Measuring and modeling elasticity distribution in the intraocular lens

Lens System

CorneaIntraocularLens

Ciliary Muscle

Zonules

Retina

Lens Anatomy

Lerman S., Radiant energy and the eye, (1980)

Helmholtz Accommodation

Coleman’s Theory of Accommodation

Schachar RA, Bax AJMechanism of human accommodation as analyzed by nonlinear finite element analysis ANNALS OF OPHTHALMOLOGY 33 (2): 103-112 SUM (2001)

Presbyopia

Presbyopia

• Onsets at about 40 years

• 100 % prevalence

• Complicates Stabismus (cross eyed)

• Increases safety risks for pilots

Conceptual Elastic Model

Zon

ules

Med

ia

Zon

ules

Cap

sule

Lasering

Zon

ules

Med

ia

Cap

sule

Zon

ules

Laser

Photodisruption

• Femtosecond pulsed laser

• Nonlinear absorption

• Breakdown only occurs above threshold

Limited to focal spot No damage to surrounding tissue Small disruption sites: 1 to 10 m Precise location

Acoustic Radiation Force

Aco

ustic

Wav

efro

nt

GasBubble

Elastic Solid

Advantages

• Reflection more efficient than absorption

• Bubbles:– Approximate perfect reflectors– High spatial resolution– High contrast for anechoic tissues like lens

• Potential in-vivo procedure

• Localized measurement

Experimental Set-up

Ultrafast Laser

Mirror

Shutter

ND Filt

erFocusing

Lens

Water

GelPorcine

Lens

Water

GelPorcine

Lens

Water

GelPorcine

Lens

Water

GelPorcine

Lens

Water

GelPorcine

Lens

Sampling

1 mm

Sampling points

Bubble Displacement (Porcine Lens)

1 3 5 7 90

10

20

30

40

Lateral Position (mm)

Max

imum

Dis

plac

emen

t (m

)

Bubble Size Dependence

(Int. Backscatter) ~ Bubble Radius

Max

imum

Dis

plac

emen

t (m

)

R2=0.97

0.15 0.2 0.25 0.320

30

40 Push #1

Push #7

Cumulative Normalized Bubble Displacement (N = 12)

Lateral Position (mm)

Rel

. Max

imum

Dis

plac

emen

t

0 2 4 6 8 100

2

4

6

Relative Stiffness – Porcine LensR

elat

ive

Stif

fnes

s

Lateral Position (mm)1 2 3 4 5 6 7 8 9

0

0.2

0.4

0.6

0.8

1

Young’s Modulus – Porcine Lens

0 1 2 3 40

5

10

15

Radial Position (mm)

Youn

gs M

odul

us (

kPa)

Conclusions

• Acoustic radiation force displaces bubble

• Ultrasound tracks bubble

• Convert displacement into elasticity

• Lens elasticity

– Not homogeneous

– Function of radial distance

Heys et. al., Experimental Setup

Heys KR, Cram SL, Truscott RJWMassive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia?Molecular Vision (2004)

Heys et. al., Results (65 year-old)

Heys KR, Cram SL, Truscott RJWMassive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia?Molecular Vision (2004)

Elasticity Distribution vs. Age

Heys KR, Cram SL, Truscott RJWMassive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia?Molecular Vision (2004)

Multilayer Model

A B C D E F G H I

Radial distance (mm)

Pol

ar d

ista

nce

(mm

) Anterior

Posterior

Zonules

Capsu

le

Lig

ht

0 1 2 3 4 5 6

0

1

2

-1

-2

Caution

• Not a direct model of presbyopia

• Ignore age-related geometry

• Separate biomechanical contributions

– Average elasticity

– Elasticity distribution

DeformedOriginal

Force

Displacement

Procedure

0.6

0.7

0.8

0.9

1.0

0.0 1.0 2.0 3.0 4.0

Layer Radial Position (mm)

No

rmal

ized

Mo

du

lus 0.25

0.51.51

Elasticity Distribution (Varying Average Elasticity)

AB

CD

EF

GH

I

Multiplier

Average Elasticity (Varying Average Elasticity)

0.00

0.10

0.20

0.30

0.00 0.02 0.04 0.06 0.08 0.10

Zonule Force (N)

Cil

iary

Dis

pla

ce

me

nt

(mm

)Soft Hard

Accommodation (Varying Average Elasticity)

29.2

29.6

30.0

30.4

0.00 0.02 0.04 0.06 0.08 0.10

Zonule Force (N)

Op

tic

al

Po

we

r (D

)

Soft Hard

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0

Layer Radial Position (mm)

Yo

un

g's

Mo

du

lus

(kP

a)

Elasticity Distribution (Varying Elasticity Distribution)

AB

CD

EF

GH

I

Average Elasticity (Varying Elasticity Distribution)

0.00

0.10

0.20

0.30

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Zonule Force (N)

Cil

iary

Dis

pla

ce

me

nt

(mm

)

Accommodation (Varying Elasticity Distribution)

24

26

28

30

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Zonule Force (N)

Op

tica

l P

ow

er (

D)

Lens Biomechanics

Radial distance

Pol

ar d

ista

nce

Elasticity Distribution (Example)

0.0

5.0

10.0

0.0 1.0 2.0 3.0 4.0

Layer Radial Position (mm)

Yo

un

g's

Mo

du

lus

(k

Pa

) High AverageFavorable Distribution

Low AverageUnfavorable Distribution

29.8

30.0

30.2

30.4

30.6

0.00 0.02 0.04 0.06

Zonule Force (N)

Op

tica

l Po

wer

(D

)

Accommodation (Example)

High AverageFavorable Distribution

Low AverageUnfavorable Distribution

Conclusions

• Multi-layer model shows accommodation

• Two presbyopia mechanisms:

– Increased average elasticity (known)

– Elasticity distribution change (new)

• Elasticity map needed for presbyopia surgery

Colleagues

• Matthew O’Donnell

• Todd Erpelding

• Jing Yong Ye

• Christine Tse

• Marwa Zhody

• Tibor Juhasz

• Gagik Jotyan

• Ron Kurtz

Biomedical Ultrasound LaboratoryBiomedical Engineering Dept.

bul.eecs.umich.edu

Center for Ultrafast Optical Sciencewww.eecs.umich.edu/CUOS/

University of Michigan

IntraLase Corporation, Irvine, CAwww.intralase.com

Supported by NIH grant R21 EY015876