2.1.

Theoretical Background of Pressure Generation

If an absorber is irradiated with laser pulses, the light absorption leads to heating and a subsequent thermoelastic pressure generation. The pressure is dependent on the absorption coefficient $\alpha$ , radiant exposure $H$ , absorber depth $z$ , and the temperature-dependent Grüneisen parameter $\Gamma$ of the material [Eq. 1]. Neglecting the temporary temperature rise caused by the absorption of the laser pulse and considering conditions of stress confinement, a spot with a diameter larger than the absorption depth and uniform irradiance across the laser beam, the pressure induced in the absorber is:^{18, 19, 20}

The induced pressure causes thermoelastic expansion of the tissue and the emission of a pressure wave. The maximum amplitude of this pressure wave at some distance is directly proportional to pulse energy and the Grüneisen parameter $\Gamma$ :²¹

With the approximation of a polynomial relation between $\Gamma$ and temperature $T$ , the maximum pressure amplitude as given in Eq. 3 results in:

2.2.

Temperature Determination from Pressure Signal

If the material constants $T_0$ and $T_{\max }$ are known for the chorio-retinal tissue, a temperature increase can be determined from the maximum amplitude of the laser-induced pressure wave according to Eq. 7. For this purpose the individually varied proportionality factor $s$ has to be determined once before each measurement. This can be performed by applying probe pulses with the known energy $E$ , detecting $p_{\max }$ at a known temperature $T=T_{\mathrm{ref}}$ of the absorbing media, and conversion of Eq. 7. For in vivo temperature determination, $T_{\mathrm{ref}}$ is the body temperature.

With the knowledge of $s$ , all parameters of Eq. 7 are defined, and the temperature increase during laser-induced tissue heating can thereafter be calculated from $p_{\max }$ according to Eq. 8:

2.3.

Experimental Setup for Determination of $T_0$ and $T_{\max }$

The ex vivo calibration experiments on porcine and rabbit retinal explants to determine $T_0$ and $T_{\max }$ were carried out within four hours postmortem. First, the macula was dissected from the eye. Then the vitreous body and neural retina were carefully removed. To prevent drying, the retinal explant was covered with physiological saline solution.

Laser pulses of a nitrogen laser pumped dye laser (LSI Laser Science, VSL337ND with Coumarin500, $\lambda =500\mathrm{nm}$ , $E\approx 5\mu \mathrm{J}$ $\tau =3.5\mathrm{ns}$ , $f=5\mathrm{Hz}$ ) were coupled to an optical fiber (Ceram Optec, $50\mu \mathrm{m}$ , $\mathrm{NA}=0.11$ ), which was directly connected to a slit lamp (sl, Zeiss, 30 SL/L). The tip of the fiber was imaged through an ophthalmic contact lens (cl, Mainster Standard or Haag-Streit 903) onto the surface of a retinal explant. By the slit lamp magnification, the laser spot diameter on the surface could be adjusted between $50\mu \mathrm{m}$ and $1\mathrm{mm}$ with a spatial top-hat beam profile. Assuming a pulse energy of $5\mu \mathrm{J}$ and a spot diameter of $0.3\mathrm{mm}$ , the light absorption in the RPE [ $\alpha =1700{\mathrm{cm}}^{-1}$ (Ref. 24)] causes a temporary maximal temperature increase of less than $3°\mathrm{C}$ . The average power for a repetition rate of $5\mathrm{Hz}$ is $25\mu W$ , which induces a negligible baseline temperature of $<50\mathrm{mK}$ .

The retinal explant was positioned in a cuvette filled with physiological saline solution. The laser-induced pressure wave propagated through the water bath and was detected by a ring-shaped ultrasonic transducer (ut, lead zirconium titanate, PZT5) embedded in the contact lens (Fig. 1 ). By means of a thermal resistor (tr) and peltier elements (pe), the ambient temperature of the saline solution and, consequently, of the retinal explant could be regulated in the range of $5\text{to}60°\mathrm{C}$ . The current temperature of the water bath was measured by a thermocouple (tc) positioned close to the retinal explant. A magnetic stirrer (Hanna, HI190M) was used to move the saline solution to prevent ambient temperature gradients within the water bath.

Fig. 1

Experimental setup for a determination of the temperature dependence of the Grüneisen parameter. sl: slit lamp; fc: fiber coupler; cl: contact lens; ut: ultrasonic transducer; rpe: RPE explant; tc: thermocouple; tr: thermal resistor; and pe: peltier element.

2.4.

Experimental Setup for Optoacoustic Temperature Determination

The ex vivo experiments on OA temperature determination were performed on whole porcine eyes within four hours postmortem with the contact lens directly positioned on the cornea.

The in vivo experiments two on rabbits were carried out under ethical guidelines for animal treatment with permission of the ethical committee of the University of Kiel.

The rabbit was anesthetized right before the measurement by a mixture of xylacinehydrochloride and ketaminehydrochloride. It was then placed in a special holding device and positioned in front of the slit lamp. The rabbit’s cornea was additionally anesthetized with xylocaine eye drops, and the pupils were dilated with neosynephrine eye drops. The contact lens with the integrated ultrasonic transducer was fixed on the rabbit’s cornea and kept stable during the measurement. For a better acoustic adaption to the ultrasonic transducer, some drops of Methocel® were used as a contact gel.

