Quantifying tissue temperature changes induced by infrared neural stimulation: numerical simulation and MR thermometry

Infrared neural stimulation (INS) delivered via short pulse trains is an innovative tool that has potential for us use for studying brain function and circuitry, brain machine interface, and clinical use. The prevailing mechanism for INS involves the conversion of light energy into thermal transients, leading to neuronal membrane depolarization. Due to the potential risks of thermal damage, it is crucial to ensure that the resulting local temperature increases are within non-damaging limits for brain tissues. Previous studies have estimated damage thresholds using histological methods and have modeled thermal effects based on peripheral nerves. However, additional quantitative measurements and modeling studies are needed for the central nervous system. Here, we performed 7 T MRI thermometry on ex vivo rat brains following the delivery of infrared pulse trains at five different intensities from 0.1-1.0 J/cm2 (each pulse train 1,875 nm, 25 us/pulse, 200 Hz, 0.5 s duration, delivered through 200 µm fiber). Additionally, we utilized the General BioHeat Transfer Model (GBHTM) to simulate local temperature changes in perfused brain tissues while delivering these laser energies to tissue (with optical parameters of human skin) via three different sizes of optical fibers at five energy intensities. The simulation results clearly demonstrate that a 0.5 second INS pulse train induces an increase followed by an immediate drop in temperature at stimulation offset. The delivery of multiple pulse trains with 2.5 s interstimulus interval (ISI) leads to rising temperatures that plateau. Both thermometry and modeling results show that, using parameters that are commonly used in biological applications (200 µm diameter fiber, 0.1-1.0 J/cm2), the final temperature increase at the end of the 60 sec stimuli duration does not exceed 1°C with stimulation values of 0.1-0.5 J/cm2 and does not exceed 2°C with stimulation values of up to 1.0 J/cm2. Thus, the maximum temperature rise is consistent with the thermal damage threshold reported in previous studies. This study provides a quantitative evaluation of the temperature changes induced by INS, suggesting that existing practices pose minimal major safety concerns for biological tissues.


Introduction
To investigate brain networks and their relationship to behavior and disease, various brain mapping methods have been developed.While optogenetic stimulation is well known, infrared neural stimulation (INS, 1,875 nm) is an optical method that does not require viral transfection of tissue, making it potentially an attractive method for human use [1,2].INS has been used for peripheral nerve stimulation [3][4][5], cochlear stimulation [6][7][8], cardiac pacemaking [9,10], as well as for mapping of brainwide neural circuits in highfield MRI [11].[Note: pulsed INS is distinct from other infrared wavelength applications such as 800-980 [12], 1470 [13], 5.6 µm [14].]INS evokes neuronal response by delivery of multiple pulse trains (each pulse train: 0.25 msec per pulse, 0.5 sec duration, 200 Hz; Fig. 1) of 1,875 nm infrared light [15][16][17].While the mechanism by which a transient temperature rise induces neural depolarization is still unclear, most studies support photo-thermal effects leading to membrane capacitance change as the primary mechanism [18][19][20].What results is a thermally confined energy transfer, resulting in a very focal activation in the region of interest.When delivered via 200-400 um optical fibers, this focality has made it amenable for targeting single cortical columns from the brain surface [17], as well as deep cortical and subcortical structures in the brain [11,21,22].Previously, Cayce et al. developed application of INS for stimulating brain regions such as thalamocortical projections, somatosensory cortex and primary visual cortex, in both ex vivo and in vivo settings [15][16][17]23].More recently, a novel technology was developed for mapping brain-wide networks in vivo in primate brains by combining INS with ultra-highfield functional magnetic resonance imaging (INS-fMRI), advancing a rapid method for mapping brainwide functional networks at mesoscale [11].INS also offers potential advantages for precision targeting of neural circuits for circuit neuromodulation for clinical [1,2] and for brain-machine interface [24] applications.To further our understanding of INS, we turn to issues of safety and assessment of local temperature changes induced by INS laser pulses.
Previous experimental assessments of INS damage threshholds were conducted via histological assessment.Using 2,120 nm irradiation coupled to a 600 µm fiber core, Wells et al. [3,5] revealed that INS applied to sciatic nerves in rat could reliably evoke response with radiant exposure of up to 0.8-1.0J/cm 2 .Similar to Wells's results, thermal damage thresholds for human spinal nerve roots in vivo were about 1.09 J/cm 2 [23].Other histological assessments of INS effects on cortical tissues in monkey [25] and human [2] have provided thresholds of energy ranging from 0.4 -1.0 J/cm 2 , depending on the stimulation paradigm and angle of incidence [26].
Empirical assessment of temperature change is challenging, as the values obtained depend on the spatiotemporal resolution of the measurement.For brain studies, MR thermometry is an approach which can map the distribution and amplitudes of temperature changes in a volume of tissue [27][28][29].Because temperature change leads to a proton resonance frequency (PRF) shift in water [30,31], these phase changes can be mapped, using specific MRI sequences, to reveal local temperature change profiles for each imaging voxel.Recently, Luo et al. [32] employed this method to determine, from T 2 *-weighted images, the temperature changes induced by different optogenetic stimulation durations.
Numerical models simulating tissue temperature increase resulting from INS have also provided valuable estimates [33][34][35].The Pennes' bioheat equation (BHTE) has been widely used [36].However, the general bioheat transfer model (GBHTM), which considers the presence of a heat source in the perfused tissue, provides a more precise prediction of temperatures in specific organs and tissue types [37][38][39].By establishing an explicit relationship between the parameters of the model and the underlying physiology, such as perfusion and blood velocity [40,41], GBHTM establishes in superior accuracy in predicting temporal and spatial temperature changes in living tissue.
In this study, we used both numerical modeling and MR thermometry to examine temperature increase induced by different intensities of INS stimulation.Our results show that the experimental stimulation parameters commonly used in most previous studies induce temperature rises of not more than 1°C.The implications of this result are discussed.

INS paradigm
A wavelength of 1,875 nm was used to stimulate target tissue due to its good thermal confinement and only several-hundred-micrometers tissue penetration depth in neural tissues [3].Additionally, it is a commonly used near infrared wavelength in INS when stimulating the CNS [11,16,17,21].
The INS paradigm consists of multiple pulses delivered in short pulse trains per trial.As shown in Fig. 1, the smallest basic unit of the stimulation was a pulse, consisting of a 0.25 ms stimulation-on period followed by a 4.75 ms stimulation-off period, at a frequency of 200 Hz.A pulse train consisted of 100 pulses and had a duration of 0.5 s.Each train was followed by a 2.5 sec interstimulus interval (ISI), and the combination of a pulse train and the following ISI was repeated multiple times (20 times in our ex vivo experiment, 50 times in simulation).

