Recently I was visiting an eye hospital in a Tier II city in India wherein I was referred to a case of unexpected spherical surprise, postoperatively. Though the patient had preoperative .77 diopter of cylinder, a non toric lens was selected as there was no toric model available,. The patient landed with a spherical surprise along with the uncorrected astigmatism/cylinder error. The objective of my article here is to analyze why some patients land up with unexpected spherical surprise when patients have a pre operative astigmatism that is not corrected with either a TORIC or an LRI.

Below is the biometry sheet of the patient. The eye operated is left eye.

According to the biometry sheet above (left eye), if a 20.50 D of IOL is implanted the patient should land up with emmetropia (-.04). Of course there will be some astigmatism left over as no Toric IOL or LRI is planned. But most clinicians would expect almost a zero spherical power with a 20.50 diopter, postoperatively.

However, in reality this is not the case. Most of us fail to realize that the value of -.04 shown against the 20.5 D IOL implanted is not emmetropia, but a spherical equivalent. Or in other words, the expected refraction of -.04 is not a spherical component only, it is a combination of spherical and cylinder power that would be closest to zero. That is, it is only a spherical equivalent.

**What is Spherical Equivalent?**

In prescription glass, a spherical equivalent is prescribed often for those patients who are unable to tolerate a sphero-cylinder glass. Thus such glasses have only spherical power.

If a patient had been initially prescribed -4+1@90deg, and the patient is not able to tolerate the sphero-cylinder glass, he or she may then be prescribed a spherical equivalent of the sphero-cylinder glass. Thus the new spherical power of such a glass will be :

**sphere + 1/2 of cylinder** :

-4+1@90

= -4+(half of +1)

= -4 +.50

= -3.50 Thus the spherical equivalent of the sphero-cylinder glass will be **-3.50**. Such a glass will have only spherical power and no cylinder.

The benefit of targeting spherical equivalent is that the ray of light will now fall as a 'circle of least confusion' or the refraction of light that goes through the glass will now create a minimum distortion that would be acceptable to the patient.

If the patient was given a sphero-cylinder lens, then the patient would have had a spectacles with -4 at 90 deg and -3 at 180 deg. Since the patient is not comfortable with such a sphero-cylinder glass, he will now wear a spherical glass of -3.50 diopters that will be a spherical equivalent of the earlier prescribed sphero-cylinder glass.

**Spherical equivalent in the Biometry chart**:

What we need to realize in the biometry chart that I provided as an example is that a 20.50 diopter IOL for the left eye **will only provide a spherical equivalent refraction of -.04. This is a combination of the patient's spherical and cylinder power, and therefore not necessarily emmetropia.**

For example, you may have a patient with a glass power of -1+2 at a certain axis, say 90deg. The spherical equivalent of this sphero-cylinder is 0 (sphere + 1/2 cylinder). Thus the patient will have significant spherical and cylinder error, yet the spherical equivalent is 0. This is the circle of least confusion, which will still be a large blur in the middle of conoid of strum.

Thus the -.04 is just a mathematical calculation that is closest to zero. Without a toric lens implanted, there would be a significant spherical and the entire uncorrected cylinder post operatively. If pre operative cylinder is uncorrected, this would also impact the patient's spherical power. Why?

This is because cylinder is merely a difference in power of two principal meridians. You cannot have a cylinder without a spherical power, but you can have a spherical power without cylinder. Thus a patient landing up with plano + .75 at 90 deg would mean the patient has +.75 of spherical power at the 180 degree meridian ( transposition).

Consider the above biometry chart. Notice in this chart, fortunately both spherical equivalent (Ref SE) and spherical power (Ref Sph) with cylinder (Ref Cyl) with axis spelled out. With a 19.50 diopter HOYA XY1A selected the spherical equivalent (Ref SE) denotes -.04. The sphere and cyliner are then shown separately as +.23 and -.53 respectively. If you calculate the spherical equivalent of the sphere and cylinder (sphere + 1/2 of cylinder) , you will get -.04.

**The Holladay IOL Consultant software:**

Since most IOL calculation formulae suggest IOL power closest to a spherical equivalent of zero, for patients who have more than .50 diopter of astigmatism, it is important to get an idea of what lies behind the suggested spherical equivalent against the IOL power.

Below is a screenshot from the **Holladay IOL consultant software**:

In the below you will see a suggested Expected Residual Rx : -.63 +.99 @12

That is if you implant a 19.50 diopter lens, the expected refraction will be -.63+.99@12. Note the spherical equivalent of this number (sphere + 1/2 cylinder) is -.13. The IOL power of 19.50 diopter is suggested as closest to spherical equivalent of zero.

**If you do not have the Holladay IOL consultant software:**

Even if you do not have the Holladay IOL consultant software, you can calculate the expected spherical power the patient will land up mentally. The trick is to take the half of the cylinder value as the spherical power, plus the expected spherical equivalent suggested against the IOL power. For example, the cylinder is 1 diopter. Half of the 1D cylinder is .50. Add the spherical equivalent refraction of -.13 to .50. You will get -.63. The sign of the spherical power will be opposite to the cylinder axis. Since the cylinder axis is in plus, the spherical will be in minus.

**More examples**

In this example the patient has a steep meridian of more than 1diopter at 0 deg. 20.5 diopter is the IOL power suggested as closest to a spherical equivalent of zero (.04). The expected Residual refraction postoperatively with a 20.5 diopter IOL implanted is indicated as -.45+.99@0 deg

If you do not have a Holladay IOL consultant software you could still calculate it. Take half of the pre operative astigmatism which is .50 and substract .04(spherical equivalent from .50). Thus -.45 is your expected spherical power ( take the sign as opposite to the astigmatism sign)

In the example on right, the patient has pre operative astigmatism of .70@90. Half of this is .35 diopter which should be the spherical component. The sign has to be opposite to astigmatism therefore we will have -.35. Add to this the spherical equivalent with a 20.5 diopter IOL power which is .16. When you substract -.35 from .16, you get the expected spherical component which in this case will be -.19.

No wonder the Holladay Expected residual refraction is showing -.19+.69@90

I have included my own excel sheet for you to enter the details and see the expected spherical power to make it easy for you. This calculator does not take into consideration the SIA effects.

**In summary** I wanted to bring to your attention why patients usually land up with a spherical error when they have an uncorrected astigmatism pre operatively. The IOL power suggested by IOL calculation formulae is not on the basis of emmetropia, but spherical equivalent for such patients. It is therefore important to go beyond the spherical equivalent. The spherical power the patient will be left with is half of the pre operative astigmatism, plus the value of spherical equivalent refraction against the IOL power selected. Of course, any added surgically induced astigmatism is going to play a role too. By understanding the expected spherical power component, you can then choose the appropriate IOL power.