### ASSORT Toric Calculator

**By Noel Alpins, FRANZCO,
FRCOphth, FACS***Available at www.assort.com*

The ASSORT Toric Calculator offers unique
features, designed for accuracy and functionality,
that are not available on other calculators
provided by implant companies or private
groups. Its primary unique feature is the ability
to calculate the most effective implant (sphere
and toricity) available from all
companies worldwide and compare
IOLs based on the target
spherocylindrical refraction that
is calculated to remain postoperatively
(Figure 1). The user can do this in a universal generic
calculation without having to visit several separate corporate
websites, some of which have inaccuracies of varying origins.^{1}

With the ASSORT Toric Calculator, accuracy is achieved by using calculations that parallel those of popular laser interferometry biometers, and the software also includes optimized lens constants for commonly used formulas, such as Hoffer, Haigis, Holladay, and SRK/T, to obtain the effective lens position (ELP). Other parameters used in the calculations include axial length, average keratometry (K) in diopters or radius of curvature, corneal toric power according to associated spherical implant power, and anterior chamber depth. The astigmatic effect of the phaco incision can be dynamically adjusted based on incision placement (Figure 2). The new parameter of corneal topographic astigmatism (CorT Total) can be employed to include an accurate measure of corneal astigmatism with inclusion of the posterior cornea. There is also an option to step up and down implant power for the available sphere and cylinder separately, with a display of calculated target spherocylindrical refraction. This is invaluable in evaluating preferred lens choice for any implant.

Another unique feature of the ASSORT Toric Calculator
is its ability to perform calculations to address postoperative
refractive surprises. The calculator can quantify both numerically
and graphically how much benefit can be obtained from
IOL rotation, IOL exchange, or LASIK to improve an unsatisfactory
outcome according to the implant used (Figure 3).^{2}
The Alpins method calculations are concurrently included to
assist in the decision-making process.^{3,4}

In summary, the ASSORT Toric Calculator displays all preand
postoperative toric implant requirements. It contains the
parameters for the most accurate calculation for any implant
desired and assists in resolving refractive cylinder surprises that
are bound to occur in some cases.^{2}

1. Goggin M, Moore S, Esterman A. Outcome of toric intraocular lens implantation after adjusting for anterior chamber depth and intraocular lens sphere equivalent power effects. JAMA Ophthalmol. 2011;129:998-1003.

2. Alpins NA, Stamatelatos G. Refractive surprise after toric intraocular lens implantation: graph analysis. J Cataract Refract Surg. 2014;40:283-294.

3. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg. 1993;19:524-533.

4. Alpins NA. Astigmatism analysis by the Alpins method. J Cataract Refract Surg. 2001;27:31-49.

### Barrett Toric Calculator

**By Graham D. Barrett, MD, FRANZCO**

*Available at www.ascrs.org/barretttoric-
calculator and www.apacrs.org/toric_
calculator/Toric%20
Calculator.aspx*

Our ability to provide excellent unaided acuity after cataract surgery improved dramatically with the introduction of toric IOLs. Nevertheless, despite accurate keratometry, precise alignment, and complex calculations, the refractive outcome after toric IOL implantation is not always predictable. Choosing the correct toric IOL for patients is more challenging than choosing a spherical IOL power, as we have to consider the magnitude and axis of the toric cylinder required. In order to avoid unexpected astigmatic outcomes, we must consider which devices should be used to measure the cornea, how to interpret the measurements, which methods to use to predict the required cylinder, and which technique will most acccurately align the toric IOL axis.

**Methods to predict the required cylinder. **Louis Émile Javal,
MD, a 19th century ophthalmologist, first noted that he could
not account for total ocular astigmatism by simply measuring
the power of the anterior cornea. This phenomenon is known
as *Javal's rule* and is thought to be due to the posterior cornea
contributing, on average, 0.50 D of against-the-rule astigmatism.

