nonlinear optical behavior of ocular tissue during laser irradiation

Nonlinear optical behaviorof ocular tissue during laser irradiation

Wei-Chiang Lin, Massoud Motamedi, and Ashley J. Welch

Apump 1cw Ho–YAG laser2 and probe 1He–Ne laser2 system was used to study the dynamics of the opticalbehavior of ocular tissue during laser heating. The nonlinear optical behavior of porcine corneal andvitreous-humor tissue was characterized in vitro by means of measurements of the radial profile of aHe–Ne laser beam transmitted through the tissue. Temperature gradients in the tissue created by theabsorption of pump radiation caused the probe beam to diverge. For constant laser power, the rate ofdivergence was made dependent on the spot size of the pump beam. The profile of the transmitted probebeam returned to its original magnitude and shape after the tissue was permitted to cool. Thisreversible change in optical behavior was attributed to the formation of a negative lens owing tothermally induced local gradients in the refractive index of the tissue.Key words: Thermal lensing, nonlinear optics, tissue optics. r 1995 Optical Society of America

1. Introduction

The optical properties of a biological medium aregenerally assumed to remain constant during laserirradiation unless the resulting temperature fieldalters the physical properties of the medium. Heat-ing that produces either coagulation or dehydrationwill affect the absorption and the scattering proper-ties of biological samples.1–7 In addition to theseirreversible changes, reversible changes in the opticalbehavior of tissue have been observed.8,9 Thermallyinduced changes in the refractive index of wateroccur,10 and for mid- and far-infrared wavelengths theabsorption coefficients of water are temperature de-pendent and reversible.11–16 Because water is themajor component of soft tissue, we expect its opticalbehavior to be temperature dependent as well. Toinvestigate irreversible and reversible changes in theoptical behavior of tissue, we have selected the corneaand the vitreous humor. These media are ideal forpump–probe laser experiments because these tissuesare normally transparent. In addition, transient

W.-C. Lin and M. Motamedi are with the Biomedical Laser andSpectroscopy Program, Biomedical Engineering Program, Univer-sity of Texas Medical Branch, Galveston, Texas 77550. A. J. Welchis with the Department of Electrical and Computer Engineeringand the Biomedical Engineering Program, University of Texas atAustin, Austin, Texas 78712.Received 17 January 1995; revised manuscript received 24 July

1995.0003-6935@95@347979-07$06.00@0.

r 1995 Optical Society of America.

changes in their optical properties might affect safetystandards as well as dosimetry for ophthalmic laserapplications, such as microsurgery with Nd:YAG la-sers.17,18We hypothesize that radial temperature gradients

produced by laser heating will induce local changes inthe index of refraction of tissue. These changesshould alter the profile of a beam of light travelingthrough the tissue. To test this hypothesis, we stud-ied the thermally induced, nonlinear optical behaviorof porcine cornea and vitreous humor with a pump–probe laser system. An infrared, cw Ho–YAG laserrapidly increased the temperature in the tissuesamples while a low-power He–Ne laser beam probedchanges in the optics of the ocular media. This studyexamined the optical behavior of ocular tissue in atemperature range in which tissue heating did notinduce any visible damage, such as whitening 1coagu-lation2 of the cornea. In addition, the optical behav-ior of water, which is frequently used to model theinteraction of infrared laser radiation with tissue,was examined.

2. Materials and Methods

Corneal and vitreous-humor tissue from porcine eyeswere used in this study. After harvesting, the eye-balls were wrapped in saline-moistened gauze andstored at 4–6 °C tomaintain the corneal water content.The cornea was excised and sandwiched between amicroscope slide 11 mm thick2 and a cover slip 10.2mm thick2. The cover-slip side was irradiated. Theaverage thickness of the cornea was measured to be

1 December 1995 @ Vol. 34, No. 34 @ APPLIED OPTICS 7979

1.2 mm 1n 5 52. The vitreous humor was drawn witha syringe after the cornea was removed and placed ina quartz container with a 2-mm path length. Allspecimens were used within 24 h post mortem. Forcomparative studies, the optical behavior of distilledwater was also characterized through the use of thesame setup and procedure.The experimental system is shown in Fig. 1. A

