Using Eye Models to Design Optical Treatments and/or Slow Progression

of the Myopic Eye

David A. Atchison

School of Optometry & Vision Science and

Institute of Health & Biomedical Innovation Queensland University of Technology

Brisbane, Australia

Content

Peripheral refraction theories of myopia development Ophthalmic treatments

§  Spectacle lenses §  Contact lenses

Eye model for adult myopia Designing lenses An option to using eye models

Peripheral refraction theories of myopia development

Optical treatments referred to are those that manipulate peripheral refraction One popular theory is that peripheral hyperopia can lead to the development of myopia, so the treatment involves adding peripheral positive power to induce peripheral myopia Alternatives to this theory are - that the eye grows until there is a balance between the tangential and sagittal shell errors (if this is possible) - that eye growth is caused by low �cone� activity when low image contrast occurs (Thibos) These theories could mean having either additional positive or additional negative power in the periphery

Ophthalmic treatments

The common ophthalmic treatments are spectacle lenses and contact lenses

For spectacle lenses, we can vary the surface curvatures and asphericities to manipulate peripheral power

For contact lenses, there are usually one or more fewer degrees of freedom because the lens must fit well onto the eye

Ophthalmic treatments - spectacles

Conventional spectacle lens design is concerned with the eye rotating behind the lens so that wherever you look through the lens there is good foveal vision Coddington raytracing equations (n’cos2I’)/t’ – (ncos2I)/t = ct(n’cosI’ – ncosI) ΔT = 1/t’ – F = T’ – F n’/s’ – n/s = cs(n’cosI’ – ncosI) ΔS = 1/s’ – F = S’ – F The eye takes no part in the design apart from providing the effective aperture stop (center-of-rotation) and the correction that must be achieved by the lens Eye aberrations are small compared with tangential and sagittal lens power errors

Ideal image surface (far point sphere)

θ

Center of rotation of eye

T’ S’

Foveal vision and rotating eye

Ophthalmic treatments – spectacles (cont.)

For peripheral vision, effective aperture stop for the lens is the eye entrance pupil If eye rotates, peripheral correction may be lost and foveal vision will be poor. As a compromise, a small part of the lens at the central (eg 10 mm wide) may be concerned with foveal correction with a fairly constant power. The peripheral refraction of the eye must be considered (not shown here)

Entrance pupil of eye

T’

S’

Peripheral vision and stationary eye

Ophthalmic treatments – contact lenses

Unlike spectacle lenses, contact lenses rotate with the eye The effective stop for the lens is the eye entrance pupil - much of the lens is used for both foveal and peripheral vision Aberrations associated with lens surfaces are high for both central and peripheral vision, and producing effects in the periphery may compromise central vision Again, the peripheral refraction of the eye must be considered

Entrance pupil of eye

T’

S’

Peripheral vision and stationary eye

Eye model for adult myopia One way to design ophthalmic corrections for myopia is to include eye model based on measurements in a population e.g. Atchison 2006, VR:

§  Four refracting conicoidal surfaces with gradient index in lenses

§  Both a co-axial form and one in which the lens and retina are tilted and decentred

§  Anterior cornea steepens as myopia increases

§  Vitreous length (and axial length) increase as myopia increases

§  The retina is oblate (steepens away from the vertex), but becomes less oblate as myopia increases §  flatter along the vertical than along the horizontal meridian

Eye model for adult myopia (cont.)

SR is spectacle refraction

medium refractive index

radius of curvature (mm)

asphericity Q Distance to next surface (mm)

air 1.0

+7.77 + 0.022SR –0.15

cornea 1.376 0.55

+6.4 –0.275

aqueous 1.3374 3.15

+11.48 –5

anterior lens

1.44

1.416 – 0.037r2 infinity

posterior lens

2.16

–5.9 –2

vitreous 1.336 16.28 – 0.299SR

x: –12.91 – 0.094SR y: –12.72 + 0.004SR

x: +0.27 + 0.026SR y: +0.25 + 0.017SR

retina

z position (mm)

0 5 10 15 20 25 30

x/y

posi

tion

(m

m)

-15

-10

-5

0

5

10

15

cornea emmetrope

x 10D myope y 10D myope

Designing lenses

Raytrace from retina back out of eye and through ophthalmic lens Useful to see what happens when parameters of eye are manipulated

Manipulate the lens parameters to achieve desired outcome Because of the theory that peripheral hyperopia leads to myopia, most lenses have additional positive power in the periphery, similar to what is being done with distance-centre bifocal contact lenses

Designing lenses (cont.)