To determine the chorioretinal temperature increase during laser heating, an experimental setup as shown in Fig. 2 was used. The fiber-coupled pulsed dye laser was connected to a slit lamp (sl, Zeiss, Visulas Argon). Additionally, the radiation of a TTT laser (CeramOptec, $\lambda =810\mathrm{nm}$ , $\mathrm{P}⩽3\mathrm{W}$ ) was coupled via a fiber concentrically into the same optical path as the probe laser radiation utilizing a dichroic mirror (dm). The two fiber tips were imaged onto the fundus of the eye using a retinal top-hat beam profile with independently adjustable spot diameters between $50\mu \mathrm{m}\text{to}1\mathrm{mm}$ (probe laser spot) and $0.5\text{to}5.5\mathrm{mm}$ (TTT laser spot). The energy of the dye laser was measured by a photodiode (pd, FND100). As in the previous setup, the ultrasonic pressure wave was detected by a ring transducer integrated into the contact lens. To verify the OA-determined temperature increase, a miniaturized thermocouple (tc, Rössel Messtechnik, type K, diameter $250\mu \mathrm{m}$ ) was positioned through the sclera below the RPE layer into the center of the TTT laser spot. For in vivo measurements on rabbit eyes, the thermocouple was inserted through a sclerotomy into the center of the irradiation spot. All data were acquired (daq) and analyzed by a personal computer (PC).

Fig. 2

Experimental setup for chorioretinal temperature determination by OA. fc: fiber coupler; pd: photodiode; dm: dichroic mirror; sl: slitlamp; cl: contact lens; ut: ultrasonic transducer; tc: thermocouple; daq: data acquisition; and pc: personal computer.

2.5.

Data Acquisition

For an online monitoring of laser-induced temperature increase, all data acquisition and analysis need to be performed in real time. The signal of the ultrasonic transducer is amplified by a preamplifier (Panametrics 5662) by $54\mathrm{dB}$ and digitized by an $8\text{-}\text{bit}$ high-speed digitizer (National Instruments, NI 5112, $100\mathrm{MHz}$ , two channel). The second channel is used for the pulse energy signal from the photodiode and as a trigger signal. The temperature measurement is achieved by a thermocouple input board (Measurement Computing PCI-DAS-TC).

The real-time signal processing and display was programmed in LabView® 6.0i software. To increase the signal-to-noise ratio, the ultrasonic transients underwent a software-based frequency filtering (Butterworth fourth order, bandpass $50\mathrm{kHz}\text{to}3\mathrm{MHz}$ ). The maximum amplitude of the first peak was recorded as $p_{\max }$ . The obtained temperature curves were filtered utilizing a fifth-order median filter.

2.6.

Analytical Modeling of Heat Diffusion

In order to compare the experimentally obtained data with temperature simulations, we used an analytical model based on two absorbing layers, assuming homogeneous and isotropic heat conduction and negligible light scattering. The changes in temperature that occur from laser exposure are described by the heat diffusion equation:

Due to heat convection arising from blood circulation in the choroid, a global perfusion term is added to the source term $\epsilon$ . This can be achieved by assuming the subtraction of a quantity of heat with a constant rate $Q$ within the whole volume. Therefore, the perfusion term $\rho c_{p}QT$ , acting as a heat sink, is subtracted from the source term $\epsilon$ .^{17, 26} As the blood circulation and hence the perfusion is physiologically localized in the choroid, the assumption of a global heat sink is an overestimation, resulting in lower perfusion rates.

The source term $\epsilon$ is dependent on the beam profile of the laser spot. With respect to the experimental setup, we assumed a top-hat laser profile in time and space. For the analytical modeling, we approximated a square laser beam profile (side length, $2a$ ) covering the same area as the circular beam spot with radius $r$ , thus $2a=r\sqrt{\pi }$ .

The fluence rate $I(x,y,z)$ in the tissue, assuming one absorbing layer of the thickness $d$ for the top-hat laser spot, is given by the Lambert-Beer law:

With the described approximations, Eq. 11 can be solved analytically using the source term of Eq. 14:^{27, 28}

2.7.

Layer Structure at the Fundus

For temperature calculations, a rabbit eye model consisting of two absorbing layers was used: the retinal pigment epithelium (RPE) and the choroid. The absorption for human RPE was reported in the range from 400- to 1100-nm wavelength.³¹ These data were used to calculate the spectral absorption coefficient for human RPE by assuming an absorber thickness of 10 μm. For rabbit RPE and choroid the absorption is known from 400- to 700-nm wavelength.^{29, 30} According to the rabbit eye geometry published by Birngruber¹⁷ the rabbit RPE has a thickness of 4 μm and the pigmented choroid of 20 μm. The rabbit absorption coefficients for the irradiation wavelength of 810 nm were derived by extrapolating the absorption data and assuming a constant ratio of absorption coefficient for human RPE to rabbit RPE respective choroid. The ratio was derived for $\lambda =650\mathrm{nm}$ . The corresponding curves are depicted in Fig. 3 . Under these assumptions a fundus geometry as shown in Fig. 4 was used for the temperature simulations. The RPE had a thickness of $4\mu \mathrm{m}$ , resulting in an absorption coefficient of $169{\mathrm{cm}}^{-1}$ for a wavelength of $810\mathrm{nm}$ . The adjacent choroid was $61\mu \mathrm{m}$ thick with melanin concentrated in the posterior third of the choroid, thus, an absorption coefficient of $156{\mathrm{cm}}^{-1}$ . The sclera was assumed to scatter the remaining light out of the regarded volume without absorption. Due to absorption and scattering in the anterior part of the eye including lens and vitreous, only 90% of the power incident at the cornea was assumed to reach the fundus of the rabbit eye.^{32, 33, 34, 35}

Fig. 3

Absorption of human RPE, rabbit RPE, and rabbit choroid as a function of wavelength derived from Refs. 29, 30, 31.

