In IOL power calculation, a formula is used that requires accurate biometric measurements of the eye, the visual axial length (AL), and the central corneal power (K). The desired “target” postoperative refraction and the estimated position of the IOL (estimated lens position [ELP]) are added to these factors for use in power calculation. Some surgeons target a slightly myopic result, the advantage of which is that it allows for some degree of near vision and reduces the possibility of a postoperative hyperopic refractive surprise.
Power prediction formulas
IOL power prediction formulas are termed theoretical because they are based on theoretical optics, the basis of which is the Gullstrand eye (see Chapter 3). In the 1980s, regression formulas (eg, Sanders, Retzlaff, Kraff [SRK] formulas I and II) were popular because they were simple to use. However, the use of these formulas often led to power errors that subsequently became the major reason IOLs were explanted or exchanged. In the 1990s, regression formulas were largely replaced by more accurate, newer theoretical or ray tracing formulas.
Geometric optics was used to generate basic theoretical formulas for IOL power calculation, an example of which is shown below. The pseudophakic eye can be modeled as a 2-element optical system (Fig 6-5). Using Gaussian reduction equations (see Chapter 1), the IOL power that produces emmetropia may be given by
P = power of the target IOL (in diopters [D])
V = index of refraction of the vitreous
AL = visual axial length (in meters)
C = ELP (in meters), the distance from the anterior corneal surface to the principal plane of the IOL
K = average dioptric power of the central cornea
A = index of refraction of the aqueous
Most of the advances in newer theoretical formulas (such as the Haigis, Hoffer Q, Hoffer H5, Holladay 1 and 2, Olsen, and SRK/T formulas) concerned improved methods of predicting the ELP, as described later in this chapter. These formulas are complex and cannot be used easily for calculation by hand. However, programmable calculators and applicable computer programs are widely available. These formulas are also programmed into automated optical biometers like the IOLMaster (Carl Zeiss Meditec, Jena, Germany) and the Lenstar (Haag-Streit, Köniz, Switzerland) and most modern ultrasonographic instruments.
Figure 6-5 Schematic eye. PC and P′C are the front and back principal planes of the cornea, respectively. Similarly, PIOL and P′IOL are the front and back principal planes of the intraocular lens (IOL). OCD = optical chapter depth and represents a mathematical construct of this simplified model and is not identical to the anatomical anterior chamber depth; S = distance between back principal plane of the IOL and retina. (The drawing is not to scale.)
(Redrawn by C. H. Wooley.)
Biometric formula requirements
Axial length The AL is the most important factor in these formulas. A 1-mm error in AL measurement results in a refractive error of approximately 2.35 D in a 23.5-mm eye. The refractive error declines to only 1.75 D/mm in a 30-mm eye but rises to 3.75 D/mm in a 20-mm eye. Therefore, accuracy in AL measurement is more important in short eyes than in long eyes.
ULTRASONIC MEASUREMENT OF AXIAL LENGTH
When A-scan ultrasonography is used to measure AL, we either assume a constant ultrasound velocity through the entire eye or measure each of the various ocular structures at its individual velocity. A-scans measure not distance but rather the time required for a sound pulse to travel from the cornea to the retina and back again. Sound travels faster through the crystalline lens and the cornea (1641 m/s) than it does through aqueous and vitreous (1532 m/s). Even within the lens itself, the speed of sound can vary in different layers and is altered by nuclear sclerosis.
The average velocity through a phakic eye of normal length is 1555 m/s; however, it rises to 1560 m/s for a short (20-mm) eye and drops to 1550 m/s for a long (30-mm) eye. This variation is due to the presence of the crystalline lens; 1554 m/s is an accurate value for an aphakic eye of any length.
The following formula can be used to easily correct any AL measured with an incorrect average velocity:
where ALC is the AL value at the correct velocity, ALM is the resultant AL value at the incorrect velocity, VC is the correct velocity, and VM is the incorrect velocity.
In eyes with AL values greater than 25 mm, staphyloma should be suspected, especially when numerous disparate readings are obtained. Such errors occur because the macula is located either at the deepest part of the staphyloma or on the “side of the hill.” To measure such eyes and obtain the true measurement to the fovea, the patient must fixate on the light in the center of the A-scan probe. If such a lighted probe is unavailable or if the patient is unable to fixate upon it, the clinician must use a B-scan technique. Optical methods (eg, IOLMaster, Lenstar) are very useful in such cases (see the following section).
