It was in 1981, when KJ Hoffer addressed IOL calculation difficulties in short
eyes for the first time in his paper entitled 'Intraocular Lens Calculation: the
Problem of the Short Eye' [1]. In a certain working setup (applanation biometry,
Binkhorst IOL formula) calculated lens powers had turned out to be too strong
thus causing a postoperative myopization of about 0.5 dptr. With immersion
biometry and different calculation algorithms, the problem vanished.
Nevertheless, these findings triggered the formulation of the empirical SRK I
formula, which, in the late 80ies, was modified to become SRK II. The
modification consisted in turning the A-constant of SRK I into an axial length
dependent function in order to overcome the tendency of SRK I to
underestimate the IOL power in short eyes. This, however, did not solve the
problem: SRK II continued to create hyperopia in short eyes. So, finally, the
empirical approach was abandoned and the original authors - like others before
and after them - turned themselves to physiological optics and published their
modification of the thin lens formula as SRK/T formula in 1981. Today,
advances in surgical techniques and intraocular lens materials have broadened
the range of axial lengths for refractive surgical procedures. So, the short eye
problem will be revisited in the following with respect to biometry, keratometry
and IOL calculation. Special allowance will be made for angle closure glaucoma
eyes, since these eyes are often met in the short axial length range.

**Measurement problems in short eyes**
By 'short eyes' we shall understand eyes with axial lengths <= 22 mm. From a database survey
covering biometry data of 15124 cataract eyes it was found [2] that the short eye percentage
amounted to 11.1 % (cf Tab.1).

--------------------------------------------------------------------------------
axial length range [mm] AL <= 22 22 < AL < 25 AL >= 25
--------------------------------------------------------------------------------
anterior chamber AC [mm] 2.69 3.14 3.48
lens thickness LT [mm] 4.69 4.46 4.40
axial length AL [mm] 21.44 23.27 27.09
corneal radius RC [mm] 7.45 7.69 7.76
total n 1 678 11 812 1 633
percentage % 11.1 78.1 10.8
--------------------------------------------------------------------------------

**Tab.1: Incidence of short and long eyes in cataract patients: biometry and
keratometry data of n=15124 eyes (from [2]).**
Fig.1 shows a typical immersion A-scan of such an eye with an axial length of 19.2 mm. It has a
thick lens (4.9 mm) and a shallow anterior chamber (2.0 mm).

**Fig.1: Typical immersion A-scan of a short eye with anterior chamber depth AC=2.0 mm,
lens thickness LT=4.9 mm and axial length AL=19.2 mm.
**

Immersion scanning is to be preferred for axial length measurements, especially for short eyes.
First, with the corneal double peak echo clearly discernible, all 4 ocular landmark echoes (cornea,
lens front and rear, back wall) may be adjusted for optimal steepness thus achieving best
orientation; second, no danger of indenting the globe exists thus preventing the axial length from
being measured too short which would later result in a postoperative myopization.

Problems may also arise from some A-scan units which - in automatic biometry mode - might not
expect an anterior chamber as shallow and/or a lens as thick. The measurement may be rejected or
even faulty. Manual mode has to be selected in this case. Another source of errors is found in the
use of a mean sound velocity instead of individual velocities for each ocular compartment. A thick
lens will lead to an underestimation of the axial length. For example, with a popular setting of 1550
m/s, the axial length of Fig.1 would be given as 19.1 mm instead of 19.2 mm.

Due to the small anatomical dimensions, ultrasonic measurements are generally more sensitive to
systematic measurement errors. In addition, different A-scan devices may produce different axial
length results as a consequence of the individual technical design features of each instrument. The
same holds for the determination of corneal power by keratometry or corneal topography. Starting
from curvature data, different keratometer indices are used for the conversion into corneal
refractive power. A 7.5 mm radius, e.g. will translate into 44.3 dpt with an index of 1.332 (Zeiss
keratometer), whereas the keratometer index (1.3375) of widely used popular Javal type
instruments had been deliberately choosen to give a corneal power of 45.0 dpt for this very radius.

So, apart from being more difficult to obtain, short eye parameters are very sensitive to the
measurement setup, i.e. the biometry and keratometry devices used for their acquisition.