There are several toric IOL calculators available. The Alcon
calculator (see *Manufacturer-Specific Toric IOL Calculators*)
uses a fixed ratio in calculating the corneal vector of the cylinder
power for a toric IOL. This can be adjusted for the posterior
cornea's contribution using the Baylor nomogram. The
Holladay calculator uses ELP to calculate the corneal vector
of the toric IOL, and it can be adjusted based on the Baylor
nomogram or direct measurement of the posterior cornea.
Another alternative is to go to the Asia-Pacific Association
of Cataract and Refractive Surgeons (APACRS) or American
Society of Cataract and Refractive Surgery (ASCRS) websites
and use a toric calculator I developed, which is also available
on the Lenstar biometer (Haag-Streit).

**The Barrett Toric Calculator.** The Barrett Toric
Calculator (Figure 4) uses the Universal II formula to predict
the required spherical equivalent IOL power. The calculator
derives the posterior corneal curvature based on a
theoretical model proposed to explain the behavior of the
posterior cornea. The toric IOL cylinder power required
to correct the corneal astigmatism—including posterior
corneal astigmatism—is calculated from the predicted ELP
using vector calculations for each eye. In a study conducted at Ein-Tal Eye Center and awaiting publication in the *Journal
of Cataract and Refractive Surgery*, the most accurate prediction
of residual astigmatism was achieved with the Barrett
Toric IOL calculator in combination with the Lenstar.

In a subsequent study I performed with my fellow Adi Abulafia, MD, in Perth, Australia, we analyzed 54 eyes implanted with toric IOLs, comparing pre- and postoperative Ks, the intended versus actual axis of alignment, and different calculators to identify the relative contribution of each of these factors to errors in predicted residual astigmatism. The results showed that errors in estimating surgically induced astigmatism (SIA) adversely affect the predictability of toric IOL outcomes and that utilizing the centroid value for SIA offers significant improvement. Similarly, eliminating errors in axis alignment offers further improvement, but the effect is less significant.

The most important benefit, however, that can be obtained in improving toric IOL outcomes comes from use of an improved calculator. In addition to the Barrett Calculator, the Barrett Rx formula is also available online (Figure 5). This formula recommends the required IOL power for lens exchange, piggyback IOLs, or the rotation of an existing toric IOL to correct for an unexpected refractive outcome.

**Techniques to acccurately align the toric IOL axis.** An error
in alignment of 1° reduces the effective correction of a toric IOL
by an estimated 3%. Although, clinically, the impact of misalignment
appears to be less than not taking into account factors
such as posterior corneal astigmatism, there are several techniques
that can be considered to improve alignment.

Today, we have sophisticated systems to help minimize errors in alignment of a toric IOL on the required axis. These include intraoperative determination of the axis with wavefront devices or image-guided systems.

I use the toriCAM app (developed by Graham D. Barrett, MD, FRANZCO; https://itunes.apple.com/us/app/ id910004717?mt=8), which is simple to use but accurate. First, I dry the limbus with a cellulose spear to prevent smearing and mark the limbus at what I perceive to be 180°. I then use the toriCAM app to align the red reference axis indicator with the limbal marks, press the camera button, and capture an image. The images are stored in the photo album of my iPhone, and toriCAM records the reference axis, patient name, and date and time of the image. I then set the desired toric axis on my marker and offset the reference axis accordingly. A custom toric marker specifically for the toriCAM app is available, allowing the surgeon to set the reference axis as indicated by the app independently from the toric axis recommended by the toric calculator. Applying the inked marker then provides accurate marks with which the toric IOL can be aligned after insertion.

Avoiding unexpected outcomes with toric IOLs is as important as selecting the appropriate spherical IOL power. Understanding the source of potential errors during measurement, prediction, and alignment—with careful attention to each step in the process—can minimize the likelihood of an unexpected astigmatic result.

