Discussing Meridian Power Calculations

I’ve added a new calculator to EyeDock that can determine the power in any meridian of a pair of spectacle lenses. 



It's located here, along with some accompanying text describing why such calculations might be useful (one of which includes insurance coverage for medically necessary contact lenses). 

However, I wanted to expand a bit on how this calculation is done, and how the power in a meridian can be estimated if needed.



First of all, getting the exact measurement of a meridian’s power is not difficult if you have the formula:


 Dc´= Ds + Dc (sin² θ)



  • Ds is the sphere component of the Rx
  • Dc is the cylindrical power
  • θ is the difference between the axis of the Rx and the meridian in question

Keep in mind that the theta (θ) value only needs to take into account the shortest distance between the cyl axis and the meridian of interest. For example, if our spectacle power is:


-2.00 -1.50 x 030


And we want to know the power at meridian 180º, subtracting the two will give us 180 - 30 = 150. 


Of course, we all know meridian 180º is the same as meridian 0º, so the shortest distance between these two angles is 30 - 0 = 0º.


So, the rule of thumb is this: If you take the difference between the two angles and it’s bigger than 90º, subtract this number from 180º.


As another example, what is the difference between 150º and 10º? 

150 - 10 = 140º

Since this result is greater than 90, subtract it from 180:

180 - 140 = 40º


So, the closest difference between meridian 10º and meridian 150º is 40º. To be honest, it’s probably easier to visualize this on an optical cross than to do it mathematically:

But I Can’t Remember Formulas!


So, what happens if you’re shipwrecked on a desert island and your survival depends on calculating a lens power in a specific meridian and you just can’t remember the above formula? Well, fortunately, this is actually pretty easy to estimate.


 Let’s consider a spectacle Rx of:


-2.00 -1.50 x 030


And let’s suppose we want to know the power in the 180º meridian.


When thinking through optics calculations, I sometimes like to think of the Rx as split into a spherical component plus a cylindrical component, like this:

For now, we can focus on the cylindrical component because this is the only where the power varies by the meridian (in other words, the spherical component isn’t very interesting because it has the same power in every meridian).


And what do we know about cylinder power? Well:

There is zero power at the cylinder’s axis, which is at 30º in this example. 

100% of the cylinder power is located 90º away from the axis, which is at (30+90=) 120º.

For everything else, we can estimate the amount of cylinder as being proportional to how far you are in between these two meridians.


So, if we want to know the amount of cylinder in meridian 180, we just need to know how far this is from the cylinder axis. Meridian 180º is 30º away from axis 30º. Since the full cylinder is 90º away from our axis, 30/90 is ⅓ of the way there.


⅓  of the total cyl power (-1.50) is -0.50.


Now that we know how much of our cylinder power is located at this meridian, we can add back in the spherical component of Rx:


-2.00 + -0.50 = -2.50 estimated total power in meridian 180º


That’s not exactly what we get when we use the formula, but it’s pretty darn close.


New universal search features

I wanted to write a little note about some new features I've added to the contact lens searches in the last couple weeks.

As a side note, this is something I'm really horrible at doing: I'm constantly tweaking and adding things to EyeDock, but then I forget to tell people about them. I like to spend my time doing the things I enjoy, which is building new features. I have to spend time doing things I don't particularly enjoy, which is keeping data up-to-date and answering support emails. Everything else always seems to fall be the wayside, which pretty much means everything related to business and marketing.

So, with that in mind, I'm going to share some new features that you probably wouldn't notice unless you happen to stumble upon them.


Distance Center or Near Center data for multifocal contact lenses.

For years, I've been kicking myself for not including database fields for categorizing soft multifocals by distance-center or near-center. As I've read more and more about how these designs factor into myopia control, I realized it's something I really needed to address. So, I added these fields to the database, wrote code to search by  them, and went through all the bifocal lenses and populated these values wherever I had the information. 

So, to search by this field, go to the contact lens searches, select the "More options", and then select "Bifocal Center" in the "even more options" dropdown.

 Bifocal Center searches


As always, you can combine this with any other search criterion. So, for example, you could search for daily disposable distance-center bifocal lenses or silicone hydrogel near-center lenses or anything else you want.