**IOL related problems in short eyes**
The intraocular lenses to be used for short eyes must usually have high dioptric powers (30 dpt or
more). Commonly, these powers are not readily available and the lenses themselves must be
especially designed and manufactured. With high-powered lenses a new problem starts to rise:
differences between total power and vertex power may not be neglected any more. Due to still
different power-labelling policies of IOL manufacturers, the diopter value for a given lens may
either denote total or back vertex power. Powers relate to the effective focal length (f', principal
plane to focal point) for total power and to vertex distance (back vertex to focal point) for vertex
power. To make things worse, these distances are dependent on the shape of the lens optic (cf.
Fig.2).

**Fig.2: Principal planes of lenses of different shape: 0: convex-plano, 1: biconvex with 1:1
ratio of anterior to posterior lens radius; 3: biconvex with 3:1 ratio. **

All lenses are situated in the same position (e.g. capsular bag). In order to focus onto the retina R, each lens
must have a different focal length f', i.e. different power.

**Fig.3: Difference between vertex power and total power vs total power for theoretical
lenses (PMMA, 7 mm optic) #1 and #3 of Fig.2. The image principal plane of the
asymmetric lens #3 is closer to its back vertex than for the equiconvex lens #1, thus, the
difference between vertex and total power is smaller than for lens #1 (cf. Fig.2).**

From Fig.3 it can be seen, that for a total power of about 30 dpt these differences may reach
nearly half a diopter for a biconvex IOL with a 3:1 radius ratio. So, two given lenses with the same
power label may optically behave completely different. Another geometry related effect can also be
seen from Fig.2: intraocular lenses of different shape, positioned at the same location require
different focal lengths i.e. different powers. An additional aspect worth noting is the fact that high
dioptric lenses literally are 'thick' lenses. IOL formulas, however, with the exception of empiric
algorithms like SRK I/II, are valid mathematically only for (infinitely) 'thin' lenses.

If the above described effects due to different biometry methods (applanation, immersion), different
keratometer calibrations und IOL related effects are combined for a short eye of 21 mm, refractive
errors of up to 2.4 dpt may result [3]. Half of this error can be attributed to IOL specifications.

How can all of these factors be made allowance for in a given clinical surrounding ? The total of the
individual biometry and keratometry intruments as well as the specifications of the individual lens
type used must be reflected in individualized lens constants. For the SRK II (see e.g. [4]) and
SRK/T formula [5], the constant to be individualized is the A-constant. Although, as has been
pointed out earlier, SRK II (and even more SRK I) should not be used any longer - especially not
for short eye calculations, this formula is still very popular. The lens constant of theoretical formulas
is related to the optical ACD and comes as ACD-constant, surgeon factor (in the HOLLADAY
formula) or personalized ACD (in the HOFFER Q). Theoretical formulas are based on geometrical
thin lens optics and are of the form (see e.g.[6]):

n n
DL = ----- - -------
L - d n/z - d
ref nC - 1
with z = DC + ----------- and DC = ------
1 - ref dBC RC
DL : IOL power
DC : corneal power
RC : corneal radius
nC : keratometer index
dBC : vertex distance between cornea and spectacles
ref : desired refraction
d : optical ACD
L : axial length
n : refractive index of aequeous and vitreous (1.336)

Theoretical formulas differ among each other by the individual recipes how biometric and
keratometric measurement data should be translated into the parameters L, d and DC of the above
basic formula.

Individualizing constants is equivalent to adjusting them so as to produce a mean zero prediction
error for not too small a data set of postoperative refractions. Instead of carrying out the
optimization for all axial lengths, better results may be obtained by using a triple individualization for
short, normal and long eyes ([7],[8]).

Another approach - advocated by us - is to use 3 constants a0, a1 and a2 in combination with the
preop ultrasonically measured ACD in order to predict the axial length dependence of the optical
ACD (cf e.g. [6]). Tab.2 summarizes some results of triple individualization for a silicone IOL.

--------------------------------------------------------------------------------
axial length range [mm] AL <= 22 22 < AL < 25 AL >= 25
--------------------------------------------------------------------------------
anterior chamber AC [mm] 2.80 3.26 3.58
axial length AL [mm] 21.76 23.38 25.56
corneal radius RC [mm] 7.47 7.73 7.83
total n 6 98 14
A-constant for SRK II 120.7 119.8 118.7
A-constant for SRK/T 119.6 119.3 119.2
--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
Haigis constants a0=2.137 a1=-0.026 a2=0.133
--------------------------------------------------------------------------------

**Tab.2: Biometric data and optimized IOL constants after triple individualization
for IOL model ADATOMED 90c after [7].**
With this concept, significantly different prediction curves for the optical ACD are obtained in Fig.4
for the three IOL models of Fig.2. For this calculation, an axial length dependent eye model has
been used ([9],[10],[11]).