Rat brain phantom
A freshly excised Sprague-Dawley rat brain was used for the ex vivo experiment.To protect the fragile tissue, it was embedded in agar, which has minimal impact on the MR Thermometry measurement and provides transparency for visually guided insertion of probes.Additionally, a plastic bar was inserted into the agar to facilitate access without leaving any fingerprints.On the opposite side of the bar, a 200 µm multimode fibre (NA = 0.22) was inserted deep into the brain.Figure 2(A) displays a photograph of the rat brain phantom, while Fig. 2(B) illustrates the positioning of the optical fiber and fiber tip.The phantom was sealed one day before scanning and placed in the MRI bore overnight to reach thermal equilibrium at room temperature.

INS stimulation
The laser control equipment used here was from CNI (Changchun New Industries Optoelectronics Technology Co., Ltd., Changchun, China), as mentioned in Ref. [11].It was connected to a 200 µm optical fiber that delivered 1,875 ± 10 nm wavelength.The laser stimulus followed a similar paradigm to the one used in previous simulations (250 µs pulse duration, repeated at 200 Hz, with 100 pulses per 0.5 sec train, as depicted in Fig. 1).Our trials consisted of 20 trains of 3 sec each (0.5s of stimulation and 2.5s off), resulting in a total trial duration of 60 sec.The stimulus was controlled using a trigger control box and a MATLAB program.To maintain consistency with previous studies on INS in CNS [16,17,25], 5 different radiant energies ranging from 0.1 to 1.0 J/cm 2 were applied, which were measured using an optical power meter from Thorlabs.The first INS train took place between the 2 nd and 3 rd MR thermometry measurements (indicated by the first white arrow in Fig. S2 in Supplement 1), while the final train (20 th ) was delivered between the 22 nd and 23 rd measurements (indicated by the second white arrow in Fig. S2).For each energy intensity, the 60-second trial was repeated 9 times.To mitigate the influence of the residual temperature of adjacent trials, a sufficient interval was provided between two trials to allow the tempature to return to the initial room temperature.All the energy intensities were tesed using the same phantom, with the lowest energy applied first and the highest energy applied last.

MRI setup
A 7 T research MR scanner (Magnetom, Siemens Healthcare, Erlangen, Germany) was used for scanning and acquiring image data.Two types of data were collected with the 7T-MRI system: structural images of the rat brain and thermometry images for measuring temperature changes.
Despite the limitations in signal-to-noise ratio (SNR) and resolution in MR Thermometry, we made every effort to utilize the best available hardware and sequence support to achieve the most reliable temperature measurement.To attain the highest possible temporal and spatial resolutions on a 7 T human MRI scanner, we applied a customized 1 Tx / 5 Rx surface loop array coil developed by Gao et al. [42].This coil consisted of a 2.5 cm-diameter transceiver loop, which was centered for focused proton excitation and MR signal reception, and four peripheral receive loops dedicated solely to signal reception.This high-performance device enabled a significant increase in both SNR and spatial resolution.
Structural images were aquired to precisely locate the optic fiber within the rat brain.After multiple attempts and quantitative evaluations, a spatial resolution of 1 mm isotropic (1µL) was found to be the optimal choice for MR Thermometry measurement.Thus, a 2D-TSE T2-weighted sequence with an in-plane resolution of 0.1 mm and a slice thickness of 0.5 mm (as illustrated in Fig. 2(B)) was employed, and the slice containing the laser tip of interest for MR Thermometry was selected (Fig. 3(B)).
The MR Thermometry technique based on the PRF shift [28] was used for measuring local temperature changes.A 3D-FLASH sequence with the following parameters: FOV = 128 mm 2 , 1 mm isotropic voxel size, TE = 3.4 msec, TR = 1.65 msec, FA = 10°, acquisition time 1.8 sec with 1 average, accelerated with a GRAPPA factor of 2, and phase/slice partial Fourier of 6/8, was employed along with the 1Tx/5Rx surface coil.For each laser energy level, a total of thirty-five 3D-FLASH scans were performed with 3 sec intervals.Two scans were acquired prior to INS, followed by twenty scans corresponded to the INS paradigm, and thirteen additional scans were acquired after the completion of INS.Aligned with the INS stimulation, the 35-scan MRI trial repeated 9 times for each radiant energy level.The acquired phase images (Fig. 3(B)) were then converted into temperature maps using a PRF shift coefficient of −0.01 ppm/°C, as commonly used for water and aqueous tissues [27,43].

Statistical analysis
Since the direct data in acquired images is phase map, it needed to be converted to temperature change according to [27]: where ϕ(T) is the phase map at current time point, ϕ(T 0 ) is the phase map of the baseline image which is measured at room temperature (before INS), γ here represents the gyromagnetic ratio of hydrogen (2.67 × 10 8 rads/Tesla, constant), α is the PRF shift coefficient of water (−0.01 ppm/°C, constant), B 0 is the magnetic field strength (7 Tesla here), and TE is the echo time of imaging sequence (1.65 msec here).And in our condition, 1 °C ≅ 0.031 rads.The temperature of the voxel at the location of the optic fiber tip was selected, and the temperature increase in the 9 isolated measurements was averaged for further analysis.ANOVA and paired-sample t-test were conducted to statistical analysis the temperature changes before and after INS, as well as the differences across different power intensities at the same time point.The data was analyzed using MATLAB.

Modeling of tissue
A cylindrical brain tissue sample with a 20 mm diameter and a 30 mm height was modeled using parameters derived from skin [56,57].The brain tissue was assumed to be uniform and normally perfused [39,44].A constant heat capacity was assigned throughout the volume, and energy was uniformly deposited in the brain tissue which is regarded as isotropic.Therefore, the model domain can be simplified into a two-dimensional rectangular zone which is a 20 × 30 mm 2 plane with a spatial resolution of 10 × 10 µm 2 .This voxel size can achieve reasonable accuracy at the cell level, as the diameter of body cells of neurons varies from 4 to 100 microns, with most intermediate-size cells ranging from 35 to 50 µm [45].Also, in mammals, the body temperature is regulated by hypothalamus, which maintains brain temperature around 36.8-37.2°C [46], depending on several factors such as cerebral blood flow and metabolism.Based on this, the initial temperature of our tissue was set at 37 °C, and the real-time temperature was calculated twice every 90 µs.