Fig. 4

Fundus geometry of a rabbit eye used for analytical modeling of temperature increase.¹⁷

As biological tissue consists mainly of water, the material specific parameters $\rho =0.993\mathrm{g}∕{\mathrm{cm}}^3$ (density), $c_p=4.179\mathrm{J}∕\left(\mathrm{g}\mathrm{K}\right)$ (specific heat capacity), and $\kappa =\beta ∕\left(\rho c_p\right)=1.51$ ${10}^{-7}{\mathrm{m}}^2∕\mathrm{s}$ (thermal diffusivity) were taken for water at $37°\mathrm{C}$ .²²

The choroidal blood flow, which was taken into account by a global perfusion term according to Eq. 15, has been measured by different groups.¹⁷ For rabbits, the determined perfusion rate $Q$ ranges from $Q=0.13{\mathrm{s}}^{-1}$ (Ref. 36) to $Q=0.6{\mathrm{s}}^{-1}$ (Ref. 37).

For the simulations, the temperature increase according to Eq. 15 was calculated for both absorbing layers separately. With respect to the linearity of the differential operators $\partial ∕\partial t$ and $\Delta$ [Eq. 10], the principle of superposition can be applied, and the sum of both temperature increases results in the total increase $T_{\mathrm{tot}}$ :

3.1.

Results from Analytical Modeling

3.1.1.

Dorsal and lateral temperature profile

In first analytical simulations, the lateral temperature increase during TTT laser irradiation was calculated for different depths in the fundus of the rabbit eye. A top-hat laser beam profile with a square length of $2a=2.66\mathrm{mm}$ was assumed, which correlates to a circular spot diameter of $3\mathrm{mm}$ . The assumed power applied to the cornea was $300\mathrm{mW}$ , corresponding to $270\mathrm{mW}$ on the retina. According to Sec. 2.7, the overall absorption at the fundus is 31.6%. The calculated temperature increase at the end of the $60\mathrm{s}$ irradiation period over tissue depth and distance to the center of the spot is depicted in Fig. 5 in an isothermal diagram. For a better visualization, the layered structure of a rabbit eye is drawn on the right side of the graph according to Ref. 17, and the irradiation spot is drawn on top. Figures 6a and 6b depict a vertical and horizontal cross section in the center of the spot and along the surface of the RPE.

Fig. 5

Calculated temperature increase after $60\text{-}\mathrm{s}$ heating with $a=1.33\mathrm{mm}$ and $P=270\mathrm{mW}$ on the retina without perfusion.

Fig. 6

(a) Calculated dorsal and (b) lateral temperature increase at the fundus of a rabbit eye after $60\text{-}\mathrm{s}$ TTT laser irradiation with $a=1.33\mathrm{mm}$ and $P=270\mathrm{mW}$ on the retina without perfusion.

The results show that the calculated temperature increase after $60\text{-}\mathrm{s}$ irradiation is $12.0°\mathrm{C}$ in the center of the spot on the RPE retina interface. The highest temperature increase of $12.2°\mathrm{C}$ is achieved in the choroid. Due to heat diffusion, the temperature in the vitreous decreases with an average gradient of about $1\mathrm{°C}∕100\mu \mathrm{m}$ . For the lateral temperature profile, $\Delta T$ decreases as the distance to the center of the spot increases. The increase in temperature at the border of the spot is 36.3% less than in the center.

3.1.2.

Influence of pigmentation on the chorioretinal temperature increase

One factor in chorioretinal temperature increase is its absorption. An especially important factor, which varies intra- and interindividual, is the density of the melanin in the RPE layer. Therefore, the temperature increase was calculated for different RPE absorption coefficients. Besides, the value used in the previous simulation with ${\alpha }_{\mathrm{rpe}}=169{\mathrm{cm}}^{-1}$ , an RPE absorption of ${\alpha }_{\mathrm{rpe}}=84.5{\mathrm{cm}}^{-1}$ and ${\alpha }_{\mathrm{rpe}}=253.5{\mathrm{cm}}^{-1}$ was assumed. The total absorptions at the fundi are thus 29.2, 31.6, and 33.9% for ${\alpha }_{\mathrm{rpe}}=84.5$ , 169, and $253.5{\mathrm{cm}}^{-1}$ , respectively. The temperature versus time is depicted in Fig. 7 for $x=y=z=0$ , assuming the same laser parameters as in Sec. 3.1.1.

Fig. 7

Influence of different RPE absorptions on the retinal temperature increase with $a=1.33\mathrm{mm}$ and $P=270\mathrm{mW}$ on the retina.

As expected, the course of the three curves is the same except for a constant factor. The maximum calculated temperature increase after $60\text{-}\mathrm{s}$ irradiation is 7.8% less in the weakly pigmented than in the medium pigmented one. At the same time, it is 7.5% higher in the heavily pigmented RPE.

