# FullMonte IOL Calculator History

In the 1990s, Sanders, Retzlaff, and Kraff developed a statistical formula called the SRK formula. It was a linear regression on two variables, axial length and keratometry. It was individualized for each lens by the well-known A-constant. It worked well on average eyes in the middle range of axial length and keratometry. However, large errors again were found on long or short eyes or eyes with different keratometry’s. To address these deficiencies, the authors developed the SRK II formula which had some adjustments for long and short eyes. Later in the 90s they developed the SRK/T formula which is based both on optical theory and linear regression. Kenneth Hoffer developed his program based on thin lens optics, but was the first nonlinear regression on the critical factor of effective lens position (ELP). In the 90’s, I developed a non-linear Neural Net IOL calculator which improved on the SRK/T formula. Jack Holladay developed formulas which utilized horizontal white-to-white distance. Most recently, Wolfgang Haigis has developed a predictor of effective lens position based on the anterior chamber depth and the axial length. And finally Thomas Olsen has added several new parameters to his formula including preoperative refraction, lens thickness, age, as well as the factors developed by the other authors.

With the prevalence of refractive surgery after the approval of LASIK, a whole new set of problems emerged. The change in shape of the cornea skewed keratometry values, making the standard formulas error-prone. John Shammas and Wolfgang Haigis adapted formulas to better predict postoperative refractions with lenses in those patients The search goes on. As you can see the trend is to add more variables and to try to do linear predictions based on those variables to arrive at key prediction of ELP. And while all the formulas rely on statistical verification of coefficients, which are mean values taken from the linear regression for the coefficients, we only receive one number and that is the IOL that will give us a certain predicted result. FullMonte IOL is different. First we utilize all of the above variables plus some new ones that we will discuss later. The process is different as well. It is not a formula, but rather a computing process that delivers not just one number but a statistical probability of achieving a certain result. This probability is constantly updated from data you supply to the software. The answer that we deliver is a graph. And from this graph, the surgeon can estimate the best lens to give him the most accurate results and she can also see how confident she can be in the final results. To see this better let’s look at some simple statistics graphs (histograms).

### Typical Probability Density Curves

On the graph you can see we have several superimposed probability densities. They all are equally accurate. By accuracy, we mean the central tendency of these probability curves. When you optimize a traditional intraocular lens formula to arrive at the single A–constant or ‘surgeon factor’, you are essentially moving the curve above along the x-axis. So all standard formulas can be adjusted to give equal average accuracy. But you are not changing the shape of the curve. You are making two assumptions: first that the data is normal, and second that the value you pick as the average will give you good results over the range of all eyes. We’ve seen that both assumptions are not valid. Long eyes, short eyes, refractive surgery eyes, and so forth, show that this is not so. It is better to look at the whole probability curve. And in this graph we can see that the central blue curve has a very high peak with very short tails. So the variance is small compared to other graphs (Precision is the inverse of variance, so it is higher). The other two graphs, while having equal accuracy, have much higher variance (lower precision) and fatter, longer tails. Those fat tails provide the errors in IOL prediction.

### Probability Graph

As mentioned previously, FullMonte IOL provides graphs of predicted results. Here is one:

Example Probability Distribution Each probability curve is calculated for different lens powers. The central probability (black line) is the most likely expected refraction after implantation with each lens. We would choose the lens with closest probability to the planned refraction. Below is a Small Series (<50) optimized MCMC graph. Notice the broad spread of probabilities, and the uncertainty in the lens power you might choose.

### Example FullMonte Probability Calculation

In two prospective, controlled studies comparing the FullMonte IOL Monte Carlo Markov Chain (MCMC) process versus the optimized SRK/T formula, the MCMC variance was found to be almost half the SRK/T formula. (0.26 vs 0.47) and (0.13 vs 0.19) In addition note the following results:

• Reduced StdDev from 0.44 (SRKT) to 0.36 (FMG)
• Significant – at p-value = 0.05478
• FMG better predictor 53 times – versus 21 for SRKT, 18 equal
• 90% of Eyes within 0.50 diopters of intended refraction
• 61% of Eyes within 0.25 diopters of intended refraction
What does refractive precision mean to you in clinical practice? You have to look at two sides of the coin. First it means you have a high chance of hitting your target in over 95% of your cases. Second, you have a much lower chance of missing your target by greater than 0.50 diopters (<2%). This means you can confidently add a ‘laser’ guarantee backing up your refractive lens surgery. I won’t go into too much about the theory behind MCMC processes. Suffice it to say, it is based on Bayes rule and intensive computational analysis. Look at the simple diagram below:

### Bayesian Diagram

In this case, with one variable, you can see that there is a theoretical prior likelihood of achieving a certain result. This would be like having perfectly balanced dice. But when we toss the dice 1000 times and find that the results are different than expected (the dice is ‘loaded’), we can combine that data with the theoretical data and then arrive at the posterior distribution which is the answer were looking for. But the answer is not a single number, but a probability distribution of likely post-op refractions with a particular lens.The evidence modifies the theory to arrive at a realistic predicted result. The FullMonte IOL MCMC computational process does this on a large scale using all the variables known to affect intraocular lens calculation (from Olsen and others).