH 4 water. The equilibrium swelling ratios and final weight concentrations were calculated and are shown in Table 13.7. In Table 13.7, the equilibrium swelling ratio is the ratio of the hydrogel in its swollen state with respect to its relaxed state, or the state at which the hydrogel was synthesized in solution. For reference, the equilibrium swelling ratios from the dry polymer state are also included.

The swelling ratio of the 7.5% AAB4N3 hydrogel in water was 12.7. For PAA, all the parameters in the swelling equations were known except

Table 13.7 Equilibrium swelling results for AAB4N3

Pressure (mmHg)

20

15

10

5

1% BAC

2% BAC

3% BAC

4% BAC

5% BAC

Increasing

BAC

368 Biomaterials and regenerative medicine in ophthalmology

As expected, the osmotic pressure exerted by the hydrogel increased with polymer concentration in the hydrogel and with decreasing crosslinker concentration. There is a non-linear increase in osmotic pressure with polymer concentration and a linear decrease with the crosslinker concentration.

The polymer concentration has the most significant impact on osmotic pressure.

For all formulations analyzed with polymer concentration between 0.5 and 2.0% and crosslinker content between 1 and 5%, the gels will swell slightly and exert a small osmotic pressure. The osmotic pressure is plotted in mmHg because the intraocular pressure is routinely expressed in this unit. Therefore, none of these hydrogel formulations exceed the normal intraocular pressure of 15 mmHg and should not cause glaucoma (Tasman and Jaeger,

2006). However, the swelling pressure may be sufficiently high that it may maintain healthy ocular function and tamponade the retina. This confirms that PAA is a good candidate for vitreous substitution because of its ability to exert a slight osmotic pressure even at low polymer concentrations in the hydrogel.

13.5Conclusions and recommendations

Knowledge of the mechanical behavior of the vitreous humor was acquired to develop in situ-forming hydrogels as permanent vitreous substitutes. One of the objectives of this research was to examine and understand fully the viscoelastic behavior of the vitreous humor and its application to its function in the eye. Its mechanical properties have been objectively tested using rheometry. A large number of porcine vitreous samples were analyzed using capillary rheometry, and the storage and loss moduli match those found by other groups who used different methods. The data showed that the vitreous humor had a higher storage modulus than loss modulus, indicating viscoelastic solid behavior similar to that of a polymeric hydrogel.

Additionally, it has been definitively shown that the composition of the vitreous humor is a mesh of collagen with hyaluronic acid coils interspersed in a gel of 99% water (Foulds, 1987). This research made it possible to develop a better, permanent vitreous substitute by mimicking the natural vitreous in form and function. Additionally, this knowledge could lead to a better understanding of the mechanism of retinal detachment and vitreous syneresis, improving the knowledge base for practicing ophthalmologists in diagnostics. The disciplines of chemical engineering, polymer chemistry, ophthalmology, and biology were applied to examine the vitreous humor from a multifaceted perspective. The results show that the vitreous body could be tested intact, which had not been done before, by employing capillary rheometry.

The review of the literature shows that there is obviously a need for a

better vitreous substitute. Hence, the second objective of this work focused on the design of a biomimetic prosthetic. It has been shown that the refractive index and viscoelastic properties of the natural vitreous can be mimicked by a copolymeric hydrogel network composed of PAA. The incorporation of a hydrophobic moiety along the polymer backbone enables hydrogel formation at lower polymer concentrations, which minimizes both the refractive index and the modulus.

The concept that sets these vitreous substitutes apart from the others is the process of in situ gelation. It has been shown that in situ gelation greatly improves the biocompatibility and efficacy of the vitreous substitute. The reversible disulfide crosslinker enables the synthesized copolymers to be liquefied and extensively purified. By the time the copolymers come into contact with ocular tissues, all monomers and low molecular weight components were removed, greatly improving biocompatibility (Swindle et al., 2008). The method of gelation in vivo also has practical benefits. Implantation of a preformed hydrogel into the ocular cavity is not feasible, and injection of a preformed hydrogel is difficult and leads to some loss of elasticity and cohesiveness.

It was also shown through modeling that the osmotic pressures exerted by these in situ-forming vitreous substitutes were low enough to avoid surgical and post-surgical complications, while high enough to tamponade the retina. The osmotic pressure that will be exerted by the vitreous substitute can be tailored by modifying the polymer concentration, crosslinker content, or the hydrophobic content.

A mixture design was used to optimize the formulation of in situ-forming hydrogel vitreous substitutes. This method of hydrogel design optimization enabled rapid screening of candidate formulations that matched the optical and mechanical properties of the natural vitreous humor. This statistical experimental design method was applied to novel polymer formulations in order to rapidly screen for an in situ-forming hydrogel vitreous substitute to be used eventually in a long-term animal study and possibly clinical trials.

By acquiring the properties of the vitreous humor, better vitreous substitutes were developed that are capable of forming in situ due to the incorporation of the disulfide crosslinker. In conclusion, the viscoelastic properties of the vitreous humor were determined, the method of in situ regelation was proven, the mechanism of retinal attachment via exertion of osmotic pressure was proven through modeling, and biomimetic hydrogel vitreous substitutes were rapidly screened using a mixture design.

13.6Future trends

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characterized, and can serve as the target values for refractive index and modulus for a biomimetic vitreous substitute. Polymeric hydrogels formed at low concentrations should be able to match both the refractive index and viscoelastic properties of the natural vitreous humor.

The concept of an in situ-forming hydrogel vitreous substitute has been proven in vitro and in vivo using model polymeric systems. The process of injecting a liquid into the eye and having it form a gel in the shape of the ocular cavity is preferable. Additionally, the use of an in situ-forming hydrogel as a vitreous substitute would require no change in the current vitrectomy technique, allowing for easier adoption by the surgical community. Other novel polymer systems with improved biocompatibility can be applied as vitreous substitutes with the incorporation of a disulfide crosslinker along the backbone, or by using other in situ crosslinking methods. A mixture design should be used to rapidly screen these new polymeric candidates and to target the formulation that will yield a biomimetic vitreous substitute.

It is possible that an in vivo-forming hydrogel vitreous substitute could be used in clinical trials shortly. Several of the fundamental questions have been answered through the completion of osmotic pressure modeling and optimization of the design of the vitreous substitutes. These methods can be applied to other polymeric systems to rapidly screen for vitreous substitute candidates for future animal studies and possibly clinical trials.

13.7Sources of further information and advice

Refojo explored polymers as ophthalmic prostheses and reviewed vitreous substitutes (Refojo, 1971; Chan et al., 1984; Giordano and Refojo, 1998).

Chirila’s group pioneered the modern research by evaluating synthetic polymeric hydrogels as vitreous substitutes. They were also the first to evaluate the viscoelastic properties of vitreous substitutes (Chirila et al., 1998; Chirila and Hong, 1998). Experimental vitreous substitutes have also been reviewed extensively by several groups (Chan et al., 1984; Chirila et al., 1998; Soman and Banerjee, 2003; Swindle and Ravi, 2007). The development of in situ-forming hydrogel vitreous substitutes has been explored by a couple of groups recently (Foster et al., 2006; Suri and Banerjee, 2006; Swindle et al., 2008).

13.8References

Aliyar HA, Foster WJ, Hamilton PD and Ravi N (2004), ‘Towards the development of an artificial human vitreous’, Polym Prepr, 45, 469–470.

Anderson MJ, Whitcomb PJ (2000), DOE Simplified: Practical Tools for Effective

Experimentation, New York, Productivity Press.

Bajpai AK, Bajpai J, Shukla S and Kulkarni RA (2004), ‘Modulation in sorption dynamics