2.1.

Optoacoustic Temperature Measurement

The temperature measurement is based on the optoacoustic effect. The temperature-dependent pressure generation is described thoroughly by Brinkmann et al.²⁸ If a laser pulse with pulse duration ${\tau }_p$ is applied to an absorber, the absorbed energy $E$ is converted to heat and the temperature of the absorber rises by

$T_0$ and $T_{\max }$ are the tissue specific parameters that were determined for rabbits by a calibration measurement of the optoacoustical signal for known temperatures²⁶ as $T_0=-17.4°\mathrm{C}\pm 0.3°\mathrm{C}$ and $T_{\max }=102.9°\mathrm{C}\pm 2.2°\mathrm{C}$.

The proportionality constant $s$ is unique for each irradiation site and contains information of the pigmentation at each irradiated area, but also on the light and sound transmission through the eye as well as the detector characteristics. It is, therefore, required to determine $s$ for each individual irradiation site prior to the application of the therapy laser radiation. If one measures the pressure $p(t,T_{\mathrm{ref}})$ at a known temperature $T_{\mathrm{ref}}$, in this case the body temperature during in vivo experiments, Eq. (5) can be solved for $s$. This step allows us to take the site-individual variations in signal into account.

2.2.

Power-Controlled Retinal Photocoagulation

In order to perform irradiations within a set time frame with a fixed desired end temperature $T_{\text{aim}}$, the laser power during the photocoagulation is adjusted depending on the site-individual temperature information. This is shown in Fig. 1.

Fig. 1

Irradiation scheme for the power-controlled dosimetry. After a calibration phase, a probe irradiation at a low power $P_{\text{probe}}$ is conducted to reveal the tissue parameters. The probe temperature $T_{\text{probe}}$ is measured and used to calculate the necessary power for the treatment irradiation $P_{\text{treatment}}$ in order to create the treatment temperature $T_{\text{treatment}}$.

Each irradiation consists of three phases. In the calibration phase of duration $t_{\mathrm{cal}}$, calibration pulses are applied to the unheated fundus tissue in order to determine the irradiation site specific parameter $s$. This calibrates the feedback signal to the base temperature of the absorber before the start of the treatment $T_{\mathrm{ref}}$ (here, the body temperature of the rabbit for the in vivo experiments). After the calibration, an irradiation at a low power $P_{\text{probe}}$ is performed for an irradiation time $t_{\text{probe}}$, during which the temperature rise $T_{\text{probe}}$ is monitored. The knowledge of $T_{\text{probe}}$ and $P_{\text{probe}}$ can be used to calculate the required power $P_{\text{treatment}}$ to reach the desired temperature rise $T_{\text{aim}}$. The tissue is irradiated with the calculated treatment laser power $P_{\text{treatment}}$ and the irradiation time $t_{\text{treatment}}$, and the temperature reaches $T_{\text{treatment}}$ in order to create the desired lesion strength at the end of the irradiation.

2.3.

Temperature Profile During Retinal Photocoagulation

When heating the rabbit fundus, the radiation is absorbed in the monolayer melanin granules of the RPE and the pigmented part and blood of the choroid. As the rabbit is a merangiotic animal, the blood vessels are confined to these regions and the absorption in the inner retina can be neglected. A model for rabbit eyes with absorption coefficients of ${\mu }_a=1204$ and $260{\mathrm{cm}}^{-1}$ with thicknesses 4 (absorbing part of the RPE) and $30\mu \mathrm{m}$ (absorbing part of the choroid), respectively,³⁵ was used for the calculations. According to the heat diffusion equation

However, $T_{\text{volume}}(t)$ is not a suitable parameter to describe the coagulation process. The peak RPE surface temperature of the irradiated volume $T_{\text{peak}}(t)$, which is located at the center of the irradiated area close to the surface of the RPE, provides a better description, as it determines the onset of the retinal coagulation. $\mathrm{\Delta }{T}_{\text{peak}}(t)$ is correlated to $\mathrm{\Delta }{T}_{\text{volume}}(t)$ via a time-dependent conversion function

The conversion function and its properties are described in detail by Schlott et al.²⁵ and the radial and axial temperature profiles are more thoroughly investigated by Brinkmann et al.²⁸ Hence, only the adjustments that are necessary for this method are described here.