INS
Taking previous in vivo brain studies aimed at targeting submillimeter functional domains into account, fiber sizes with diameters of 100, 200 and 400 µm were selected to deliver lasers with a wavelength of 1,875 nm at 5 different radiant intensities respectively.Throughout the entire stimulation, the fibers were embedded in the tissue with the fiber tip positioned along the center axis of the modeled tissue and 10 mm below the top surface.To understand the temperature evolution during longer exposure durations, each trial in our simulation comsisted of 50 pulse trains, which is 1.5 times longer than a trial in above ex vivo experiment.We conducted two different simulations: one using a top-hat profile and the other using a quadratic profile.Our results indicate that the top-hat profile is conservative.Consequently, we assumed that the power density is uniform at every point on the fiber tip plane when employing the top-hat profile.

Generic bioheat transfer model
During simulations, the in vivo tissue heating was computed by solving the GBHTM, which is derived using first principles and has been validated in swine, demonstrating more accurate heating predictions in in vivo tissue compared to the traditional Pennes' BHTM [41].The GBHTM model consists of two coupled differential equations representing the tissue sub-volume and the blood sub-volume, respectively, both of which predict an appropriate blood tissue heat transfer rate term for transient cases [37]: where ρ is the tissue density (kg•m −3 ), C p is the specific heat at constant pressure (J•kg −1 •K −1 ), C ti and C bl is the heat capacity of tissue and blood (J•kg is the blood-tissue heat transfer rate term, P is the local perfusion, and Q is power density (W•m −3 ).Subscripts bl and ti represent blood and tissue, respectively.Pennes' BHTM, as in Eq. ( 4), is widely used to predict in vivo temperature because of its simplicity. where represents the volumetric perfusion rate, and other parameters are similar with Eq. ( 2).However, the Pennes' BHTM lacks a formal derivation; it is therefore difficult to interpret or evaluate the variables and parameters in Pennes' BHTM based on the underlaying physiology because the blood perfusion-related parameter (w(C p ) bl (1 − ζ)) always needs adjustment to minimize the error between modeled and measured temperatures for reasonable estimates.Furthermore, according to Shrivastava et al. [39], blood temperature is considered constant in Pennes' BHTM, which artificially forces the tissue temperature to track closely to blood temperature, potentially causing underestimation of tissue heating in deep tissue regions.By considering heat transfer in blood and tissue volumes respectively, GBHTM can address these issues and potentially contribute to a better understanding than Pennes' BHTM.Since thermal properties do not depend on stimulation wavelength and have been widely studied, the brain's thermal parameters were used for modeling.Relevant thermal parameters are the same as those used in Ref. [44].In the modeling, the following thermal properties of the brain were used: tissue density, ρ = 1,000 kg•m −3 , specific heat at constant pressure, C p = 3,600 [47,48].
C language was used to program the equation, and the finite difference technique was employed to implement the numerical simulation.The initial condition was set at 37 °C, and the boundary condition was adiabatic.
As for the optical part, the GBHTM requires, as input, laser induced power density in the tissue, and its distribution follows the Beer-Lambert Law (Eq.( 5)).
where I 0 is the irradiation intensity used to stimulate tissue, z is the propagation depth of light in Z-direction, and µ = µ a + µ s , µ a and µ s correspond to absorption and scattering coefficients respectively.However, despite many INS-related studies, there is limited available data regarding brain tissue at wavelengths above 1,850 nm [33][34][35][49][50][51][52][53][54].In the absence of direct data, we assumed that the values in the brain would fall within the range of values measured in other tissue types, such as the skin.Optical parameters of the skin were selected for several reasons: a) Optical properties of water were widely used in previous simulation studies.Although water is the major component of cells [1], there are still significant amounts of proteins, lipids and pigments in cells, which can influence the light absortion and scattering of the tissue.b) The target tissue of INS in the CNS, such as cerebral cortex, basal ganglia and brain stem, are composed of dense neurons, dense axons and little cerebrospinal fluid (CSF), and the combination of these components would significantly alter the optical characters of tissue.c) Skin is also a tissue composed of dense cells and has similar thermal properties to brain tissue [47].d) Skin is the most widely measured tissue with available measurements at various wavelengths [55][56][57], and according to available optical parameters of brain, skin and water, the differences between brain and skin tissue are smaller than those between brain and water [50,[54][55][56][58][59][60][61][62] (surveyed absorption coefficient of different media of various wavelength is listed in Supplement 1 Fig.S3, Table S2).According to our survey, for wavelengths over 1,000 nm, the available absorption coefficients of the brain were either similar to the values of skin or fell within the range of the minimum and maximum coefficients of skin.Therefore, we chose two sets of parameter that cover the entire range of the total absorption coefficients: an absorption coefficient and a reduced scattering coefficient of 1.97 cm −1 and 12.50 cm −1 respectively for Case 1 and 11.38 cm −1 and 10.46 cm −1 respectively for Case 2, which are the lower and upper limit [56,57].Tissue heating was simulated for both sets of optical parameters to evaluate the potential range of heating using GBHTM.The spatial and temporal resolution in MR Thermometry is much lower than in the simulation.Thirty-five sequential phase maps were obtained using the 3D-FLASH sequence on the slice of interest, which included two images before INS started and thirteen images after INS ended.Subsequently, these phase maps were converted into temperature changes according to Eq. ( 1), and the map after the last train was presented in Fig. 3(B) (the entire figure of the 35 phase-temperature maps can be found in Supplement 1 Fig.S1).

MR thermometry
In order to study the temperature changes, the data from the voxel containing the fiber tip were extracted and plotted as curves, illustrating the progression of temperature variations at the stimulation site (Fig. 3(A)).After two baseline measurements, the first INS train produced about 0.8 °C temperature increase in the tissue (at maximum energy intensity).Due to the temporal resolution limitations, only the overall temperature change after an INS train could be observed.As depicted in Fig. 3(A), the tissue temperature exhibited a continuous increase during the first several INS trains, consistent with the simulation, and began to reach a plateau starting from the 7 th train, which occurred much earlier than the simulation results.This pattern was consistent across exposure intensities except for the lowest one, and the stable temperature rise was proportional to INS intensity.At the end of a trial, INS induced significant heating of the tissue under all conditions, except when stimulating with 0.1 J/cm 2 .Additionally, it was observed that after the INS trial ended, the tissue temperature dropped to less than 50% of the maximum temperature reached during stimulation within 3 sec and returned to around the baseline level (< 0.1 °C) within 10 sec, even when the highest exposure intensity was employed.

