**Ophthalmic Viscosurgical Devices (OVDs) are used to maintain intraocular space when performing eye surgery and to give protection to the corneal endothelium from mechanical trauma. These viscoelastic solutions or gels consist of components such as methylcellulose, chondroitin sulfate or hyaluronic acid or its sodium salt. **

Since they are polymeric, they have the tendency to be viscoelastic with their properties greatly influenced by factors such as molecular architecture, molecular weight, concentration and intra- or inter- molecular interactions in solution.

## Types of OVDs

Based on their 'cohesiveness or dispersiveness', OVDs are classified as cohesive OVDs or dispersive OVDs. These characteristics of OVDs are related to their rheological properties.

Cohesive OVDs are high viscosity materials which adhere to each other through molecular associations. They are highly shear-thinning materials with higher molecular weights and surface tension. Their high viscosity allows them to create space by pressurizing the eye in order to insert the optical implant (lens). Cohesive OVDs can also be removed easily after the surgery as their cohesiveness makes the entire mass stick together.

Conversely, dispersive OVDs are more Newtonian, with lower molecular weight. With lower viscosities and surface tension, they can coat and adhere better to tissues and surgical instruments, and can be used for lubrication during the insertion of the optical implant.

However, removing dispersive OVDs after surgery is a difficult process because of their higher fluidity. As well as these two types, combination OVDs, with both dispersive and cohesive properties, and visco-adpative OVDs, which exhibit different properties based on the conditions of use, are also available.

## Rheological Characterization

ISO15798:2013 is the International Standard describing the requirements for OVD characterization in terms of their physical, chemical, and biological characteristics. This article focuses on a particular section of the standard that deals with rheological characterization.

According to the standard, testing of the product must be performed in its finished and sterilized state at 25°C for rheological testing. Both oscillatory and steady shear testing are performed for characterization of viscoelastic and flow characteristics, such as complex viscosity, dynamic viscosity, and viscoelastic moduli.

The complex viscosity measurement is performed as function oscillation frequency using logarithmic increments to illustrate the resistance to flow and deformation of the OVD formulation simultaneously. The specified frequency range is 0.001 - 1000 Hz but the range of 0.01 - 100 Hz is considered acceptable on the condition that the zero shear viscosity plateau at diminishing frequencies is accessible.

For higher viscosity materials, this will happen at lower frequencies. Achieving 100 Hz is often impossible on a rotational rheometer because of inertial limitations. Therefore, it is necessary to aim for the highest achievable frequency. The OVD’s elasticity or viscoelasticity is characterized through G' and G" and is quantified simultaneously with η* up to a frequency of 100 Hz ideally, or to the maximum possible value based on inertia limitations. Data must be shown on a double logarithmic scale against frequency, or as a graph of percent elasticity against log frequency.

For steady shear measurements, the recommended shear rate range is from 0.001 s^{-1} to approximate the zero shear viscosity, representative of conditions within the anterior chamber, to a shear rate of roughly 100 s^{-1}, to reproduce conditions when injecting the viscoelastic fluid into the eye through a cannula. It is essential to increase the shear rates in logarithmic increments. Steady shear viscosity data should be presented on a double logarithmic scale as a function of shear rate.

It is problematic to measure low viscosity fluids at low shear rates. Hence, the lowest shear rate at which it is possible to attain the zero shear viscosity is deemed acceptable. The zero shear viscosity plateau appears for low viscosity materials at higher shear rates and for high viscosity materials at lower shear rates. Therefore, it is not necessary to have low shear rates at all times. It is to be noted that the steady shear zero shear viscosity must correspond with the equivalent value of η* quantified using oscillatory testing.

## Experimental Procedure

The experiment involved analysis and comparison of an OVD formulation consisting of hyaluronic acid at concentrations of 15 mg/ml, 18 mg/ml and 25 mg/ml as outlined in the IS015798:2013 standard. A Kinexus rotational rheometer with a Peltier plate cartridge was used to perform rotational rheometer measurements. Oscillatory measurements and viscometry tests were carried out using a 4°/40 mm cone-plate measuring system and a 2°/20 mm cone-plate, respectively.

A constant and controllable loading protocol was applied on both samples using a standard loading sequence. All rheology measurements were carried out at 25°C. A strain controlled frequency sweep within the pre-determined linear viscoelastic was carried out to measure G' ,G" and η* as a function of frequency. An equilibrium table of shear rates test was carried out to measure the steady state shear (dynamic) viscosity as a function of shear rate.

## Experimental Results

## Oscillation Testing

Figure 1 shows the complex viscosity curves as a function of angular frequency (ω = 2 πf), which are characteristic of a viscoelastic fluid. In this case, the complex viscosity is low, so more elastic, at high frequencies and increases with decreasing frequency due to conversion of elastic energy into viscous energy, culminating in a consistent viscosity plateau. All samples with higher viscosities and concentrations show this constant viscosity or zero shear viscosity plateau (η*0).