### TORIC RESULTS ANALYZER

**By Mark S. Hansen, MD;
John P. Berdahl, MD; and
David R. Hardten, MD***Available at www.astigmatismfix.com*

The Toric Results Analyzer calculator was developed by Drs. Berdahl and Hardten as a tool for dealing with residual astigmatism following toric IOL implantation. Residual astigmatism often remains after surgery, and this is confirmed by the fact that surgeons have used the Toric Results Analyzer for more than 20,000 IOL calculations over the past 2 years.

This easy-to-use calculator helps surgeons determine if residual astigmatism following toric IOL implantation can be corrected by simply rotating the lens. It also provides information that can be used to determine the ideal rotation of the lens to correct residual astigmatism and can provide information for an IOL exchange if a higher or lower toric power is needed. In cases in which rotation or exchange would not be useful, most surgeons opt for laser vision correction.

The information required to use the calculator includes the patient's current refraction (in plus or minus sphere), the intended IOL axis, and the toric lens information (spherical power and cylinder power at corneal plane), including the current axis (Figure 6).

After this information is entered, the calculator indicates the axis the lens should be rotated to in order to decrease the amount of astigmatism to an acceptable level (Figure 7).

If the predicted refraction after rotation is acceptable as the intended target, then rotating the lens can be attempted. If the expected refraction after rotating the lens would not be acceptable, then a lens exchange or laser vision correction can be considered.

Following is a step-by-step approach to easily integrate this application into clinical use:

• Measure manifest refraction.

• Measure the IOL axis and determine the power and
toricity. It is important to get the axis measurement
accurate. This can best be achieved at the slit lamp
when the patient is dilated. Align a slit beam with the
axis of the toric lens marks. Then use a smartphone
app (such as Axis Assistant) to determine the axis of
the beam.

• Enter the information at www.astigmatismfix.com.

• Determine whether rotating the lens will neutralize the
astigmatism and whether the resulting spherical equivalent
is appropriate.

• Determine a surgical plan; if the lens can be rotated easily,
mark the current and ideal axis, loosen the IOL with
an OVD, and rotate the lens to align with the ideal axis.

The basic concept of this tool is to determine whether simply rotating the lens to the ideal axis will sufficiently reduce the amount of unexpected postoperative astigmatism.

### Holladay IOL Consultant

**By Jack T. Holladay, MD, MSEE, FACS***Available at www.hicsoap.com*

The Holladay IOL Consultant software features both a Toric PreOp Planner for forward calculation and a Toric PostOp Back Calculator for back calculation.

**Toric PreOp Planner.** The Toric PreOp
Planner allows the user to determine the
ideal toricity and axis of placement for a
toric IOL using K readings and
the expected SIA from the
cataract incision. It does not
use a constant ratio of 1.46
to determine the ideal toricity
of the IOL from the corneal astigmatism—an approach
used by some other calculators that can result in errors with
low- and high-powered IOLs. Before using the planner, the
surgeon should confirm that the K readings and the axes for
the flat and steep Ks are correct. The magnitude and axis of
the manifest refraction are irrelevant, as the crystalline lens
will be removed.

Next, the surgeon enters the magnitude of the SIA. For modern small-incision cataract surgery, this value is usually between 0.00 and 0.50 D. For a given surgeon, if pre- and postoperative Ks have been entered, the mean value (centroid) may be found on the Aggregate Surgically Induced Refractive Changes (SIRC) on the main menu (Figure 8).

The SIRC from K's button and Minus Cylinder must be checked to obtain the correct value. In the example in Figure 8, the magnitude of the SIA is -0.21 D with the incision at 152° in the left eye. The user would enter 0.21 D, ignoring the sign. The meridional location of the cataract incision must be entered (152°). As soon as the magnitude and axis of the cataract incision have been entered, a black arcuate trapezoid is shown at the limbus on the drawing (Figure 9).

A drop-down list of available toric IOLs is displayed. The user selects the toric IOL model and the IOL formula to be used (Holladay 2 is recommended). Once this has been done, the steep axis of the cornea and the calculated correct axis for the IOL are shown. Displayed below the picture is the axis of placement, the ideal toricity of the IOL, and the remaining residual refraction with the nearest available toric IOL. All available toricities are shown, with the nearest to the ideal toricity highlighted in bold print and the residual refraction for each available toricity.