Temperature distribution induced by INS
Despite the limited spatial resolution, a rough representation of the temperature distribution in the tissue was possible.A magnified plot depicting the thermal distribution immediately after the final INS train is shown in Fig. 3(B), captured under the highest intensity setting.
Our findings indicate that the heating effect was confined to a small, focal region encompassing only a few voxels.This may be due to the radiant penetration, with tissue on the side away from fiber implantation (and tissue near the fiber tip) exhibited greater temperature increase and a more noticeable thermal gradient than the other side, consistent with Monte Carlo simulations of light distribution.

Temperature change measurements
The tissue temperature was recorded right after an INS train ended, providing the maximum temperature achieved during that train.The first INS train typically resulted in a significant temperature increase for most conditions.For instance, laser radiant intensities ranging from 0.1 to 1 J/cm 2 resulted in temperature increases of -0.09 °C, 0.28 °C, 0.08 °C, 0.64 °C and 0.72 °C.The temperature reached a plateau about 27 sec after the start of MR Thermometry measurement and stabilized until the end of INS trial.The temperature difference between 10 sec after the end of the last INS pulse train (t = 73 sec) and beginning of the INS trial (t = 3 sec) was less than 0.3 °C for all conditions, indicating the baseline temperature remained stable across the experiment (detailed values in Supplement 1 Fig.S3, Table S6 and S7).
A formula describing the relationship between radiant exposure and temperature rise was provided in Ref. [39,63]: where ∆T is the temperature rise, µ a is the wavelength-and tissue-dependent absoption coefficient, H is the radiant exposure intensity to tissue, ρ and c are constant as in Eq. ( 2), representing tissue density and specific heat of tissue respectively.Note that in Izzo's study, this formula was used to estimate the temperature rise when other parameters were already known, in which the absorption coefficient of water was used.We attempted to find temperature increase and corresponding energy intensity data in many other studies, but few of them provided both temperature and intensity data.Thus, our ex vivo experiment results were also used to calculate the absorption coefficient of the ex vivo rat brain.The temperature change at the end of each trial was used as ∆T, the radiant exposure H was the corresponding power intensity delivered in the current trial, and the density and specific heat of tissue were the same as before.The calculated µ a of the ex vivo rat brain was 6.75 cm −1 (SD = 0.22), which appeared to fall within the range of optical properties used in our simulation.For a 0.5 sec train, the temperature exhibited slight fluctuations that repeated 100 times with corresponding INS pulses, resulting in an upward trend.It is not surprising that the final temperature of a train varied depending on fiber size and energy intensity, with a larger fiber diameter and higher intensity resulting in greater temperature increase.When using the same energy intensity, the temperature rises per pulse duration (0.25 msec pulse on) were found to be consistent during the initial period of an INS train, regardless of the chosen optic fiber diameter.However, there were variations in the temperature decreases (occurring during the 4.75 msec interval) among the different fiber sizes of 100, 200, 400 µm, with wider fibers resulting in smaller temperature drops.Therefore, within the same time frame, a 400 µm fiber would transfer more thermal energy to the tissue compared to a 100 µm fiber.As the number of delivered pulses increased, the tissue temperature rose, and the heating effect of pulse duration on tissue diminished slightly, while the temperature reduction during the interval gradually increased.In the case of lower radiant exposure transmitted by a small fiber, the temperature changes exhibited a nearly balanced rise and fall pattern during the last several pulses of a train, indicating a stable temperature level.The plots also depicted the linear relationship between temperature change and energy intensity when a specific fiber size was selected.

Simulations
The long-time temperature changes during a 150 sec trial were also explored .As described above, a 0.5 sec train, triggered every 3 seconds, was repeated 50 times to form a trial.These curves are plotted in Fig. 5 and shared similar characters with that of a single 0.5 sec train.For each curve, there were 50 peaks that demonstrate a similar time-dependent temperature increase as in Fig. 4 and the maximum temperature after a train.Although the initial temperatures of separate pulse trains were different, for the condition with the most significant temperature change (Case 2, 400 µm and 1 J/cm 2 ), the maximum temperature increase at the end of the first pulse train was almost the same as that of the last pulse train (the difference was around 0.3 °C), while the temperature decrease during ISI for the first and last pulse train was different, which was approximately 1 °C.Furthermore, these curves exhibited more pronounced cross-train fluctuations than in Fig. 4 (cross pulses), with the maximum difference between adjancent peaks and troughs exceeding over 12 °C (Case 2, 400 µm and 1 J/cm 2 ).In most conditions, the temperature decrease was nearly equal to the temperature increase in the last several trains, and the tissue temperature eventually reached a plateau.The temperature increase caused by a pulse train was relatively larger when the tissue was stimulated with higher intensity or a laser fiber with larger diameter was used, and it would take a longer time to reach a plateau.Based on Fig. 5, the variations between the peak temperatures of each train could be ignored after 10 trains (30 sec) for all cases or fiber sizes when using intensities of 0.3 J/cm 2 and below.

Temperature distribution induced by INS
Since regions far from the fiber tip in the tissue were not subjected to heating, a 4 × 7 mm 2 region was chosen to display the temperature gradient images.The fiber tip was positioned at the center of the horizontal plane and 1 mm below the upper surface plane of the tissue (as depicted in Fig. 6).To facilitate the comparison of thermal gradients after a train under different conditions, the maximum radiant exposure intensity (1 J/cm 2 ) was selected to yield more intuitive results.Due to the difference between the two sets of tissue optical properties, the heated zones showed distinct patterns.In case 1, characterized by a lower absorption coefficient, a cone-shaped heated region was observed, with a maximum temperature increase of approximately 5 to 6 °C.As for Case 2, the region was shorter but exhibited higher temperatures (over a 10 °C increase), resembling an inverted water drop in shape.The heated volume positively correlated with optic fiber size and changed slightly with increasing energy intensity.The penetration depth can be roughly discerned in Fig. 6.It appears that after an INS train, the maximum temperature point (pixel) in Case 1 is deeper than in Case 2, consistent with the difference in penetration depths, although both points are located beneath the fiber tip (refer to the next Section).However, the widest cross-sectional plane of the heated region remains at the surface of the fiber tip following a train.
When the stimulation was extended to a trial, the thermal gradient distribution followed a similar pattern to that observed after an INS train.The main differences were that the heated volume was significantly larger (the surrounding tissue experienced a slight temperature rise due to thermal conduction) and the overall temperature of the region just beneath the fiber tip was higher.