When ultrasonography is used to measure the AL in biphakic eyes (ie, a phakic IOL in a phakic eye), it is difficult to eliminate the effect of the sound velocity through the implanted phakic lens. To correct for this potential error, one can use the following published formula:
1555 = the measured AL of the eye at a sound velocity of 1555 m/s
C = the material-specific correction factor, which is +0.42 for PMMA, −0.59 for silicone, +0.11 for collamer, and +0.23 for acrylic
T = the central thickness of the implanted phakic IOL
Published tables list the central thickness of phakic IOLs available on the market (for each dioptric power). The least degree of error (in terms of AL error) is associated with use of a very thin myopic collamer lens, and the greatest amount of error is associated with use of a thick hyperopic silicone lens.
The primary A-scan techniques—applanation (contact) and immersion (noncontact)—often give different results (Figs 6-6, 6-7). Although the immersion method is accepted as the more accurate of the 2 techniques, it is more difficult to perform and less widely employed than the applanation method. The applanation method is susceptible to artificially shortened AL measurement because of inadvertent corneal indentation.
Figure 6-6 In applanation ultrasonography, the probe must contact the cornea, which causes corneal depression and shortening of the axial length reading.
(Courtesy of Kenneth J. Hoffer, MD.)
Figure 6-7 Ultrasonography techniques. A, In immersion ultrasonography, the probe is immersed in the solution, placing it away from the cornea. B, Prager shell for immersion A-scan. C, Ultrasound probe and Kohn shell. D, B-scan of an eye with staphyloma, showing the difference between the anatomical length (A) and the visual length (V).
(Courtesy of Kenneth J. Hoffer, MD.)
Figure 6-8 An optical biometer (left) and view of the instrument’s axial length screen (right).
(Courtesy of Kenneth J. Hoffer, MD.)
OPTICAL MEASUREMENT OF AXIAL LENGTH
Optical biometry uses a partial coherence laser for AL measurement (Fig 6-8). In a manner analogous to ultrasonography, this device indirectly measures the time required for infrared light to travel to the retina. Because light travels at too high a speed to be measured directly, light interference methodology (interferometry) is used to determine the transit time and thus the AL. This technique does not require contact with the globe, so corneal compression artifacts are eliminated. This instrument was developed such that its readings would be equivalent to those of the immersion ultrasound technique. Because this device requires the patient to fixate on a target, the length measured is the path the light takes to the fovea: the “visual” AL. The ocular media must be clear enough to allow voluntary fixation and light transmission. Thus, in dense cataracts (especially posterior subcapsular cataracts), ultrasound biometry is still necessary (in 5%–8% of cataract patients). Compared with ultrasonography, this technique provides more accurate, reproducible AL measurements. In addition, optical measurement is ideal in 2 clinical situations that are difficult to achieve using ultrasonography: eyes with staphyloma and eyes filled with silicone oil, although such measurements require adjustment.
If removal of the silicone oil is not intended, additional optical accommodations must be made. Because of the element of reduced vergence (see Chapter 1) introduced by a medium of a different refractive index, IOL power must be increased to achieve the intended refractive target. This problem is further compounded by the decreased refractive power achieved at the interface between the posterior surface of the IOL and the silicone oil. When these elements are not considered, Grinbaum and colleagues demonstrated that patients exhibit a mean postoperative hyperopic surprise of close to 4 diopters (D). This hyperopic shift may be minimized by avoiding the use of IOLs with convex posterior surfaces.
Dong J, Tang M, Zhang Y, et al. Comparison of Anterior Segment Biometric Measurements between Pentacam HR and IOLMaster in Normal and High Myopic Eyes. PLoS One. 2015; 10(11): e0143110.
Freeman G, Pesudovs K. The impact of cataract severity on measurement acquisition with the IOLMaster. Acta Ophthalmol TablScand.2005;83(4):439–442.
Grinbaum A, Treister G, Moisseiev J. Predicted and actual refraction after intraocular lens implantation in eyes with silicone oil. J Cataract Refract Surg. 1996;22(6): 726–729.
Corneal power The central corneal power, K, is the second most important factor in the calculation formula; a 1.0 D error in corneal power causes a 1.0 D postoperative refractive error. Corneal power can be estimated by keratometry or corneal topography, neither of which measures corneal power directly. The standard manual keratometer (Fig 6-9A) measures only a small central portion (3.2-mm diameter) of the cornea and views the cornea as a convex mirror. The corneal radius of curvature can be calculated from the size of the reflected image. Both front and back corneal surfaces contribute to corneal power, but the keratometer power “reading” is based on measurement of the radius of curvature of only the front surface and assumptions about the posterior surface.
Two imaging systems are commonly used in measuring corneal power. The Pentacam (Oculus Optikgeräte GmbH, Wetzlar, Germany, Fig 6-9B) system uses a single Scheimpflug camera to measure the radius of curvature of the anterior and posterior corneal surfaces, as well as the corneal thickness, for the calculation of corneal power. Early studies questioned the accuracy of the Pentacam in eyes that had undergone laser corneal refractive procedures. Newer software has made dramatic improvements. The Galilei (Ziemer Ophthalmic Systems AG, Port, Switzerland) system measures corneal power by use of a dual Scheimpflug camera integrated with a Placido disk.
