The problem of intraocular lens (IOL) power calculation in eyes that have had corneal refractive surgery is well known. This stems from the inability of instruments to measure the true corneal power in these eyes. With the increasing popularity and proliferation of various designs of phakic refractive IOLs to correct myopia and hyperopia, the question arises whether these IOLs will affect the results of normal ultrasound axial length (AL) measurements. I use the terms biphakia and biphakic to describe the state of a phakic eye with a refractive IOL regardless of its position in the eye. Because the speed of sound through the various materials of phakic IOLs is widely different and is different from the average velocity used to measure the eye, a variable but definite error occurs. This paper presents a method to correct this error.
Materials and Methods
Mathematical analysis of a phakic eye containing an artificial lens reveals that because the sound traveling through a phakic IOL travels faster or slower than the average speed at which the ultrasound unit is set to measure, the AL the instrument provides includes a false element in the total measurement. This is the phakic IOL thickness error (TE). To correct the AL, this error must be subtracted from the measured AL and then the actual true central thickness (TA) of the phakic IOL added back.
The TA can be obtained from the manufacturer. The Appendix shows the thickness of all commercially available phakic IOLs based on their power.
Next, the TE is calculated, starting with the fact that there is a directly proportional relationship between the TA of the lens and the true sound velocity (VA) of the material of the phakic IOL and the TE and incorrect velocity (VE) used by the ultrasound instrument. This can be expressed as
which means that
If we solve this equation for TE,
The value that must be subtracted can be determined by knowing the VA though the material of the phakic IOL and the velocity the instrument uses for the measurement. Many ultrasound instruments are set at average sound velocities from 1530 to 1560 meters per second (m/s); often they are set at 1550 m/s. Since 1974, I have used the mathematically determined average velocity of 1555 m/s, published in 1994,1 which is best for eyes with an AL in the normal range. That paper also gave the sound velocities through various IOL materials (Table 1).
Next, the erroneous value of thickness in equation 1 is replaced with that in equation 4 to produce
Pulling TA from the last 2 factors produces
Therefore, what must be added to the measured AL is the value (1 – VE/VA) multiplied by TA.
Using the ultrasound velocities of the materials from Table 1 and the average velocity of 1555 m/s for VE produces the values to be used, which are shown in Table 2. The correction value for Collamer IOLs is very small, with 11% of the phakic IOL thickness added to the AL. This will not have a major effect on AL in eyes with myopic phakic IOLs with very thin centers. In contrast, for silicone phakic IOLs, 59% of the thickness must be subtracted from the AL reading; this can be significant, especially with thick-centered hyperopic phakic IOLs (1.09 diopters [D]). For poly(methyl methacrylate) (PMMA) IOLs, 42% of the IOL thickness must be added and for acrylic IOLs, 23%.
Phakic IOLs have a variable effect on the ultrasound measurement of the AL. How much depends on the power of the IOL and its material. The greatest effect will occur with a silicone IOL in an eye with very high hyperopia, and the least effect will occur with a Collamer lens in an eye with very high myopia. As the central thickness of the only currently available myopic phakic IOL (Medennium, Table 2) is always 0.05 mm, 0.03 mm must be subtracted from the AL in eyes with a myopic silicone phakic IOL.
The premise of this formulation is based on using an average sound velocity of 1555 m/s for measuring the AL. Those who cannot change the velocity in their A-scan units may be concerned. I therefore analyzed the effect if the velocity used were as low as 1530 m/s (average velocity for a 30.0 mm eye) or as high as 1560 m/s (average velocity for a 20.0 mm eye). As seen in Table 3, the effect is so minimal that it need not be a concern. When measuring cases of extreme AL, it is appropriate to adjust for the change in average sound velocity. This can be done by changing the velocity on the A-scan instrument or by using the Holladay CALF method,8 which measures the eye at 1532 m/s (as if it were all aqueous–vitreous) and adding the CALF factor of 0.32 mm. Either way, the correction for the phakic IOL described is valid. Central thickness for the available dioptric ranges of 5 phakic IOLs are shown in the Appendix.
These formulations will be tested for accuracy in the real world by comparing AL measurements before and after implantation of phakic IOL of various materials and powers. But with the limitation of the errors in ultrasound accuracy, this may be more difficult to accomplish. The Zeiss IOLMaster may be a better means of comparison once the manufacturer provides the capacity for phakic IOL correction.
After the AL has been corrected by the above formula, it is important to use the correct formula to calculate the IOL power to be implanted. I recommend the Hoffer Q formula9 for eyes shorter than 22.0 mm, the Holladay 1 formula10 (not the Holladay 211) for ALs between 24.5 mm and 26.0 mm, and the SRK/T formula12 for those longer than 26.0 mm.
1. Hoffer KJ. Ultrasound speeds for axial length measurement. J Cataract Refract Surg 1994; 20:554-562
2. Arnold ND, Guenther AH. Experimental determination of ultrasonic wave velocities in plastics as functions of temperature. J Appl Polym Sci 1966; 10:731-743
3. Folds DL. Experimental determination of ultrasonic wave velocities in plastics, elastomers, and syntactic foam as a function of temperature. J Acoust Soc Am 1972; 52:426-427
4. Kono R. The dynamic bulk velocity of polystyrene and polymethylmethacrylate. J Phys Soc (Japan) 1960; 15:718-725
5. Asay JR, Lamberson DL, Guenther AH. Pressure and temperature dependence on the acoustic velocities in polymethylmethacrylate. J Appl Physics 1969; 40:1768-1783
6. Hartmann B, Jarzynski J. Ultrasound measurements in polymers. J Acoust Soc Am 1974; 56:1469-1477
7. Encyclopedia of Polymer Science and Engineering, 2nd ed. New York, NY, Wiley and Sons, 1989; Vol 1:147–149
8. Hoffer KJ. Modern IOL Power Calculations: Avoiding Errors and Planning for Special Circumstances. Focal Points, Clinical Modules for Ophthalmology. San Francisco, CA, American Academy of Ophthalmology, 1999; 17(12)
9. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993; 19:700-712; errata, 1994; 20:677
10. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988; 14:17-24
11. Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000; 26:1233-1237
12. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990; 16:333-340; correction, 528
Central thickness for the available dioptric ranges of 5 phakic IOLs.