3.1.3.

Influence of perfusion on the chorioretinal temperature increase

In a further simulation, the influence of perfusion on the retinal temperature increase was calculated. In Fig. 8a , the calculated temperature increase over time is shown. The assumed laser parameters are the same as in Sec. 3.1.1. In contrast to the temperature curve without perfusion, the calculated temperature increase with heat convection reaches a constant temperature during irradiation time. At thermal equilibrium, the heat induced by the laser irradiation is equal to the energy leaving the area by heat conduction and blood flow. Figure 8b depicts the influence of the perfusion rate to the maximum temperature increase after a $60\text{-}\mathrm{s}$ irradiation. As shown, the final temperature increase does not linearly decrease with the perfusion rate. With a perfusion rate of $Q=0.13{\mathrm{s}}^{-1}$ (according to Ref. 36), the maximum temperature rise $\Delta T=7.4°\mathrm{C}$ is 38.5% lower compared to the value $\Delta T=12.0°\mathrm{C}$ obtained without perfusion. An even higher drop of 65.1% is seen for the maximum perfusion rate of $0.6{\mathrm{s}}^{-1}$ reported in Ref. 37.

Fig. 8

Influence of perfusion on the temperature increase at the RPE surface with $a=1.33\mathrm{mm}$ and $P=270\mathrm{mW}$ on the retina. (a) Temperature increase over irradiation time. (b) Maximum temperature after $60\mathrm{s}$ of irradiation over perfusion rate. (c) Lateral temperature increase for different perfusion rates. (d) Ratio of $\Delta T$ in the center to the border of the spot versus perfusion rate.

In Fig. 8c, the lateral temperature profiles after $60\text{-}\mathrm{s}$ irradiation for different perfusion rates are depicted. Due to the perfusion, the temperature within the spot is more constant with an increasing temperature gradient to the border of the spot.

Another simulation concerns the ratio of temperature increase induced in the center of the laser spot $(x=y=0)$ to the border ( $x=a$ , $y=0$ ). The result is shown in Fig. 8d. Without perfusion, the calculated temperature ratio between the center and border is 1.57. The ratio increases with increasing perfusion up to a factor of 1.98 for a perfusion rate of 1.0.

3.2.

Determination of the Temperature-Dependent Tissue Parameters

The maximal amplitude of the pressure wave in dependence of the temperature of retinal explants was measured for 12 porcine and two rabbit retinal explants. The explants were dissected from the globes and positioned in a cuvette. The cuvette was then filled with saline solution of $55°\mathrm{C}$ temperature.

Afterward, the radiation of the probe laser was applied to the explant. Within $30\min$ , the water bath was cooled down to $15°\mathrm{C}$ . During that time, about 100 data points were gained, with every data point being an average value of 30 pressure maxima for the same RPE temperature. Every measured maximal pressure was normalized to the corresponding pulse energy, thus compensating for pulse-to-pulse energy deviations of the laser source according to Eq. 3. The curves observed for the different retinal explants were normalized to a temperature of $37°\mathrm{C}$ and averaged. The standard deviation is less than 3% for all data points between 20 and $50°\mathrm{C}$ .

According to Eq. 7, a second-order polynomial was fitted to the averaged data. In Fig. 9 , the temperature dependence of the detected pressure maximum for rabbit and porcine retinal explants is depicted. The graph shows averaged curves for 12 porcine and two rabbit eyes. For the fitting parameters $T_0$ and $T_{\max }$ , values of $(-20.5\pm 1.1)°\mathrm{C}$ and $(114.4\pm 7.8)°\mathrm{C}$ were obtained for the porcine RPE explants. The constants for rabbit RPE explants are $T_0=(-22.5\pm 1.3)°\mathrm{C}$ and $T_{\max }=(150.4\pm 17.3)°\mathrm{C}$ , with the uncertainty being the error of the parameter value obtained by the non-linear curve fit. From 37 to $50°\mathrm{C}$ , the pressure maximum increases by 15.1% (pig) and 16.5% (rabbit).

Fig. 9

Temperature dependence of maximum detected ultrasonic pressure signal for porcine and rabbit RPE explants and typical pressure transient as detected by the ultrasonic transducer.

The insert in Fig. 9 depicts a typical pressure transient as detected by the ultrasonic transducer. The observed oscillation of the signal shows the response function of the transducer.

In all of the following experiments, the average values of $T_0$ and $T_{\max }$ were used for calculations of the chorioretinal temperature increases using Eq. 8.

3.3.

Temperature Determination on Porcine Eyes (Ex Vivo)

The chorioretinal temperature increase during TTT was determined by OA as well as by a thermocouple (TC) inserted transsclerally below the RPE layer for a quantification of the measurement accuracy. For the OA temperature determination, a retinal spot diameter of $0.3\mathrm{mm}$ and a pulse energy of $5\mu \mathrm{J}$ was used. The retinal diameter of the TTT laser spot was $2\mathrm{mm}$ . The irradiation was increased in four steps. With consideration of 6% reflectance of the Mainster Standard contact lens, and the assumption of 16% absorption in the anterior ocular media as measured for human eyes,³² retinal irradiances between 1.01 and $3.36\mathrm{W}∕{\mathrm{cm}}^2$ were applied. The position of the eye, the probe laser spot, and the TTT laser spot were kept stable between the measurements. To obtain the individually different scaling factor $s$ , 20 probe pulses were applied before each measurement and the average pressure maximum was detected at known ambient temperatures. The induced temperature increase during TTT laser irradiation over time is plotted in Fig. 10 . Figure 10a shows the thermocouple measurement for the four different irradiations, while Fig. 10b depicts the corresponding OA determined temperatures. The deviation of the temperature courses is shown in Fig. 10c.