Other new lens fields

 While I was at it, I added several other database fields that I felt were long overdue, including:

  • Keratoconus
  • Prosthetic 
  • Novelty
  • Bandage lens

As a result, you can search for lenses by these factors now too.


Smarter Universal Search

I call the search bar at the top of the page the "Universal Search" because it has a TON of built in functionality. For one, it can be used to search all the databases: Soft Lenses, GP lenses, and Topical ophthalmic medications,and even link to  external sites for things like ICD-10 searches. However, there are a lot of features that I'm sure have flown under the radar. 

For soft lenses, you can search by:

1. Lens name (of course)

2. Abbreviations. For example, type "AOFA" as a quick way to search for "Acuvue Oasys for Astigmatism"

Searching by abbreviation


3. Search by company. For example, typing "Alcon" will let you see all of Alcon's lenses.

Searching by company


4. Keyword searches. This is fairly new, but the search will now recoginze a bunch of keywords. Some examples would include:

  • High dk
  • bandage
  • center-near
  • toric 
  • daily replacement

And many combinations of these things, such as toric bifocal high dk lenses:

Keyword searches


5. Searching by refraction. This is a subscriber only feature, but I believe it is EyeDock's greatest feature. I've written entire posts about searching by refraction so I won't go in to too much detail here but, if you haven't tried it, you're really missing out!

Searching by refraction



Well, that's all I'll share with you today. There are a lot more things I should probably share with you, though, so I'm going to have to try to push out a few more posts like this so one. I need to make sure you're using EyeDock to it's fullest potential!

All the best,


Todd M Zarwell OD FAAO



Error in EyeDock's Pazeo listing

It was brought to our attention yesterday that we had an error in our Pazeo listing. The recommended pediatric dosage for this medication is 2 years. Our listing incorrectly listed it as 2 months. 

We completely understand the significance of such an error and truly regret that it happened. These listings are manually, but very carefully, entered into our database by us. They are double and triple checked, but this mistake managed to slip through our evaluation process. We apologize for allowing this to happen and will increase our efforts to prevent something like this from happening again.



Todd M Zarwell OD FAAO

Updated Oblique Crossed Cylinders Calculator

I've made an update to EyeDock's [oblique crossed cylinder calculator]( It still uses your trial toric lenses power, rotation, and over refraction to determine which toric lens to try next. toric lens calc screenshot However, I realized that this was still leaving some unnecessary work for the practitioner using this calculator. For one, it's nice to know that the *best* lens is one that corrects -4.25 diopters of cylinder with an 86 degree axis. However, I know that most lenses I regularly work with do not come in those exact powers. Traditionally I have looked up what powers the lens *does* come in and tried to find the closest match. This required rounding to the closest axis, reducing the cyl to the closest power the lens comes in. To make matters worse, I usually also need to adjust the sphere power to maintain the spherical equivalent to make up for my cyl power adjustments. Once I've made all these changes I start to wonder how big of an impact my compromises will make on the final result. How much will my axis rounding and cyl power reducing affect my patient's visual acuity? This is what I attempted to address with these calculator updates. I've added a feature that lets you enter which brand of trial contact lens you have on your patients eye. oblique CL brand screenshot With this information the calculator can look up the available lens parameters on EyeDock and find the best match to the *ideal* lens. It will intelligently round to the best axis, adapt the cyl power to the closest option, and make adjustments to the sphere power as needed. oblique brand suggestion It also gives you a sense of how close you are to the ideal lens by calculation the uncorrected Rx. From here it makes a prediction about what the potential visual acuity will be with this lens, which will enable you to make a decision about the lens's worthiness. Of course, the calculator may throw in its own 2 cents: If the potential vision seems poor it will suggest you try another lens brand. (1) Here's a little walkthrough of the calculator: I hope this allows my fellow clinicians to save a little time in their busy practices. As always, let me know if you have any thoughts or comments! -Todd Todd M Zarwell OD FAAO (1) If another brand was suggested, I was really, really tempted to have the calculator suggest some alternatives. However, I decided this was beyond the scope of this tool. For one, the calculator does not even know the patient's true refraction. For two, the oblique cross cyl calculator is making decisions based on how this particular brand rotates on the eye, but we can't necessarily expect another brand to behave the same way. Do to these information limitations I decided it would be presumptuous to try to make a suggestion about alternative lens brands and powers. My advice would be to type in the patient's original refraction into the search bar and start from scratch.

