Continuing Education
Correcting Astigmatism With Contact Lenses
By PETER D. BERGENSKE, O.D.
November 1998
When prescribing contact lenses for your astigmatic patients, maximize the relationship between the lens surface and the toric cornea
It's 1998. You can correct virtually any astigmatic patient with either soft or rigid contact lenses. Most of the time, you can do it with a modest degree of know-how, cleverness and luck, but sometimes a dose of head-scratching and consultation is in order. Understanding the optics and dynamics of how lens surfaces interact with the toric cornea will help you avoid the occasional tight spot and more importantly, will make you a hero to the astigmat who wants to try contact lenses one more time.
Astigmatism and Toricity
The word "astigmatism" means "without a point." "Astigmatism" refers to the optical aberration that occurs when light is refracted by non-spherical surfaces, resulting in not a point, but a spread of focus. When dealing with contact lenses, we are challenged by both the optical problem of astigmatic refraction and the physical obstacles of toric surfaces. The term "toricity" refers to the non-spherical surface of a contact lens or an eye, which usually follows the mathematical rule that the curvature of shortest radius is perpendicular to the curvature of longest radius.
The human cornea is neither a true spherical nor a true toric surface. Rather, it is a relatively complex aspheric surface with the degree of asphericity, or rate of peripheral flattening, varying in each of the principle meridians. Advances in corneal topography have greatly facilitated the understanding of corneal toricity. Differences in power graphically represent the differences in corneal contour along not only the principal meridians, but also the entire central cornea, therefore demonstrating the differences in asphericity between the principle meridians. As the corneal toricity is evaluated in terms of the optical zone and diameter of the lens being fitted, contact lens fitting software can further display the relevant characteristics of the toric cornea and predict lens behavior (Fig. 1).
The Spherical Rigid Lens
A rigid lens with spherical front and back surfaces is often the simplest way to correct astigmatism. If the astigmatic refractive error arises from a toric corneal surface, then a spherical rigid lens will neutralize the astigmatism, independent of lens rotation or cylinder axis. Refraction occurs when light strikes an interface of two different refractive indices at an angle. The spherical front curve and convex surface of the lens assures uniform refraction when light strikes it, resulting in a point focus. At the back surface of the lens, the light diverges slightly and uniformly as it emerges from the index of the lens to enter the lesser index of the tears. With a toric cornea, the tear layer is thicker for the meridian of greatest curvature (shortest radius), creating a tear lens of 1.336 index with a spherical front surface and a toric back surface. Light traveling through the thicker part of the tear lens arrives at the back surface of the tear lens later and a bit more diverged, thus adjusting for the astigmatic error. The corneal curve and the curve of the tear layer are the same. The tear lens index is only slightly different than the assumed index of refraction for the keratometer (1.3375, which includes a correction for the back surface of the cornea), so little refraction occurs at this surface. For all but the most extreme degrees of corneal toricity, a rigid spherical lens will create a nearly perfect neutralization of the corneal astigmatism. This principle is worth understanding in order to comprehend what happens when the lens surfaces need to be made toric.
As long as the degree of corneal toricity is not too great, the physical fit of the spherical rigid lens on a toric lens surface is not only acceptable, but often preferable to the fit obtained on a spherical cornea, where lens movement can be restricted and tear exchange limited. In theory, a spherical rigid lens is fit in approximate alignment with the flattest corneal meridian, although in practice, the optimum lens is often slightly steeper than the central corneal curvature. This allows for a modest degree of bearing in the periphery of the flat meridian and avoids excessive clearance and rocking in the steeper meridian.
Residual Astigmatism
Morton D. Sarver, O.D., M.S., defined residual astigmatism as the astigmatic refraction present when a contact lens is placed on the cornea to correct existing ametropia. Residual astigmatism occurs when the lens or fluid interface between the lens and the cornea fails to neutralize the total refractive cylinder of the eye, or creates more astigmatism. This may be due to flexure of the lens (resulting in inadequate tear layer lens with the soft lens being the extreme example), toric anterior or posterior surfaces on the contact lens or the presence of internal astigmatism. Internal astigmatism is most often attributed to the crystalline lens, but may also be due to differences in the principal meridians of the back surface of the cornea or a variety of less likely suspects.