Fig. 10

Temperature increase during TTT on a porcine eye (ex vivo) $(d=2\mathrm{mm})$ . (a) TC measurement; (b) OA determination; and (c) deviation of (a) and (b).

The TTT laser was switched on $10\mathrm{s}$ after the OA measurement started and lasted for $60\mathrm{s}$ . Right after the irradiation started, the temperature steeply increased with a maximum temperature at the end of the irradiation. In Table 1 , the maximum temperature increases at the end of the irradiation in dependence on the irradiance $I$ for TC measurement and OA determination are shown. For all curves, the OA determination shows a slightly higher temperature increase than the direct measurement. The maximum temperature increases are $5.5°\mathrm{C}∕(\mathrm{W}∕{\mathrm{cm}}^2)$ measured by the TC, and $5.8°\mathrm{C}∕(\mathrm{W}∕{\mathrm{cm}}^2)$ derived from OA determination. In Table 1, the deviation of $\Delta T_{\max }$ is given in absolute values, and relative to the TC measurement. The maximum deviation is hereby up to $1.2°\mathrm{C}$ with a highest percentage deviation of 8.6%.

Table 1

Maximum temperature increases for different irradiations on porcine eyes for TC measurement, and optoacoustic determination and deviation between the two measurement techniques.

As shown in Fig. 10c, the deviation varies with the irradiation time. The highest deviations occur at the beginning and right after the irradiation, caused by high differences in the slopes. The maximum temperature deviations are given in Table 1. The last column in Table 1 represents the average deviation for the irradiation time of $60\mathrm{s}$ .

The maximum deviation increases with the irradiance. The highest temperature deviation of $6.0°\mathrm{C}$ was observed for an irradiance of $3.36\mathrm{W}∕{\mathrm{cm}}^2$ right after the TTT laser was switched on. The highest average temperature deviation of $1.7°\mathrm{C}$ was also derived for the same irradiance.

3.4.

Temperature Determination on Rabbit Eyes (In Vivo)

Our first in vivo experiment served to investigate the correspondence and accuracy between OA and TC temperature determination on rabbits. Therefore, a miniaturized TC was inserted through a sclerotomy $1\mathrm{mm}$ posterior to the corneal limbus in the rabbit’s eye. The tip of the TC was positioned into the center of the TTT laser spot into the subretinal space resting on top of the RPE.

Figure 11 shows a photograph of the rabbit fundus taken during TTT irradiation through the ocular of the slit lamp. The TC and its central position can clearly be seen. During the irradiation the TC was handheld.

Fig. 11

Photograph of a rabbit fundus during TTT with a TC positioned in the center of the laser spot.

For the experiment, a retinal spot diameter of $2\mathrm{mm}$ with a power of $129\mathrm{mW}$ measured in front of the contact lens was used for heating. Due to a reflectance of 2.8% in the Haag-Streit contact lens for $810\text{-}\mathrm{nm}$ wavelength and assuming an absorption of 10% in the globe,^{33, 34} the retinal irradiance was $3.59\mathrm{W}∕{\mathrm{cm}}^2$ .

For the probe laser, a pulse energy of $6.3\mu \mathrm{J}$ was used at a retinal spot diameter of $0.3\mathrm{mm}$ . Five measurements were performed consecutively with neither moving the laser spot nor changing the laser settings. Three temperature curves were determined by OA and two by means of the handheld TC, as depicted in Fig. 12 .

Fig. 12

Temperature increase at the fundus of a rabbit eye during TTT (in vivo). OA and TC measurement and calculated data are shown. ( $d=2\mathrm{mm}$ , $I=3.59\mathrm{W}∕{\mathrm{cm}}^2$ ).

As expected from temperature calculation [Fig. 8a], a constant temperature plateau within the irradiation time was achieved due to perfusion. In the described experiment, this plateau was reached $20\mathrm{s}$ after starting the TTT laser irradiation. The obtained plateau temperature measured by the TC is between 4.1 and $6.2°\mathrm{C}$ . The temperature data as determined by OA are mainly within the TC range.

For a comparison with analytical data, a calculated temperature curve was fitted to the experimental data assuming a fundus geometry and absorption coefficients as described in Sec. 2.7. The best accordance to the averaged experimental curves with a maximum temperature increase of $5.5°\mathrm{C}$ was achieved with a global perfusion rate of $0.13{\mathrm{s}}^{-1}$ .

The same rabbit was used for another experiment to quantify the influence of perfusion on the chorioretinal temperature increase during TTT. The temperature increase was determined by OA at the same area pre- and postmortem while keeping the position of the rabbit stable. The retinal irradiation was set to $3.90\mathrm{W}∕{\mathrm{cm}}^2$ with a spot diameter of $2\mathrm{mm}$ . The probe laser parameters are the same as in the previous experiment. The rabbit underwent two irradiations in vivo and five postmortem. The averaged curves are plotted in Fig. 13 . The error bars indicate the standard deviation of the averaged measurements.

