4 IOL Power Calculation: Principles and Concepts



10.1055/b-0036-134475

4 IOL Power Calculation: Principles and Concepts

Thomas Olsen

4.1 Introduction


The quest for accurate intraocular lens (IOL) power calculation has existed ever since the first IOL was implanted by Sir Harold Ridley in 1949. The surgery went well, but the postoperative refraction was found to be – 20 D. Ridley soon realized that the error was due to the higher refractive index of Perspex (polymethyl methacrylate [PMMA]) as compared to the crystalline lens, the dimensions of which he had been trying to copy. 1


Nowadays a prediction error of 0.5 D, be it spheric or cylindrical, can make the difference between success and failure, especially with multifocal and toric implants. Hence the question of improved accuracy to the first decimal point is not just of academic interest but is also clinically relevant for the patient’s quality of life.


This chapter discusses the principles and the sources of error behind IOL power calculation, beginning with the fundamentals of the “thin-lens” IOL power calculation formula. Next, the text describes the conditions for improved IOL power calculation using ray tracing and newly developed methods for the prediction of the IOL position. The benefit of using physiological optics is stressed. However, the calculation of IOL power is not just a question about optics. The eye is a biological tissue of small dimensions, which requires an understanding of how clinical measurements combine with physical optics to meet the clinical reality. As the demands and complexity of patients seem to rise in parallel, practitioners face significant challenges in future IOL power calculations.



4.2 Thin-Lens IOL Power Formulas


According to Gaussian optics (paraxial imagery) the refractive power of any spherical surface can be calculated as 2


F=n2-n1rF={{n}_{2}-{n}_{1}\over{r}} 1

where F = refractive power of the surface in diopters (D), n 1 = the index of refraction of the material before the surface, n 2 = the index of refraction of the material after the surface, and r = the radius of curvature in meters.


Vergence is another important concept describing the diopteric power of paraxial rays at a certain distance. It is defined as the reciprocal of the “reduced” distance, defined as distance divided by refractive index:


V=ndV={n\over{d}} 2

where V = vergence of rays in diopters, d = distance in meters, and n = refractive index of the material. When a lens of power F is added to a bundle of rays the resulting vergence can be calculated by addition:


V2=V1+F{V}_{2}={V}_{1}+F 3

where F = refractive power of the lens in diopters, V 1 = vergence before the lens, and V 2 = vergence after the lens. The reduced distance to the new focal point can be calculated as the reciprocal of V 2.


From these basic equations we can now construct the thin-lens IOL power calculation formula: consider an eye of corneal power F, length Ax, and a thin IOL at a distance d from the cornea. The focal distance, that is, the vergence after the cornea, assuming incoming parallel rays is 1/K. When the rays hit the lens plane, the vergence is changed by the distance d/n 1, where d is the distance in meters and n 1 is the refractive index of the aqueous. Thus the vergence V 1 at the front surface of the lens plane can be calculated as the reciprocal of the new reduced distance according to equation 2:


V1=11K-dn1{V}_{1}={1\over{\left({1\over{K}}-{d\over{{n}_{1}}}\right)}} 4

To be focused on the retina, rays leaving the lens plane must have a vergence (V 2) defined by the distance from the lens plane to the retina:


V2=n2Ax-d{V}_{2}={{n}_{2}\over{\left(Ax-d\right)}} 5

where n 2 = refractive index in the posterior segment and the other variables as defined earlier. Thus the power of the IOL needed to focus the rays on the retina can be found by subtracting vergence V 2 from V 1, which gives


P=n2Ax-d-11K-dn1P={{n}_{2}\over{\left(Ax-d\right)}}-{1\over{\left({1\over{K}}-{d\over{{n}_{1}}}\right)}} 6

where P = power of IOL for emmetropia, K = corneal power, Ax = axial length, d = effective lens plane (ELP), n 1 = refractive index of aqueous, and n 2 = refractive index of vitreous (Fig. 4.1). This equation is the general thin-lens formula found in all the thin-lens formulas, that is, the Fedorov, 3 Colenbrander, 4 Binkhorst, 5 Hoffer, 6 ,​ 7 SRK/T, 8 Holladay 1, 9 and Haigis 10 formulas.

Fig. 4.1 Thin-lens intraocular lens (IOL) power calculation model. The thin-lens formula assumes the cornea and the IOL to be thin lenses of infinite thickness. The ELP is the effective lens plane that predicts the refraction from the K-reading (K) and the axial length (Ax).

However, for it to work in clinical practice several key elements in the equation need to be addressed. Important questions pertain to how the corneal power is determined, how the ELP is predicted, how the axial length should be measured accurately, and how to deal with higher-order aberrations of the cornea and the IOL.



