ASCRS 2010 April 9 – 14, 2010, Boston, MA, USA On the origin of the corneal data in the Gullstrand eye Wolfgang Haigis, MS PhD AssProf Dept. of Ophthalmology,

ASCRS 2010April 9 – 14, 2010, Boston, MA, USA

On the origin of the corneal datain the Gullstrand eye

Wolfgang Haigis, MS PhD AssProfDept. of Ophthalmology, University of Wuerzburg, Germany

The author has no financial interest in the subject matter of this poster

On the origin of the corneal data in the Gullstrand eyeBackground and Purpose

The Gullstrand eye

• is a theoretical (schematic) eye in different modifications (exact, simplified, without accommodation or under maximum accommodation),

• has been used for decades as an eye model for theoretical-optical calculations,

• serves as a basis for the calibration of ophthalmic instruments (e.g. keratometers, topographers, etc.

Question

• To which extent does the cornea of the Gullstrand eye reflect true biometric measurements ?

• Do applications and instruments based hereupon produce realistic results ?

W.Haigis 2010

Gullstrand eyeExact schematical eye in accommodative rest for optical

calculations

From: Siebeck R: Optik des menschlichen Auges. Springer Berlin Göttingen Heidelberg 1960

The Gullstrand theoretical eye provides exact data for all components of the optical system ‘eye‘, i.e. it gives intraocular distances, indices of refraction of the ocular media, and radii of curvature of the corneal and lenticular interfaces, together with the cardinal points (principal, focal and nodal points) of the eye.All this data describe a self-consistent model eye.

The exact schematical eye in accommodative rest is axially 1D hyperopic.

W.Haigis 2010

+

1

1

R

nCn

2

2 R

Cnn

☺ ?

The cornea is a meniscus lens with 2 surfaces. Both of them determine its refractive power, yet only the anterior radius is measured by kerato-metry. The posterior radius and thus the posterior surface power is not known.

Gullstrand eye and corneal powerKeratometer index for instrument calibration

Haigis W: Corneal power after refractive surgery with myopia: the contact lens method. J Cataract Refract Surg 29(7):1397-1411,2003

Deriving the corneal power from a measurement of the ante-rior corneal radius alone makes only sense if there is a fixed ratio between posterior and anterior radii of curvature. If this ratio is given by the

Gullstrand ratio R2/R1 = 6.8/7.7

then it is possible to calculate the corneal power K according

to

where KI : keratometer index and R1: anterior corneal radius.

It can be shown that with• KI =1.3315 (Zeiss index) the total (equivalent) power • KI =1.3375 (Javal index) the (back) vertex power

of the cornea is obtained.

(In eyes not following the Gullstrand ratio (e.g. after refractive

surgery), neither index produces any reasonable results.)

1

1 RKIK

Surface refractivepowers:

W.Haigis 2010

Hermann von Helmholtz1821-1894

On the origin of the corneal data in the Gullstrand eyeMethods

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909

Allvar Gullstrand1862-1930

MethodsLiterature research to trace down the numerical properties of the cornea of the Gullstrand eye to their individual origins, especially for the anterior and posterior corneal radii of curvature, the corneal thickness and the refractive indices of cornea and aqueous.

Gullstrand published his schematic eye(s) in a separate chapter entitled ‘Die Dioptrik des Auges‘ (Dioptrics of the eye) in Hermann von Helmholtz‘s famous ‚Handbuch der physiologischen Optik‘ (Handbook of physiologic optics).

W.Haigis 2010

Gullstrand eye: refractive index of aqueous/vitreousMeasurement values from contemporary literature

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.285

• 1.3365 : own measurements by Gullstrand [1].• 1.338 : measurements by Chossat, cited in [1].• 1.3366 : measurements by Brewster, cited in [1].• 1.3420 : measurements by Krause, cited in [1] . • Comparative results from a compilation of various refractometric studies are cited in [2].

1.336 adopted by Gullstrand

[1]: H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Verlag von Leopold Voss, 1909, S.87

[2]: Freytag G. Vergleichende Untersuchungen über die Brechungsindizes der Linse und der flüssigen Augenmedien des Menschen und höherer Tiere in verschiedenen Lebensaltern. Wiesbaden 1907

W.Haigis 2010

Gullstrand eye: refractive index of the corneaMeasurement values from contemporary literature

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.279

• 1.3770 and 1.3721 : refractometrically measured on a 50 year old male and a baby aged 2 days by Aubert and Matthiesen [1].

• 1.3746 : calculated from measurement results for the individual corneal components [2].

• 1.3763 : last compilation by Matthiesen [3].