**Fig.4: Optical ACD vs axial length for theoretical eye model and 3 model lenses (PMMA,
7 mm optic). Lens annotations as in Fig.2.
**

To improve the quality of IOL calculation in general and especially in short eyes, patients have to
be followed up and their stable postoperative refractions have to be measured. These values are
then taken to improve the (triple) individualization of lens constants. Thus, with every new patient,
the results will get better and more predictable.

**Measurements on glaucomatous eyes**
We retrospectively analyzed the results of IOL implantations in patients with short eyes (AL <= 22
mm) and shallow anterior chambers. Among them were 9 cases without glaucomatous history
respectively no optic disc damage and no loss of visual field. 3 patients were suffering from chronic
angle glaucoma, 4 had a history of acute angle closure and 11 eyes showed a primary open angle
glaucoma with narrow angle. The biometric findings for these patients are compiled in Tab.3.

--------------------------------------------------------------------------------
grp n AC [mm] LT [mm] AL [mm] LT/AL AC/LT
--------------------------------------------------------------------------------
1 9 2.03 ± 0.22 5.15 ± 0.61 21.33 ± 0.43 0.241 ± 0.028 0.404 ± 0.086
2 3 2.02 ± 0.06 5.51 ± 0.34 21.39 ± 0.04 0.257 ± 0.015 0.368 ± 0.032
3 4 1.79 ± 0.14 5.61 ± 0.42 21.08 ± 0.76 0.266 ± 0.014 0.323 ± 0.050
4 11 2.18 ± 0.23 5.29 ± 0.55 21.82 ± 0.58 0.242 ± 0.026 0.421 ± 0.087
--------------------------------------------------------------------------------

**Tab.3: Biometric findings in 27 short eyes <= 22 mm. Group 1: normal; group 2:
chronic angle closure glaucoma; group 3: acute angle closure glaucoma. group 4:
primary open angle glaucoma with narrow angle.**
It is well known that lens thickening with age contributes to the possibility of angle closure
glaucoma ([12], [13]). WOLLENSAK et al. [13] observed the mean lens thickness in angle
closure glaucoma to be 0.5 mm greater than in normal eyes. We found a mean difference of +0.32
mm in lens thickness between eyes with acute angle closure glaucoma and primary open angle
glaucoma and a value of +0.22 mm for the difference between chronic closure glaucoma and
primary open angle glaucoma.

The lens thickness/axial length factor LT/AL (LAF) which is mentioned in literature as an indicator
for potential risk of angle closure (>0.229) ([12],[13],[14]) was higher in all our groups (between
0.241 (normal and primary open angle glaucoma) - 0.266 (acute angle glaucoma)). This may be
due to the small sample numbers and the extremely short eyes of our groups.

The ratio AC/LT between the anterior chamber and the lens thickness was 0.323 in those eyes
which had already suffered an acute angle closure attack. Chronic closure glaucoma eyes showed
this ratio to be 0.368, whereas normal (0.404) and glaucomatous eyes without a closure history
(0.421) presented with a higher ratio. Again, the statistical significance out of such small samples is
questionable.

The patients of groups 1 - 4 were supplied with 11 RAYNER 755U lenses and 10 memory lenses
type MENTOR U940A. The prediction errors of postoperative refraction (true refraction -
calculated refraction) for these cases is summarized in Tab.4.

--------------------------------------------------------------------------------
true - calculated refraction [dpt]
grp IOLs implanted optimized default
--------------------------------------------------------------------------------
1 5 x RAYNER 755U +0.47 ± 0.62 -0.19 ± 0.57
2 3 x MENTOR U940A no useful refraction measurable
3 2 x RAYNER 755U -0.48 ± 1.25 -0.96 ± 1.28
2 x MENTOR U940A -2.14 ± 1.50 -2.09 ± 1.44
4 4 x RAYNER 755U -0.09 ± 0.67 -0.78 ± 0.61
5 x MENTOR U940A -0.05 ± 1.03 -0.58 ± 0.95
--------------------------------------------------------------------------------

**Tab.4: Prediction error of postoperative refraction (true refraction - calculated
refraction) for short eyes with and without optimization of lens constants.**
Refraction was calculated using the manufacturer's constant (755U: A=118.0, 940A: A=119.0,
denoted by 'default' in Tab.4) as well as the optimzed constants a0, a1, a2 ('optimized' in Tab.4),
which were derived earlier from the stable postoperative refractions of two different patient groups
(n=13 for MENTOR U940A, n=83 for RAYNER 755U). The individual axial length dependences
of the optical ACDs of the 2 lenses are depicted in Fig.5. The different axial length behaviour is
clearly visible.

