Measuring and modeling elasticity distribution in the intraocular lens

Lens System Zonules Cornea Intraocular Lens Retina Ciliary Muscle

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

Helmholtz Accommodation

Coleman’s Theory of Accommodation Schachar RA, Bax AJ Mechanism 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 Zonules Capsule Media Zonules

Lasering Zonules Media Capsule 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 mm Precise location

Acoustic Radiation Force Gas Bubble Acoustic Wavefront 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 Water Gel Water Gel Water Gel Porcine Lens Water Gel Porcine Lens Water Gel Porcine Lens Water Gel Porcine Lens Water Gel Porcine Lens Shutter Focusing Lens ND Filter Ultrafast Laser Mirror

Sampling 1 mm Sampling points

Bubble Displacement (Porcine Lens) 40 30 Maximum Displacement (mm) 20 10 1 3 5 7 9 Lateral Position (mm)

Bubble Size Dependence (Int. Backscatter) ~ Bubble Radius Maximum Displacement (mm) R2=0.97 0.15 0.2 0.25 0.3 20 30 40 Push #1 Push #7

Cumulative Normalized Bubble Displacement (N = 12) Lateral Position (mm) Rel. Maximum Displacement 2 4 6 8 10 Normalized for int. backscatter, mean curve normalized for 5 mm std. Error of the mean

Relative Stiffness – Porcine Lens Lateral Position (mm) 1 2 3 4 5 6 7 8 9 0.2 0.4 0.6 0.8

Young’s Modulus – Porcine Lens

Conclusions Acoustic radiation force displaces bubble Ultrasound tracks bubble Convert displacement into elasticity Lens elasticity Not homogeneous Function of radial distance Lifetime 4.9x longer in nucleus assuming outer4 = cortex, inner3 = nucleus Lifetime 8.1x longer in nucleus assuming 4 mm = nucleus, avg(1mm 9mm) = cortex Stiffness 3.0x in nucleus, assuming nucleus = inner3, cortex = outer4 Stiffness 4.3x in nucleus, assuming nucleus = 5 mm, cortex = 2mm & 8mm

Heys et. al., Experimental Setup Heys KR, Cram SL, Truscott RJW Massive 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 RJW Massive 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 RJW Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Molecular Vision (2004)

Light Multilayer Model Anterior Polar distance (mm) Zonules Capsule 2 Light 1 I H G F D E Polar distance (mm) C A B Zonules -1 Capsule -2 Posterior 1 2 3 4 5 6 Radial distance (mm)

Caution Not a direct model of presbyopia Ignore age-related geometry Separate biomechanical contributions Average elasticity Elasticity distribution

Procedure Deformed Original Force Displacement

Optical Power the degree to which a lens converges or diverges light, equal to the reciprocal of the focal length ra = anterior radius of curvature rp = posterior radius of curvature t = polar lens thickness n1 = index of refraction for lens n2 = index of refraction for vitreous

Elasticity Distribution (Varying Average Elasticity) Multiplier A B C D E F G H I

Average Elasticity (Varying Average Elasticity)

Accommodation (Varying Average Elasticity)

Elasticity Distribution (Varying Elasticity Distribution) H G F E D C B A

Average Elasticity (Varying Elasticity Distribution)

Accommodation (Varying Elasticity Distribution)

Lens Biomechanics Polar distance Radial distance

Elasticity Distribution (Example) High Average Favorable Distribution Low Average Unfavorable Distribution

Accommodation (Example) Low Average Unfavorable Distribution High Average Favorable Distribution

Conclusions Multi-layer model shows accommodation Two presbyopia mechanisms: Increased average elasticity (known) Elasticity distribution change (new) Elasticity map needed for presbyopia surgery Lifetime 4.9x longer in nucleus assuming outer4 = cortex, inner3 = nucleus Lifetime 8.1x longer in nucleus assuming 4 mm = nucleus, avg(1mm 9mm) = cortex Stiffness 3.0x in nucleus, assuming nucleus = inner3, cortex = outer4 Stiffness 4.3x in nucleus, assuming nucleus = 5 mm, cortex = 2mm & 8mm

Colleagues Matthew O’Donnell Todd Erpelding Jing Yong Ye Christine Tse Marwa Zhody Tibor Juhasz Gagik Jotyan Ron Kurtz

Biomedical Ultrasound Laboratory Biomedical Engineering Dept. bul.eecs.umich.edu Center for Ultrafast Optical Science www.eecs.umich.edu/CUOS/ University of Michigan IntraLase Corporation, Irvine, CA www.intralase.com Supported by NIH grant R21 EY015876