2.1.

Animals

Twelve adult male C57BL/6 mice (20–27.25 g) were used in the experiments. Animals were housed in a room with a 12 h light/dark cycle (lights on at 6:00 AM) and food and water ad libitum. All experiments were done in compliance with the guidelines of the European Community (EUVD 86/609/EEC) and were approved by the local ethics commission of the State of Sachsen-Anhalt.

2.2.

Craniotomy Surgery

We induced anesthesia by applying urethane (Sigma-Aldrich, St. Louis, USA) intraperitoneally at a concentration of $1.25\mathrm{g}/\mathrm{kg}$ of animal weight. Experiments commenced after a deep level of anesthesia was attained and the animal lost all motor reflexes. We also injected 0.1 ml of a $0.2\mathrm{mg}/\mathrm{ml}$ solution of glycopyrronium bromide (Robinul, $0.2\mathrm{mg}/\mathrm{ml}$) to reduce airway secretions and stabilize the preparation.

Mice were fixed in a stereotaxic frame, and a craniotomy was performed over the right parietal cortex. Drilling was done under saline to prevent excessive heat generation. As a final step, we let the surface of the dura mater dry completely⁶ and used dental acrylic to attach a brass holder to the occipital bone. We performed the experiments at 24°C and waited for the surface temperature of the craniotomy to stabilize before we started imaging. Due to slow radiative heat loss, the typical baseline temperature of the exposed brain was approximately 30°C during the experiment, in accordance with previous studies.^7,8 At the end of an experiment, the animals were euthanized.

2.3.

Measurement Setup

For thermography, we used an Optris PI 230 infrared camera (Optris GmbH, Berlin, Germany). The detector of the camera is an uncooled focal plane array with $160\times 120\text{pixels}$. The sampling rate is fixed by the camera at 128 Hz. We used a lens that provided a field of view (FOV) of 23 by 17 deg. In combination with the sample distance of 20 mm, this setup yields a single pixel resolution of $50.9\mu \mathrm{m}$. Data acquisition was done through the PI Connect software provided by the camera manufacturer. The camera was calibrated by setting a custom emission factor of 0.95 to match measured optical properties of the brain surface and loading the manufacturer-supplied lens and array calibration file. This procedure matched the reading of our camera to that of a needle probe at equilibrium on the brain. Since the recording could not be triggered externally, blocks that contained all trials of an experiment were acquired. The onset of illumination was then determined from a thermal reference made from the exposed filament of a microlightbulb and placed in the FOV.

For laser illumination, we used five custom optical paths with the following laser sources: three diode-pumped solid-state lasers of 473 nm [blue, module from Changchun New Industries Optoelectronics Technology Co., Ltd. (CNI)], 532 nm (green, module from DHOM UltraLasers, Inc.), and 589 nm (yellow, module from CNI), as well as two diode lasers with wavelengths of 633 nm (red) and 450 nm (royal blue). Each laser was collimated into the proximal end of the fiber with an aspheric lens. The clean-cut distal end of the fiber was placed directly in the field of view, as described below. Due to propagation within the fiber, the beam profile in air exiting the fiber approximates a super-Gaussian profile [Fig. 1(g)]. This condition is usually typical for optogenetics experiments with multimode fibers, but might not always be present, e.g., due to coupling angle. To control the timing of illumination, lasers were driven in continuous wave mode and shuttered (SR474; Stanford Research Systems). Light intensity was adjusted by a variable neutral density filter. Typically, we used an illumination intensity of 10 mW for 500 ms if not specified otherwise. For experiments that are not wavelength-specific, we used the 450-nm laser because of its high stability.