Time curve of penetration depth of maximum temperature point with INS
Similar to the temperature change, the penetration depth of the maximum temperature also changed over time.The distance between the pixel with maximum temperature and the optic fiber tip was measured during an INS train as shown in Fig. 7.This distance was independent of the exposure intensity and consistent with the penetration depth of laser radiation, which is determined by laser wavelength, beam diameter, and the optical parameters of the tissue [63].In contrast to the penetration depth of the laser, which is held constant in this simulation, the thermal accumulation and diffusion evolves over time and INS pulses.This results in a shift in the location of maximum temperature [64].Although the optical penetration depth at wavelength of 1,875 nm was approximately 1.2 mm [55], the depth of the maximum temperature point increased gradually with INS pulses stimulating and eventually leveled at a depth of about 0.1 to 0.3 mm in the tissue.Specifically, the thermal penetration depth was approximately 270 ± 10 µm in Case 1 and 140 ± 10 µm in Case 2, when using a laser with a 100 µm beam diameter.With a larger diameter, the peak temperature point was slightly deeper (about 1 to 3 pixels, equivalent to 10 to 30 µm).However, limited by the spatial resolution of our simulation, differences of less than 10 µm were not observed.

Temperature change measurements
To further quantify the temperature increase, the temperature change during the last INS pulse in a train and the temperature during the last INS train in a trial were recorded.As described above, both higher energy intensity and a larger fiber diameter resulted in a higher resulting tissue temperature.Case 1 (lower boundary) had a lower maximum temperature and a more stable temperature than Case 2 (upper boundary) due to differences in optical parameters.
Within a single INS train, the temperature fluctuation was small, and the tissue temperature increased noticeably at the end of a train.As demonstrated in Sec 3.1.1,the first INS pulse duration results in the same temperature increases regardless of the fiber size, assuming equal exposure intensity.A pulse duration of 1 J/cm 2 resulted in a temperature increase of 0.16 °C in Case 1 and 0.46 °C in Case 2. The variation of temperature change among different fiber diameters was primarily determined by the thermal diffusion in tissue during the 4.75 ms interval period, and tissue stimulated with a 100 µm fiber experienced a significantly larger temperature decline compared to those stimulated with 200 and 400 µm (∆T in Case 1: 0.030, 0.011, 0.01 °C, ∆T in Case 2: 0.121, 0.071, 0.070 °C).In the subsequent INS period, the fluctuation magnitudes changed over time, specifically, according to the current temperature and the thermal distribution in the tissue.At the end of the first INS train, the tissue temperature reached its temporal maximum within 0.5 sec, as shown in Fig. 4 (detailed values in Supplement 1 Fig.S3, Table S2).
Among all the considered conditions, temperature change was the greatest when a 400 µm fiber was used to deliver 1 J/cm 2 power intensity laser, and the biggest temporal temperature change was 6.71 °C in Case 1 and 13.26 °C in Case 2. Although the immediate temperature after the last pulse the first train was relatively high, the subsequent 2.5 sec interval was long enough for the thermal energy to transfer to the surrounding tissue, and the temperature decreased by 5.56 °C in Case 1 and 11.74 °C in Case 2, respectively.
The subsequent trains would continuously stimulate the tissue and led to intermittent thermal accumulation and diffusion.After 20 trains (60 sec, the same as in ex vivo experiment), the temperature change rate became lower or even approached 0 in some conditions.And the greatest temperature rises among all the considered conditions, i.e., using a 400 µm diameter and 1 J/cm 2 power intensity, were 4.07 and 4.77 in Case 1 and Case 2 before the 21 st pulse train.The temperature increases at the end of the last (50 th ) train exceeded 6 °C for all the conditions at the radiant energy level of 1 J/cm 2 (except for the 100 µm in Case 1 which is 3.77 °C) and even exceeded 11 °C when using 400 µm fiber (more details in Supplement 1 Table S3).However, the maximum temperatures were ephemeral and would drop sharply just after the INS was turned off.The final temperature increase after a complete 150 sec trial for all the conditions was below 6 °C (Supplement 1 Fig.S3, Table S4), i.e., 43 °C, which appears to be a safe temperature for tissue [65].

Discussion
To assess the safety of using INS (1,875 nm wavelength light, pulse width 0.25 ms, delivered at 200 Hz for 0.5 sec) as a brain stimulation method, we investigated temperature changes in brain tissue using MR thermometry of an ex vivo rat brain and GBHTM numerical modeling methods.Both methods used 0.5sec pulse trains, with 2.5sec ISI, for a total of 20 pulse trains, delivered at 5 different stimulation intensities (0.1, 0.3, 0.5, 0.7, 1.0 J/cm 2 ).Data from both methods exhibited similar time-dependent temperature curves, initially showing a steep rise over the first several trains, reaching a plateau, and then rapidly declining at the cessation of the pulse trains.Both methods showed that the magnitude of maximum temperature change rose with increases in stimulation intensity.MR thermometry revealed that the maximum temperature reached by the highest intensity (1.0 J/cm 2 ) did not exceed 2°C, and did not exceed 1°C for the most commonly used experimental conditions in primates (0.1-0.3 J/cm 2 ) (Shi et al. 2021, Yao et al. 2023).In the simulation, the maximum transient temperature rises in all conditions remained below 20°C, and the final temperature after completing the entire INS trial was below 6 °C.These results indicated that the likelihood of tissue damage occurring in vivo due to this specific INS paradigm was minimal.