Estimated lens position All formulas require an estimation of the distance at which the principal plane of the IOL will be situated behind the cornea—a factor now known as the ELP. Initially, most IOLs were either anterior chamber or prepupillary IOLs. Thus, in the original theoretical formulas, this factor was called the anterior chamber depth (ACD), and it was a constant value (usually 2.8 or 3.5 mm). This value became incorporated in the A constant of the regression formulas of the 1980s.
Figure 6-9 Instruments for measuring corneal power. A, Manual keratometer. B, Oculus Pentacam.
(Part A courtesy of Reichert Technologies; part B courtesy of Oculus Optikgeräte GmbH.)
In 1983, using pachymetry studies of posterior chamber IOLs as a basis, Hoffer introduced an ACD prediction formula for posterior chamber lenses that was based on the eye’s AL:
ACD = 0.293 × AL − 2.92
Other adjustments (second-generation formulas) were also based on the AL. The Holladay 1 formula used the K reading and AL value as factors (in a corneal height formula by Fyodorov), as did the later SRK/T formula, whereas the Hoffer Q formula used the AL value and a tangent factor of K (all these formulas are third generation). Olsen added other measurements of the anterior segment, such as the preoperative ACD, lens thickness, and corneal diameter (this formula is fourth generation). Subsequently, Holladay used these factors, as well as patient age and preoperative refraction, in his Holladay 2 formula. Haigis eliminated K as a prediction factor and replaced it with the preoperative ACD measurement. These newer formulas are more accurate than those of the first and second generations, and all are currently in use (Fig 6-10).
The most accurate way to measure the preoperative ACD or the postoperative ELP is by optical means, using scanning slit topography, Scheimpflug imaging, or optical interferometry. Ultrasonography is usually less precise and provides a shorter reading.
Most formulas use only one constant, such as the ACD, the A constant, or the surgeon factor (SF). One exception is the Haigis formula, which uses 3 constants (a0, a1, a2). The A constant, developed as a result of regression formulas, was widely used in the 1980s, so much so that manufacturers assigned each lens design a specific A constant, as well as an ACD value. Even though regression formulas (eg, SRK formula) are no longer recommended and rarely used for IOL calculation, the A constant still exists for the SRK/T formula.
Figure 6-10 Accuracy range of commonly used formulas by axial length.
(Courtesy of Warren Hill, MD.)
Holladay developed 2 formulas that convert a lens’s A constant to another factor. The first converts the A constant to an SF for the Holladay formula:
SF = (0.5663 × A) − 65.6
where A is the IOL-specific A constant and SF is the Holladay surgeon factor. The second formula converts a lens’s A constant to a personalized ACD (pACD) for the Hoffer Q formula:
where A is the IOL-specific A constant and pACD is the Hoffer pACD (ELP). So, for example, an A constant of 113.78, 116.35, or 118.92 converts to a pACD of 2.50 mm, 4.00 mm, or 5.50 mm, respectively.
It is prudent to calculate the power of an alternate IOL before surgery. If not calculated in advance, the power of an IOL intended for bag placement can be decreased for sulcus placement with subtraction of 0.75–1.50 D, depending on the AL value (Table 6-1). This need to reduce IOL power is not necessary if posterior optic capture is performed. If the haptics are in the sulcus but the optic is “buttonholed” through the anterior capsulorrhexis into the capsular bag, no IOL power adjustment need be made.
Careful attention to avoiding IOL tilt is important, especially in cases of sutured-in IOLs. Such tilt will induce astigmatism of oblique incidence. For plus-power IOLs, the induced astigmatism will be of with-the-rule orientation in the case of a lens tilted about the horizontal axis and against-the-rule astigmatism in the case of an IOL tilted about the vertical axis. The opposite holds true for the much less common minus-powered IOLs.
Douthwaite WA, Spence D. Slit-lamp measurement of the anterior chamber depth. Br J Ophthalmol. 1986;70(3):205–208.
Millar ER, Allen D, Steel DH. Effect of anterior capsulorhexis optic capture of a sulcus-fixated intraocular lens on refractive outcomes. J Cataract Refract Surg. 2013;39(6):841–844.
Savini G, Hoffer KJ, Lombardo M, Serrao S, Schiano-Lomoriello D, Ducoli P. Influence of the effective lens position, as predicted by axial length and keratometry, on the near add power of multifocal intraocular lenses. J Cataract Refract Surg. 2016;42(1):44–49.