Fig. 1

Overview of the setup, measurements, and our mathematical model describing temperature variation. (a) Schematic representation of our setup. Light is emitted by a laser, attenuated by a variable neutral density filter (ND), gated by a blade shutter (Sh), and focused into the fiber by a collimation lens (L). The brain is imaged by an IR-camera system. A small thermal reference is placed within the field of view to trigger acquisition events (Ref). (b) Close-up view of the craniotomy; the fiber is placed on top of the exposed surface of the brain and the illuminated spot is imaged with the IR-camera. (c) Thermography image of the craniotomy during laser illumination. The craniotomy is distinguishable from the surrounding bone by its difference in thermal emission. (d) Example of a temperature-time diagram with illumination pulses of 2000 ms; blue rectangles indicate timing of laser illumination. (e) Equations corresponding to the rising phase fit function and the falling phase fit function. The rising phase was fitted with a logarithmic model that is defined by three parameters: $\mathbf{a}$ (scaling), $\mathbf{b}$ (timing adjustment), and $\mathbf{c}$ (shape). The falling phase was fitted with an exponential decay model, where ${\mathbf{g}}_{\mathbf{1}}$ and ${\mathbf{g}}_{\mathbf{2}}$ are the magnitude parameters and ${\mathbf{h}}_{\mathbf{1}}$ and ${\mathbf{h}}_{\mathbf{2}}$ are the time parameters. (f) Measured data ($\text{mean}\pm \text{standard deviation}$ in gray) and model fits. The dashed line corresponds to the extrapolated prediction of a model obtained by fitting only the first 500 ms worth of data for the rising phase ($n=35$ trials). (g) Measured data ($\text{mean}\pm \text{standard deviation}$ in gray) and model fits for an illumination time of 20 s. The dashed line corresponds to the extrapolated prediction of a model obtained by fitting only the first 500 ms worth of data for the rising phase ($n=38$ trials). (h) Beam shape and relative irradiance from $200\text{-}\mu \mathrm{m}$ fiber recorded through the IR camera.

The camera, timing reference, and delivery fiber tip were all mounted onto a stable optical breadboard together with the anesthetized animal [Figs. 1(a) and 1(b)]. The camera was fixed at a 45 deg angle in relation to the platform and the brain surface. The fiber tip was positioned with a micromanipulator and held at a 45 deg angle in relation to the brain surface. This results in a slightly oval shape of the resulting illuminated spot, but balances spot size distortion and measurement access. Also, a $200\mu \mathrm{m}$ multimode fiber with a numerical aperture of 0.22 was used. The numerical aperture was fully filled by the lasers.

A measured beam distribution is given in Fig. 1(g), showing the super-Gaussian beam shape as seen from the position of the IR camera. Due to the projection of the fiber aperture onto the brain surface at an angle, power densities in parts of the spot are lower than what would be seen with perpendicular illumination. This might lead to a slight underestimation of actual heating, which we attempted to compensate for by measuring the warmest pixel in the spot. Even though the fiber projection shape is elliptical due to the tilting of the fiber, we can assume an illumination area equal to the fiber tip to calculate power densities of our illumination paradigms, since we are measuring the maximum temperature increase in the illumination area. The approximate area of our $200\text{-}\mu \mathrm{m}$ fiber is $0.03{\mathrm{mm}}^2$, for the $100\mu \mathrm{m}$ is $0.008{\mathrm{mm}}^2$, and for the $400\mu \mathrm{m}$ is $0.13{\mathrm{mm}}^2$.

2.4.

Measurements and Analysis

After experiments, data from the PI Connect software were exported as a text file and analyzed in MATLAB 2013a (Mathworks) and Mathematica 10.0.1 (Wolfram Research). The analysis code is available for inspection in Ref. 9. Figures other than Fig. 4 (animal variability) were made with multitrial data sets from individual representative animals to demonstrate qualitative differences.

Trials were segmented from raw data based on thresholding the timing reference temperature. The baseline mean temperature was subtracted to obtain the relative temperature increase. We then conducted nonlinear model fits to various empirical models as described below. Bootstrapping was conducted within trials to estimate the variability of our model fits for individual experiments. To assess model fits, we calculated $R$-squared metrics. To assess statistical differences between wavelengths, we used a Wilcoxon signed-rank test for the parameter values, where a $p$-value $<0.05$ was considered a significant result. All analyses, figures, and tables for the results section were generated using standard Mathematica functions.