Temperature fluctuation and quantification of damage possibility
The INS train consisted of a series of 0.25 msec wide INS pulses with a 4.75 msec interval between pulses, and the 2.5 sec interval between different INS trains was five times longer than the 0.5 sec train.It was therefore not surprising that the tissue temperature fluctuated with the on and off cycles of INS stimulation, as shown in Fig. 4 and Fig. 5.In our simulations, after 50 pulse trains and at maximum energy of 1.0 J/cm 2 , the tissue experienced substantial heating during INS stimulation, with the temperature reaching 13.26°C (Fig. 4) after a single train and 18.53°C (Fig. 5) after completing the entire 50-train trial.
Our modeling shows consistent numbers.Note that in experimental conditions in nonhuman primate studies, which use a 200 µm fiber in brain tissue, the maximum number of pulse trains delivered is 3-4 pulse trains with radiant exposures not exceeding 0.3 J/cm 2 [21,22].This corresponds to, according to the model, temperatures not exceeding ∼1°C (Case 1) and ∼2°C (Case 2) (see Fig. 5).In the first human study [2], where INS was applied to cortical tissue prior to resection in epilepsy patients, a 400 µm fiber was placed at a 60°angle to the surface of cortex, and single (not multiple) pulse trains delivered every 8-10 sec.For a 400 µm fiber and a single pulse train, these values do not exceed 2°C (Case 1) and 3.7°C (Case 2) (see Fig. 5).Thus, these numbers are only slightly higher than the experimentally determined temperature rises (see Discussion below).
In numerical three kinds of variables were taken into account: radiant exposure intensity, fiber size, and the tissue optical property.Both radiant exposure and fiber size were proportional to the temperature increase.However, the relationship between radiant exposure intensity and tissue temperature increase was linear, whereas the relationship between fiber size and temperature change was not.The two sets of tissue properties also resulted in different temperature due to their different absorption coefficients, and the temperature increase in Case 2 was about one-fold higher than that in Case 1 (details about the two sets of parameters are provided in the next section).Based on these findings, delivering an INS trial at 2 W/mm 2 by a 400 µm fiber to tissue, as in Case 2, resulted in the highest thermal variation compared to all other conditions, reaching 55.53 °C.Although this is a high value, it lasted less than 0.3 sec before dropping by 50%.As shown in [49,66], the local thermal damage threshold was identified at approximately 60 °C in in vitro spiral ganglion neurons.Despite the discrepancies in the experiment material between their studies and ours, the thermal damage threshold and activation mechanism would be similar at the single neuron level because of their comparable cell structures, in which impedance plays a crucial role in INS stimulation and modification [49,67].Additionally, the damage threshold might be higher in vivo due to the thermodynamics environment.The final temperature after a 150 sec trial was much lower than the maximum temperature, as the last interval following the last train provided enough time for the temperature to decrease.The largest temperature change observed (2 W/mm 2 by 400 µm for Case 2) was 12.76 °C lower than the temperature before the interval, indicating that none of these conditions would lead to a tissue temperature over 43 °C after the entire 150 sec INS stimulation.
Previous animal studies have demonstrated that CNS could withstand temperatures of 42-42.5 °C for a duration ranging from one third to one hour, or at 43 °C for ten to thirty minutes [65].Also, the photothermal mechanism was the widely accepted as the light-tissue interaction of INS evoking neuron activities, while the local temperature change and temperature gradient caused by this interaction would lead to the alternation of cells or neurons and further contribute to the tissue activities.It has also been suggested that temperatures ranging from 40 to 45 °C might lead to reversible injury in cells [68,69], such as thermal denaturation of enzymes, and tissue would still be denatured, which was repairable via repair mechanisms of cell, between 42 to 50 °C, and tissue necrosis would require a minimum temperature of 60 °C [64].
In the ex vivo experiment, the temperature rise was lower, less than 2 °C with 1 J/cm 2 (equal to 2 W/mm 2 ).There were several reasons that could explain this phenomenon: a) The spatial resolution of MR Thermometry was 1 mm isotropic, which was 5 times the fiber diameter used for delivering radiation.Therefore, the measured value in the voxel with the highest temperature actually represented the average temperature in the 1 mm 3 zone.This equalization of temperature between the stimulation site and adjacent regions would definitely result in a reduction of the measured maximum temperature.b) It took 1.8 sec to finish one-shot phase mapping, which was much longer than an INS train, and thus, not only the 0.5 sec heating duration would be recorded, but also 1.3 sec of the 2.5 sec long interval with the INS off.As mentioned earlier, once the INS train was off, the tissue temperature would decrease shapely, so the limitation of temporal resolution would also lead to a lower measured temperature than the real temperature.c) The total duration of one trial in the ex vivo experiment differed from the simulation.In the simulation, 50 INS trains per trial were set to estimate the maximum temperature rise that could be reached by INS stimulation in biological CNS tissue, as it would not cause actual damage.Conversely, only 20 INS trains were used per trial in the ex vivo experiment, aligning with previous INS in CNS experiments [15][16][17], in order to verify the temperature change in in vivo scenarios.Taking the INS train number into account, the temperature increase in simulation was compared with the MR Thermometry measurement, while keeping all other conditions the same (200 µm, consistent intensities).The maximum temperature increased immediately after the 20 th INS train and the final temperature at 60 seconds were 6.04 and 2.05 °C, respectively, for 1 J• cm −2 (2 W• mm −2 ) in Case 1, and they were 10.72 °C and 2.56 °C for 1 J• cm −2 in Case 2. The temperature before the 21 st train was only slightly higher than the MR Thermometry measurement.Considering the MR Thermometry reflected the average temperature over space and time, it is reasonable to conclude that the results of simulation and experiment are consistent with each other.These findings, suggest that the temperature increase induced by the current INS paradigm is within the range that does not cause tissue damage.
The overall trend in both simulation and experiment was similar, while the plateau in ex vivo experiments (after the 7th train, around 21 sec) came earlier than in simulation (at least after the 25th train, around 75 sec) for 2 W/mm 2 .For the other radiant exposure intensities, the time point of reaching the plateau would be early (about 40-50 sec for 1.4 and 1.0 W/mm 2 , similar to in ex vivo for 0.6 and 0.2 W/mm 2 ).The reason for this discrepancy might be that the ex vivo tissue lacked perfusion and the measured temperature was an averaged value.

