Intraocular Lenses

Removing a cataract removes about 20 D of the eye’s focusing power, and the intraocular lens that replaces it sets the patient’s refraction for the rest of their life. Choosing its power is a vergence problem, solved before surgery from a few measurements; this chapter is about that calculation, what goes wrong with it, and the optics of toric, multifocal and other special lenses.

#Calculating the power

Treat the pseudophakic eye as two thin lenses, the cornea (power K) and the IOL, a distance ELP apart, in front of a retina at the axial length AL. Light from a distant object leaves the cornea with vergence K, travels to the IOL, and must leave the IOL with exactly the vergence that focuses it on the retina. With lengths in millimetres and the index of the eye 1.336, the IOL power for emmetropia is

AL and K are measured. The effective lens position (ELP) is not: it is where the lens will act, which is only known after surgery. The first theoretical formulas used this equation with one fixed ELP for every eye; the first regression formula, SRK, fitted outcomes directly:

where the A-constant belongs to the lens model (and is refined for each surgeon and biometer). Second-generation formulas (SRK II) let the constant vary with axial length. Third-generation formulas (Hoffer Q, Holladay 1, SRK/T), still built on the vergence equation, predict the ELP from AL and K. Later formulas use more measurements: Haigis predicts it from the anterior chamber depth and AL, without K; Holladay 2 adds lens thickness, corneal diameter, age and refraction; Barrett Universal II and Olsen use the anterior chamber depth, with lens thickness; Hill-RBF and Kane draw on large outcome datasets. Traditionally the Hoffer Q was preferred for short eyes and SRK/T for long eyes; the newer formulas perform well across the range. In long eyes, older formulas tend to leave the patient hyperopic (an axial length adjustment such as Wang–Koch corrects this), and very long eyes may need low or minus lens powers. Steep keratoconic corneas also tend to give a hyperopic surprise.

The figure shows how sensitive the result is. In an average eye, a 1 mm error in axial length shifts the refraction by roughly 2.5 D (often quoted as 2.35 D; about 3.75 D in a 20 mm eye and 1.75 D in a 30 mm eye), and a 1 D error in keratometry by about 1 D. Short eyes forgive least. The figure holds the lens position fixed and gives a little more in average and short eyes (a little less in very long ones); formulas that predict the lens position from the axial length partly offset the error. A dioptre of IOL power is worth only about 0.7 D of spectacle refraction in an average eye: a ratio of about 1.4 to 1.5 that recurs in sulcus, piggyback and toric lens calculations.

#Biometry

• Optical biometry (partial coherence interferometry or swept-source OCT) measures the axial length without touching the eye, to the retinal pigment epithelium, and is the standard. A dense cataract or poor fixation can defeat it.
• Ultrasound converts the echo time to length with an assumed sound velocity: about 1550 m/s averaged over a phakic eye, 1532 m/s in aqueous and vitreous, 1641 m/s in the lens and cornea. Applanation biometry presses on the cornea and shortens the reading, which leads to too strong a lens and a myopic surprise; immersion biometry avoids the compression. Silicone oil, with a sound velocity of only about 980 m/s, makes an uncorrected ultrasound axial length far too long, and also changes the power the IOL needs.
• Keratometry must be accurate and repeatable; dry eye, contact lens warpage and irregular astigmatism all distort it. Contact lenses are left out before biometry (Chapter 15).
• Check the two eyes against each other: a difference of more than about 0.3 mm in axial length or 1 D in K between fellow eyes, or a result that doesn’t fit the refractive history, should be repeated.

#After refractive surgery

Standard calculations after myopic LASIK or PRK give too weak a lens and a hyperopic surprise, for three reasons that all push the same way:

1. Instrument error: keratometers measure a ring a few millimetres across (about 3 mm for a manual keratometer, 2.3 to 2.5 mm for optical biometers), which can lie outside a small flattened optical zone and read steeper than the centre.
2. Index error: the keratometric index (1.3375) assumes a normal ratio between the anterior and posterior corneal curvatures. Laser ablation flattens only the anterior surface, so the index now overestimates the corneal power.
3. Formula error: formulas that predict the ELP from K read the flat cornea as a sign of a shallow anterior chamber, predict the lens sitting farther forward, and choose a weaker lens.