Changes to plaquenil risk calculations

A new study investigating plaquenil (hydroxychloroquine or HCQ) toxicity and dosing, The Risk of Toxic Retinopathy in Patients on Long-term Hydroxychloroquine Therapy 1, was published last year. This has prompted me to reevaluate and rewrite EyeDock’s plaquenil risk calculator.

I was actually quite happy to do this as the new recommendations provided some clarification about how suggested plaquenil dosages should be calculated.

The previous convention2 suggested a daily dosage no higher than 6.5mg/kg of body weight daily. The recommendation was to use ideal body weight - a calculated value using your patient’s gender and height - rather than real body weight.

However, as I wrote my original calculator, I found that there were some significant differences in the recommended daily dosages when using real vs. ideal body weight. At that time I decided to write about this in a blog post, Daily Plaquenil Dosage - Crunching Numbers.

Due to these concerns I decided to make EyeDock’s original plaquenil dosage calculator cover all of its bases by making recommendations based on real AND ideal weight. This resulted in an awkward and admittedly confusing results, especially for overweight patients. This is nicely illustrated in this screenshot:

New Recommendations

Thankfully Melles and Marmor’s 2014 study removes a lot of this ambiguity:

… because of these findings, we have used real body weight for all subsequent presentations in this article and 5.0mg/kg of real body weight as a division between judicious and excessive use.

How does this affect our calculations?

As a consequence, I have rewritten EyeDock’s calculator to take use these new recommendations. The result is a more succinct and less confusing calculator:

Safe plaquenil dose by true weight
“Safe” plaquenil dose by true weight

Of course, changing this formula will change the results of my calculator. As always, I highly recommend that people using this calculator understand what conventions it uses. It’s critical to understand its output so you can interpret the information, assess risk, and make proper decisions for your patients.

Let’s take look at at how the new recommendations affect the calculations of plaquenil risk. It’s not difficult to predict what we’ll see when we look at true weight and simply compare the old standard, 6.5mg HCQ / kg weight, to the new recommendation, 5.0mg HCQ / kg weight: The new recommendations will recommend a lower “safe” dosage across all weights:

Since 200mg bid (400mg/day) has traditionally been considered a “typical” dosage, we’ll look closely at this value.

Using 6.5mg HCQ/kg weight = 400mg HCQ, and solving for weight:

400 mg / (6.5mg/kg) = weight

weight = 61.54 kg

61.5 kg * 2.20462 lbs/kg = 135 lbs

Therefore, a 400mg daily dose of plaquenil (or less) would have been considered appropriate for anyone weighing at least 135 lbs.

Now let’s do the same thing for the new recommendation, 5.0mg HCQ/kg weight:

400 mg / (5.0 mg/kg) = weight

weight = 80.0 kg

80.0 kg * 2.20462 lbs/kg = 176 lbs

With the new recommendation, a patient should not take 400mg plaquenil daily unless their weight is at least 176 lbs.

As I discussed above, the old recommendations also suggested taking into account ideal weight as opposed to true weight, although it was a little unclear as when and where this should be done (this was focus on my aforementioned blog post ). I decided to explore this more closely in the folowing graph.

green zone is normal BMI, orange is underweight, blue is overweight
green zone is normal BMI, orange is underweight, blue is overweight

The green (6.5mg/kg) and blue (5.0mg/kg) lines look “safe” HCQ dosage calculated by true body weight and are virtually identical to the previous graph.

To calculate ideal body weight we need to know the gender and height of our subject, so I chose an average 5’4“ (64 inch or 1.625 meter) tall woman (women are more likely to be taking plaquenil). I discussed how ideal body weight is calculated in my previous post and I will not repeat it here. Most importantly, a 5’4” woman’s ideal weight will be 120.6 lbs (54.7 kg). Because her ideal weight will not change, calculating her recommended maximum safe dosage of plaquenil will always be:

6.5mg/kg * 54.7kg = 355.6 mg HCQ

This is represented by the yellow line in the above graph. Since the ideal weight is independent of her true weight the yellow line is perfectly horizontal. By this standard, a 5’4" woman’s ideal plaquenil dose is always 356 mg/day or less.