For the power-controlled irradiation, the conversion function is not just one continuous function but has to be determined for the probe phase and the treatment phase independently. We used a mathematical model to derive $f(t)$ for the two irradiation phases at the rabbit fundus. The commercially available software COMSOL Multiphysics 4.2 is a finite-element numerical simulation software, which was used here to solve the heat diffusion equation [Eq. (6)]. The light–tissue interaction is not modeled directly but rather treated as a heat source $Q(\overrightarrow{r},t)$, which describes the laser energy deposition per time and volume in $\mathrm{W}/{\mathrm{m}}^3$ and can be described within the irradiated volume during the irradiation as

Table 1

Layer thicknesses and absorption coefficients of the rabbit fundus as used in the numerical model.

Light scattering is not incorporated in the model. The geometry is more thoroughly discussed by Schlott et al.²⁵ and shown in Fig. 2(a). The origin $(x,y,z)=(0,0,0)$ is at the center of the square irradiated area at the surface of the RPE. The temperature rise is shown for the end of the treatment at $t=50\mathrm{ms}$ with a calibration power $P_{\mathrm{c}\mathrm{a}\mathrm{l}}=3\mathrm{mW}$ (which corresponds to a pulse energy of 3 µJ applied with a repetition rate of 1 MHz), a probe power $P_{\text{probe}}=10\mathrm{mW}$ and a treatment laser power $P_{\text{treatment}}=20\mathrm{mW}$ in a vertical $x\text{-}z$-slice through the fundus layers, where $x$ is one of the radial coordinates and $z$ is the axial coordinate with the upper edge of the RPE located at $z=0$. The axial temperature profile development over time (b) as well as the profile in $x$-direction (c) is also shown.

Fig. 2

Fundus layer geometry and temperature distribution for the temperature simulation on the rabbit fundus, displayed for (a) a vertical slice through the rabbit fundus with isothermal contours indicating the regions with a temperature rise of 1, 4, 6, 8, 10 and 12°C, (b) along the z-axis, and (c) on the surface of the RPE along the x-direction for 1, 10, 20, and 40 ms after the calibration phase, which corresponds to t = 11, 20, 30, and 50 ms, respectively. The displayed temperature profile occurs at the end of the treatment at t = 50 ms. The edge length of the irradiation beam (arrow) is d = 200 μm.

In the model, the remaining tissue parameters are assumed to be that of water [$\rho =993\mathrm{kg}/{\mathrm{m}}^3$; $C_p=4176\mathrm{J}/(\mathrm{kg}\mathrm{K})$; $k=0.627\mathrm{W}/(\mathrm{m}\mathrm{K})$]. The temporal temperature development of $\mathrm{\Delta }{T}_{\text{peak}}$ and $\mathrm{\Delta }{T}_{\text{volume}}$ as calculated from the temperature profiles is shown in Fig. 3.

Fig. 3

Simulation results for $\mathrm{\Delta }{T}_{\text{peak}}(t)$ (solid line) and $\mathrm{\Delta }{T}_{\text{volume}}(t)$ (dashed line) over the course of an entire irradiation, consisting of 10-ms calibration phase, 20-ms probe phase, and 20-ms treatment phase. $P_{\text{probe}}$ was chosen as 10 mW and $P_{\text{treatment}}$ was chosen as 20 mW.