pump–probe systemwas employed to study the nonlin-ear optical behavior of cornea, vitreous humor, andwater. Tissue heating was induced by a cryogeni-cally cooled, cw Ho–YAG laser at l 5 2.09 µm1rare-earth medical2 while a low-power He–Ne laserwas used to detect the changes in optics of the sample.To change the spot size of the Ho–YAG laser beam,samples were placed at several locations in front ofthe focal plane of a plano–convex lens 1 f 5 11 cm2 thatwas used to focus both the pump and the probe beams.The optical alignment and the beam profile of bothlaser beams were measured after the lens by use of aknife-edge technique and a CCD camera. Althoughthe pump and the probe laser beams were focused atdifferent locations, their optical paths were almostidentical in the range of 3–5 mm in front of the focalplane, where the experiments were conducted. Themeasured spatial distributions of both laser beamswere Gaussian.The profile of the He–Ne laser beam was monitored

at the observation plane 120 cm behind the lens2 witha standard-frame-rate 130 frames@s2 CCD camera.Profile changes were assumed to indicate the extentof the nonlinear optical properties of the sample.The irradiance of the transmitted beam on the CCDarray was adjusted with a neutral density 1ND2 filterto prevent image saturation. Video images wererecorded through the use of a time-code generatorthat was synchronized with the laser shutter 1videotimer and VCR2. Images were then digitized andanalyzed, frame by frame, with a 33-ms temporalresolution to follow the dynamics of the probe-laserbeam profile.To minimize and account for artifacts we con-

Fig. 1. Schematic diagram of the pump–probe laser system formonitoring the thermally induced nonlinear optical behavior ofcorneal and vitreous-humor tissue.

7980 APPLIED OPTICS @ Vol. 34, No. 34 @ 1 December 1995

ducted control experiments. First, reference mea-surements were made with only the microscope slidesor the quartz cuvette, i.e., without any sample.Next, measurements were performed with varioustissue samples at different locations along the optical1z2 axis. For each experiment the transmitted profileof the He–Ne laser beam at the observation plane wasrecorded in the absence of Ho–YAG radiation. Thisbeam profile provided a reference for the normaliza-tion of the measurements that were performed dur-ing the laser-heating procedure. At each selectedlocation on the sample the measurements were re-peated three times. Sufficient time was allowedbetween irradiations for the sample to return to roomtemperature. The output power of the Ho–YAG la-ser was 500 6 20 mW for all experiments. Theexposure time, controlled by an external-cavity shut-ter with a 3-ms response time, was set at 500 or 300ms, depending on the structure of the sample and thespot size 1irradiance2 of the heating beam. At thehighest irradiance it was necessary to limit the expo-sure time to 300 ms to prevent visible coagulation atthe cornea.The incident irradiance was altered by a change in

the position of the sample along the optical axis.Corneal samples were positioned at three differentz-axis locations, resulting in spot sizes with a 1@e2diameter D of 1.0, 1.2, and 1.4 mm for the Ho–YAGlaser beam. The corresponding incident irradianceswere 570, 400, and 290 mW@mm2, respectively.Vitreous-humor samples were also tested at threedifferent z-axis locations and had estimated incidentirradiances of 850, 400, and 220mW@mm2 forD5 0.8,1.2, and 1.6 mm, respectively. For water, one posi-tion was selected, resulting in an incident irradianceof 400 mW@mm2 forD 5 1.2 mm.

3. Results

In the absence of any absorbing media such as tissue,the transmitted He–Ne laser beam profile remainedconstant for all experiments during Ho–YAG irradia-tion of the microscope slides and the quartz container.After the sample was placed in the pump–probe setupand heated with the pump-laser radiation, the trans-mitted He–Ne laser beam began to diverge. Thisdecreased the spot area of the transmitted probebeam at the observation plane. An illustration of theprobe-laser beam trajectories extrapolated from thisobservation is presented in Fig. 2. The transmittedHe–Ne laser beam returned to its original profile afterthe sample had cooled. A sequence of images of thebeam profile of the transmitted He–Ne laser beamobtained from one of the corneal samples is shown inFig. 3. Note that the spot area of the probe beamdecreased and the central irradiance increased as thecorneal sample was heated for 500 ms.The optical behavior of corneal tissue for different

pump-radiation spot sizes is shown in Fig. 4. Expo-sure of corneal tissue to high irradiance 1of the orderof 570 mW@mm2 for D 5 1.0 mm2 induced a fasterconvergence in the spot area as compared with lower

irradiances 1400 mW@mm2 for D 5 1.2 mm and 290mW@mm2 for D 5 1.4 mm2. After a 300-ms exposuretime, the measured spot area of the probe beamdecreased 50%, 27%, and 18% for pump-beam irradi-ances of 570, 400, and 290 mW@mm2, respectively.An irradiance of 570 mW@mm2 for 500 ms coagulatedthe cornea; the irradiated spot became white, whichdistorted the effects of thermal defocusing on thetransmitted probe-laser beam profile.The reversible feature of the thermally induced

reduction in the spot area is seen in the smalldifferences among the error bars on the curves shownin Fig. 4. Sufficient time for the tissue to cool off wasprovided between irradiances, and sites not coagu-