4.2.1 Effective Lens Plane


One of the most important variables in any IOL power calculation formula is the predicted position of the IOL after surgery. In fact, this is the only true “prediction” that needs to be made by the formula, and the actual method by which the different IOL formulas perform this task makes them differ in performance. The rest is “just” optics.


Some confusion may arise about the exact meaning of the ELP. The thin-lens formula (equation 6) requires an ELP holding all the refractive power of the IOL. The ELP may, however, be different from the actual position of the IOL. The reason for this is the way such formulas were developed and how they were made accurate. Usually the procedure of optimization proceeds as follows: From a large database of known refractive outcome the exact ELP required with the formula to produce that outcome from the preoperative measurements and the IOL power is calculated in retrospect for each case. Next, the dependence of the ELP on preoperative measures, such as the axial length and the K-reading, is analyzed, often by regression analysis. Such analysis will most probably show that the ELP depends on the axial length (because the IOL tends to locate deeper in a long eye than in a short eye); therefore an improvement of the formula could be to implement a function of the axial length in the prediction of the ELP. The same procedure might be done for other variables, giving rise to two-variable, three-variable, or multiple-variable formulas of increasing complexity.


A formula developed in this way may be accurate for the sole reason that it is based on actual clinical data. Even though it may be theoretically wrong, adjustments to the virtual, “hidden” variable, called the ELP, can make it work in practice. However, if the formula uses the K-reading based on the index of 1.3375 (most thin-lens formulas do) the corneal power may be approximately 1 diopter (D) too high, as will be described later in this chapter. Consequently, the IOL power will be underestimated by almost the same amount. The formula may, however, compensate for this error by assuming a deeper position of the IOL than is really the case, thereby increasing the estimated IOL power. This is the main reason why the ELP of most thin lens formulas is deeper than the real IOL position.



4.3 The IOL Power Calculation Revisited



4.3.1 Modern Conditions for IOL Power Calculation


The clinical environment for IOL power calculation has taken a quantum leap since the early days of IOL implantation, improving the condition for accurate IOL power calculation in several ways:




  1. Thanks to small incision techniques—whether done by hand or with laser—the corneal anatomy is almost undisturbed by the surgery with minimally induced astigmatism if not deliberately aimed for. This gives less variability of the corneal power in IOL power calculation and makes it feasible to target the astigmatism by selecting the appropriate toric power of the implant.



  2. Thanks to the standardized opening of the lens capsule—whether done by hand or with laser—there is less variability in the position of the implant after surgery. Most surgeons prefer to use the continuous curvilinear capsulorhexis (CCC) technique 11 to create a circular opening of the capsule, providing a predictable environment for in-the-bag placement of the IOL. The size of the rhexis is usually selected so that the anterior edge of the capsule will symmetrically overlap the peripheral parts of the optic. As the capsule eventually contracts it will fixate the IOL not only in the axial position but also in the lateral position with minimal tilt and rotation.



  3. Thanks to laser biometry for the measurement of the axial length 12 we can now measure this important variable with unsurpassed accuracy. According to the manufacturers the accuracy of optical biometers is often stated to be within 0.020 mm between repeated measurements. Recalling that 1 mm axial length error is the equivalent of a 2.5 D error in the spectacle plane you will find that the laser error accounts for only 0.05 D error in the IOL refractive prediction error.



  4. Thanks to the development of diagnostic equipment for corneal refractive surgery we now have sophisticated tools for the analysis of corneal shape and function. Although the familiar K-reading still forms a cornerstone in IOL power calculation (to be discussed), there is abundant evidence that the corneal refraction is only partly measured by recording the curvature of the front surface in a paracentral ring area of ~ 3 mm. When it comes to post–laser in situ keratomileusis (post-LASIK) cases, nonregular astigmatism, and keratoconus, a standard K-reading is simply not adequate for an accurate analysis of the true, effective corneal power. For a complete description the posterior surface as well as the higher-order aberrations of the cornea should be taken into account.



  5. Although there is little documentation in the scientific literature we must assume that the optical quality of modern IOLs has improved considerably over the years due to improvement in manufacturing standards. More than 20 years ago the author of this chapter found significant deviations between the labeled and the true power of the IOL in many cases. 13 The power checks were performed using a keratometer-like setting with measurement of the curvature of both IOL surfaces in two meridians, and errors were found in the region 0.5 to 1 D in terms of both spherical and cylindrical power. Considering the low error of modern IOL power calculation with mean absolute prediction errors well below 0.5 D there seems to be less room for major IOL labeling errors in present manufacturing.



  6. Finally, the art of IOL power calculation per se has improved. 14 However, the concept of “garbage in … garbage out” also works for the ideal formula. Therefore, to have the best results with the best formula we must understand the principles behind its use and avoid the pitfalls.

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Jun 3, 2020 | Posted by in OPHTHALMOLOGY | Comments Off on 4 IOL Power Calculation: Principles and Concepts

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