Many patients fit with spherical lenses show measurable and visually significant residual astigmatism. Several remedies are available, but the dilemma we face is the question of whether the remedy is justified. Patients often tolerate small degrees of residual astigmatism well in the context of the many visual advantages of contact lenses. There are situations, however, where a lens design modification significantly improves visual result over the standard spherical lens.
Flexure -- When the refractive astigmatism is with-the-rule, and a spherical RGP induces a residual astigmatism that is against-the-rule, a thin, flexing RGP is often successful. The residual astigmatism occurs in this situation because the corneal toricity exceeds the refractive cylinder, so a lens that flexes on the eye will create less astigmatic correction, reducing the residual error.
Conversely, when a spherical rigid lens results in an undercorrection of with-the-rule astigmatism, evaluate the lens in situ using keratometry of the front surface of the lens to check for flexure. Flexure can usually be corrected by increasing lens thickness. Keep in mind that if the residual astigmatic error is against-the-rule and the corneal toricity is against-the-rule, a lens thin enough to flex on the eye will increase the residual astigmatism. Note that perhaps the most common method today for preventing the residual astigmatism that would otherwise occur with a rigid lens is to fit the virtually completely flexible soft lens on eyes having corneal toricity yet spherical refractive error.
Astigmatic Spectacles -- A rarely mentioned method of dealing with residual astigmatism is to combine astigmatic spectacles with spherical rigid or soft contact lenses. Patients with extreme refractive errors are especially open to the option of wearing a less complex and perhaps more comfortable contact lens that yields reasonable acuity and a light, attractive pair of spectacles when vision is more critical. The contact lens power is commonly adjusted to the spherical equivalent of the residual astigmatic error, yet patients may consider spectacles for further refinement.
The Front Surface Toric -- Besides correcting residual astigmatism with flexing lenses and astigmatic spectacles, it's sometimes necessary to fit lenses with one or more toric surfaces. These lenses present an additional fitting challenge because rotation must be limited. Pioneered with rigid lenses, the early efforts of limiting rotation still have application, although there have been great advances with the development of toric soft lenses. In 1963, Irving Borish presented a paper reviewing 500 cases of patients wearing front toric, prism ballasted rigid lenses. As a testimony to the success of the toric soft contact lens, it's doubtful that today there are as many cases of this lens fit by all practitioners in the United States combined.
The front surface toric, prism ballast, spherical base curve rigid lens provided the prototype for the soft toric lens of similar construction used today. Although truncation of the bottom edge can can be advantageous, it's largely found to be unnecessary with soft and rigid lenses of this style. Today, the front surface toric, spherical base curve rigid lens is principally used for against-the-rule residual astigmatism that occurs after neutralization of irregular or oblique corneal astigmatism by a spherical base lens. Although this is a limited application, it is valuable to have at hand when the appropriate situation arises.
Front toric rigid lenses should be designed with what would currently be considered a relatively small diameter (8.6 to 8.9mm) but with a proportionately larger optical zone (7.7mm with 8.9mm diameter). The aim is to achieve a lens with a tendency to center but with enough stability to resist excess rotation. Adding a small degree of prism maintains lens orientation so that the smaller the diameter, the less average thickness will be required. Most of the blink action is in the upper lid, and the lower lid action only enhances it, so it's generally safe to consider the direction of the upper lid action alone when analyzing the forces that make a lens rotate. The upper lid action generates a motion that's vertical and also has a temporal-to-nasal vector. During a blink, the upper lid will have the greatest ability to rotate the lens when it encounters the thickest meridian of the lens. If a spherical trial lens overrefracts cylinder axis 90 for each, you should order lenses with axis 80 for the right eye and axis 100 for the left to compensate for the temporal-nasal rotation anticipated for the apex of the lens. Virtually all rigid contact lenses of this design are prescribed to compensate against-the-rule astigmatism, which is why a plus cylinder axis of about 180 is added to the front surface, making the lens thickest in the 90-degree meridian. Excessive rotation can often be controlled by thinning the superior edge, especially at the temporal aspect.