Fig. 2. Illustration of the self-defocusing action with the tissuelocated in front of the focal plane. The solid lines represent theoriginal beam paths, and the dashed lines represent the modifiedbeam paths that are due to thermal lensing.

lated were irradiated three times. The error barsrepresent the maximum and minimum spot-areavalues at different time intervals during pump-laserirradiation for the three exposures at each site. Thechange in the probe-beam spot area was highly repro-ducible.Transient changes in the spot area of the He–Ne

laser beam transmitted through vitreous-humor

Fig. 4. Plot of the changes in the spot area of the transmittedHe–Ne laser beam as a function of the exposure time for threedifferent spot sizes for the pump laser 1D 5 1.0, 1.2, and 1.4mm2 forcorneal tissue. The curves represent the averages of themeasure-ments; the error bars indicate the maximum andminimum values.

Fig. 3. Sequence of images showing the changes in the profile of the probing beam transmitted through the cornea, which was heated witha Ho–YAG laser 1D 5 1.2 mm, at 400mW@mm2 for 500ms2: the reference image taken at 1a2 t5 0ms, 1b2 t5 33ms, 1c2 t5 165ms, 1d2 t5 330ms, and 1e2 t 5 500 ms.


samples when various incident irradiances were usedto heat the samples are shown in the Fig. 5. Therate of change of the spot area of the transmittedprobe beam increased as the diameter of the heatedspot decreased. This change was similar to that seenin the corneal-tissue results. When a vitreous-humor sample was located 3 cm in front of the focalplane of the 850-mW@mm2 pump-laser beam withD 5 0.8 mm, the spot area reached a minimum, whichwas approximately 45% of its original size, within 100ms after the onset of exposure. After 100 ms, thetransmitted spot became distorted; its beam profilelost its symmetry as the irradiation continued. Weattribute the distortion of the He–Ne laser beamprofile to the laser-induced free convection in thissample. When the vitreous-humor sample wasmoved 1 cm forward 1for a 400-mW@mm2 pump-laserbeam with D 5 1.2 mm2, between 150 and 200 mswere necessary to reach a minimum spot area, which

Fig. 5. Plot of the changes in the spot area of the transmittedHe–Ne laser beam as a function of the exposure time for threedifferent spot sizes for the pump laser 1D 5 0.8, 1.2, and 1.6 mm2for vitreous-humor tissue. The curves represent the averages ofthe measurements; the error bars indicate the maximum andminimum values. The asterisks indicate the onset of distortion ofthe probe-laser beam profile.


was approximately 40% of the initial value. Afterthat, the distortion of the probe beam as described forthe case above was observed 1see Fig. 62. When thesample was located 5 cm in front of the focal plane 1a220-mW@mm2 pump-laser beam with D 5 1.6 mm2,the observed spot size decreased by 50% by the end ofthe 500-ms irradiation.In the experiments with water, dynamic optical

behaviors similar to those seen during irradiation ofthe corneal and vitreous-humor samples for thetransmitted He–Ne laser beam was observed. Dur-ing irradiation with the 400-mW@mm2 pump-laserbeam with D 5 1.2 mm, the spot area of the probe-laser beam decreased rapidly within the first 100 msof the irradiation 1see Fig. 72. After a maximumdecrease of 50% in the spot area was observed atapproximately 100 ms, the beam profile of the trans-mitted probe-laser beam spot gradually became dis-

Fig. 7. Plot of the changes in the spot area of the transmittedHe–Ne laser beamwith 400mW@mm2 of the pump laser on cornea,vitreous humor, and water. The curves represent the averages ofthe measurements; the error bars show the maximum and mini-mum values in these measurements. The asterisks indicate theonset of convection-induced distortion of the probe-laser beamprofile. An irradiance of 400 mW@mm2 for 500 ms did notcoagulate the cornea.

Fig. 6. Sequence of images showing the distortion, caused by free convection, of the He–Ne-laser beam profile as the beam travels throughvitreous humor for images taken at 1a2 t 5 0 ms 1the reference beam profile2, 1b2 t 5 233 ms 1the beam profile before the onset of distortion2,and 1c2 t 5 400 ms 1the distorted beam profile2.

torted until the end of the irradiation. A comparisonof the nonlinear optical behaviors of water, vitreoushumor, and corneamade with data from an irradianceof 400 mW@mm2 for D 5 1.2 mm over 500 ms showedchanges in the spot area of the transmitted He–Nelaser beam during the irradiation. The results areshown in Fig. 7.