Fig. 2

Effects of the illumination power and wavelength. (a) Increased illumination power leads to higher temperature changes with similar time profile at 450 nm (means from $n=38$ trials per power value). (b) A linear increase of the $\mathbf{a}$ parameter of our model reflects these changes; the shape parameter $\mathbf{c}$ remains constant. Error bars correspond to the 1% to 99% confidence intervals from approximately $1:4$ bootstrapped data. (c) Temperature increase profile for different wavelengths of laser light (10 mW). Different temperature change trends are seen (means from $n=40$ trials per wavelength). (d–f) Different wavelengths differentially affect the model $\mathbf{a}$ and $\mathbf{c}$ parameters, representing different absorption magnitude and kinetics. The remaining $\mathbf{b}$ parameter remains around a fixed value of 1, as explained in the text. Data for eight animals (40 trials per animal and per wavelength) are represented as a box-and-whiskers plot showing the median, quartiles, and maximum/minimum values for each wavelength. The black dots correspond to mean values (40 trials) for the parameters for each wavelength and animal. The parameter values for different wavelengths corresponding to the same animal are connected with gray lines. Significant differences between parameter values of different wavelengths are marked with a star ($p$-value $<0.05$, Wilcoxon signed-rank test). Table showing the median as well as the first ($Q1$) and the third quartiles ($Q3$) for $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ parameters at all studied wavelengths.

3.1.

Deriving a Parametric Model to Fit Thermographic Recordings

Upon laser illumination, a clear temperature rise can be seen in the several camera pixels sampling the heated area [Fig. 1(c)]. This area of elevated temperature decays rapidly with spatial distance from the heated area. Since the heated area only covers several pixels and we are primarily interested in the maximum temperature rise due to illumination, we assumed a local point-like process at the tip of the illumination fiber and took the maximal pixel temperature in the region of interest as a measure of the heated tissue temperature. We avoided taking the mean temperature of the region of interest, since border pixels only partially covering the illuminated/heated area would dilute the mean and lead to a false underestimate. The temperature rise in response to heating appears at first glance to be exponential, as some models seem to predict.⁴ Upon closer inspection, however, we found that regardless of the measurement duration within our time frame of up to 2000 ms, the temperature would continue to rise and not equilibrate [Fig. 1(f)]. We selected the simplest mathematical model matching these characteristics: a logarithmic rise, scaled by an amplitude constant $\mathbf{a}$ and a time constant $\mathbf{c}$:

To evaluate this model qualitatively, we first recorded from individual animals without pooling the data (to avoid interanimal variability, which is discussed later). A total of 40 trials of illumination were recorded per animal with a 450-nm laser at 5 mW optical power for 2 s. The standard sample number for each illumination paradigm throughout this report will be 40 trials per animal unless specified otherwise. As can be seen in Fig. 1(e), our logarithmic model fits the temperature rise over 2000 ms exceptionally well ($r^2$-goodness of fit: 0.997). Fitting the same temperature rise during the initial 500 ms interval still results in a good fit when extrapolated out to 2000 ms worth of data ($r^2=0.943$), with improved precision for the earliest part of the temperature increase. Of note, this earliest phase of temperature rise features kinetics that are fast compared to the 7 ms sampling interval of our camera and, thus, are subject to more error and instability in model fitting than the later, more stable phases of rise. During subsequent experiments, the fit interval was tailored to the desired pulse and train lengths. Increasing the illumination to the time scale of tens of seconds produces the same results as seen in Fig. 1(g). Our model is able to fit an illumination time of 20 s, meaning the temperature trend is still logarithmic; this should not change for any illumination time, as long as the temperature increase is within the range where brain heating does not cause irreversible changes in tissue biophysical characteristics. The fit of the initial 500 ms also results in a reasonable prediction when extrapolated to the full 20 s, and the final predicted temperature increase lies well within our variability interval.

The temperature fall during the cooling phase shows an exponential-like time course. In contrast to the rising phase, which is logarithmic, the falling phase is indeed exponential with a limit equilibrium tissue temperature of the surrounding tissue (in this case, the exposed craniotomy field). A simple exponential did not fit the data sufficiently well, especially in the initial rapid fall, but a double-exponential provided excellent fits (Fig. 1, $r^2$-goodness of fit: 0.997). Based on this finding, we propose the following empirical model:

3.2.

