measuring and modeling elasticity distribution in the intraocular lens
TRANSCRIPT
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