Pediatric Patients
CUSTOMIZED IOL POWER
As discussed earlier, the refractive error (De) is governed by the product of (m1N1) and (m2N2), or by both of the refractive rate function (mj) and the axial length growth rates (Nj) which must be personalized, particularly for those eyes having the (mjNj) values deviating too much from the typical values of m1=0.5 m2, N1=0.2 N2, and m2=2.7 (D/mm), N2=0.3 (mm/year).
As illustrated in Figure 21.3, the Lin’s double-rate growth theory provides two situations (a) for fixed Nj, higher mj develops higher myopia progress; and (b) for
Fig. 21.3: Myopia power (De) progress versus age (A) in Lin’s double-rate theory for two cases: (a) fixed axial growth rate N=dL/dA (mm/year), comparing high and low m = -dDe/dL (diopter/mm); (b) fixed m, and comparing high and low N
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fixed mj, higher Nj results higher myopia. Therefore, the adjusted under-corrected IOL-power, P=Po-Dadj, should be customized accordingly, where Po is the IOL-power for emmetropia.
For example, for different vitreous cavity length X=(16, 18, 20) mm, one may use the emmetropic-state condition Pt=1336/(X/Z) to find m2=(3.4, 2.7, 2.2) (D/mm), respectively, for a typical value of Z=0.806. Therefore, for given axial growth rates of N1 and N2, short vitreous cavity eyes (or smaller X) having a higher (about 25%) m2 values would suffer greater myopia. In comparison, longer X (or L, say X=20 mm) having a smaller m2 would have a narrower range of myopia progress and can be easily adjusted. Furthermore, as shown in Figure 21.1 and Eq.
(1.c), m2 is proportional to the square of the total power Pt, or the implanted IOL-power which is age (Ao) dependent.
On the other hand, for a fixed mj rates, the higher Nj rates (with N2 > 0.4 mm/yr) would also suffer greater myopia and more difficult to be adjusted. Therefore, a true customized IOL-power should be adjusted not just by the age of surgery (Ao) (proposed by Wilson et al 5), but also by the individual rates (mj)(Nj), to be discussed further.
The Adjusted IOL-power
The age-adjusted De of Wilson et al is shown in Table 21.1 for various age when the cataract surgery is performed (Ao).
According to Lin’s formula, Dadj = B(Po-P), with Po being the IOL-power for plano (at age Ao), and B is a conversion factor having typical values of B = 0.7 and 0.816 for S = 5.0 and 3.0 mm, respectively.
According to Lin’s double-rate theory, the above mean Dadj should be further revised by 5 to 15% lower or higher for lower mN and higher mN which should be estimated pre-operatively. The new adjusted De should count for (mN) value deviating up to 50% of the mean (typical) values of (m2N2)=2.7 × 0.3 = 0.8 (D/year) and (m1N1)=1.39 × 0.03 = 0.03 (D/year), for dS = 0.1dX, or N1 = 0.1N2 (for age 0 to 3) and dS = 0 (for age 3 and up).
It was reported by Vasavada for the rate of axial growth after congenital cataract surgery5 depends on the
age at surgery (Ao). The 5-year average growth of axial length (dL) is reported as: dL = 4.04 mm (for Ao<1 year);
1.07 mm (for Ao = 1 to 3 years); 0.97 mm (for Ao = 3 to 10 years).
In above examples, the mean N2 = (4.0, 1.0, 0.3) (mm/
yr), respectively, for various As ranges if one ignores the contribution from N1. Therefore, the corresponding myopia induced due to dL is given by De = -M(dL) = -(9.0, 4.0, 1.5) diopter, respectively, for a mean M = 2.8 (D/mm), where M = m2 when dL = dX (with dS = 0).Based on these data, the IOL-power should be adjusted by –De to compensate the myopic-shift after cataract/IOL. These reported values, however, are only good for average over the studied subjects. For individual eyes, these adjustment should also consider the personalized values of M and N. It should be noted that M (or m2) is proportional to the square of the total power of the pseudophakic which decreases by age as shown in Figure 21.1.
Adjusted Factors
Depending on the environment factors such as nearwork of the patient, the personalized Dadj for teenagers (A=10 to 18) may be pre-estimated based on the historical values for age between 10 and 12 years. In other words, the above Table for Dadj (for age 6 to 14) should be further adjusted for eyes with abnormal axial growth rate due to nearwork.
Other factors impacting the Dadj are summarized as follows (see also Fig. 21.4):
a. Genetic factor: abnormal axial growth rate of (N1, N2) may occur for children having myopic parent (one or both). Greater Dadj than the mean value shown in Table 21.1 are needed.
b. IOL-power (Po) for emmetropia at surgery age (Ao):
For the same age child but having different Po, a higher Po would result in higher value of m2, as shown by Eq.
(1.c). Therefore, the myopic progress would be more for the same axial growth rate (N). The mean Dadj in Table 21.1 should be revised based on the following (Fig. 21.5).
