Biometry for Cataract - The art of applying Mathematics to Biology

Updated: May 11

On a cold winter morning, twenty years back, as my friends and I sat for the class in the university, our professor shared an unique experience. He detailed us about his experience learning a new subject called biometry of eye, as he cared for his mother who developed cataract to undergo surgery. To the question, what is Biometry, our professor said in as many words, " Well from what I gathered, it seems that is an art of applying a combination of mathematics and statistics to our body (eye) ".

Little did I know, that I have to learn more, when destiny brought me closer to the field of applying science to biology. However, an understanding of the history of development of biometry formula, would help us to appreciate this science more. Lets take a walk down the history to understand more about modern biometry.

The first IOL, as we all know, was implanted by Sir Harold Ridley, post World War II. However the biometry machines found life no earlier than the late sixties or the early seventies. What this indicates is that the art of IOL implantation predates the science of biometry. The IOL power in the pre biometry days was a subject of individual judgement, though strategies like the Basic Refractive Error (BRE) was largely popular. In BRE, the surgeon would implant a 18.0 diopter lens to an emmetrope, but would deduct or add 1.25 D to the lens for every 1 D of myopia or hyperopia, respectively.

As the biometry machines started seeing the light of the day, a host of first generation theoretical formula got introduced. Notable of these are the Fyodorov, Collabander, Binkhorst, etc. These formulas were theoretical, two lens formula, which only took into consideration the two lenses in the eye (consider the cornea ). Of the many troubles associated, there was one bright point. The anterior chamber lenses were largely stable, unlike the later generation IOLs that were implanted in the capsular bag. As the axial stability of the lens was more (considering there was no bag contraction effect on anterior lenses ), the need for more sophisticated formulas was not felt, till the advent of phacoemulsification.

With phaco, surgeons understood, that the capsular bag was the right place to implant an IOL. But one of the many challenges initially associated with phaco, was the stability of the IOL implanted in the bag. Thus came a host of second generation formulas, notable among them P=A-2.5L-.9K   - yes the SRK. Despite its many challenges, the SRK was revolutionary in the sense that it for the first time introduced the concept of a constant. This constant accounts for the lens design and factor.

To cut a long story short, the next fifteen years of Sanders et al were devoted to further improving the formula, largely by improving the constant based on individual eye features. Thus while the SRK II modified the A constant with the individual Axial Length finding, the more advanced SRK T linked the same to the Keratometry reading also. Nevertheless, the original SRK formula, gives us an idea of how important and precise the axial length calculation needs to be, as any error on the axial length calculation is multiplied by almost three times, as reflected in the formula.

A paper published by Holladay in 1996, however has slowly revolutionized the concept of lens power calculation. Holladay in a series of pioneering work, showed the world that some of the basic assumptions that were made in the eighties and nineties, were not scientific. Notable of this is that, the SRK T assumes that a higher axial length would be associate with a higher anterior chamber depth, and hence the Effective Lens Position (ELP) further away from the cornea. This is not always true. What you see as the Holladay II (Holladay IOL Software) and incorporated in different manufacturer machines, hence takes into account seven variables - all in the interest of understanding the ELP more precisely.

The last five years has been very exciting in the ophthalmic world. We have seen the introduction of a host of new age laser biometry, topographers, tomography. The world of IOL power calculation has not failed us to live up to the expectation of the patient, and the many scientific discoveries. The Olsen formula, Barrett Universal II, the papers published by Wang & Koch for high myopia patients, the Hill RBF, centroid SIA, are all revolutionary concepts. The efficacy of the Barrett formula lies in this, that it takes into account the changes in the principles plane of refraction of an IOL, as you move from the higher to the lower diopter of the manufacturer.

Despite the many improvements that we have seen in Biometry in the last few years, achieving the target refraction is still eluding in many a practice. This may be because, achieving the target refraction and a smiling face is not just a factor of science, but an art - a combination of surgical skill and biological factors of the patient post operatively. Notable among these variables are the rhexis and the capsular contraction of the individual patient. While we perfect the science, the art remains an art. Let us hope for the best art.


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