Fig. 13

Temperature increase at the fundus of a rabbit eye during TTT (in vivo), influence of perfusion ( $d=2\mathrm{mm}$ , $I=3.9\mathrm{W}∕{\mathrm{cm}}^2$ ).

In contrast to the living rabbit, the $\Delta T$ postmortem rose over the $60\mathrm{s}$ of irradiation. The averaged maximum temperature increase without perfusion was $8.6°\mathrm{C}$ compared to $5.3°\mathrm{C}$ with perfusion. Thus, $\Delta T_{\max }$ increased by 62.2% postmortem.

The average standard deviation for the temperature increase with perfusion (two measurements) was $0.24°\mathrm{C}$ , whereas for the determination without perfusion a value of $0.47°\mathrm{C}$ was obtained.

The temperature slopes were calculated analytically. For the vital rabbit, a perfusion rate of $0.22{\mathrm{s}}^{-1}$ shows the best correspondence to experimental data. The results of the calculation are also plotted in Fig. 13. Both simulations for the vital and dead rabbit are in good accordance to the experimental gained data, with an average deviation during irradiation of $0.30°\mathrm{C}$ respective of $0.24°\mathrm{C}$ compared to the averaged experimental data.

In a further experiment, another rabbit underwent five TTT irradiations using slightly differing intensities on different retinal areas. For all irradiations, the temperature increase was determined by OA. Before the irradiation, the retina was marked by high intensity radiation of a diode laser coupled into an indirect ophthalmoscope with a retinal spot diameter of $0.5\mathrm{mm}$ . The distance between the rectangularly arranged spots was $5\mathrm{mm}$ in each direction. This marking was necessary for a better identification of the treated areas in fundus images.

The power of the TTT laser ranged from $115\text{to}148\mathrm{mW}$ . Due to a reflectance of the Mainster Standard contact lens of 6% and a retinal spot diameter of $2\mathrm{mm}$ , retinal irradiances between 3.10 and $3.96\mathrm{W}∕{\mathrm{cm}}^2$ were achieved. The retinal diameter of the probe laser spot was $0.3\mathrm{mm}$ with a pulse energy of $6.3\mu \mathrm{J}$ . Figure 14 shows a fundus image of the rabbit eye after the laser irradiations. The five treated areas are marked by white circles, with the spot numbers in chronological order. The whole experiment took $30\min$ with at least five minutes between two irradiations. In the third irradiation (spot 3), a whitening of the retina occurred after $40\mathrm{s}$ of irradiation time.

Fig. 14

(a) White light fundus image of rabbit eye after laser irradiation. The white spots are coagulations caused by the diode laser radiation. (b) Corresponding temperature increases $(d=2\mathrm{mm})$ .

The corresponding temperature slopes over time are plotted in Fig. 14b. It is shown that for irradiations 1, 2, 4, and 5 with irradiances between 3.10 and $3.77\mathrm{W}∕{\mathrm{cm}}^2$ , an almost constant temperature increase was reached after $10\text{-}\mathrm{s}$ irradiation time. The temperature increases for the plateaus are between 6.4 and $9.7°\mathrm{C}$ , while the temperature level is not linear in comparison to the individual irradiation. For the third irradiation with $3.96\mathrm{W}∕{\mathrm{cm}}^2$ , an extraordinary high temperature increase of more than $20°\mathrm{C}$ was obtained, even though the irradiation was only 5.0% higher than irradiation 5. The moment the lesion became visible to the ophthalmologist during the irradiation is demarcated with an arrow.

4.1.

Analytical Modeling

As many laser therapies in ophthalmology evoke a therapeutic effect due to heating, several temperature calculations have been performed, particularly models for laser photocoagulation at the retina with exposure times up to $300\mathrm{ms}$ .^{16, 17, 24, 38} However, the calculated temperatures are not linearly transferable to long exposure times like in TTT, since the perfusion in the choroid cannot be neglected for exposure times of seconds to minutes.

In the analytical model used for this work, the results should be understood as adjuvant for a general understanding of the temperature increases during laser irradiation of the fundus and the influence of the different tissue properties on it. The temperature increase and temporal course depend on the absorption of the different layers, their thickness and distances, as well as on the blood perfusion for long irradiation times as in TTT. The different influences are discussed in the following sections.

For exposure times of $60\mathrm{s}$ , the lateral temperature decreases as the radial distance to the center of the spot increases, as shown in Fig. 6b. For a treatment, this fact should be accounted for by using spot diameters larger than the diseased area to obtain a sufficient temperature increase over the whole diseased area. However, the temperature difference between center and border of the spot might result in a central coagulation without having any effect to the outer area. To achieve a constant temperature profile over the whole irradiated area, it is necessary to change the lateral laser spot profile in such a way that the intensity is increasing with the distance to the center, e.g., by a ring profile or torus (doughnut mode).