Positive power (negative refraction) in periphery of lens-eye combination

T’

S’

Designing lenses - some results Refraction results for different forms of ‒4 D spectacle and contact lenses with the model eye along the horizontal field meridian n Spectacle lens F1 = 0D - considerable peripheral hyperopia n Spectacle lens F1 = +4 D (very steep) - negligble peripheral refraction. A yet more curved lens or adding asphericity is needed to produce peripheral myopia n The soft contact lens with spherical surfaces provides considerable peripheral myopia and the aspheric version provides little effect. n Lens design affects astigmatism

Angle (degrees)

0 10 20 30 40

90-1

800

astig

mat

ism

J18

0 (D

)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

mea

n sp

here

M (D

)

-1.0

-0.5

0.0

0.5

1.0

SL - plano base SL - 4D base CL - Q 0 CL - Q -0.25

SL - plano base SL - 4D base CL - Q 0 CL - Q -0.25

-4 D lenses

-4 D lenses

An option to using an eye model

If the peripheral refraction of the eye is known or can be predicted, an eye model is not needed Instead, the peripheral refraction of the eye can be combined with the peripheral power of the lens This is useful if the eye model has shortcomings e.g. mine overemphasises oblique astigmatism by about 50% and does not show all of the mean sphere difference between horizontal and vertical field meridians

An option to using an eye model (cont.)

Eccentricity (degrees)

-40 -30 -20 -10 0 10 20 30 40

M (D

)

-10

-8

-6

-4

-2

0

Temporal Nasal

+0.75 to-0.50 (n = 32/12)

-0.61 to -1.50 (n = 24/8)

-1.61 to -2.50 (n= 16/2)

-2.61 to -3.50 (n = 12/7)

-3.61 to -4.50 (n = 7/3)

-4.61 to -5.50 (n = 7/2)

-5.61 to -6.50 (n = 7/3)

-6.61 to -12.00 (n = 11/5)

Data of peripheral refraction along the horizontal meridian(Atchison et al. 2006, Vision Res) give equations ΔM(K) = ‒(0.000206K + 0.00027)θ2

J180(K) = ‒(0.00023K + 0.00098)θ2

ΔM(K) relative spherical equivalent refraction of eye J180(K) = astigmatism of eye K is on-axis refraction θ is angle of light out of eye in degrees

An option to using an eye model (cont.)

ΔM(K) = �(0.000206K + 0.00027)θ2

J180(K) = �(0.000023K + 0.00098)θ2

Peripheral refraction for combined lens and eye are given by ΔM ≈ ΔM(K) – (ΔT + ΔS)/2 J180 ≈ J180(K) � (ΔT � ΔS)/2 ΔΤ, ΔS are tangential and sagittal power errors of lens Lens can be manipulated to get the desired peripheral refraction

An option to using an eye model – example

Angle (deg)

Pow

er (D

)

-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Ray Traced Power

Horizontal Power

Vertical Power

Power (D)

0.501.001.502.002.503.003.504.00

0.00-0.50-1.00-1.50-2.00-2.50-3.00-3.50-4.00

Vertical TargetVertical Lens

Horizontal TargetHorizontal Lens

Nasal Field

Temporal Field

Lens designed and made to correct my right eye along the horizontal field (Atchison et al. 2013, OVS)

An option to using an eye model – example (cont.)