4. Discussion

The important phenomenon observed in this studywas that the transmitted probe-laser beam undergoesreversible self-defocusing when the ocular sample isheated with the pump-laser beam. We believe thisreversible optical behavior is due to the temperaturedependence of the refractive index19–25 of ocular me-dia, which is approximately governed by

n1r, z2 5 n0 1 DT1r, z, t21dndT2 , 112

where n0 is the background refractive index, DT1r, z, t2is the change in temperature, and dn@dT is the totalchange in the index of refraction with a change intemperature. Because the probe laser beam con-verges during the heating process of ocular media, thedn@dT of corneal and vitreous-humor media must benegative: the higher the temperature, the lower therefractive index. The slightly temperature-depen-dent value of the dn@dT for water is known to be21.2479 3 1024@°C at 30 °C 1see Fig. 82. Althoughthe dn@dT for the cornea and the vitreous humor arenot available, we might anticipate that they should beclose to the value of water because of the high watercontent of these ocular media 178% for the cornea26and 98% for the vitreous humor272.Because of the Gaussian profile of the Ho–YAG

laser beam and the axial absorption of its radiation, atemperature gradient in the radial, as well as theaxial, direction of the tissue is generated. Thistemperature gradient results in a gradient in therefractive index for both axes. In this study, theincident-ray trajectories are approximately parallel tothe axial direction; thus the effect of the axial gradi-ent of the refractive index on the probe laser beam is

Fig. 8. Plot of the temperature dependence of the refractive indexand the dn@dT value for water at 404.66 nm 1see Ref. 102.

small and can be neglected.28 It is known that thelocal variation in the refractive index is directlyproportional to the incident power and is inverselyrelated to the square of the spot size of the pump laserbeam.21 Thus the smaller the spot size of theHo–YAGlaser on the sample, the higher the irradiance and theresulting temperature. The lensing effect in themedia is more pronounced as a result of the steepergradient of the refractive index. This increase ex-plains why the defocusing rate of the probe beamshown in Figs. 4 and 5 increases as the spot size of thepump laser decreases. Local variation in the refrac-tive index eventually vanishes as the temperaturegradients disappear. However, irreversible changesin the transmitted probe-laser beam profile occur ifthe heat induces permanent changes in the structureof the corneal sample.The temperature dependence of the refractive in-

dex comprises two components: temperature- andstress-dependent variations. The dn@dT hence canbe separated into two independent terms, that is,

dn

dT5 1≠n≠T2r 1 1≠n≠r2T

≠r

≠T, 122

where r is the density of the medium.19 The firstterm 1right-hand side2 of Eq. 122 represents the tempera-ture-dependent change in the refractive index at aconstant density. This term is related to the absorp-tion coefficient and can be either positive or negative,depending on the characteristics of the thermallyinduced shift of the absorption spectrum of the me-dium. The second term on the right-hand side of Eq.122 characterizes the change induced by thermal expan-sion, which is negative. Because the cooler surround-ing tissue constrains the hotter tissue during laserheating, a gradient in density is produced. Thisdensity gradient in turn produces refractive-indexvariations.19,20 Because photoelastic and thermal-expansion coefficients for the ocular media are notavailable, we could not evaluate the significance ofthermal expansion in dn@dT. Although thermal-expansion-induced bulging, which causes a lensingeffect,20 of the front face of samples has been reportedin nonbiological media, in the current study thesurfaces of ocular samples were constrained to be flatby the container or the holder.In the experiments with the vitreous humor, the

rate of defocusing increased after a certain point inthe heating process 1see Fig. 52. This phenomenonwas not observed in the experiments with water andcornea and may be due to heat-induced liquefaction ofthe vitreous humor.29,30 This liquefaction processcauses major changes in the mechanical properties ofvitreous humor, especially its viscosity. Further-more, the optical and thermal properties of vitreoushumor may also be affected by this process. Theseheat-induced variations in the physical properties ofvitreous humor therefore change the rate of theself-defocusing action of the probe-laser beam.The thermal-defocusing phenomenon is known to

be very sensitive to free-convection currents in liquid


media.19 High absorption of 2.09-µm laser radiationby water and by ocularmedia leads to the formation ofa steep density gradient that is due to thermalexpansion. This expansion initiates free convectionfor low-viscosity media, such as water at 0.8904 cp at25 °C,10 and heated vitreous humor. A free-convec-tive flow in amedium leads to an asymmetric tempera-ture profile. As a consequence, an asymmetric lensis formed that causes beam deflection and distortionof the laser beam profile, as seen in Fig. 6.The similarity between the self-defocusing action of