The simulations on the dorsal temperature profile after $60\mathrm{s}$ of TTT irradiation show that the temperature within the absorbing layers of the eye is almost constant due to heat convection and the long exposure time. The long exposure time is also the reason why the total absorption of the fundus is of much higher interest for the temperature increase than the detailed absorption of RPE and choroid. By convection, the induced heat disperses over all fundus layers. The longer the exposure time, the smaller the influence of location and thickness of every absorbing layer, i.e., the influence of RPE pigmentation plays a minor role for this wavelength. The RPE absorption in the rabbit (6.54% for $\lambda =810\mathrm{nm}$ ) compared to the choroidal absorption (26.80% for $\lambda =810\mathrm{nm}$ ) is rather low. With increasing absorption ratio, the differences in RPE pigmentation might have a stronger influence on the temperature increase.

For shorter exposure times (e.g., photocoagulation with $\tau \approx 100\mathrm{ms}$ ), the RPE pigmentation has a much higher influence. For humans the calculated contribution to the total temperature increase from RPE layer is 65% compared to a choroidal contribution of 35%.²⁴ In this case, individually varied RPE pigmentation might result in high temperature differences.

Even though choroidal perfusion has a negligible effect in retinal photocoagulation,³⁹ the influence on the chorioretinal temperature increase during TTT was clearly shown. Even with a comparatively small perfusion rate of $0.1{\mathrm{s}}^{-1}$ , the maximum $\Delta T$ is 33.9% less than without perfusion. This might have a significant influence on TTT, because areas of high temperature might occur within the irradiated area, in which the individual perfusion is low. On the other hand, the temperature increase induced on areas above the main vessels might be obviously less than in surrounding areas.

The simulations that monitored the influence of perfusion on the temperature course [Fig. 8c] and the ratio of temperature increase induced between the center and the border of the spot [Fig. 8d] indicates that the temperature gradients at the border of the laser spot increase with perfusion. Increasing perfusion averages the temperature profile within the irradiated area with a rather steep gradient at the rim of the spot. In perfused tissue, the heated area is more localized within the spot, even though the maximum temperature is less.

In a medical application, the perfusion rate also depends on the intraocular pressure, which can be varied by the pressure of the contact lens to the cornea. Therefore, a higher pressure might result in reduced perfusion and thus induce a higher temperature increase during laser irradiation.

Overall, the utilized analytical model is adequate for a general understanding of the influence of tissue parameters on the shape and slope of the laser-induced temperature increase.

The main limitation is given by the assumption of a global perfusion rate, as the rabbit’s physiology differs from this assumption. A thermal model with perfusion localized only in the choroid might result in much higher perfusion rates and different temperature slopes. Moreover, the assumption of a constant perfusion rate, independent of the observed area, does not reflect a retinal laser treatment very well, since for large spot sizes the blood will already accumulate heat as it crosses the irradiated spot. Such considerations cannot be implemented by analytical modeling and will be part of a numerical temperature model currently under development.

When observing a central temperature increase, the influence of a rectangular spot instead of a circular profile will have a minor influence, since the central heating induced by the border of the spot is comparably small. This is no longer valid if the temperature increase at the border shall be considered.

For large spot diameters, as given in TTT, the assumption of neglected scattering is appropriate, because most of the scattered light is absorbed within the irradiated area anyway, especially if a temperature increase in the center of the spot is regarded.

The influence of tissue heterogeneities like single melanosomes within the RPE is negligible for long irradiation times, as the heat conduction leads to an almost constant depth temperature profile during heating time. However, the results obtained in simulations are appropriate to generally describe temperature courses at the fundus. For a more realistic examination, a numerical model considering local perfusion in the choroid and a circular irradiation is needed. The implementation of such models is in progress.

4.2.

Temperature Dependence of the Grüneisen Parameter $\Gamma$

The temperature dependence of the pressure wave maximum for porcine and rabbit retinal explants show an analog course in the measured temperature range. The findings for porcine retinal explants are similar to results obtained by Schüle in related experiments, using a wavelength of $527\mathrm{nm}$ and a pulse length of $1.7\mu \mathrm{s}$ with a linear approximation, who obtained an increase in $p_{\max }$ of 14.6% from 37 to $50°\mathrm{C}$ .¹⁴ The increase of $p_{\max }$ for water in the same range is with 30% about twice as large as for an eye fundus.¹⁹

In order to receive an adequate signal-to-noise ratio for every single pressure transient, it is desirable to obtain the highest possible pressure amplitude. It is therefore beneficial that the specimen shows a high absorption for the used laser wavelength. Due to the absorption curve for melanin,³¹ the main absorber in the RPE, a maximum amplitude can be achieved using a wavelength in the visible range. The shorter the wavelength, the higher the absorption. The second important factor is the pulse duration. For a pulse duration longer than the acoustic transit time ( $t_{\mathrm{trans}}=2.7\mathrm{ns}$ for rabbit RPE with $d=4\mu \mathrm{m}$ ), the induced pressure amplitude decreases almost exponentially with the pulse duration.¹⁸ With respect to these two factors, the choice of a $500\text{-}\mathrm{nm}$ wavelength with a pulse duration of $3.5\mathrm{ns}$ is adequate.

4.3.

Temperature Determination on Ex Vivo Eye Globes

A general comparison between OA temperature determination and TC measurement on porcine eye globes shows a very good accordance.

