Measurement, modeling, and prediction of temperature rise due to optogenetic brain stimulation

Abstract

Optogenetics is one of the most important techniques in neurophysiology, with potential clinical applications. However, the strong light needed may cause harmful temperature rises. So far, there are no methods to reliably estimate brain heating and safe limits in actual optogenetic experiments. We used thermal imaging to directly measure such temperature rises at the surface of live mouse brains during laser illumination with wavelengths and intensities typical for optogenetics. We then modeled the temperature rise with a simple logarithmic model. Our results indicate that previous finite-element models can underestimate temperature increases by an order of magnitude. We validate our empirical model by predicting the temperature rise caused by pulsed stimulation paradigms. These predictions fit closely to the empirical data and constitute a better estimate of real temperature increases. Additionally, we provide a web-based app for easy calculation that can be used as a tool for safe design of optogenetic experiments.

Keywords: modeling; optogenetics; thermal imaging.

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.

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.

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.

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).

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%.

Fig. 6

Effect of time elapsed since craniotomy on tissue heating, for both (a–c) dead and (d–f) alive mice. (a) The temperature increase in brain tissue from a dead animal due to optogenetic illumination grows higher as time passes after death. (b, c) This increase is reflected in the value of model parameter $\mathbf{a}$, whereas parameters $\mathbf{a}$ and $\mathbf{c}$ remain constant throughout time. (d) The temperature increase after illumination in brain tissue from a living animal remains constant in time. (e, f) Accordingly, none of the parameters for our model show trends in their variability.