After hyperopic LASIK the errors reverse, giving a myopic surprise. Special methods estimate the true corneal power: the clinical history method (the pre-LASIK K minus the refractive change at the corneal plane), methods that need no history (Haigis-L, Shammas, Barrett True-K No History), and measurements of the posterior cornea by Scheimpflug imaging or OCT. Online calculators average several of them. After radial keratotomy both corneal surfaces flatten together, so the index error is small, but the optical zone is often 3 mm or less, so keratometers overestimate the central power and standard calculations again give a hyperopic surprise. RK-specific methods are used and a slightly myopic target is wise: the cornea fluctuates through the day, drifts hyperopic over the years, and swells after cataract surgery, causing a temporary hyperopic shift that should settle before any lens exchange is considered.

#Where the lens sits

A lens of given power is more effective the farther forward it sits, just as a plus spectacle lens is (Chapter 6). The figure above shows that moving the optic 0.7 mm forward leaves the eye about 1 D myopic; because a dioptre of refraction is about 1.4 D at the IOL, the model would need about 1.3 D less power. So:

• Sulcus placement, when the bag cannot hold a lens (for example after a posterior capsule rupture) but the anterior capsule rim can support one, needs a lens about 1 D weaker than in the bag for average powers (0.5 D for low powers, 1.5 D or more for high powers), unless the optic is captured back through the capsulorhexis. With no capsular support at all, the options are an anterior chamber lens or a lens fixed to the iris or sclera. Only lenses designed for the sulcus, usually three-piece lenses, belong there: a single-piece acrylic lens in the sulcus rubs on the iris, causing pigment dispersion, uveitis, glaucoma and hyphaema.
• Anterior chamber lenses sit farther forward still, with a lower A-constant: roughly 3 D less power than a lens in the bag.
• Piggyback lenses: a second lens in the sulcus in front of the first. Primary piggybacks provide powers beyond the usual range for very short eyes; two acrylic lenses in the bag are avoided, because cells grow between them (interlenticular opacification). A secondary piggyback corrects a refractive surprise without removing the original lens: its power is about 1.5 times the spherical equivalent of a hyperopic error, and about 1.2 to 1.3 times a myopic one (a minus lens).

A refractive surprise can also be managed with spectacles or contact lenses, laser refractive surgery, or by exchanging the lens, which is easiest in the first weeks, before the capsule fibroses; exchange suits a wrong lens, a piggyback suits a well-tolerated lens in a stable eye. In an eye filled with silicone oil, a biconvex IOL behind the oil loses power at its back surface and needs roughly 3 to 3.5 D more.

#Toric lenses

A toric IOL corrects regular corneal astigmatism. Its axis marks are aligned with the steep corneal meridian, and its cylinder, specified at the IOL plane, is larger than the astigmatism it corrects at the cornea, by a factor of about 1.4 to 1.5 in an average eye (it varies with the eye’s dimensions): a lens with 3.00 D of cylinder corrects about 2 D of corneal astigmatism. Three things matter:

• The posterior cornea. Keratometers measure the front surface and infer the rest. The back surface adds, on average, about 0.3 to 0.5 D of against-the-rule astigmatism, so measured with-the-rule astigmatism overstates the total and against-the-rule astigmatism understates it. Modern toric calculators allow for it, along with the astigmatism induced by the incision.
• Alignment. The eye rotates when the patient lies down, so the reference axis is marked with the patient sitting up, or tracked with image guidance.
• Rotation. A toric lens off its axis by θ leaves $2C\sin \theta$ of astigmatism (Chapter 13): about 3.3% of its effect per degree, half at 15°, and all of it at 30°, beyond which it makes the astigmatism worse. A rotated lens is best repositioned within the first weeks.

#Multifocal and extended depth of focus lenses

A monofocal lens focuses one distance; the pseudophakic eye cannot accommodate. Lenses that extend the range of clear vision all trade image quality for it:

• Diffractive multifocals split the light between two or three foci. A diffractive bifocal puts about 40% of the light at each focus and loses nearly a fifth to higher diffraction orders; trifocals add an intermediate focus.
• Refractive multifocals use zones of different power, so their performance depends on pupil size and centration.
• Extended depth of focus lenses stretch a single focus over a range of about 1 to 1.5 D, giving good distance and intermediate vision with fewer haloes but limited near vision.
• Monovision with monofocal lenses (one eye for distance, the other a little myopic) is a well-tolerated alternative.