**Figure 1. **Frequency sweep data showing complex viscosity as a function of angular frequency for 25 mg/ml (◊), 18 mg/ml (_{o}) and 15 mg/ml (Δ) HA solutions.

G' and G" curves over the same frequency range for the three HA solutions are presented in Figure 2, showing the dominance of the elastic modulus G' at high frequencies. This is related to a low value of η* and deteriorates with decreasing frequency (increasing time) owing to the conversion of elastic energy into viscous energy, consistent with the increase and eventual plateau in η*.

**Figure 2. **Frequency sweep data showing G’ (red) and G” (blue) as a function of angular frequency for 25mg/ml (x), 18mg/ml (∇) and 15mg/ml (◊) HA solutions.

The G'/G" crossover reveals a shift from elastic dominant (pseudo-gel like) behavior to liquid dominant behavior. The inverse of the crossover frequency 1/ωc represents the longest relaxation time of the material or the time taken for the dissipation of roughly 63% of the elastic energy or stress when the polymer relaxes. The modulus at this crossover point is termed as the 'crossover modulus' (G_{c}), providing the total stiffness at this angular frequency.

With η*, the HA solutions with the highest concentrations exhibit the largest values of G' across all frequencies and have the longest relaxation time. This is in good agreement with a higher number of inter-molecular interactions or entanglements, allowing these materials to show more elasticity for longer when stressed.

## Viscometry Testing

Figure 3 presents the steady state flow curves for the three HA solutions. All samples are pseudoplastic or shear-thinning, and their viscosity decreases with increasing shear rate, largely reflecting the complex viscosity vs. angular frequency curves shown in Figure 1.

**Figure 3. **Equilibrium flow curve data showing dynamic viscosity as a function of shear rate for 25mg/ml (_{o}), 18mg/ml (+) and 15mg/ml (∇) HA solutions.

This is a key reason behind the plotting of complex viscosity data against angular frequency, as it is possible to equivocate angular frequency with shear rate, and for simple liquid and polymeric systems η*(ω) ≈ η(γ') as ω tends to zero. Here, η and η* data agree very well in the low frequency, low shear rate region with comparable values of η_{0} and the same concentration trend.

## Data Analysis

Direct estimation of the zero shear viscosity is possible by taking a single point or an average of several points within the zero shear viscosity plateau. Applying a rheological model that fits curves of this type very well is another approach. The Cross and Carreau models are such models incorporated into the rSpace software.

It is possible to fit these models to both both η*(ω) and η(γ') data, provided that the coefficient of correlation is high for the fit. A Cross model fitted to viscosity-shear rate data for the 15 mg/ml HA solution is illustrated in Figure 4, demonstrating the suitability of this model to fit the data.

**Figure 4. **Equilibrium flow curve data showing dynamic viscosity as a function of shear rate for 15 mg/ml HA (Δ) fitted with a Cross model (red line).

Table 1 summarizes zero shear viscosity for all samples based on cross model fitting of η*(ω) and η*(γ) data as well as automated crossover analysis data for G' and G" curves.

**Table 1. **Reported values for the zero shear viscosity (η0), crossover frequency (ωc) and crossover modulus (G_{c}) following cross model fitting and crossover analysis respectively.

HA Concentration |
η0 (Pa.s) |
η*0 (Pa.s) |
ω_{c} (rad/s) |
G_{c} (Pa) |

15 mg/ml |
365 |
389 |
0.768 |
62 |

18 mg/ml |
623 |
660 |
0.094 |
85 |

25 mg/ml |
1867 |
1919 |
0.064 |
145 |

Higher values of η0 reveal lower mobility and therefore more cohesive properties, whereas lower values represent better dispersiveness. In terms of G' and G" data, a more cohesive structure is characterized by a lower cross over frequency (ωc) and higher crossover modulus (G_{c}), whereas a more dispersive system is characterized by a higher value of ωc and lower value of G_{c}.

In general, cohesive OVDs tend to have η0 values anywhere between 100 and 100 000 Pas and dispersive OVDs to have below 50 Pas, with these higher viscosities usually related to lower values of ωc and higher values of G_{c}. Based on these conditions, the three solutions analyzed would be categorized as being more cohesive than dispersive in nature.

## Conclusion

A Kinexus rotational rheometer was used to evaluate the rheological properties of an HA based OVD at three different HA concentrations, as outlined in the ISO15798:2013 standard. This included the measurements of the steady state dynamic shear viscosity, complex viscosity and viscoelastic moduli (G' and G"). The characterization and comparison of the different samples were performed in terms of their zero shear viscosities and relaxation profiles, respectively, to achieve better classification based on their 'cohesive and dispersive' properties.

This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.

For more information on this source, please visit Malvern Panalytical.