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
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)