The light that is out of focus is not lost from the retina: it veils the focused image, lowering contrast sensitivity and causing haloes and glare around lights at night. A defocus curve, acuity against the distance looked at, shows the trade:

Good candidates are motivated patients with otherwise healthy eyes. Macular disease, glaucoma with field loss, irregular corneas and heavy night driving argue against diffractive multifocals, and residual astigmatism or refractive error, dry eye and posterior capsule opacification all reduce their benefit. Other approaches include small-aperture lenses, which extend depth of focus by the pinhole effect, and the light-adjustable lens, whose power is refined after surgery with ultraviolet light.

#Aspheric lenses

The average cornea has positive spherical aberration (Chapter 5). A young crystalline lens partly cancels it, but a spherical IOL adds more. Aspheric IOLs with negative spherical aberration offset the cornea’s and improve contrast with large pupils; aberration-neutral designs add none and are more forgiving of decentration and tilt.

#Materials and design

• PMMA: rigid, needing a large incision; still used for some anterior chamber and sulcus lenses.
• Silicone: foldable, but silicone oil clings to it, so it is avoided in eyes likely to need vitreoretinal surgery.
• Hydrophobic acrylic: the commonest material. Higher refractive indices allow thinner lenses. Small fluid-filled vacuoles, glistenings, can appear within the optic, usually without affecting vision.
• Hydrophilic acrylic: can calcify, especially after gas is injected into the anterior chamber, as in endothelial keratoplasty.

A sharp, square posterior optic edge reduces posterior capsule opacification by blocking migrating lens epithelial cells. Some lenses add a yellow chromophore to filter blue light; a protective benefit for the macula has not been shown.

#Dysphotopsias

Positive dysphotopsia is unwanted light: streaks, arcs, flashes or haloes, often from internal reflections at the edge of a square-edged, high-index acrylic lens. Negative dysphotopsia is a dark temporal crescent or shadow, typically after uncomplicated in-the-bag implantation; one explanation is a gap on the nasal retina between light refracted by the optic and light passing outside it. Both often fade with time. Persistent negative dysphotopsia may respond to placing a lens or the optic in front of the anterior capsule (a sulcus piggyback or reverse optic capture) or to a nasal anterior capsulotomy; persistent positive dysphotopsia may need exchange for a lower-index lens with a rounded edge.

#Children

A child’s eye keeps growing and becomes more myopic, so the IOL is chosen to leave the child hyperopic, more so the younger the child, with the residual corrected by glasses (in the Infant Aphakia Treatment Study, +8 D at 4 to 6 weeks of age and +6 D up to 6 months). In infants aged 1 to 6 months with a unilateral congenital cataract, that randomised trial found no difference in visual acuity at 4½ years between IOL and contact lens correction, but more adverse events and additional surgery with the IOL.

#Recap

• IOL power = $\frac{1336}{\text{AL}-\text{ELP}}-\frac{1336}{1336/K-\text{ELP}}$; SRK: P = A − 2.5 AL − 0.9 K.
• 1 mm of axial length ≈ 2.35 D (more in short eyes); 1 D of K ≈ 1 D. Applanation shortens the axial length: myopic surprise.
• After myopic LASIK, standard calculations give a hyperopic surprise (instrument, index and formula errors); after hyperopic LASIK, myopic.
• Sulcus: about 1 D weaker for average powers; only lenses designed for the sulcus, never a single-piece acrylic. AC lens: about 3 D weaker. Secondary piggyback ≈ 1.5 × a hyperopic error, 1.2–1.3 × a myopic one.
• Toric IOL: IOL-plane cylinder ≈ 1.46 × corneal-plane; allow for the posterior cornea (about 0.3–0.5 D ATR); rotation leaves $2C\sin \theta$.
• Multifocals trade contrast and night haloes for range; choose healthy eyes and motivated patients.
• Positive dysphotopsia: square-edged, high-index lenses. Negative: a temporal shadow after in-the-bag lenses.

#Test yourself

#Further reading

• American Academy of Ophthalmology, Basic and Clinical Science Course, Section 3 (chapter on intraocular lenses) and Section 11: Lens and Cataract.
• K. J. Hoffer (ed.), IOL Power. SLACK.
• S. R. Lambert et al., Comparison of contact lens and intraocular lens correction of monocular aphakia during infancy (Infant Aphakia Treatment Study). JAMA Ophthalmology 132 (2014) 676–682.