For the experiments, we used a fiber with a square core, so the integration in Eq. (7) was carried out in carthesian coordinates. This also necessitates the simulation being run in three-dimensions, because there is no radial symmetry. The simulation parameters were chosen to be $P_{\mathrm{c}\mathrm{a}\mathrm{l}\mathbf{i}\mathrm{b}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}=3\mathrm{mW}$ which corresponds to a pulse energy of 3 µJ applied with a repetition rate of 1 MHz, $P_{\text{probe}}=10\mathrm{mW}$, $P_{\text{treatment}}=20\mathrm{mW}$ and $d=200\mu \mathrm{m}$. By taking the ratio of $\mathrm{\Delta }{T}_{\text{peak}}$ and $\mathrm{\Delta }{T}_{\text{volume}}$ according to Eq. (9), one can determine the conversion function $f(t)$. We split the conversion function into two parts, $f_{\text{probe}}(t)$ and $f_{\text{treatment}}(t)$, corresponding to the probe and treatment phase, respectively.

From Fig. 1, the ratio of powers $P_{\text{treatment}}/P_{\text{probe}}$ can be correlated to the ratio of temperatures $\mathrm{\Delta }{T}_{\text{treatment}}/\mathrm{\Delta }{T}_{\text{probe}}$. If the tissue was allowed to cool down to $\mathrm{\Delta }{T}_{\mathrm{ref}}$ prior to applying $P_{\text{treatment}}$, then $P_{\text{treatment}}/P_{\text{probe}}=\mathrm{\Delta }{T}_{\text{treatment}}/\mathrm{\Delta }{T}_{\text{probe}}$, because the temperature rise is proportional to the introduced heat.³⁶ However, if the temperature is not completely cooled down when the treatment phase starts, $f$ becomes a function of the spot size used, the time of the probe phase and the time gap to the start of the treatment phase. Therefore, we used the mathematical model to calculate the relationship between the ratios. The temperature rise from the two successive phases was simulated by varying the laser powers $P_{\text{probe}}$ and $P_{\text{treatment}}$ for different beam diameters and calculating the temperatures. By plotting $\mathrm{\Delta }{T}_{\text{treatment}}/\mathrm{\Delta }{T}_{\text{probe}}$ over $P_{\text{treatment}}/P_{\text{probe}}$, we found a linear correlation that could be fitted according to $\mathrm{\Delta }{T}_{\text{treatment}}/\mathrm{\Delta }{T}_{\text{probe}}=m*P_{\text{treatment}}/P_{\text{probe}}+b$, where $m$ is the slope of the curve and $b$ is the intersection with the temperature axis. We found $m=1$ for all diameters, but the intersection was radius-dependent, as is shown in Fig. 4. The simulated data were fitted with a parabola.

Fig. 4

Irradiation diameter dependency of the intersection $b$ for the linear approximation between the ratio of temperature rises and the laser powers.

The powers $P_{\text{probe}}$ and $P_{\text{treatment}}$ consist of the laser power of the therapy beam $P_{\mathrm{th}}$ and the mean power introduced by the measurement laser pulses $P_{\text{pulse}}$ ($P_{\text{probe}}=P_{\text{probe},\mathrm{th}}+P_{\text{probe},\text{pulse}}$, $P_{\text{treatment}}=P_{\text{treatment},\mathrm{th}}+P_{\text{treatment},\text{pulse}}$). $P_{\text{pulse}}$ remains the same for the successive irradiations ($P_{\text{probe},\text{pulse}}=P_{\text{treatment},\text{pulse}}=P_{\text{pulse}}$). Using this and solving for $P_{\text{treatment},\mathrm{th}}$ yields

$P_{\text{treatment},\mathrm{th}}$ is the power that is required during the treatment phase in order to reach $T_{\text{aim}}$ at the end of the treatment phase. Of particular interest is the conversion function $f_{\text{treatment}}(q,t)$ for different ratios of laser powers $q=P_{\text{probe}}/P_{\text{treatment}}$. This is depicted in Fig. 5. After calculating $P_{\text{treatment}}$, the temperature is monitored using the corresponding conversion function based on $q$.

Fig. 5

Conversion functions $f_{\text{treatment}}$ for the treatment phase for different ratios of $P_{\text{probe}}$ and $P_{\text{treatment}}$.

3.1.

