Numerical Studies of the Importance of Changes in Lens Geometry and Stiffness in

Causing Presbyopia

Harvey Burd - Department of Engineering Science, Oxford UniversityStuart Judge - Physiology Laboratory, Oxford University

ScopeA - Finite element model of the ageing lens; what

factors cause presbyopia?B - Preliminary model of lens-refilling procedures

Geometric model of the lens(See Burd, Judge and Cross 2002)

Rcb

RL

r

x

∆

TA

TP

tA

tP

hδ

Cortex

Nucleus

5th order polynomial

MRI Studies (Strenk et al. 1999)

Ciliary body diameter (mm)

0

5

10

15

20 30 40 50 60Age

Lens diameter (mm)

0

5

10

20 30 40 50 60Age

Ciliary body movement (mm)

0

0.5

1

20 30 40 50 60Age

Stiffness of Cortex and Nucleus(Fisher 1971)

0

1

2

3

4

5

0 20 40 60Age in years

E/10

00 (N

/m2 )

Cortex

Nucleus

Axisymmetric Finite Element Lens Meshes

29 year 45 year

δcbδcb

Capsule

Cortex

Nucleus Zonule

Deformed Mesh for 29 Year Lens

AccommodatedUnaccommodated

Computed optical power

22

24

26

28

30

32

34

36

38

0 0.1 0.2 0.3 0.4Ciliary body displacement (mm)

Lens

opt

ical

pow

er (D

)

29 Year45 Year

29 Year 45 YearLensAccommodationamplitude

9.49D 2.94D

EyeAccommodationamplitude

7.68D 2.38D

Bennett and Rabbetts (1998):

Eye accommodation amplitude

Lens accommodation amplitude= 0.81

Aqueous and vitreous refractive index = 1.336 Lens refractive index = 1.422

Factors Contributing to PresbyopiaChanges in:

(a) Lens, zonule and ciliary body geometry(b) Ciliary muscle activity(c) Lens stiffness(d) Capsule stiffness(e) Spatial variation of capsule thickness

Not included in this study:· Lens refractive index

Finite Element Parametric StudyA1 A2 A3 A4 A5 A6

Geometry 29 45 29 29 29 29Lens stiffness 29 29 45 29 29 29Capsule stiffness 29 29 29 45 29 29Variation of capsule thickness 29 29 29 29 45 29Ciliary body movement 29 29 29 29 29 45Eye accommodation amplitude 7.68D

B1 B2 B3 B4 B5 B6Geometry 45 29 45 45 45 45Lens stiffness 45 45 29 45 45 45Capsule stiffness 45 45 45 29 45 45Variation of capsule thickness 45 45 45 45 29 45Ciliary body movement 45 45 45 45 45 29Eye accommodation amplitude 2.38D

A1 A2 A3 A4 A5 A6Geometry 29 45 29 29 29 29Lens stiffness 29 29 45 29 29 29Capsule stiffness 29 29 29 45 29 29Variation of capsule thickness 29 29 29 29 45 29Ciliary body movement 29 29 29 29 29 45Eye accommodation amplitude 7.68D 3.55D 7.14D 7.44D 8.70D 6.03D

B1 B2 B3 B4 B5 B6Geometry 45 29 45 45 45 45Lens stiffness 45 45 29 45 45 45Capsule stiffness 45 45 45 29 45 45Variation of capsule thickness 45 45 45 45 29 45Ciliary body movement 45 45 45 45 45 29Eye accommodation amplitude 2.38D 5.40D 2.64D 2.62D 2.05D 3.57D

1

2

345

A Factorial Model for Presbyopia

CTCSLSCBG fffffAA 29

45 =

A45= Amplitude of accommodation of 29 year eye

A29 = Accommodation amplitude of 45 year eye

= 2.2

= 1.3

= 1.1

= 1.06

= 0.91

fG = Geometry factor

fCB = Ciliary body amplitude factor

fL = Lens stiffness factor

fCS = Capsule stiffness factor

fCT = Capsule thickness factor

Performance of the Factorial Model

Accommodation Amplitude

0

2

4

6

8

10

0 2 4 6 8 10

Finite element analysis (D)

Fact

oria

l mod

el (D

)

29 Year45 Year

A Factorial Model for Presbyopia

CTCSLSCBG fffffAA 29

45 =

A45= Amplitude of accommodation of 29 year eye

A29 = Accommodation amplitude of 45 year eye

f

fG = Geometry factor = 2.2

CB = Ciliary body amplitude factor = 1.3

fL = Lens stiffness factor = 1.1

fCS = Capsule stiffness factor = 1.06

fCT = Capsule thickness factor = 0.91

B - Preliminary model of lens-refilling procedures

Step 1

Initial geometry for 84 year lens

Step 2

Injection of liquid polymer at pressure

PInternal pressure, P

Steps 3 and 4 - Curing the injected polymer

E = 3.6 kPaν = 0.49999

Step 3

Increase lens stiffness to

simulate curing of the polymer

Step 4

Remove injection pressure

Step 5 - Simulate stretching of the lens

Step A

Apply new boundary conditions

Step B

Stretch the lensδcb = 0.6 mmδcb = 0.6 mm

24

26

28

30

32

34

36

-0.1 0 0.1 0.2 0.3 0.4 0.5Lens equator radial displacement (mm)

Lens

opt

ical

pow

er (D

)

Polymer injection

Stretching

Start of injection

Stretched state

Results of Polymer Refilling Model

Polymer curing

Koopmans et al. (2003). IOVS

Stretching device Results

Results of finite element

model

Conclusions

(a) Based on data used for the study, lensgeometry and ciliary muscle activity are more significant then lens stiffness in the development of presbyopia

(b) A lens re-filling model compares well with previous in-vitro tests.