Toric Soft Contact Lenses
Toric soft contact lenses are categorically designed to correct residual astigmatism. Virtually every combination of with-the-rule or against-the-rule correction is available in both front surface toric and back toric designs. Both types of toric design are also available in prism ballast and double slab-off thin zone designs to provide rotational stability (Figs. 2a & 2b).
There are theoretically two advantages of back toric soft lenses-- the back surface cylinder should help to stabilize the rotation of the lens on the eye, and the spherical front surface should not cause lid effects that vary with the axis of the cylinder. The optic zone of the back toric soft lens is small relative to the lens diameter (typically an ellipse about 6mm in the steep meridian by 8mm in the flat meridian). The fitting curve, which is typically specified as the base curve, is in fact a large secondary curve that provides most of the fitting characteristic of the lens. Back toric soft lenses tend to fit such that there is a small but measurable tear lens effect, necessitating power modification beyond what you'd expect based on vertex alone. You can't always predict this effect, so make an adjustment after overrefraction of a trial lens or rely on the manufacturer's recommendations based on refraction and corneal curvature measurements. As a general rule, if the axis of the corneal toricity and the axis of the refractive astigmatism are approximately the same, a back surface toric soft lens will fit better and more reliably than a lens with an entirely spherical base, despite the fact that soft lenses drape the cornea.
Because soft contact lenses are so large, they're created with lenticulated front peripheral curves. This minimizes the effect of a toric front optical zone, so the principle reason for choosing a front toric zone is more for its spherical base curve than for its toric front curve. The spherical base, front toric soft lens is best for cases where there is poor agreement between the axis of the corneal toricity and the axis of the refractive astigmatism, or when there is significant astigmatism and a nearly spherical corneal curve. On the other hand, due to the flexible nature of soft lenses, many patients with toric corneas are successfully fit with spherical base curve lenses.
Rotational stability is the sine qua non of lenses that are intended to correct residual astigmatism. If a toric lens rotates so that the cylinder axis of the lens is displaced, you can easily calculate compensation for the rotation using the left add, right subtract (LARS) rule, and if the resultant lens rotates the same as the original, all will be well (Table 1). In some cases, the rotation of the lens and the tear layer effect will combine to induce a residual astigmatism that is not easily added to the power of the trial lens. In cases where the axis of the residual cylinder is significantly different from the axis of the lens, you must apply the crossed cylinder formulae to determine the desired resultant lens.
K For the resultant cylinder power: C^{2} = A^{2} + B^{2} + 2AB cos 2 a; where C is the resultant cylinder power, A and B are the crossed cylinders, and a is the angle between their axes.
K For the axis of the resultant cylinder: sin 2 b = B/C sin 2 a; where b is both the angle between the first cylinder axis and the resultant axis.
K For the resultant sphere: S = (A + B - C)/2. (This is added to the sum of the sphere power of the trial lens and the sphere power of the overrefraction).
Fortunately, these calculations are available on preprogrammed calculators, or they can be set up on a spread sheet on a personal computer. Most contact lens manufacturers have consultants who will make the calculations for you. Thomas Quinn, O.D., M.S., has pointed out that in order for the calculations to be correct, you must correct for the rotation of the lens on the eye prior to making the calculation, and then again correct for the rotation that is predicted to occur with the new lens power (Table 2).
The choice of prism ballast versus thin zone design is largely one of preference, but also comes from trial and error. The thin zone design is perhaps most dependent on lid forces for orientation, so patients with very loose lids may fail to keep it in place but do well with a prism ballast design. Anthony Hanks, O.D., and others have shown that most of the stabilization of rotation is determined by the direction of the blink and its effect on the wedge shape of the lens (the so-called watermelon seed effect), rather than by gravity. The thin zone design is beneficial for patients who require a toric lens on one eye only, as no differential prism is induced.
Rigid Lenses with Back Surface Toricity
The toric back surface of rigid lenses serves most often to obtain an optimum lens-cornea relationship rather than to correct for residual astigmatism. Due to the effect of surface power, however, the back surface cylinder that will fit a toric cornea will typically create an unwanted cylinder power on the eye. To determine the amount of cylinder power created by the toric surface when it is on the eye, you must consider the indices of refraction of the lens material, the tear film and the assumed index of the keratometer.