For a posterior implanted IOL (with S=5.0 mm), the typical parameters for (L, X, P’, Po) meeting the emmetropic condition are shown as follows:
Table 21.1: The adjusted mean power (Wilson et al, 2005) at age of surgery (Ao)
Ao (year) 0.1 0.2 0.4 1-2 2-4 4 5 6 7-10 10-14 >14
Dadj (Wilson) +12 +9 +8 +6 +5 +4 +3 +2 +15-1.0 +0.5 plano
Fig. 21.4: Flowchart of factors for the adjusted IOL-power calculation (Dadj) shown in Table 21.1 (see also text)
Fig. 21.5: The adjusted IOL-power (Dadj) versus cataract surgery age (Ao) for emmetropic. IOL-power (Po) being higher than equal to, or lower than the mean value, shown by curve (a), (b) and (c), respectively
A (year) L X P’ Po
0 17 12 45 57
1-2 19 14 44 43
3-6 21 16 43 32
>10 24 19 43 23
For individual ocular parameters (or IOL-power needed for emmetropia) deviated from the above “mean”
values, the adjustment of Dadj may be calculated based on the following situations.
(i) For same P’, but different Po due to different X:
dM = (2Z2/X)(dPo) = C(dPo), (5.a)
dPo = Po’ – Po, (5.b)
which gives C = (0.07 – 0.12) for A = (0 – 14) year (for S=5.0 mm, Z=0.7). For example, for Po changes from 40 to 50 D, a change of dM=(0.7 – 1.2) (D/mm) corresponding to the increase of about (1.0 – 1.8) D of Dadj is needed, (for axial growth (dL) of 1.5 mm.
(ii) For same X, but Po changes due to different P’:
dM = -(2ZS/X2)(dP’) = C’(dP’), (6) which gives C’ = (0.02 – 0.06) for A = (0 – 14) years. For example, corneal power change of dP’ = B(dPo) = 8.4 D, for IOL-power change of dPo=10 D, and dM=(0.17 – 0.5), or dDadj=(0.26 – 0.8) D is needed (for dL=1.5 mm) which is less sensitive to case (i).
(c) Corneal power (P’): The role of P’ on m2 is calculated as follows: (for fixed IOL-power, P=30 D), m2=(3, 3.46, 3.9), for P’=(39, 43, 47). That is, a change of 10% of P’
results in about 12 to 13% change of m2.
(d) Implant position of IOL. The IOL-power for emmetropia (Po) is governed by the effective anterior chamber depth (S), axial length (L) and corneal power (P’) by
Po = 1336 / (L-S) – 1336 / (1336/P’ – S). (7) For example, L=23 mm and P’=43 D, Po=(19, 23) D, respectively, for anterior implanted IOL (such as in the ciliary suleus) with S=3.0 mm, and for posterior IOL (in lens capsular bag) with S=5.0 mm. Therefore, the m2 value is about 46% higher in posterior IOL which also requires a higher Dadj accordingly.
(e) Secondary IOL-power, P(2), may be calculated by a new formula of Lin which does not require the knowledge of axial length and is given by
P(2)=(Ppre-P”)/B, (8)
where Ppre is the pre-IOL refractive error and P” is the residual error, B is a conversion factor given by B=Z2, with Z=1-S(P’/1336), P’ being the corneal power. For example, for P’=43 D, B=(0.82, 0.7), for S=(3, 5) mm, respectively, depending on the secondary IOL position.
(f) For early age stage (0 to about 2 year), the rate function of the anterior chamber depth (m1) is proportional to the corneal power square, shown by Eq.(1.d). Therefore, steeper cornea results in a higher myopic progress due to the growth of S, the same trend as that of steep lens (or higher IOL-power), and a higher Dadj is needed. Figure 21.4 summarizes the above adjustment factors for revised Dadj accordingly.
Comparing to the Wilson’s Dadj (which is only valid for average population), the Dadj (new) of Lin is
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customized based on the estimated pre-operative rates functions m and N which, in general, are age dependent.
CONCLUSION
The myopic-shift after pediatric cataract surgery may be compensated by a new adjusted IOL-power which is age-dependent and governed by rate functions (mj and Nj, with j=1,2). In comparison to the mean-value method of Wilson et al, the Lin’s new Dadj is personalized by the measured (or estimated) pre-operative mj and Nj which may deviate from their mean (typical) values. Greater details for the discussion of Lin’s double-rate theory was published elsewhere.2
REFERENCES
1. Lin JT. The new IOL formulas based on Gaussian optics. In:
Garg A and Lin JT, Ed. Mastering IOLs: Principles and Innovations. New Delhi: Jaypee Brothers, 2006;56-65.
2. Lin JT. Analysis of refractive state ratios and the onset of myopia. Ophthal Physiol Opt 2006;26:97-105.
3. Wilson ME, Trivedi RH. Eye growth after pediatric cataract surgery. Am J Ophthalmol 2004;38:1039-40.
4. Trivedi RH, Wilson ME. Intraocular lens power calculation for children. In: Mastering the Techniques of IOL power calculations. Garg A et al, (ed). Jaypee Brothers: New Delhi 2005;98-108.
5. Vasavada AR, Raj SM, Nihalani B. Rate of axial growth after congenital cataract surgery. Am J Ophthalmol 2004;138:
915-24.
6. Gordon LA, Donzis PB. Refractive development of the human eye. Arch Ophthalmol 1985;103:785-89.