Stiffness and elasticity of contact lens materials

Recent months have seen a variety of reports describing the increased incidence of various ocular complications associated with the continuous wear of silicone hydrogel lenses. Many of these quote that the complications are related to the stiffness modulus of the lens material. Increasingly, this stiffness value is given prominence when any new lens is introduced, as it has a significant effect on the lens performance.
The aim of this article is to review this physical property, describe how it might be measured and to look again at the sorts of effects upon the eye that lens stiffness exerts.

Material Properties of Contact lenses
The behaviour of a contact lens upon the eye depends on many factors. Comfort and ocular health are significantly influenced by the ability of the material to be kept adequately wet when worn, and also to allow sufficient oxygen to the underlying cornea (as discussed in the previous two articles in this series).
All plastics will by definition change shape under the influence of an external force. This may be provided by, for example, the lids when a plastic lens is on the eye, or by the fingers when a lens is held. For this reason, the way the material responds to this force will have a bearing on both the handling of a lens and the performance of the lens on the eye.
A very flexible hydrogel lens will drape itself over the cornea easily and is therefore likely to provide a good degree of comfort while exerting minimum influence upon the insides of the lids during blinking. On the other hand, the lens may be difficult to handle and, if very flexible, may fail to provide a stable optical image.
The ease with which a gas-permeable lens bends under force is less likely to offer differences in the ease with which it is handled. But flexure on the eye is going to have some influence on the optical stability, the tear exchange and the movement of the lens on blinking (the dimensional stability obviously having an effect upon the fit of the lens).
In the long term, the durability of a lens both on the eye and also on repeated handling will be influenced by the material's ability to withstand repeated external force. It will also influence the risk of the material warping during manufacture and hence the reliability of parameter states.
For these reasons, some specification of the lens material's external forces is described by manufacturers when describing any particular lens. A variety of terms, some interchangeable, have been adopted and may be quoted using a variety of units. Their use is sometimes confusing to say the least.

Strength versus Modulus
The way in which any particular material changes in response to some deforming force is described in terms of its strength or modulus.
The strength of a material may be defined as the force per unit area required to cause failure of the material when it is subjected to a particular type of testing procedure. Hence, one might measure tensile (stretching) strength, shear, impact or tearing strength. The tearing strength relates to the force required to tear a material subsequent to a notch or surface disruption, the exact nature of which should be specified as it clearly will influence the ease of tearing.
If failure of the material is not the required end point, but rather deformation, then the term modulus may be used. The modulus is defined as the force per unit area (the stress) required to produce the deformation (the strain) and the modulus is usually specified relating to the direction of the force applied. Hence, stretching to produce deformation might result in a tensile modulus, compression in a rigidity modulus.
The stress, or force per unit area, may be specified in a variety of units and one is as likely to see imperial units in some texts as metric. Consequently, stress may be specified as tsi (tons per square inch), psi (pounds per square inch), kilograms or grams weight per square millimetre, and dynes per square centimetre. The SI unit of stress, and hence the one that perhaps should be the standard, is newtons per square metre (Nm-2) also known as a Pascal, but it is worth noting that this is an extremely small value for common materials and may well be stated as mega-newtons per square metre (106 Nm-2).
For conversion purposes, the following holds true:

1 dyn cm-2 = 0.1 Nm-2 = 10-7megaNm-2
= 1.45 x 10-5 psi
= 6.46 x 10-9 tsi
= 1.02 x 10-8 kg mm-2