Tissue related thermal gradient distribution
The thermal distribution plays a crucial role in achieving precise stimulation.In most INS in CNS studies, a wavelength of 1,875 nm was selected to provide focal stimulation and proper penetration depth in biological tissue [4,11,16,23].As shown in Fig. 6, the INS train would locally heat a region less than 4 mm width beneath the optic fiber tip.The penetration depth of the heated region varied depending on the assumed tissue optical parameters.Additionally, the heated volume was greater when using larger diameter fibers, and as a result, the maximum temperature point on the symmetry axis would experience less heat transfer to its neighbors, leading to a higher likelihood of thermal energy accumulation and relatively higher temperature.This may also explain the faster increase in temperature at the maximum temperature point and the larger temperature change, which is in agreement with the temperature-time curve.The penetration depth, as mentioned above, was also an important factor.It was unexpected at first that the maximum temperature point was not at the fiber tip but serveral hundred microns beneath it, and it would become deeper over time.This phenomenon was observed in both simulation and ex vivo experiment, indicating that the actual stimulation site was not only located at the fiber tip but also involved some neurons in deeper tissue.This is because most neurons had a width of 30 to 50 µm, which might help guide INS with more accuracy.
The optical properties used in this study encompassed two end values of skin's optical properties.It was assumed that this range covered the potential optical properties of brain tissue.Although many previous studies selected the optical properties of water as the substitute of brain tissue [33,53,70], which were rarely measured at the 1,875 nm wavelength, the optical properties of skin seemed to be a more suitable choice for several reasons as follows: a) Most previous studies about INS safety or potential thermal damage focused on situations where the optic fiber was not inserted into tissue, but rather stimulating tissue without direct contact, such as in in vitro studies and in the cochlea, where the medium for laser radiation before reaching the target tissue might be more similar to water.b) The reason why the absorption coefficient of water was used was because it is the main component of cells, and infrared around 2,000 nm wavelength is strongly absorbed by water [1].However, brain tissue, unlike PNS where axons are organized in parallel bundles in nerves, is a much more complex neuronal network composed of massive neurons, including cell bodies, dendrites and axons, glial cells and many other structures, such as microtubule and synaptic complexes.The presence of these components introduces other substances which affect the optical properties of tissue, such as fat and protein [61,64].c) Skin is the largest organ in the human body, consisting of three layers, one of which is the dermis.The dermis is a thick layer of living cells containing vessels, nerve endings, and glands.It exhibits certain similarities to the brain.Also, the optical properties of the skin have been extensively studied across a broad range of wavelengths, from 400 to 2,000 nm in human and up to 2,500 nm in rat This provides valuable guidance for inferring the properties of other biological tissues that share similar components and structures.d) According to Eq. ( 6), we calculated the absorption coefficient of the ex vivo rat brain with our ex vivo experiments, which turned out to be 6.75 cm −1 and fell within the range of optical properties used in our simulations.Recently, Genina et al. [71] measured the optical properties of brain tissue in rats from 400 to 1,800 nm, studying the optical coefficient of brain tissue above 1,300 nm for the first time and providing more information to compare the optical properties of skin and brain.Although the absorption value of brain fell in the range of coefficient of skin for most conditions, the minimum absorption coefficient was a bit greater than the value in Genina's study (1.54 cm −1 and 1.36 cm −1 ) at 1,727 nm.However, the absorption coefficient measured in their study was also lower than values reported in most other previous studies within the known wavelength range (400-1,200 nm), which may be due to the methods of measurement [50].Meanwhile, the measured optical properties would differ when different regions of brain were used, which is due to the difference in anatomical structure and tissue components, i.e., nerve, grey matter, white matter, cerebellum and ganglia.
Based on the aforementioned reasons, we believe it is reasonable to employ the optical parameters of skin as substitutes for brain parameters in our simulations.Future studies with optical parameters of brain tissue may offer additional insight.

Comparison to previous studies
Many studies have discussed the potential thermal damage and possible damage threshold in INS due to the critical importance of ensuring INS safety.However, there were large diversities among these studies, including but not limited to radiant wavelength, INS paradigm, the unit of threshold, and the type of target tissue.When it came to the unit of the damage threshold, there were three kinds of unit: Celsius degree (°C), Joule per square centimeter (J/cm 2 ) and safety ratio.
The unit "J/cm 2 " was commonly used in previous studies.Chernov et al. [25] applied INS, sharing a similar paradigm with ours but with a trial duration of 30 minutes, to the brains of rats and squirrel monkeys.They performed histological assessments and found that the safe radiant exposure was in the range of 0.3 and 0.4 J/cm 2 for the rat cortex, around 0.6 J/cm 2 for the somatosensory cortex of the squirrel monkey.Higher intensity resulted in sponge-like tissue damage.It also illustrated that there might be a slight variation between different cortex types or creature species.Despite the similarity in INS paradigm, wavelength and target tissue, the longer trial duration (less than 3 min in our study, but 30 minutes in Chernov's study) and the different stimulation mode (fiber insertion in our study, but non-contact positioning in Chernov's study) might result in different conclusions.According to our simulation results, the relatively stable tissue temperature (initial temperature: 37 °C) after 150 sec was between 38 to 40.37 °C (minimum and maximum transient temperature), which was considered a safe temperature range.However, due to the INS duration being 10 times longer in Chernov's study, this temperature no longer appeared to be safe.As shown in [65], the maximum temperature for normal brain during such a long time was in the range of 38 to 46.3 °C.On the other hand, the non-contact stimulation method might also contribute to the differences.If the optic fiber was inserted into tissue, the thermal energy was gradually accumulated in the tissue, and the maximum temperature point would not always be confined to a specific site, which was significantly different from the non-contact method.Also, the fiber itself would transit some energy.Recently, Pan et al. reported similar results to Chernov et al., using almost the same method, but for the first time targeting the human brain [2].Both in vitro and in vivo experiments was conducted and indicated a damage threshold estimate of about 0.6 J/cm 2 .Apart from its application in the CNS, another study [68] used a 600 µm fiber to deliver a laser at a wavelength of 2,120 nm with a pulse duration of 0.35 sec at variable frequency to determine the INS injury in rat sciatic nerve.They reported that the energy intensity between 0.66 to 0.70 J/cm 2 was safe, with a maximum duration of 4 minutes at 2 Hz.Without considering delayed nerve damage, the radiant exposure could even reach up to 1.0 to 1.2 J/cm 2 .Cury et al. reported a higher INS threshold for the rat and rabbit sciatic nerve by utilizing a fiber with a beam size of 0.12 mm 2 to deliver infrared at 1,470 nm, revealing a threshold of neural activation at 3.16 ± 0.68 J•cm −2 [72].
Although the unit "J/cm 2 " is a commonly used index when describing radiant energy intensity, it is inadequate for fairly evaluating the consistency of results in different experiments when other parameters such as tissue type, radiant wavelength, stimulation paradigm, total duration etc. were diverse.Celsius degree would be a better measure in this case, providing more standardized and quantified data for damage probability assessments.However, only a few studies have discussed the damage threshold in terms of Celsius degrees.Brown et al. [49] conducted a study using cultured spiral ganglion neurons to study the energy-dependent INS damge probability.They found that the local damage threshold was about 60 °C using the patch-clamp recording method, which was consistent with our results.Dremin et al. [73] simulated the thermal field distribution in brain and skin tissue, and the tissues were stimulated by 760, 1,064 and 1,267 nm infrared wavelengths while the optic fiber was placed at the tissue surface.Their results indicated that, in the selected wavelength range, the temperature rise in skin tissue (4.5, 3.0 and 3.5 °C increase per 50 mW) was higher than in brain tissue (1.9, 1.7 and 1.6 °C increase per 50 mW) and the temperature after 10 min 250 mW radiant exposure at 760 nm wavelength was 59.1 and 46.2 °C.The reason why the final temperatures were higher than ours might be because the INS stimulation paradigm was significantly different, i.e., had intervals between INS or not.On the other hand, if the temperature rise in the skin were higher than that in the brain, our results could also demonstrate the safety of our INS paradigm and radiant exposure intensity using in the CNS.The maximum tolerable temperature and heat duration in brain had already been widely studied [32,65], providing valuable guidance for evaluating and addressing safety concerns in our study.
The safety ratio, which is the ratio of the ablation threshold to the simulation threshold, has also been employed in safety assessment.An in vivo experiment conducted by Cayce et al. demonstrated a safety ratio of 2:1, wherein activation occurred at 0.53 J/cm 2 and damage was observed at 1.09 J/cm 2 [23].Human spianal nerve roots of were the target of stimulation using 2,120 nm wavelength laser.Assuming that the safety ratio and damage threshold from this study are applicable to our results, the maximum transient temperature rise (approximately 9.26 °C) would be sufficiently high to excite neuronal action potential.However, this temperature was only half as low as the data reported in [53], which utilized a 1,940 nm wavelength laser at a power of 600 mW and a frequency of 10 Hz.The discrepancy could stem from the variation between in vivo and in vitro enviornments, as well as differences in temperature measurement methods.It may also serve as evidence supporting the notion that the INS damage threshold surpasses 1 J/cm 2 .Throckmorton et al. studied the rat sciatic nerve and established distinct thermal threshold for diversity radiant wavelengths [70].They compared the energy intensity corresponding to the 50% probability of exciting action potential, known as H 50 [74], at wavelengths of 1,450 nm, 1,875 nm, and 2,120 nm.Their findings revealed that the laser at 1,450 nm and at 1,875 nm shared a similar H 50 value of about 1.0 J/cm 2 , consistently higher than the H 50 of 2,120 nm (approximately 0.7 J/cm 2 ).This led to the establishment of 3:1 safety threshold, suggesting that the damage threshold for 2,120 nm was nearly 2.1 J/cm 2 , significantly higher than previously reported.
The INS-fMRI studies employing the same INS paradigm as in our study, it was observed that 0.1-0.3J/cm 2 was adequate to evoke a BOLD response at the stimulation site as well as in the interconnected neurons of the amygdala and cortex.In line with the simulation results, the maximum temperature was 3.22 °C, while the minimum temperature was 0.62 °C.
The results of previous studies exhibited a range of diversity, initially leading to confusion.However, the majority of these findings corroborated our results in this study, suggesting radiant exposure below 1 J/cm 2 would be deemed safe for INS in the CNS, particularly when the fiber was inserted into the tissue.Furthermore, the temperature increase remained within 20 °C, ensuring that the overall temperature stayed below 60 °C.