Influence of Illumination Intensity on Brain Heating

Increased illumination strength naturally causes increased heating of the tissue. We first tested this qualitative relationship by exposing the brain of a single animal to several intensities within the range used in optogenetic experiments (2.5, 5, 7.5, and 10 mW) and by measuring and modeling the resultant temperature increases [Figs. 2(a) and 2(b)]. By changing the illumination power coming out of a fiber with the same diameter ($200\mu \mathrm{m}$), we are effectively changing the power density of the illumination and therefore studying its effects on brain heating. For the given intensities, the respective power densities amount to 83.3, 166.6, 250, and $333.3\mathrm{mW}/{\mathrm{mm}}^2$. The fiber tip was placed in a blood vessel free area at the beginning of the experiment, and its position was kept constant to avoid introducing variability from differences in blood vessel density on the surface of the brain. The same procedure was followed in all experiments, except for those in which deviations were inevitable, such as when we measured the influence of fiber diameter.

A linear increase in temperature with power indicates that energy influx dominates the final temperature outcome, whereas a nonlinear relationship would indicate a substantial dynamic involvement of other processes such as cooling. A priori, one would expect the former situation given the massive amount of power input from illumination (e.g., $10\mathrm{mW}/0.03{\mathrm{mm}}^2$ would amount to a power input of 33 W in $1{\mathrm{cm}}^2$, comparable to the total power of an incandescent desk lamp or small soldering iron). As expected, our results show a linear increase in temperature with illumination intensity or power density [Fig. 2(a)]; this linear increase is reflected in our model parameter $\mathbf{a}$ but not on model parameters $\mathbf{b}$ or $\mathbf{c}$ [Fig. 2(b)].

During exposure to 10 mW of 450 nm light for 500 ms, the brain heats up to an average of 6.35 K above baseline ($200\text{-}\mu \mathrm{m}$ fiber). This would encroach upon the maximal tolerable temperature increase without permanent tissue damage (6 to 8 K).^1,2 Out of the calculated model parameters, the $\mathbf{a}$ parameter increases linearly with power, while the shape parameter $\mathbf{c}$ (as well as the timing adjustment parameter $\mathbf{b}$) remain largely unaffected [Fig. 2(b)].

3.3.

Influence of Illumination Wavelength on Brain Heating

The interaction of light with tissue and transfer of heat energy is mainly determined by two separate physical processes: scattering and absorption. Scattering is mainly due to heterogeneities in the refractory index within nervous tissue. Absorption in a relatively transparent tissue such as the brain is governed, to a significant extent, by hemoglobin. Both processes cause a wavelength dependence of heat transfer to the tissue. Scattering increases exponentially at shorter wavelengths,^10,11 but absorption is complex and depends mainly on the hemoglobin absorption spectrum. In the visible light range, which is used in optogenetics, it generally decreases with wavelength.

To establish a quantitative relationship between various wavelengths and heating, we tested four additional wavelengths typically used in optogenetics [Figs. 2(c)–2(f)]: blue (473 nm), green (532 nm), yellow (589 nm), and red (633 nm). In this experiment, we used data obtained from eight animals to obtain global estimates of parameter values for the predictive equation and for our web-based calculation app to predict brain heating due to optogenetic illumination. For every animal, we measured the temperature increase during 40 trials for each of the four previously mentioned wavelengths, illuminating at 10 mW of power for 500 ms through a fiber of $200\text{-}\mu \mathrm{m}$ diameter. The largest temperature increase in a typical animal was seen with blue and green light [Figs. 2(c) and 2(d); blue 1.39 K, green 1.34 K). Yellow light caused a medium increase (0.91 K) and red light caused the smallest increase (0.33 K). This is directly reflected in the values of the first ($Q1$) and third ($Q3$) quartiles for the $\mathbf{a}$ parameters of the fits [blue 0.39 to 0.771, green 0.418 to 0.808, yellow 0.287 to 0.664, and red 0.077 to 0.271; Fig. 2(g)]. The $\mathbf{c}$ parameters showed a similar trend for these wavelengths [blue: 0.02 to 0.097, green: 0.026 to 0.118, yellow: 0.02 to 0.088, red: 0.017 to 0.054; Fig. 2(g)], which is likely a manifestation of deeper penetration of longer wavelengths.

