Does the tear film removehigher order wavefrontcorrections?

Charles Campbell

The role of tear film on therefractive state of the eyen The strongest refracting surface of the eye is

the air/tear film interface

n However, if the tear film has a constantthickness it may be considered to be a zeropower element

The role of tear film on therefractive state of the eye

n If the tear film is constant thickness, i.e.a zero power element, the cornealsurface may be considered as the firstrefracting element

n In refractive surgery it is the cornealsurface that is changed and this is theeffect that is usually considered - thetear film is neglected

The role of tear film on therefractive state of the eye

n But suppose the tear film is not constantthickness and so the air/tear surfacedoes not replicate the corneal surface

n Now the tear film is no longer a zeropower element and must be considered

n When can this happen? How will effectrefractive corrections?

Effect of a tear film of non-constant thickness

n If a tear film initially of constantthickness covering a local correction inform a local depression

n Flows and fills in that depression,much the corrective effect is removed

The flow of thin fluid films

n Will the tear film flow to partially eraselocal refractive corrections ablated intothe corneal surface in the time betweenblinks?

n To answer this question we need toconsider how and why thin fluid filmsflow

The flow of thin fluid films

n Parameters effecting flown Surface tension (s)

n Mean surface curvature gradient (—M)

n Viscosity (m)

n Film thickness (h)

The flow of thin fluid films -surface tension (s)

n The surface tension at a gas/fluid interface -such as the air/tear film surface - acts tominimize surface area

n Surface area is minimized when the localmean surface curvature, M, is constant overthe interface surface

n Surface tension in a curved interface causesa pressure difference, P,between the gas andthe fluid to be exist

†

P = 2sM (Young-Laplace formula)

The flow of thin fluid films - meansurface curvature gradient (—M)

n A gradient in the mean surfacecurvature,—M, creates a pressuregradient,—P,in the fluid film

n The pressure gradient causes fluid toflow from areas of higher curvature toareas of lower curvature until meancurvature, and hence the pressure, isequalized

The flow of thin fluid films -viscosity (m)

n In a flowing fluid film in contact with airon one side and solid on the othern the fluid in contact with the solid surface

moves at exactly the same speed as thatsurface

n the fluid at the air interface flows withhighest velocity with respect to the solidsurface

The flow of thin fluid films -viscosity (m)n We may think of the thin flowing film as being

made of thin layers sliding with respect to oneanother

n Viscosity may be thought of as a ‘friction’between the layer that slows flow by inhibitingmovement between layers

n The flow restricting force due to viscosity isproportional to the velocity gradient,F=m∂V/∂h air

corneaFlow rate

The flow of thin fluid films -film thickness (h)

n For a given surface velocity, the thinner thefilm, the higher the velocity gradient must beand the greater the viscosity will resist flow

n Film flow rate is found to be proportional to h3

- as the film gets thinner the flow rate quicklyslows

Tear film dynamics – initialconditions – change with time

n The initial film after a blink – can thetear film be modeled as initially having aconstant thickness?

n How does the thickness change withtime?

Can we assume the tear film startslife with a constant thickness?

n To answer this question, we turn to coatingflow theory, the theory of creating thin film viaa wiper or dipping action widely usedindustrially forn Flow of paint

n Creation of thin emulsion films

n Coating surfaces - such as spectacle lenses

n For the eye, the wiper is the upper eye lidmoving over the corneal surface

Creation of a thin film by amoving wiper- coating flow

upper lid

+

upper lipmeniscus

Rm

hf tear film thickness

U

h(x)x

hl lubrication film thickness

y

n For coating flow the shape of the underlying surfacedoes not effect film thickness

†

hf = 1.3375Rm mU /s( )2 / 3

Thin film flow dynamics – changein thickness with time

†

∂h x, y( )∂t

=s3m

∂∂x

∂M x, y( )∂x

h x,y( )3( )Ê

Ë Á

ˆ

¯ ˜ +

∂∂y

∂M x, y( )∂y

h x, y( )3( )Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

n Equation giving the time rate of change of thesurface air/fluid surface height

n This equation allows the change in surfaceheight over short periods of time to be directlycalculated

Simulation of tear film flown Assume an initial constant tear thickness (~ 6 m)n Assume the tear film surface assumes the initial shape

and local curvature of the corrected wavefront errorn Calculate the local curvature values from the surface

elevation valuesn NOTE – second order surfaces have constant mean

curvature i.e. —M = 0

n Using the differential thickness change equationcalculate the rate of thickness change for a short periodof time ~ 10 ms

n Find the new surface shape and curvature valuesn Iterate the process for a length of time representative of

the time between blinks

†

∂h x, y( )∂t

=s3m

∂∂x

∂M x, y( )∂x

h x,y( )3( )Ê

Ë Á

ˆ

¯ ˜ +

∂∂y

∂M x,y( )∂y

h x, y( )3( )Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

Simulation for an eye with an aboveaverage amount of higher orderaberrations.

n The change in tearfilm thickness fromthe initial conditionof constantthickness

Simulation for an eye with an aboveaverage amount of higher orderaberrations.

n The change in tearfilm thickness fromthe initial conditionof constantthickness

RMS error change = 0.009micron @ 1/61 l

Experiment observation of tear filmflow via live corneal topography video

n Simulation is fine but can these effectsbe physically measured?

n Flow effects can be observed byrecording live corneal topographyvideo and observing surface curvaturechanges as the corneal topographermires change shape.

Tear film relaxation following blink ina 4 day post op PRK corneal surface

Motion just after a blink -4 dayspost-op PRK

Untreated cornea having a 50 yearold scar at about 165° that induceshigher order aberrations

Conclusionsn Tear film flow following initial film formation by

a blink can be demonstrated by computersimulation and observed with live cornealtopography video

n For surface variations of the size expectedfrom wavefront corrections the change in thetear film surface is too small to causenoticeable changes in visual image quality

n Tear film dynamics will not erase theeffects of ablative corrections for higherorder aberrations.