Limitations
Our study had several limitations.Firstly, the simulation and experiment were conducted in vivo and ex vivo respectively.This difference in conditions could lead to variations due to factors such as perfusion and metabolism.Nonetheless, the radiant exposure was consistently maintained to examine the potential temperature changes.An ex vivo rat brain was used because deceased tissue lacks the ability to regulate temperature itself and would not be affected by anesthetic.Secondly, there were no available optical parameters for brain tissue at a wavelength of 1,875 nm, and the optical properties of the skin were used as a substitute.This choice might limit the accuracy of the temperature increase estimation but can still help address the issue of safety.Moreover, different structures within the brain possess different properties, but they were considered as a uniform tissue in the simulation.However, since a range of possible optical parameters were selected, the parameters of different structures might fall into this range.Furthermore, in the ex vivo experiment, the use of 1 mm isotropic spatial resolution and 1.8 sec temporal resolution in MR Thermometry limited the precision of temperature increase measurement, despite our efforts in hardware and sequence for improved spatiotemporal resolutions.Additionally, it should be noted that we only focused on a specific INS paradigm which was mainly used for inserted INS in the CNS, and specifically examined the impact of radiant exposure and fiber diameter on temperature elevation.Other parameters were not considered in this analysis.

Conclusion
This study aimed to examine the temperature change and temperature distribution in brain tissue when stimulated with INS using optical fibers of three different sizes, delivering radiant exposures ranging from 0.1 to 1.0 J/cm 2 .Both numerical simulation and ex vivo experiments were conducted to assess the potential risk of thermal damage.The simulation and the MR Thermometry experiment yielded consistent and reliable results.Previous studies have indicated that the temperature increase remains within the range of safety threshold.Therefore, the current findings provide us with enhanced confidence in the safety of INS, allowing us to proceed with further INS investigations along this direction.

Fig. 2 .
Fig. 2. The ex vivo rat brain phantom.(A) Photo of the rat brain phantom.The three arrows point to the agar (yellow), rat brain (white) and 200 µm optical fiber (red).(B) Anatomical MRI image of key slice of the rat brain, showing optical fiber insertion.See Supplement 1.

Fig. 3 .
Fig. 3.The MR thermometry results.(A) The evolution of the temperature change at one single voxel involving the laser tip.The paired-sample t-test is conducted cross the Temperature change of 3 sec and 63 sec.The significant levels are shown in the legend, *p < 0.05, **p < 0.01, ***p < 0.001.(B) Enlarged version of the selected slice, which represents the temperature change after the last (20 th ) pulse train.In this slice the maximum temperature change is 1.874 °C.

3. 1 . 1 .
Time course of temperature change induced by INS

3. 2 . 1 .
Time course of temperature change induced by INSHere, due to the lack of good parameters for brain tissue, we model temperature change in tissue based on models of skin parameters[56,57].During INS, the temperature showed a sawtooth pattern following the switching of the stimulation on and off.The time-dependent curves of tissue temperature recorded at the pixel corresponding to the center of the stimulation site (the optical fiber end face) are presented in Fig.4(an INS train) and Fig.5(an INS trial).Regardless of the conditions (including different optic fiber sizes and radiant exposure intensities), the curves corresponding to the same INS duration followed a similar pattern.

Fig. 4 .
Fig. 4. Simulated temporal maximum temperature increase in brain.The subplots show the temperature evolution during a 0.5 sec train when 5 radiant exposures were delivered through fiber of 3 different diameter for two sets of optical parameters.

Fig. 5 .
Fig. 5.The time course of heating in the brain tissue model within 150 sec for the two cases.

Fig. 6 .
Fig.6.Temperature distributions after a train.Upper: left three subplots are for Case 1 and right three for Case 2, and for each case three fiber sizes are shown, while laser power is 1 J/cm 2 .The horizontal solid line in the 2 nd and 5 th subplot represented the plane of fiber tip surface.The vertical is the axis of symmetry of both fiber and tissue.Lower: the width and depth of the heated volume for different fiber sizes.The inset in the right inset shows the enlarged plot of the width-depth within 3 mm beneath the fiber tip.The heated volume and temperature increase are both positively correlated to the fiber size.

Fig. 7 .
Fig. 7.The distance between the fiber tip and the point of maximum temperature over time.The point of maximum temperature gradually moves away from the fiber tip.Left subplot is for Case 1 and right for Case 2.