To assess the statistical significance of this qualitative result, we performed a Wilcoxon signed-rank test for the parameter values in which a $p$-value $<0.05$ was considered significant. This test was chosen given the asymmetric and nonnormal nature of our data set, which is mainly due to two outlier samples. For parameter $\mathbf{a}$, we obtained significant differences between red and yellow, red and blue, red and green, yellow and green, and, finally, yellow and blue [Fig. 2(d)]. Although the trend was similar to the values for the $\mathbf{c}$ parameter, only the differences in yellow and green wavelengths were significant based on our statistical assumptions [Fig. 2(d)].

3.4.

Influence of Fiber Diameter on Brain Heating

Next, we tested the effect of fiber diameter on heating. Thinner fibers achieve higher local power density and are therefore expected to induce more local heating, as indicated by our results regarding the effects of illumination intensity on the brain heating. In the most ideal circumstances, we would expect the brain heating to be scaled by the power density, which is inversely proportional to the illumination area and inversely proportional to the square of the fiber diameter. However, this linearity might not hold at different fiber diameters due to factors such as the surface/volume-relationship of the illuminated spot or the increased probability of illuminating a significant blood vessel with larger fiber diameters.

To test this hypothesis experimentally, we used three different fiber diameters (100, 200, $400\mu \mathrm{m}$) with constant input numerical aperture and constant power (5 mW),with a fixed wavelength (450 nm) (Fig. 3). For each fiber diameter, the respective power densities are 625, 166.6, and $38.5\mathrm{mW}/{\mathrm{mm}}^2$. We performed the measurements in one animal and recorded 40 trials for each of the fiber diameters. Due to slight changes in the position of the fiber tip during fiber exchange, some additional variability is to be expected in these measurements. We found the largest temperature increase for the $100\text{-}\mu \mathrm{m}$ fiber (1.79 K) but no difference between 200 and $400\mu \mathrm{m}$ (1.48 and 1.49 K, respectively). This violates the predicted effect due to differences in power density; this is likely due to the unavoidable illumination of blood vessels with larger fiber sizes. The $\mathbf{a}$ parameter of the model did not differ between fiber diameters, but the $\mathbf{c}$ parameter decreased with the diameter [Figs. 3(b) and 3(c)], indicating a change in the heating process, e.g., less local heating.

Fig. 3

Effect of fiber diameter on heating. (a, b) Thinner fibers have higher local irradiance and therefore induce more local heating, in general. No clear difference is seen between 200 and $400\mu \mathrm{m}$ fibers, likely due to the unavoidable illumination of blood vessels with larger fiber sizes (see text). Plots and error bars are as in Fig. 2. (c) Table representing the model fit values. Changes are mainly seen in the $\mathbf{c}$ parameter.

For the larger diameters, especially $400\mu \mathrm{m}$, it was difficult to avoid larger surface vessels. To investigate this confound, we compared temperature rise with a $200\text{-}\mu \mathrm{m}$ fiber placed both (a) directly above and (b) as far as possible from large surface blood vessels. We found a large difference in temperature rise: direct illumination of the vessel for 500 ms with a 450-nm wavelength laser at 5 mW of power caused a twofold increase in temperature (1.22 K) over illumination away from visible blood vessels (0.66 K) [Fig. 4(a)]. We take this twofold difference as an index of the variability of heating due to the presence or absence of blood vessels. This increase in heating with blood vessel illumination suggests that the heat diffusing capacity of blood is negligible compared to its increased energy absorption. The effect is linked to a change in the $\mathbf{c}$ parameter of our model [Fig. 4(b)].

Fig. 4

Biological variability in brain heating. (a) Differences in the vascularization of the illuminated tissue have a significant effect on the temperature increase. Illumination of an area containing a visible blood vessel leads to twofold higher temperatures than illumination of an adjacent area without a vessel (means from $n=37$ to 40 trials each). (b) Vascularization leads to a change in the $\mathbf{c}$ parameter of our model, indicating different absorption kinetics. Error bars are as in Fig. 2(b). (c) Interanimal variability from five different mice imaged under the same conditions, as discussed in the text (means from $n=37$ to 40 trials per animal). (d) This interanimal variability in heating is reflected in large differences in the $\mathbf{a}$ and $\mathbf{c}$ parameters of the model indicating different magnitude and kinetics of absorption, similar to the variability seen in (a). The $\mathbf{b}$ parameter remains around a fixed value of 1, as explained in the text. Error bars are as in Fig. 2(b).

3.5.