**Fig.5: Optical ACD vs axial length for theoretical eye model and real lenses RAYNER
755U (755) and MENTOR 940A memory lens (940).**

Although, as already mentioned, the group totals are rather small, an optimization effect can clearly
be seen in group 4 (cf. Tab.4).

In general, without individualization of constants, the calculated
refractions tended to be more myopic.

For more reliable results, the number of followed up patients with short eyes and glaucoma
conditions has to be increased. This is done in a continuing study.

[1]: HOFFER KJ (1981) Intraocular lens calculation: the problem of the short eye. Ophthalmic
Surg 12 (4): 269-272

[2]: HAIGIS W (1996) Biometrie bei komplizierten Ausgangssituationen, in: 9.Kongr. d. Deutsch.
Ges. f. Intraokularlinsen Implant., Kiel 1995, Springer-Verlag, Berlin, Heidelberg, New York,
17-26, 1996

[3]: HAIGIS W (1995) The short eye problem - revisited. Lecture presented at 13th Congress of
the European Society of Cataract and Refractive Surgeons, Amsterdam, Oct. 1-4, 1995.
Publication in preparation.

[4]: HAIGIS W (1998) IOL calculation using the SRK II formula :
http://www.augenklinik.uni-wuerzburg.de/uslab/ioltxt/srk2e.htm. Last revision: Feb.12, 1998.

[5]: RETZLAFF J, SANDERS DR, KRAFF MC (1990): Development of the SRK/T intraocular
lens implant power calculation formula. J Cataract Refract Surg 16 (3): 33-340

[6]: HAIGIS W (1998) IOL calculation according to HAIGIS :
http://www.augenklinik.uni-wuerzburg.de/uslab/ioltxt/haie.htm. Last revision: Feb.12, 1998.

[7]: HAIGIS W, DUZANEC, Z, KAMMANN J, FISCHER A (1997) Klinische
Individualisierung von IOL-Konstanten, in: Vörösmarthy D, Duncker G, Hartmann Ch (Hrsg):
10.Kongr.d. Deutsch. Ges. f. Intraokularlinsen Implant., Budapest 1996, Springer-Verlag, Berlin,
Heidelberg, New York, 281-287

[8]: HAIGIS W, DUZANEC, Z (1995) Clinical individualization of IOL constants for lenses of
different geometry. Lecture at ASCRS Symposium on Cataract, IOL and Refractive Surgery,
Apr.1-5, 1995, San Diego, California, USA

[9]: HAIGIS W, HARTMANN J (1996) Theoretical eyes from biometric data and their use in
IOL calculations. In: Proc. of the 16th biannual Congress of SIDUO (Societas Internationalis pro
Diagnostica Ultrasonica in Ophthalmologia), München, June 2-6, 1996, G Hasenfratz et al (Hrsg),
in print

[10]: HAIGIS W (1995) Lens shape, IOL constants and the calculation of intraocular lens power.
Lecture at ASCRS Symposium on Cataract, IOL and Refractive Surgery, Apr.1-5, 1995, San
Diego, California, USA

[11]: HAIGIS W (1998) Lens shape and ACD prediction in IOL calculation. In: SIDUO XVII:
Proc. of the 17th Biennial Congress of the International Society for Ophthalmic Ultrasound, June
7-11, 1998, Los Angeles, California, USA. HJ Shammas (ed), in print

[12]: MARKOWITZ SN, MORIN JD (1984) Angle closure glaucoma. Relationship between lens
thickness, anterior chamber depth, and age. Can. J. Opthalmol. 19:300

[13]: WOLLENSAK J, ANDERS N (1992) Biometrische Daten von Augen nach Glaukomanfall.
Klin. Monatsbl. Augenheilkd. 201:155-158

[14]: PANEK WC, CHRISTENSEN RE, LEE DA, FAZIO DT, FOX LE, SCOTT TV (1990)
Biometric variables in patients with occludable anterior chamber angle. Am. J. Ophthalmol.
110:185-188