Comparing the yellow line (ideal weight) to the other two lines (which use real weight), we can see the ideal weight recommendations are always lower for our overweight patients. However, the opposite is also true: ideal weight recommendations are higher than real weight calculations in underweight individuals. This latter issue may be of greater importance, as Marmor and Melles state in their 2014 paper1:

… the prevalence of retinal toxicity relative to real body weight is essentially independent of body habitus, whereas the risk is much higher in thin individuals using their ideal body weight.

The concept of using ideal weight for an overweight individual seems, on the surface, very logical. Adipose tissue does not absorb hydroxychlorquine and therefore shouldn’t be considered in “safe” dosage calculations. The concern was that, if real weight is used in these calculations, it may overestimate the dosage and put our patients at risk for retinotoxicity. This can be seen in the blue zone on the right side of the above graph. While calculations using 5.0mg/kg (the blue line) do recommend higher dosages than those using ideal weight (the yellow line), they are significantly less than the former calculations that used 6.5mg/kg (the green line).

On the other hand, the opposite situation is also true. An underweight individual will have an ideal weight that is greater than their true weight. If ideal weight is used to estimate the appropriate plaquenil dosage it will suggest a higher daily dose than would be appropriate. This can be seen in the orange zone on the graph. The ideal weight calculations (the yellow line) recommend higher daily dosages than the other two. The 6.5mg/kg (the green line) recommends a lower dosage, but the 5.0mg/kg (the blue line) recommends the lowest of the three.

In a nutshell, the new recommendations (5.0 mg HCQ / kg of REAL body weight) will recommend lower dosages for underweight (and normal weight individuals too, actually). It does allow for higher dosages for overweight individuals as compared to calculations using ideal weight, but not as high as the older formula that recommended 6.5mg/kg of real body weight. While this sounds nice and logical we need some science to back it up. Fortunately Melles and Marmor 1 provided that too:

We calculated the receiver operating characteristic curves to assess the sensitivity and specificity of real vs ideal body weight in predicting retinal toxicity and found that real body weight is a better predictor of retinal toxicity.

Math and graphs are nice, but …

As always, it is very important to remember that these calculations are intended to find a daily dosage that minimizes risk. It does not mean risk is eliminated. In fact, Melles and Marmor’s study found that

Patients with a mean daily use exceeding 5.0 mg/kg had approximately 10% risk of retinal toxicity within 10 years of treatment and an almost 40% risk after 20 years. Patients using an intermediate amount of 4.0 to 5.0 mg/kg had a risk of less than 2% within the first 10 years of use but almost 20% risk after 20 years.

Knowing that risk still exists with lower dosages - and that the overall prevalence of hydroxychloroquine retinopathy is as high as 7.5% - the most critical issue is that we are monitoring our patients for early signs of toxicity. Dr. Marmor summed this up best in an email to me last year:

… More important, from my own experience, is that optometrists and ophthalmologists get quality 10–2 fields (ideally Humphrey with SITA program and pattern deviation plots for white targets; or with red targets). And that they know how to recognize early suggestive damage. I see too many cases with severe toxicity because they either had no fields done (just fundus images) or the doctor got odd fields that were too large or insensitive or with defects discounted as artifactual variation. The adjunct of high resolution SD-OCT is also a very powerful early screening tool, and optometrists should do this or link with an office that can do this! Neither fundus exam nor fundus images by themselves are adequate or proper for screening, and can lead to lawsuits and blindness.

  1. Melles & Marmor. The Risk of Toxic Retinopathy in Patients on Long-term Hydroxychloroquine Therapy. JAMA Ophthalmolol. 2014;132(12):1453–1460.

  2. Marmor, M. F., et al. Revised Recommendations on Screening for Chloroquine and Hydroxychloroquine Retinopathy. Ophthalmology, Vol. 118, No. 2, February, 2011