It is common to speak of rigid lens base curves in terms of diopters K. However, in calculating surface power effects, recall that diopters K indicates surface power for a substance of index 1.3375 when in air. The back surface of the contact lens neither has an index of 1.3375, nor functions in air. Nevertheless, the diopters K designation is useful, and it is simple to convert from this designation to actual lens surface power in air or on the eye (Table 3).
The index of refraction of the lens is greater than that of the tears, so the back toric rigid lens with a spherical front surface will create greater cylinder correction than will a lens with spherical front and back surfaces. This is useful in cases of against-the-rule corneal cylinder, where refractive cylinder is commonly greater than the corneal cylinder, so the excess correction is desirable. For example, if the cylinder component of the refractive error is -4.00 x 90, and the corneal toricity is 2.75, a lens with a spherical base curve will neutralize 2.75D cylinder leaving 1.25D residual. If the lens (index 1.48) is made with a base of 2.75 diopters K toricity, an additional cylinder correction of 2.75 x 0.42 = 1.15 will be created. Such a lens will need to be stable on the eye, but the back surface cylinder will inhibit rotation as well as improve the bearing relationship, and a small degree of prism may be added if needed. Note that the choice of material may impact the outcome, as index of the lens material influences the degree of additional cylinder correction. A lens with index of 1.43 will have a conversion factor of 0.28, thus adding only 0.77D of additional cylinder correction.
You can determine the sphere power of the back toric lens by fitting a spherical lens with a base curve that is the same as the flat curve of the desired toric lens and then overrefracting. Add the sphere power of the overrefraction to the power of the trial lens, and this is specified as the power of the toric lens in the flat meridian. You need not specify the power of the steep meridian, as it will be determined by the back surface toricity. The power measured on the lensometer will show the specified sphere power, but will show greater cylinder power (1.42 times greater) than the power indicated by the diopter K indication of the base or the amount of cylinder desired on the eye. It's important but not necessary to be aware of this calculation so that the discrepancy is expected upon lens verification.
The most common toric RGP is the bitoric lens, since the excess cylinder correction induced by the back surface cylinder must often be neutralized by a front surface cylinder. In the case where the front cylinder exactly neutralizes the excess cylinder that is created with the lens on the eye, the bitoric lens will behave optically as a spherical lens on the eye, with rotation not being a concern. The spherical power effect (SPE) bitoric lens was originally described by Dr. Sarver, and then later reintroduced by Drs. Sarver, Rodger Kame and C. Edward Williams. This design is very useful when a toric base is desired to improve the lens-to-cornea relationship, but a spherical lens would provide neutralization of the refractive astigmatism.
The SPE design is elegantly simple: the cylinder power of the lens in air (the difference in absolute powers of the principal meridians) is equal to the back surface cylinder expressed in diopters K. For example, a lens requiring a base curve of 43.00 x 46.00 (3.0 diopters K cylinder), must have a 3.00 diopters cylinder such as -1.00 @43.00 and -4.00 @46.00 for the lens to have spherical power effect on the eye. The principle advantage of this design is that the rotation of the lens on the eye will have no effect on vision. Another significant advantage is that the power can be calculated without knowledge of K readings or refractive error; you need only that which is obtained from trial lens fitting: the overrefraction and the specifications of the trial lens. This is particularly useful when fitting distorted corneas where keratometer readings are of little value.
If the SPE bitoric results in significant cylinder overrefraction and the orientation of the principal meridians of the contact lens are close to or the same as the principal meridians of the residual cylinder, a cylinder power effect bitoric lens is useful. The overrefraction can simply be added to the SPE design powers. The simplest and most reliable way to determine the power for a cylinder power effect bitoric is to trial fit with an SPE lens to determine the residual cylinder and orientation when the lens is on the eye. The overrefraction can simply be added to the SPE lens powers, keeping the base curves the same. For example, if an SPE lens that measures 43.00 x 46.00, -1.00/-4.00 (-1.00 - 3.00 cyl) results in overrefraction of -1.00 diopters cylinder, the cylinder power effect lens would be ordered as -1.00/-5.00 (-1.00 - 4.00 cyl).