Horizontal grating

-30 -20 -10 0 10 20 30

Gra

ting

Acu

ity (l

og(3

0/SF

))

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2best correction correction on-axisspecial lens

Vertical grating

temporal Visual Field Angle (degrees) nasal

-30 -20 -10 0 10 20 30

Gra

ting

Acu

ity (l

og(3

0/SF

))

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2best correctioncorrection on-axisspecial lens

On-axis correction Variable loss, up to 0.4 log (2.5 times) in temporal field Special lens Largely restores acuity

THE END

Best correction Off-axis acuity H gratings > V gratings Asymmetric with steady loss in nasal field, but little variation in temporal field 10-30° On-axis correction Variable loss, up to 0.4 log (2.5 times) in temporal field Special lens Largely restores acuity Poor at 5, 10°temporal for H grating Improved at 20-30°temporal for H grating!

Results - grating acuity

Horizontal grating

-30 -20 -10 0 10 20 30

Gra

ting

Acu

ity (l

og(3

0/SF

))

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2best correction correction on-axisspecial lens

Vertical grating

temporal Visual Field Angle (degrees) nasal

-30 -20 -10 0 10 20 30

Gra

ting

Acu

ity (l

og(3

0/SF

))

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2best correctioncorrection on-axisspecial lens

Aberration-free forms

Lens power (D)

-50 -40 -30 -20 -10 0 10 20

Bac

k su

rfac

e po

wer

(D

)

-60

-50

-40

-30

-20

-10

0

peripheral, no J180peripheral, no DM

K -4 D, K2 -6 D

+ve DM reduces-ve J180 increases

K -4.0 D, K2 -6 D

angle (degrees)

0 5 10 15 20 25 30 35

Per

iphe

ral r

efra

ctio

n (D

)

-1.0

-0.5

0.0

0.5

1.0

1.5 Q2 0, J180Q2 0, DMQ2 +17, J180Q2 +17, DMQ2 -19, J180Q2 -19, DM

Peripheral refraction theories of myopia development

Optical treatments referred to are those that manipulate peripheral refraction The popular idea that peripheral hyperopia can lead to the development of myopia is based on a misunderstanding of Hoogerheide et al (1971). It is widely believed they found that young male hyperopes and emmetropes with peripheral hyperopia went on to develop myopia However, they measured peripheral refraction after people did, or did not, develop myopia Recent longitudinal studies have not been able to find that relative peripheral hyperopia leads to progression of myopia. One study found weak evidence that relative peripheral myopia was a protection against developing central myopia.

nM0 young children, 30° temporal fieldy = +0.17x - 0.46, R^2 0.051, p < 0.001

Relative peripheral refraction (D)-4 -3 -2 -1 0 1 2 3 4 5

Cen

tral

ref

ract

ion

chan

ge a

t 1-y

ear

(D)

-3

-2

-1

0

1

2

3Atchison et al., 2015 IOVS

Eye models

Li et al. (IOVS 2015)

Chinese children

≈ 2000 7-year olds

≈ ≈ 2000 14-year olds

7-year

14-year

emmetropic eyes 5 D myopic eyes

posterior cornea

retina

n  One way to design ophthalmic corrections for myopia is to include an eye model based on measurements in a population

n  This is a 3 refracting eye model that I helped develop for Chinese children n  This is inadequate for the purpose because it is a paraxial model only – in

particular, it lacks a curved retina

GROW! STOP!

Hyperope accommodating 1 D

Emmetrope, corrected

GROW! STILL GROWING! STOP, BUT TOO LATE

Future myope, while still hyperopic

Future myope, while emmetropic

Myope with correction

Initially uncorrected myopes become corrected biomechanical limitation no biomechanical limitation

STOP! STILL GROWING!

z2

1/L 1/L2’

image surface

θ’ y

Lens power K, back surface power K2, refractive index n

1/L’

Center of rotation of eye

T’ S’

Foveal vision and rotating eye

Entrance pupil of eye

T’

S’

Peripheral vision and stationary eye

Peripheral refraction theories of myopia development (cont.)

Alternatives to this theory are - that the eye grows until there is a balance between the tangential and sagittal shell errors (if this is possible) - that eye growth is caused by low �cone� activity when low image contrast occurs (Thibos)