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# Front Surface Sphere: The Toric RGP "Special Case"

*BY LEE NEWTON, OD
*September 2000

When designing a toric RGP lens to provide an optimal fit on a moderately to highly toric cornea, common sense dictates that the front surface must also be toric to obtain the proper correction in each meridian. Otherwise, the difference in index of refraction between the contact lens and the tear lens will create residual astigmatism:

**EXAMPLE 1**

- Corneal-vertexed refraction: 2.00 3.00 x 180
- Ks: 42.00/46.25 @ 090
- Material: Fluoroperm 60 (n=1.473, ct = 0.12mm)
- Base curves: 8.04mm (42.00D)/7.40mm (45.62D)
- Back vertex powers needed: 2.00 (flat meridian), 4.37 (steep meridian lacrimal lens)
- Front surface powers needed: +56.57D (flat)/+59.26D (steep)

This lens, if made with a spherical front surface, will be off by 2.69D in one meridian or by more than 1.25D in each meridian not a desirable correction.

Even though Example 1 shows that using a front surface sphere RGP (a back surface toric) would create substantial residual astigmatism, you can use such a lens design in certain situations without compromising the optics of the correction. Back surface toric designs are possible with certain CPE (cylindrical power effect) RGP lenses, particularly those in which the difference in back vertex powers is equal to a conversion factor times the difference in base curves. Back surface torics are not SPE (spherical power effect) RGP lenses, in which the difference in back vertex powers equals the difference in base curves. SPE lenses require a toric front surface.

**Approximate Accuracy?**

In
"Back Surface Toric
RGPs" (Dr. Thomas G. Quinn, "Prescribing for Astigmatism," *Contact Lens Spectrum*, October 1999), Dr. Quinn introduced a calculation to determine if the relationship between the base curves and back vertex powers will allow you to order a back surface toric contact lens. However, the accuracy of this approximation depends on the index of refraction of the specific lens material used. The indices of commonly used RGP materials fall within a tight range (Table 1), but there is sufficient difference between the high and low ends to introduce clinically significant error into this approximation. In essence the keratometer (calibrated for index n= 1.3375) measures both the curvature and the power of the cornea, while the radius of curvature of a contact lens (transposed to diopters) is the corneal-referenced curvature of the back surface of the lens and is not the dioptric power, in air, of the lens.

To design a back surface toric RGP, you must convert ^BC (the difference in base curves of the contact lens referenced to n=1.3375. Note that ^BC probably will not equal ^K, depending on the fitting philosophy) to ^D (the difference in back vertex powers [in air] of the contact lens), due to the difference in index of refraction between the cornea and contact lens. It can be shown that Dr. Quinn's conversion factor of 1.4 is valid only for an index of refraction of 1.4725. This means that if the RGP material is index 1.4725, and the difference in back surface powers is exactly 1.4 times the difference in base curves, only then will you have a back surface toric lens.

Table 1 shows that there are five RGP materials (identified with an asterisk) that are close enough in index of refraction to validate this approximation. The "true" conversion factor of these materials is close enough to 1.4 that any error introduced is clinically insignificant.

MATERIAL | INDEX OF REFRACTION |
CONVERSION FACTOR |
ERROR INTRODUCED PER DIOPTER |

Boston 2* | 1.471 | 1.396 | 0.004 negligible |

Boston 4* | 1.468 | 1.387 | 0.013 negligible |

Boston RXD | 1.435 | 1.289 | 0.111 significant |

Boston Equalens | 1.439 | 1.301 | 0.099 significant |

Boston ES | 1.443 | 1.313 | 0.087 significant |

Boston 7 | 1.428(low) | 1.268 | 0.132 significant |

Boston EO | 1.429 | 1.271 | 0.129 significant |

Fluoroperm 60* | 1.473 | 1.401 | 0.001 negligible |

Fluoroperm 30* | 1.475 (high) | 1.407 | 0.007 negligible |

TransAir* | 1.475 (high) | 1.407 | 0.007 negligible |

**Calculating Error**

But what if we were to use Boston 7 material, index 1.428, in this same situation? The "true" conversion factor is (1.428-1)/(1.3375-1) or 1.268.

EXAMPLE 2 (Dr. Quinn's example from 10/99)

- Base curves: 40.50 D/43.00D
- Back vertex powers: 5.75D/9.25D
- Difference in back vertex powers: 3.50D
- Using approximate conversion factor: 1.4 x 2.50 = 3.50D (implying a back surface toric would work)
- Using true conversion factor: 1.268 x 2.50 = 3.17D (implying that a back surface toric would provide back vertex powers that were either off by 0.33D in one meridian or off by 0.16D in each meridian).

In this example, the patient may not notice the residual astigmatism, but ANSI standards are violated. Furthermore, in different situations (such as corneal-vertexed refraction of 3.00-6.75 x 180, Ks 42.00/47.00 @ 090, base curves 42.00/46.25), it is also possible to satisfy the criterion of 1.4 * 4.25 (the difference in base curves) = 6.00D (the difference in powers needed). This time the error would be 0.61D in one meridian or 0.30D in each meridian depending on which curve the lab chooses for the front surface of the lens.

**It Won't Work...Or Will It?**

The 1.4 approximation falls short another way as well. There are situations in which a back surface toric would work nicely, but if you use 1.4 as a conversion factor you may be misled:

EXAMPLE 3

Corneal-vertexed refraction: +1.00 6.50 x 180

- Ks 42.25/47.50 @ 090
- Material: Boston 7 (n=1.428)
- Base curves: 42.25D/ 46.75D
- Difference in back vertex powers: 5.75D
- Using approximate conversion factor: 1.4 x 4.50 = 6.30D (implying back surface toric won't work)
- Using true conversion factor: 1.268 x 4.50 = 5.71D (close enough to 5.75D to verify that a back surface toric will work)

In this example, our front surface would require powers of +54.34D and +54.29D close enough to employ a back surface toric and yet the 1.4 approximation told us it wouldn't work as well. The appropriate front surface radius of curvature would be either (1.428-1.000)/54.34D = 7.876mm or (1.428-1.000)/ 54.29D = 7.883mm too close to differentiate with a radiuscope! Furthermore, if the refraction included 6.25D of cylinder rather than 6.50D, we would be off only by 0.20D (or 0.10D in each meridian); yet, the 1.4 approximation indicates more than 0.75D of residual cylinder.

If employing a bitoric design results in "optical nirvana," does any amount of residual astigmatism create "optical turmoil?" It depends on the particular case presentation and the patient's tolerance to blur. Unless you have an understanding of the relevant optics, you might obtain a lens from the lab with parameters slightly different than expected.

The basic purpose in fitting toric RGP lenses is to provide patients with a better physical fit and visual acuity than other means of correction can provide. A lab representative stated that a typical back surface toric lens would cost a practitioner about $10 less than a bitoric lens. Labs generally prefer back surface torics because they say these lenses are easier to manufacture and provide better optics than bitoric lenses. I feel that to provide better optics, you must first fully correct the patient's refractive error. A back surface toric lens is certainly appropriate if the optics and fit warrant it.

*To receive references via fax, call (800) 239-4684 and request document #64 (Have a fax number ready).*

*Dr. Newton, a 2000 graduate of the Michigan College of Optometry, is purchasing a private practice in Bay City,
Michigan.*