Lens material choice is best left to the laboratories, as they have a better knowledge of which lens material will be most adaptable to your lens design and most stable under their manufacturing techniques. A non-flexing, easily wetting material of reasonable permeability is all that is required.
Toric trial lens sets are a luxury, and often the first lens ordered must be considered a trial lens anyway. Most laboratories are willing to loan trial lenses, but this causes a delay that may be avoidable. You can gather a great deal of information from trying to fit a spherical lens. It may be helpful to use a topical anesthetic to give the patient adequate comfort with the spherical lens. If this lens will center and not flex, the overrefraction provides much of the information needed to determine toric lens power and design. Assess lens flexure by taking a keratometry reading of the front surface of the lens on the eye. Observation of the fluorescein pattern with a spherical lens on the eye allows you to assess corneal topography in a way that is very meaningful with regard to contact lens design.
Lens Verification
For rigid lenses, it has always seemed imperative that practitioners have the ability to verify toric lenses in the office. Only if we know the exact specifications of trial lenses and ordered lenses are we able to make sound decisions for changes in lens design. It's also extremely important to record the complete specifications of lenses that are working well so they can be duplicated if lost or damaged.
Although as important for soft lenses as for rigid, few soft toric lenses are reliably verified by either manufacturers or practitioners. Determining whether or not the lens scribe marks accurately indicate the cylinder axis, or even whether or not the lens power indicated on the package is the power of the lens is time-consuming and rarely accurate enough to be of much help. CLS
This article is dedicated to the memory of Morton D. Sarver, O.D., M.S., from whom much of this material was learned, and on whose work much of this is based. Thank you, Dr. Sarver. We're still learning from you.
Dr. Bergenske practices in Madison, Wisc.
FIG. 1: Sample computer-aided design.
ASTIGMATISM
TABLE 1
Example of the Left Add, Right Subtract (LARS*) rule to compensate for lens rotation:
RIGHT EYE | LEFT EYE | |
-3.00 -1.00 x 90 | Refraction | -3.00 -1.00 x 90 |
10 degrees counter clockwise (base moves right) |
Observed rotation | 15 degrees clockwise (base moves left) |
subtract 10 degrees | LARS applied | add 15 degrees |
-3.00 -1.00 x 80 | Lens ordered | -3.00 -1.00 x 105 |
* L = observer's left
FIG. 2a: CIBA Focus Toric (8mm)
FIG. 2b: FreshLook Toric (8mm)ASTIGMATISM
TABLE 2
Crossed cylinder calculation with correction for lens rotation.
First correct for rotation of the trial lens using the reverse of LARS. |
For example, a right trial lens is: -1.75 -2.00 x80. |
If this lens rotates 10 degrees clockwise on the eye (base moves left), and overrefraction is +0.50 -2.00 x100 |
1) compensate for trial lens rotation: -1.75 -2.00 x70 |
2) combine the cylinders -1.75 -2.00 x70 +0.50 -2.00 x100 Resultant: -1.37 -3.76 x85 |
3) Correct for the expected 10 degree clockwise rotation using LARS (now add 10): |
Lens ordered: -1.37 -3.75 x95 |
TABLE 3
Lens Surface Conversion
TO CONVERT FROM | TO | MULTIPLY BY |
K reading of the lens surface | lens surface power in air | 1.42a |
lens surface power on the eye | 0.43b | |
^{N}contact lens = 1.48 | ||
^{N}tears = 1.336 | ||
^{N}keratometer = 1.3375 | ||
^{N}air = 1 | ||
a) ^{N}air - ^{N}contact lens _______________ ^{N}air - ^{N}keratometer |
1-1.48 = _______ 1-1.3375 |
= 1.42 |
b)^{ N}tears - ^{N}contact lens _________________ ^{N}air - ^{N}keratometer |
1.336-1.48 = ________ 1-1.3375 |
= 0.43 |