Experimental Setup

The experimental setup is shown in Fig. 6. The therapy laser is a frequency doubled Nd:YAG (Visulas 532 s, Carl Zeiss Meditec AG, $\lambda =532\mathrm{nm}$, cw). After starting the irradiation via a footswitch, the PC opens the shutter that blocks the measurement laser radiation (Uniblitz LS6, aperture 6 mm, time to open: 0.7 ms). The temperature measurement is performed using light from a frequency doubled Q-switched Nd:YLF laser (QC-523-1000, CrystaLaser, $\lambda =523\mathrm{nm}$, $\tau =75\mathrm{ns}$, $f=1\mathrm{kHz}$), which emits one pulse every millisecond. The radiation is coupled via a microscope objective into a multimode fiber (square core with edge length $d=70\mu \mathrm{m}$, $\mathrm{NA}=0.11$). The fiber is connected to a laser slit lamp (LSL 532s, Carl Zeiss Meditec AG), which guides the light through a contact lens. The lens is a modified commercial lens (Mainster Focal Grid, OMRA-S, Oculus Instruments) with a laser spot magnification of 1.05 into which an annular piezoceramic ultrasonic transducer with a center frequency of $f_{\mathrm{p}}=1\mathrm{MHz}$ and a bandwidth of 410 kHz was embedded to detect the incident pressure waves. The light is then focused onto the rabbit fundus for the irradiation. The measurement light induces the optoacoustic ultrasound waves from the retinal layers, which travel through the ocular media and reach the contact lens with the embedded transducer, where they are converted into electrical signals that are amplified and recorded via a digitizer card (CompuScope 8347, Gage Applied Technologies). The data processing and feedback control are performed by a custom made LabVIEW routine. The measured pressure provides the temperature information according to Eq. (5).

Fig. 6

Set-up for the power-controlled retinal photocoagulation.

The light from the therapy laser after opening the shutter (Uniblitz LS6) is superimposed with the light from the measurement laser and both are coupled into the fiber. This way the measurement irradiation is guaranteed to irradiate the same volume as the therapy irradiation. The laser power is controlled using an input/output card (NI PCIe-6341, National Instruments) to perform the treatment during the treatment phase.

3.2.

Animal Model

The experiments on chinchilla gray rabbits in vivo were carried out according to the German law for protection of animals, approved by the Ministry of Agriculture, the Environment and Rural Areas of Schleswig-Holstein, Kiel, Germany. Prior to the irradiation, the rabbits were anesthetized using ketamine (10%, 0.5 to $0.7{\mathrm{mL}·\mathrm{kg}}^{-1}$) and xylazine (2%, 0.2 to $0.25{\mathrm{mL}·\mathrm{kg}}^{-1}$).

3.3.

Treatment Scheme

After the animal was narcotized, it was fixed in a custom-made holding device in front of the slit lamp. The modified contact lens was placed on the rabbit’s eye and mechanically fixed. In order to adapt the acoustical and optical properties of the contact lens and cornea, methylcellulose gel (2%) was used as a contact gel. The body temperature was measured rectally. The beam edge length was set to $300\mu \mathrm{m}$ on the slit lamp, which results in a beam edge length of $d=200\mu \mathrm{m}$ on the rabbit fundus. The calibration phase time was chosen to be $t_{\mathrm{cal}}=10\mathrm{ms}$ and the probe and treatment phase times were both set to $t_{\text{probe}}=t_{\text{treament}}=20\mathrm{ms}$, bringing the resulting total irradiation time per site to 50 ms. During the calibration phase, the shutter for the therapy laser remains closed and was opened at the beginning of the probe phase. The therapy laser power during the probe phase $P_{\text{probe},\mathrm{th}}$ was chosen so that $T_{\text{probe}}$ at the end of the probe phase was $\sim 45°\mathrm{C}$. This ensured that the temperature rise during the probe phase would not result in irreversible coagulation effects of the tissue, while at the same time ensuring that the temperature rise is above noise level and can be fitted well. The therapy laser radiation heats the fundus tissue and the resulting temperature curve during the probe phase is fitted with a curve as described by Schlott et al.²⁵ to determine $T_{\text{probe}}$, which is then used to determine the required laser power during the treatment phase $P_{\text{treatment},\mathrm{th}}$. The calculation of $P_{\text{treatment},\mathrm{th}}$ and the adjustment of the therapy laser can be carried out within $<1\mathrm{ms}$ during the irradiation. The aim temperatures were chosen as 50°C, 55°C, 60°C, 65°C, 70°C, and 75°C. For the first five rabbits (group 1), only the aim temperatures of 50°C, 55°C, 65°C, and 75°C were used in order to find the ED50 value for ophthalmoscopic visibility. Two additional rabbits (group 2) were irradiated with the aim temperatures 60°C, 65°C, 70°C, and 75°C to resolve the ED50 value more thoroughly. The measurement pulse energy was adjusted between 3 and $5\mu \mathrm{J}$, depending on the quality of the pressure signal. The measurement pulse energy has to be high enough in order to create a strong photoacoustic signal, but at the same time low enough to prevent it from noticeably heating the tissue during the calibration phase. While the exposure to the measurement pulses in this case is above the threshold values for the maximum permissible exposure, the applied energy does not lead to a denaturation of the tissue that would influence the measurement of the temperature. Regardless, the mean power of the pulses has to be considered for the following therapy as shown in Eq. (12).