In general physical terms, the moduli most often described are Young's modulus, bulk modulus and shear modulus. Young's modulus (or tensile modulus or elastic modulus) relates to how much an object's length will change when tensile stress is exerted. This is described more fully later.
The bulk modulus or beta value is determined by how the volume of an object changes when subjected to pressure changes. The bulk modulus denotes the ratio of the change in pressure to the fractional volume compression. The reciprocal of the bulk modulus is described as the compressibility of a material and is therefore in some ways related to the flexibility and rigidity modulus as explained later, these values being obtained using a compression indentation force.
The shear modulus, though most complex, is analogous to how the top sheet of a pile of papers moves relative to the bottom sheet when a horizontal force is applied to the top sheet. Though any one of these might yield useful values for the materials student looking into contact lens behaviour, the latter two are rarely quoted or measured in this field.
As stated earlier, it is obvious that strength and modulus may be measured for both tensile (stretching) stress and compression or flexing stress. Tensile tests use a tensometer to measure extension of a given material upon stress being applied. The stress-to-strain curve so produced may yield not just Young's modulus, but also the strength of the material (that is the stress needed for the material to fail), the extension or elongation before the failure, and 'toughness', which is represented by the area under the whole stress-strain curve. While strength and modulus are represented as units such as Nm-2 as stated, the elongation at the point of break is more typically described as a percentage value.
Compression tests may use a variety of instruments, usually allowing indentation of the sample by a small sphere under a constant load, and the resultant effect measured as a function of time.
Upon removal of the load, measurement may also be made of the recovery of the material over time. As the sample tested is rarely destroyed and as it can be very small in size for measurement, the rigidity modulus so measured has historically been useful for rigid gas-permeable materials.
Generally speaking, the flexing of the lens on the eye is most important for an RGP lens and hence the flexural modulus or rigidity modulus are most often quoted (relating to compressive stress). For soft lenses, tensile properties are more useful as the durability of the lens on repeated handling is significant.
Such properties include Young's modulus, percentage elongation, tensile strength and tear propagation strength. It should also be pointed out that Young's modulus, though strictly speaking relates to tensile stress, may be used to predict material behaviour under both tension and compression. Hence its popular use in connection with newer soft lens materials.

Rigidity modulus, hardness and flexibility
The rigidity modulus describes the compressive stress related to the strain. It does give indications about the flexibility of a material but it should be remembered that it is quite different to the tensile (Young's) modulus. The values for a wide range of lens materials have been assessed, typically using some form of micro-indentation apparatus such as the CSM instrument in Figure 1.
A low rigidity modulus will give improved comfort compared to a much more rigid and less compressible material, but conversely will suffer from poor parameter stability so giving less acceptable visual performance.
Micro-indentation using a flattened indenter (as opposed to the sphere mentioned earlier) has been used to replicate the influence of the lids upon a material and may examine the modulus with stress similar to that exerted by the lid on closure (about 2.6 x 104 dyn cm-2).
Such studies have been found to correlate well with clinical findings. Lens materials found to deform and recover slowly, such as HEMA, tend to be acceptable clinically, while hydrogels showing large and rapid deformation and poor recovery tend to give visual instability and perform less well on the eye. This was the case with some of the very first high water content conventional hydrogel lenses.
Hardness relates to the resistance of the material to penetration so may be thought of as an extension of compression (and also may be measured using similar equipment to that for the rigidity modulus). As well as looking at indentation and recovery to the point of penetration, hardness has been measured in terms of the resistance of a material to scratching.
As stated both the Young's (tensile) modulus and the rigidity (compressive) modulus give reasonable prediction of the flexibility of a material on the eye. Rigid lenses will have better transmissibility if thinner, but will also be more flexible. The flexibility in the eye will affect the lens performance.
However, the variable thickness of a lens and its viscoelastic nature (changing behaviour with time, such as when a spherical lens on a toric cornea assumes a degree of toricity with wear) make the use of the modulus reading somewhat generalised.
A relatively simple and yet clinically useful method of looking at lens flexibility has been to place the lens within a carrier and placing increasing weights to bear upon one edge. Changes in the total diameter may then be measured along any particular axis depending on the orientation of the lens within the carrier (Figure 2).

Young's Modulus
Thomas Young (1773-1829) was a scientist whose work spanned many disciplines and whose legacy is still influential today, not least upon eye care professionals. An authority on the eye and vision, he formulated what is now known as the Young-Helmholtz colour vision theory, revived the wave theory of light and described astigmatism.
Young developed the idea of a 'stiffness' or elastic modulus from the work of Hooke. Young defined stress as the force (F) upon a given cross-sectional area (A) pulling upon a material (Figure 3).

Stress = F/A

The strain is related to the amount of change induced by the stress and could be defined as the ratio of the change in length of the material under the tensile stress (L1 Ð L0) compared to the original resting length (L0).

Strain = (L1 Ð L0)
(L0)

Hence, the modulus (often denoted as sigma or E) is thus:

E = stress
strain
which may be written as:

E = L0 F
(L1 Ð L0)A
This would relate to the gradient of the graph achieved if the stress and the strain were plotted (as in Figure 4).
It is worth noting that a truly elastic material will follow this pattern, whereas one such as a viscoelastic material, as is the case with contact lens materials where there may be a change in the material under stress, will not give a straight line representation.
Elastic theory allows an exact derivation of the modulus as follows:

E = µ (3l + 2µ)
µ + l

In this instance, the values of µ and l represent what are described as the Lam