### prescribing for astigmatism

# Taking the BS Out of Back Surface Toric RGPs

*BY PETER D. BERGENSKE, OD
*October 2001

I want to set the record straight about the back surface toric RGP lens design. It is a common misunderstanding that if you choose the base curves wisely, you can "get away" with a back toric design rather than a bitoric.

back toric design rather than a bitoric. You will get away with it only if the patient needs, or simply tolerates, over-correction of the corneal cylinder.

**The Theory**

Let's compare the geometric optics to the myths of the "BS theory" and show why it is wrong.

** Myth:** If you express the difference between the two base curves in diopters K and multiply that value by the lens's index of refraction, you get the in-air cylinder.

Is this true? Say a lens has base curves of 42.00 x 44.00, or 2.00 diopters K. The radii would be 8.03mm and 7.67mm. If we had a lens of index 1.5, by BS theory the cylinder in air would be 1.5 x 2.00 = 3.00D. If we use surface power formula to calculate the actual powers, we find the two back curves have surface power of 62.25D and 65.18D. So the cylinder in air is really close to 3.00D. Not bad.

** Myth:** Reverse the formula to determine how much toricity on the back surface will neutralize a known amount of refractive cylinder. Divide the refractive cylinder by the index of the material. This should give you the dioptric difference between the flat and steep curves of the lens to neutralize the refractive cylinder.

Let's see how this works. Take Ks of 42.00 x 45.00 and refraction 2.00 3.00 x 180. (Note the difference in K equals the refractive cylinder, so a spherical lens would provide full cylinder correction) Divide the refractive cylinder (3.00D) by the index (1.5) = 2.00D. Using the same lens as above, with radii of 8.03mm and 7.67mm (base cylinder of 2.00D K) calculate the powers on the eye, assuming index of tears = 1.336.

The surface power of the two meridians on the eye work out like this: (1.336-1.5)/.00803 = 20.42 and (1.336 1.5)/.00767 = 21.38. This back surface creates about 1.00D cylinder on the eye that we don't need! The steeper fitting curve displaces a portion of the tear layer with plastic, which has a higher refractive index and creates an unwanted cylinder effect on the eye.

**The Fundamental Flaw**

The BS theory is often referred to as the rule of two thirds: that is the proportion of the refractive cylinder used for the base cylinder in the calculation. This relies on an index of 1.5, which simply does not yet exist in RGP materials. There is no proportion that would be correct, so there is always an over-correction.

The theory's fundamental flaw is that the optics of a back surface toric lens on the eye are quite different from the optics in air. You must take into account the difference between the index of the lens and the index of the tears.

No matter how you design it, the back toric surface will create additional cylinder power on the eye. The theory's persistance is really a testimony that patients are pretty tolerant of the over-correction.The magnitude will actually be a little less than half the value of base curve toricity in diopters K with the axis along the flat meridian.

The one useful place for the back toric contact lens is in cases of high against-the-rule cylinder, where the refractive cylinder commonly exceeds the corneal cylinder. If you don't need this extra correction, neutralize it with a front surface plus cylinder. This creates a spherical power effect bitoric design that will provide more accurate and stable correction.

*Dr. Bergenske, a Past Chair of the American Academy of Optometry's Section on Cornea and Contact Lenses, has practiced for over 20 years in Wisconsin and now is on the faculty at Pacific University College of Optometry. E-mail him at:
berg1101@pacificu.edu.www.clspectrum.com*