In order to evaluate the visibility of the lesions, fundus images were taken 1 h after the treatment using a fundus camera (VISUCAM^®, Carl Zeiss Meditec AG). The visibility of the lesion was judged from these fundus images by four independent observers. The lesion was classified as “visible” (1), if three of four observers agreed on seeing the lesion and as “invisible” (0) otherwise.

4.1.

Accuracy of Aim Temperatures

The distribution of the final treatment temperatures $T_{\text{treatment}}$ and the corresponding irradiation powers $P_{\text{treatment},\mathrm{th}}$ are shown in Table 2 and displayed with their standard deviations ${\sigma }_T$ and ${\sigma }_P$, respectively, in Fig. 7, as well as the standard error for $T_{\text{treatment}}$ $\sigma /\sqrt{N}$. The end temperatures of $N_{\text{total}}=1001$ irradiations could be evaluated. To better compare the standard deviations of the temperature and the laser powers, the relative deviation ${\sigma }_{\mathrm{rel}}$ for both is given in %. For the temperature, one has to consider the error on the temperature rise $\mathrm{\Delta }{T}_{\text{treatment}}=T_{\text{treatment}}-T_{\mathrm{ref}}$ in accordance to Eq. (12), so the relative error ${\sigma }_{\mathrm{rel},T}$ is, therefore, given as ${\sigma }_T/\mathrm{\Delta }{T}_{\text{treatment}}$ with $T_{\mathrm{ref}}=38°\mathrm{C}$. There is no such offset for the power, so ${\sigma }_{\mathrm{rel},P}$ is simply ${\sigma }_P/P_{\text{treatment},\mathrm{th}}$. The dashed line in Fig. 7 represents the bisecting line through the origin for the temperature axis, that is, the line on which the measured temperatures should fall.

Table 2

Aim temperatures, measured treatment temperatures, corresponding treatment powers, and number of irradiations for the power-controlled coagulations.

Fig. 7

Power control treatment temperatures and laser powers. The dots denote the mean value of the temperatures at the end of the treatment with their respective standard deviations. The triangles show the mean value of the treatment phase therapy laser power for each aim temperature with their respective standard deviations ${\sigma }_T$ and ${\sigma }_P$. The symbols for the powers are shifted slightly to improve visibility.

The mean measured temperatures (dots) agree very well with the target values (dashed line). The standard deviation of the temperatures increases with higher aim temperatures. For all temperatures, the corresponding treatment laser powers $P_{\text{treatment}}$ (triangles) show a larger standard deviation than the temperatures (about twice the relative deviation), indicating that the algorithm used laser powers over a wide range to reach the desired end temperature.

4.2.