the probe beam 1He–Ne laser2 in the experiments withwater, vitreous humor, and cornea suggest that watermight be the key component responsible for thisnonlinear optical behavior. However, the validity ofthe use of water to model the response of ocular mediaduring infrared laser radiation is questionable. Therate of the self-defocusing action in the experimentswith water, vitreous humor, and cornea as shown inFig. 7 indicates the variations in the thermal re-sponses among these media that result from thedifferences in their optical and their physical proper-ties. Water has a greater absorption coefficient11,12,311µa 5 35–40 cm212 and a penetration depth 1285–333µm2 at the 2.09-µm wavelength compared with vitre-ous-humor and corneal tissue, with an absorptioncoefficient32–34 µa 5 20 cm21 and a penetration depthof 500 µm. Heat deposition during Ho–YAG laserirradiation in water is more superficial compared tothat in the ocular media. Water has a relativelygreater thermal diffusivity35 11.4433 3 1027 m2@s2 thando other ocular media 11.4143 3 1027 m2@s or less35,362,and water responds more quickly to changes in thethermal environment. In contrast, the vitreous hu-mor and the cornea, which have a lower thermaldiffusivity, take a longer time to reach a new equilib-rium condition. In addition, free convection occursin water and in vitreous humor because of their lowviscosities, which distort the temperature profile inthe medium as well as in the laser beam. All thesefactors introduce considerable deviations in the ther-mal response between water and ocular media.Hence we believe that water may not serve as a goodmodel to evaluate the thermal response or the ther-mally induced nonlinear optics of ocular media, espe-cially the cornea, during Ho-YAG laser irradiation, orfor any tissue and any pump laser.The nonlinear optical properties of ocular media

reported in this paper may influence some ophthalmiclaser applications and their safety considerations.Safety standards assume that a laser beam is repre-sented as a point source and a minimum spot occursat the retina. For wavelengths from 0.95 to 1.3 µmthe penetration depth 11@e2 in water is 1–2 cm.Absorption by the cornea, lens, and vitreous humor inthis wavelength band will undoubtedly affect the spotsize at the retina and thus estimates of retinalirradiances. In Ho–YAG laser photothermal kerato-plasty, success relies on the precision one has tocontrol collagen shrinkage in the treated cornea and


on the capability to maintain the integrity of thesurrounding tissue, especially the endothelium. Thethermally induced lensing effect in corneal tissue, asdemonstrated in our study, will lead to the changes inthe local fluence rate. This in turn alters the rate ofheat generation inside the cornea andmay change thetherapeutic results. In a laser posterior capsu-lotomy, a nanosecond or picosecond Nd:YAG laserpulse is focused into the transparent tissue to produceoptical breakdown, which disrupts the tissue. Thesize of the area of tissue disruption is controlled by thevariation of the energy of each pulse. If a strongerdestructive effect is needed, a burst of laser pulseswith a high repetition rate 1e.g., 50 Hz2 may beused.17,18 Applying laser pulses to the anterior tar-get in the eye at such a high repetition rate couldpotentially induce a small, nonuniform temperatureelevation in the cornea and create some degree of thethermal-lensing effect. The outcome of this laserapplication therefore could be changed because thelensing effect alters the spot size of the laser beam onthe target. Besides, the strong light 1electromag-netic2 field could also induce the observed changes inthe refractive index by means of other mechanismssuch as the Kerr effect,19,37 which also leads to alensing effect in the cornea. The significance of theinfluence of the nonlinear optical properties of ocularmedia in ophthalmic laser applications needs furtherinvestigation, and we will report the results of ourfurther investigation in the future. For any math-ematical model36 that simulates the thermal responseof ocular tissue to laser radiation, the influence oftemperature-dependent thermal lensing should betaken into consideration to achieve accurate predic-tions.

5. Conclusion

This study demonstrated the nonlinear, thermo-optical behavior of the cornea and the vitreous humorduring laser heating. The local index of refraction ofthese ocular media decreases as the temperatureincreases. A self-defocusing phenomenon in thetransmitted probe laser beam is transient and disap-pears as the temperature gradient vanishes. Theexistence of temperature-dependent optical nonlineari-ties of ocular tissue could affect the outcome of variouslaser applications in ophthalmology.

This study was supported in part by the NationalScience Foundation under grant BCS-9110257 andthe Department of Energy under grant DE-FG05-91-ER-61226. The authors thank J. P. Wicksted for hisvaluable comments.A. J. Welch is the Marion E. Forsman Centennial

Professor of Electrical and Computer Engineering atthe University of Texas at Austin.

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nonlinear optical behavior of ocular tissue during laser irradiation

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