Intersubject Variability in Heating

Increased heating associated with the presence of blood vessels directly below the fiber suggests that a relatively large variability may occur depending on precise localization of illumination. When possible, our experiments avoided large blood vessels; however, having small veins and capillaries in the illumination field is inevitable. This issue is of particular concern for experiments with implanted fibers, where the location of vessels relative to the fiber tip cannot be controlled at all. We therefore tested a standard condition (450 nm, 500 ms, 5 mW, $200\text{-}\mu \mathrm{m}$ fiber diameter) of illumination in five different animals [Figs. 4(c) and 4(d)]. As expected, temperature increases varied significantly between animals, leading to a final temperature increase of 1.3 to 3 K under the same conditions [Fig. 4(c)]. This variability could be attributed to changes in both the $\mathbf{a}$ and $\mathbf{c}$ parameters [Fig. 4(d)] and is discussed later. That real measurements show such variability speaks further against the practical applicability of precise but inaccurate estimates based on finite-element modeling and speaks for our approach of emperical modeling based on actual thermal measurements.

3.6.

Validation for Typical Optogenetic Pulse Paradigms

For most of our experiments, we used a 500 ms constant illumination to measure the biophysical response to illumination in a controlled manner. However, this type of illumination is rather uncommon in optogenetic experiments, where pulsed light paradigms prevail. To test whether our model could account for such paradigms as well, we selected three commonly used frequencies (10, 20, and 40 Hz) and a standard pulse length of 10 ms (20 mW). In addition, we recorded the effect of constant illumination at the same time.

We find that the model $\mathbf{a}$ parameter derived from constant illumination data can be scaled by the pulse duty cycle to yield an accurate estimate of the cumulative heating from the pulse train. For example, in a 10 Hz stimulation paradigm with 10 ms pulses that gives a 10% duty cycle, we scaled the value for the model parameter $\mathbf{a}$ to 10% of that obtained with constant illumination. We tested both yellow (589 nm) and blue (473 nm) light, and found a good match between prediction based on duty cycle and actual measured data from pulsed illumination [Figs. 5(a) and 5(b)]. Although this method does not allow the precise prediction of instantaneous maximum temperatures, the method is robust and does provide an estimate of pulsed temperatures across the frequencies tested.

Fig. 5

Heating from pulsed illumination can be approximated by duty cycle scaling. (a) The average temperature profiles for different frequencies of pulsed illumination are plotted in blue (473 nm, 20 mW, 10 ms pulses; means from $n=33$ to 38 trials per pulse frequency). The model was fitted as previously to data from constant illumination (fit from $n=39$ trials) and scaled by the respective duty cycles of the pulse trains (black dashed lines). (b) Data and fit prediction similar to (a) for yellow light illumination (589 nm; means from $n=38$ to 39 trials per pulse frequency; model fit from $n=39$ trials). For both wavelengths, the actual temperature increase from pulsed illumination is well approximated by scaling the fitted constant illumination model. For example, delivering 10 ms pulses at 10 Hz results in a 10% duty cycle, and the heating is accurately predicted by scaling the constant illumination model by 10%.

In principle, we can use our rising and falling phase equations [Fig. 1(e)] in combination to predict the instantaneous pulsed temperature time course (i.e., individual time points along the sawtooth-like temperature trajectory). However, in practice, we find that this leads to systematic accumulating overestimation of the temperature, which we attribute to heating history effects that are not fully accounted for by our current falling phase model. For the purposes of the current report, the duty cycle scaling gives accurate results overall, and since the pulse paradigms commonly used do not feature higher duty cycles, the sawtooth-like peaks are not significantly higher than the overall temperature rise trend (Fig. 5). However, the scaled values should be interpreted in light of this slight underestimate of instantaneous maximum temperature. We intend to investigate this issue further in detail in a report to follow.

3.7.

Web and Smart Phone Interface for Easy Predictions

As described previously, one main goal was to provide an empirical model with which one can predict brain heating to assist in the design of optogenetic experiments (Fig. 1). To simplify this process, we provide a web-based calculation app, which can also be used on smart phones.¹² This can be used to predict an approximate safety limit for cortical illumination, but for other tissues, histological differences in absorbance and other characteristics may change model parameters and limit actual predictability. For further caveats, see Sec. 4.