Visibility Threshold of Irradiations

Figure 8 shows a fundus image of the power-controlled irradiation sites for the different aim temperatures taken 1 h after the end of the irradiation for one of the rabbits from group 1, Fig. 9 shows the same for one of the rabbits from group 2. The images show the appearance of the irradiation sites for the different aim temperatures.

Fig. 8

Fundus image of power-controlled irradiation sites in vivo for $T_{\text{aim}}=50°\mathrm{C}$, 55°C, 65°C, and 75°C. Marker lesions for orientation are marked as “M.”

Fig. 9

Fundus image of power-controlled irradiation sites in vivo for $T_{\text{aim}}=60°\mathrm{C}$, 65°C, 70°C, and 75°C. Marker lesions for orientation are marked as “M.”

Visible lesions appear as white areas due to the increased scattering of the coagulated tissue. The bright white lesions marked with an “M” are marker lesions that are used for orientation. Within a square that is formed by four marker lesion areas, nine study irradiations with the same $T_{\text{aim}}$ were performed.

The irradiation sites for $T_{\text{aim}}=50°\mathrm{C}$ and 55°C almost exclusively show no visible coagulation effects and the irradiation sites for 60°C and 65°C are in the transition regime between invisible and visible effects, where the 60°C mostly remain invisible and the majority of the 65°C lesions become visible as mild coagulations. The irradiation sites for 70°C and 75°C are almost exclusively visible and are more pronounced than the lesions for 60°C and 65°C. The intensity of those lesions is compatible with the current clinical treatment recommendation for panretinal photocoagulation treatment.

The visibility for each $T_{\text{aim}}$ is presented in Table 3. The number of irradiation areas where the visibility could be evaluated $N_{\mathrm{irr}}$ is compared to the number of visible irradiation outcomes for each aim temperature $T_{\text{aim}}$. The fraction of these two values is given in %.

Table 3

Number of evaluable irradiation areas Nirr and the number of visible lesions among them for each Taim.

The evaluation of the visibility of the lesions from the fundus images and the corresponding temperatures can be used to find the ED50 value for ophthalmoscopical visibility, which is the temperature at which there is a 50% probability that the lesion becomes visible. The value is determined by performing a probit analysis of the binary data (visible and invisible) of the lesions. The result can be seen in Fig. 10, the visible lesions are indicated as black crosses in the top row, and the invisible lesions are at the bottom of the graph.

Fig. 10

Probit-plot evaluation of the ED50 value for ophthalmoscopical visibility 1 h after irradiation.

A total of 920 lesions in 11 eyes of 7 rabbits was evaluated. The number is lower than the number of irradiated sites, as not all areas could be imaged with the camera. Additionally, we omitted regions where image quality was too poor to give reliable results. The probit curve is displayed as the solid line, the ED50 value was calculated to be 65.3°C with a 95% confidence interval (indicated by the dashed lines). As the total number of visible and invisible lesions is difficult to assess from the graph, as the crosses conceal each other, the density of the visibility is shown for distinct temperature intervals (bars). The bar graph shows the normalized visibility per temperature interval, i.e., the number of visible lesions divided by the total number of irradiations in a temperature interval $N_{\mathrm{int}}$, where $T_{\mathrm{c}}$ is the temperature the bar is centered on, with a temperature range of $\pm 2.5°\mathrm{C}$. For example, the bar centered at $T_{\mathrm{c}}=60°\mathrm{C}$ represents the fraction of visible lesions among the total irradiations, where $T_{\text{treatment}}$ was measured between 57.5°C and 62.5°C. The numerical values for these visibility fractions for the temperature intervals of 50°C to 80°C are shown in Table 4.

Table 4

Total number and fraction of visible lesions in a temperature interval of 5°C centered on Tc.

5.1.

Accuracy of the Power Controlled Temperature Dosimetry

Figures 8 and 9 show the fundus image of the irradiations for different aim temperatures. Most of the irradiations with the aim temperatures $T_{\text{aim}}$ of 50°C and 55°C remained subvisible (261 out of 264), despite a wide range of treatment powers $P_{\text{treatment}}$. This shows that the site-individual absorption was accounted for and provides a reliable option to perform treatments with subvisible outcome. The breakdown into each category is shown in Table 3. In the transition regime with $T_{\text{aim}}=60°\mathrm{C}$ and 65°C, about 40% of the lesions become visible and are visibly less pronounced than the lesions created with $T_{\text{aim}}=70°\mathrm{C}$ and 75°C, which are visible in $>95\%$ of the cases.