As for TTT, the maximum temperature increase might cause the highest retinal damage; the measurement accuracy given by the deviation of $\Delta T_{\max }$ between TC measurement and OA determination is important for the applicability of this technique. The deviation between TC measurement and OA temperature determination is comparatively small at the end of the irradiation compared to the beginning. The OA determination shows a much higher temperature gradient at the beginning. This might indicate that the position of the TC is too deep in the eye, resulting in a slower temperature increase. Another fact is that the spherical tip of the thermocouple with a diameter of $250\mu \mathrm{m}$ detects an average temperature of the tissue integrated over the contacted area. With increasing irradiation time, the difference is decreasing because the whole tissue is heated up with only marginal temperature differences resulting from depth (see Sec. 3.1.1).

The induced temperature increases proportionally to the applied laser power. The calculated temperature after a $60\text{-}\mathrm{s}$ irradiation is $5.5°\mathrm{C}∕(\mathrm{W}∕{\mathrm{cm}}^2)$ derived from the TC measurement and $5.8°\mathrm{C}∕(\mathrm{W}∕{\mathrm{cm}}^2)$ derived from OA determination.

The temperature curves for the OA determination are much noisier than the according TC measurements. Possible reasons are that the cable from the transducer to amplifier might act as an antenna inducing noise, which is thereafter also amplified by $54\mathrm{dB}$ , as well the noise of the amplifier itself.

4.4.

Temperature Determination and Simulation In Vivo

Comparable OA temperature determination and TC measurement on a living rabbit show on one animal that the OA temperature determination is within the two temperature curves gathered by a thermocouple. As the thermocouple was handheld during the measurement, a precise positioning in the center and on the RPE without evoking lesions or retinal bleedings over the whole irradiation time is almost impossible. Even though the direct absorption of radiation of the thermocouple is negligible, the insertion from the same direction as the laser radiation causes differences in the heating process due to reflecting the radiation and causing shadowing on the fundus.

Compared to the ex vivo experiments on porcine eyes, the noise on the temperature data in rabbits is higher. The main reason is that the amplitude of the induced pressure wave is less due to a weaker absorption of the probe laser pulse in the rabbit’s fundus. Another reason is a poorer acoustic adaption of the ultrasonic transducer to the cornea. The contact lens is designed for the radius of a human cornea, having the same radius as porcine cornea. Rabbit’s corneal radii are smaller, resulting in poorer matching to the contact lens.

The calculated temperature increase for this experiment shows good correspondence to the average obtained experimental data by assuming a global perfusion rate of $0.13{\mathrm{s}}^{-1}$ . This is a realistic value for rabbit choroidal blood flow.¹⁷ In further simulations, the assumed global perfusion rate needs to be reduced to a choroidal perfusion for a better comparison to literature data.

The proposed influence of perfusion to the chorioretinal temperature increase during TTT is verified experimentally for the first time. The calculated temperature curves are in very good accordance to the experimentally gained data. In this in vivo experiment, the assumed global perfusion rate of $0.22{\mathrm{s}}^{-1}$ is higher than in the previous experiment (Fig. 12), even though the experiments were performed on the same rabbit. This might indicate that the probe laser spot was positioned on a higher perfused area like a main vessel.

In the last experiment on rabbits, the influence of intraindividual factors on the retinal temperature increase can clearly be observed. In contrast to the ex vivo experiment on porcine eyes, (Fig. 10), the temperature slopes obtained at different retinal areas are not linearly increasing with the intensity. The individual factors accounting for an individual temperature increase cannot be determined beforehand. The areas appeared equal without hints for higher or lower pigmentation or choroidal perfusion rates under white light examinations.

The slope of the temperature increase observed for irradiation 3 is more comparable to slopes determined in ex vivo experiments. This might indicate that the perfusion for this irradiated area was very weak, causing the high temperature increase. This leads subsequently to a coagulation, which became visible as a whitening of the retina. The quantified temperature threshold of $21°\mathrm{C}$ is comparable to results by Ip, Kroll, and Reichel,⁴⁰ who obtained coagulation necrosis above $60°\mathrm{C}$ retinal temperature within $0.5\text{to}1\mathrm{s}$ .

In clinical TTT, the online determined temperature increases could have predicted this lesion before occurrence. The laser power could have been lowered, or the laser could even have been switched off to prevent such damage.

4.5.

Implications on Transpupillary Thermotherapy

It was shown that the presented OA technique is sufficient for a retinal temperature determination during cw-laser irradiation. The instantaneous temperature increase caused by the absorption of the laser pulse can be estimated by $\Delta T=\alpha H∕\rho c_V$ .¹⁹ For a pulse energy of $5\mu \mathrm{J}$ and a spot diameter of $0.3\mathrm{mm}$ , this leads to an $\Delta T$ of less than $3°\mathrm{C}$ , assuming an absorption coefficient of $1700{\mathrm{cm}}^{-1}$ as realistic for human RPE.²⁴ This temporary temperature increase does not contribute significantly to the baseline temperature, as it is negligible at the occurrence of the following pulse.

The developed technique is safe for the patient and might also be used as a temperature-based dosimetry control to prevent under- and especially overtreatment during TTT. Further, the technique can be used to evaluate if an optimum treatment temperature exists, in which a therapeutic effect is evoked while below the coagulation temperature. Due to prosperous results, the power of the TTT laser might be automatically feedback controlled by the temperature information gained from the OA determination. Within the measurement accuracy, it should be possible to achieve a constant temperature increase independent of the individual tissue parameters of the patient, thus leading to a customized TTT application.