1.376 adopted by Gullstrand

[1]: Aubert H: Grundzüge der physiologischen Optik, Leipzig, 1876

[2]: Lohnstein Th: Über den Brechungsindex der menschlichen Hornhaut. Arch. f. d. ges. Physiologie. LXVI, 1897

[3]: Matthiessen L. Die neueren Fortschritte in unserer Kenntnis von dem optischen Baue des Auges der Wirbeltiere. Hamburg 1891

W.Haigis 2010

Gullstrand eye: corneal center thicknessMeasurement values from contemporary literature

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.280-282

• 0.482 – 0.668 mm: determined ophthalmometrically by Blix [1] for 10 eyes in vivo.

• 0.506 – 0.576 mm: results of Blix if 1 eye with extreme values is excluded (i.e.n=9).

• 0.46 und 0.51 mm: own measurements by A.Gullstrand [2] in vivo on 2 eyes of different subjects.

0.5 mm adopted by Gullstrand

[1]: Blix M: Oftalmometriska studier. Upsala Läkareförenings Förhandlingar. XV. 1880

[2]: H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Verlag von Leopold Voss, 1909

W.Haigis 2010

Gullstrand eye: anterior corneal radius RaMeasurement values from contemporary literature

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.272

• 7.858: (8.396 – 7.280) mm: average for 110 males (m) [1].• 7.799: (8.487 – 7.115) mm: average for 46 females (f) [1]. 7.829 mm: mean (m,f), adopted by Helmholtz [2] henceforth.

• 7.843 mm: average of 1916 Augen [3].• 7.723 mm: average [4] with n smaller than in [3].

7.80 mm (8.50 - 7.00) mm adopted by Gullstrand

[1]: Donders FC: On the anomalies of accommodation and refraction. London, 1864

[2]: Helmholtz H. Handbuch der Physiologischen Optik. 2. Auflage. Hamburg und Leipzig, 1885

[3]: Steiger A. Beiträge zur Physiologie und Pathologie der Hornhautrefraktion. Wiesbaden, 1895

[4]: Sulzer, zit, in: H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Verlag von Leopold Voss, 1909

W.Haigis 2010

Gullstrand eye: posterior corneal radius RpGullstrand‘s own measurements (n=6)

# Ra/Rp Rp/Ra Rp [mm] *)

1 1.1822 0.846 6.60

2 1.1811 0.847 6.60

3 1.1864 0.843 6.57

4 1.1734 0.852 6.65

5 1.1486 0.871 6.79

6 1.1427 0.875 6.83

mean ± sd 1.169 ± 0.019 0.856 ± 0.014 6.67 ± 0.11

Gullstrand‘s measurements of the ratio Ra/Rp with a keratometer according to Blix:

*): calculated for Ra = 7.8 mm (selected by Gullstrand as ‘ophthalmometric average‘ of contemporary measurements)

Tscherning, Lagrange et Valude. Encyclopédie d’ Ophthalmologie. III S.109, Paris 1904: Rp=6.5 mm

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.283-284

W.Haigis 2010

Gullstrand eye: corneal radii Ra and RpJustification for Gullstrand‘s choice of Ra and Rp

Ra = 7.80 mm: choosen as average from contemporary measurements.

Rp = 6.67 mm: obtained from own measurements (n=6).

Rp / Ra = 6.67 / 7.80 ≈ 6.70 / 7.80 = 0.859.

But: Rp / Ra = 6.80 / 7.70 = 0.883 adopted in final Gullstrand eye.

Gullstrand‘s reasoning: Measurements are performed in the optical zone (optical axis), not at the intersection of the cornea with the fixation axis. Due to the measurement, Rp/Ra is smaller than real, hence Rp must be larger and Ra must be smaller than measured.

Thus: Rp = measured value (6.7) + 0.1 mm = 6.8 mm.Ra = measured value (7.8) – 0.1 mm = 7.7 mm.

Rp = 6.8 mm, Ra = 7.7 mm adopted by Gullstrand

H. von Helmholtz: Handbuch der Physiologischen Optik. 3.Auflage, ergänzt und herausgegeben in Gemeinschaft mit Prof.Dr. A.Gullstrand und Prof.Dr.J.von Kries von Prof.Dr.W. Nagel. 1.Band, Hamburg und Leipzig, Verlag von Leopold Voss, 1909, S.285

W.Haigis 2010

On the origin of the corneal data in the Gullstrand eyeSummary and Conclusion

Summary

• Values for the optical properties (refractive indices, thickness, radii of curvatures) of the corneal system of the Gullstrand eye were mainly

derived from the scientific literature of the late 19th century.

• Only few measurements were performed by Gullstrand himself.

• Particularly the determination of the posterior corneal curvature is based on a very small number of measurements.

Conclusion

• Although the Gullstrand eye plays an important role as a self-consistent theoretial model eye in visual optics, it does not seem to be apt to serve as a realistic biometrical model for the cornea.

W.Haigis 2010