The mean value for the end temperature $T_{\text{treatment}}$ for the irradiations with $T_{\text{aim}}=50°\mathrm{C}$, 57°C, and 65°C is very close to the desired aim temperature, but the standard deviation increases.

For all temperatures, the corresponding treatment laser powers $P_{\text{treatment}}$ show a larger standard deviation (about twice the relative deviation) than the temperatures, so the site-individual temperature feedback is crucial for a reliable dosimetry.

The subvisible irradiations achieved the highest temperature accuracy regarding the absolute temperature values. Looking at the temperature distribution of the different power-controlled lesions as shown in Fig. 7, the subvisible irradiations showed the least deviation in achieved temperature with a standard deviation of 2.1°C ($T_{\text{aim}}=50°\mathrm{C}$) and 3.8°C ($T_{\text{aim}}=55°\mathrm{C}$). The standard deviation increases with the aim temperature $T_{\text{aim}}$, though it does not exceed 5°C. The increase is probably mostly caused by the propagation of errors during the determination of the probe phase temperature $T_{\text{probe}}$. The broader the gap between $T_{\text{probe}}$ and $T_{\text{treatment}}$, the more an error in the determination of the temperature $T_{\text{probe}}$ is exacerbated for the treatment irradiation. Additionally, the temperature determination is most accurate close to the point of reference that is determined during the calibration phase.

One thing to consider specifically for higher temperatures already causing tissue denaturation is the increased light scattering. In this case, less probe and treatment laser light reaches the RPE. Furthermore, the tissue parameters and thus the Grüneisen-parameter [Eq. (3)] change. As a consequence, the temperature measurement loses its accuracy and deviations need to be taken into account, which become stronger the more the denaturation zone moves toward the inner retina.

5.2.

Temperature Measurement

The time controlled dosimetry introduced by Schlott et al.²⁵ and Koinzer et al.³⁰ was shown to be effective in creating uniform lesions across a wide range of irradiation laser powers. However, with their approach, the irradiation time varies depending on the laser power and the degree of pigmentation from a few milliseconds to well over 500 ms in some cases. In rare occurrences, the temperature threshold for ophthalmoscopic visibility could not be reached at all, regardless of the irradiation time. This is due to the fundus tissue reaching a thermal equilibrium, where the outflux of the heat is equal to the heat induced by the absorption of the laser light. Irradiations that are too short lead to an inaccurate determination of the temperature due to the increased influence of noise in combination with the limited number of temperature data points. Also, there is a technical limitation to the response time of the algorithm at about 4 ms. On the other hand, if the irradiation time is too long, the temperature measurement is more likely to be subject to errors due to eye movement. The variation of the irradiation time would make this approach unsuitable for automated pattern photocoagulation, where the individual irradiation has to be completed within 10 to 50 ms. Also it was shown that while the lesions are of the same diameter, they can differ in appearance for different irradiation times.³⁰

With the demonstrated approach here, there was no instance of not being able to reach the aim temperature up to 75°C, improving the reliability of the dosimetry when compared to the time-variable approach. Additionally, as the treatment time is fixed at 50 ms, the appearance of the lesions is less prone to variations. The reliable time frame also makes the power-controlled dosimetry approach suitable to combine with some of the pattern coagulator systems operating in this time regime. The efficacy for shorter durations would have to be examined for application in pattern coagulators that operate in the 20-ms regime.

We have found that the most critical phase during the irradiation is the probe phase, where only a slight increase in temperature is desired. It is imperative that the temperature rise above the start temperature is high enough to be fitted reliably. Several steps were taken to increase the accuracy of the temperature determination of the probe phase.