**Toric PostOp Back Calculator.** The Toric PostOp Back
Calculator allows the surgeon to determine the exact amount
that the toric IOL should be rotated to produce the smallest
residual astigmatism. Two methods can be used to achieve
this. One method uses the postoperative Ks and postoperative
refraction, and the other uses the IOL meridian observed
at the slit lamp and the postoperative refraction; both
determine (1) the toricity of the IOL and its current placement
axis, (2) the ideal placement axis, (3) the amount of
clockwise rotation necessary to achieve the ideal placement
axis, and (4) the predicted residual refraction at the ideal
placement axis. Then a green line appears in the diagram to
illustrate the ideal axis of placement for the IOL (Figure 10).

It is prudent to measure both the postoperative Ks and observed IOL meridian along with the postoperative refraction to double-check the amount of rotation required to rotate the IOL to the ideal axis of placement. The two methods should agree to within a few degrees. When they do not match, something is wrong, and measurements should be repeated until they agree.

As with forward calculation using the Toric IOL Planner, the equations for back calculation are exact and utilize the ELP and IOL power and toricity. Approximation calculators that use a constant ratio (~1.46) to convert the cylinder at the IOL plane to the cylinder at the corneal plane will not get the same answer, especially for low- and high-power IOLs. If a calculator does not require the spherical equivalent power of the IOL as input data, the calculator uses the approximation method.

All IOL powers in the Holladay IOL Consultant are given as spheroequivalent power (SEQ) and toricity. The SEQ power of an IOL is equal to the sphere plus one-half of the toricity.

For example, a 20.00 D SEQ and 2.00 D of toricity is actually 19.00 D of sphere with 2.00 D of toricity. All US and most European manufacturers label IOLs with SEQ power and toricity, as required by the American National Standards Institute (ANSI) and International Organization for Standardization (ISO), especially so that if one drops down or up a toric step size, the SEQ power of the recommended IOL power never changes; if sphere and toricity are reported, then this is not true, and both values must change so that the SEQ remains constant. In short, calculators that report sphere and cylinder require the surgeon to determine the SEQ power when ordering an IOL, whereas this is done automatically in the Holladay IOL Consultant.n

**Noel Alpins, FRANZCO, FRCOphth, FACS**

•
Medical Director, NewVision Clinics, Melbourne, Australia

• CEO, ASSORT Surgical Management Systems

• alpins@newvisionclinics.com.au

• Financial disclosure: Developer (ASSORT Toric Calculator)

**Graham D. Barrett, MD, FRANZCO
**

• Clinical Professor of Ophthalmology, The Lions Eye Institute,
Nedlands, West Australia

• Consultant Ophthalmologist, Sir Charles Gairdner Hospital,
Nedlands, Western Australia

• graham.barrett@uwa.edu.au

• Financial disclosure: Developer (Barrett Toric Calculator,
toriCAM)

**John P. Berdahl, MD
**

• Vance Thompson Vision, Sioux Falls, South Dakota

• jberdahl@vancethompsonvision.com

• Financial disclosure: Developer (Toric Results Analyzer)

**Mark S. Hansen, MD
**

• Minnesota Eye Consultants, Minnetonka, Minnesota

• mshansen@mneye.com

• Financial disclosure: None

**David R. Hardten, MD
**

• Minnesota Eye Consultants, Minnetonka, Minnesota

• dhardten@mneye.com

• Financial disclosure: Developer (Toric Results Analyzer)

**Jack T. Holladay, MD, MSEE, FACS
**

• Clinical Professor of Ophthalmology, Baylor College of
Medicine, Houston, Texas

• Founder, Holladay Consulting

• holladay@docholladay.com

• Financial disclosure: Developer (Holladay IOL Consultant)