The transducer signal carries not only the pressure data, but also noise and disturbances influence the pressure value determination. It is, therefore, important to match the transducer properties to the expected signal. In order to minimize the effect, the transient curves are filtered using a bandpass filter. Based on simulations realizing the photoacoustic signal generation for an irradiation with a diameter of $200\mu \mathrm{m}$ and a pulse duration of 75 ns, we expect a central frequency of the transient pressure wave of 1.2 MHz. The transducers used in this work, therefore, have a resonance frequency at $f=1\mathrm{MHz}$ with a bandwidth of 410 kHZ. According to these considerations, the bandpass filter’s upper and lower bounds were chosen to be 400 kHz and 1.5 MHz, respectively.

Additionally, one has to consider the irradiation time. We found that 20 ms is a suitable irradiation time for $t_{\text{probe}}$. This results in 20 data points to fit the temperature curves, which proved to be sufficient to achieve a reliable temperature assessment in order to calculate the power needed for the treatment phase $P_{\text{treatment}}$. However, probe repetition rate can be increased for higher accuracy.

The presented results are derived using a model for the rabbit fundus. When adapting the technique for the human fundus, some changes to the model are necessary. The different structure of the rabbit and the human eyes requires some alteration of the layer structure used for the determination of the conversion function. Additionally, the holangiotic nature of the retina requires the consideration of the absorption of laser light in the inner retina.

5.3.

Visibility Threshold

The first visible lesions appear at a temperature of about 55°C, albeit very rarely. For our treatment time of 20 ms, the ED50 temperature value of creating a lesion is at 65.3°C. This is in good accordance with results published earlier,²⁵ where an ED50 value of 61.7°C for 20 ms can be extrapolated. However, there is no data for irradiation times of 20 ms to directly compare it to, as the previous experiments usually had longer irradiation times. Additionally, the fit curve derived by Schlott et al. seems to underestimate the temperatures for lower irradiation times, indicating that the ED50 value for this particular irradiation time agrees very well with the data presented here. Denton et al. have determined the threshold temperature for RPE damage as 53°C in the time range of 100 ms to 1 s, which is considerably lower than the ED50 value found here. However, their experiments were performed on RPE cell culture and with longer irradiation times.³⁷ According to the Arrhenius theory, one would expect the threshold temperature for shorter irradiation times to be higher than for longer ones. Additionally, the threshold for RPE damage is lower than for ophthalmoscopically visible effects, because the heat has to be conducted into to retinal layers in order to denature the tissue.

The comparison between Tables 3 and 4 shows that the fraction of visible lesions in a temperature regime is very similar to the fraction of visible lesions for a given aim temperature. This shows that the desired coagulation effect is achieved by the method.

The ED50 value found here also compares quite well with the damage threshold temperature of 63°C found by Sramek et al.¹¹ for the peak temperature for 20-ms irradiations in rabbits. Those temperatures were not measured directly, but inferred via a mathematical model based on the Arrhenius damage model.

When looking at the visibility of the lesions in Fig. 10, there is an overlap in visible and invisible irradiations between 60°C and 70°C. The reason for this might be uncertainties in the determination of the temperature. The conversion function to determine the peak temperature from the measured mean temperature assumes the ratio of the absorption coefficients of the RPE and the choroid ${\mu }_{\mathrm{RPE}}/{\mu }_{\mathrm{chor}}$ to be fixed. However, it was shown that the conversion function, and therefore, the laser-induced peak temperature can vary up to 9% if the ratio of absorption coefficient changes by a factor of two.³⁸ Also there are different tissue effects, for example, the creation of edema, which lead to a whitening of the fundus area, which cannot be distinguished from thermal denaturation on the fundus image. Thus, ophthalmoscopic visibility after 1 h might not be the best criterion to judge the treatment outcome. We are currently investigating the visibility thresholds of alternate modalities, such as fluorescein angiography and OCT, based on a classification system published by Koinzer et al.³⁹ Finally, it is also conceivable that there is a variance of the biological reaction to identical heat stimuli caused, for example, by a locally varying blood vessel distribution in the choroid.