Selective Infrared Neural Inhibition can be Reproduced by Resistive Heating

Abstract

Objectives.

Small-diameter afferent axons carry various sensory signals that are critical for vital physiological conditions but sometimes contribute to pathologies. Infrared (IR) neural inhibition (INI) can induce selective heat block of small-diameter axons, which holds potential for translational applications such as pain management. Previous research suggested that IR-heating-induced acceleration of voltage-gated potassium channel kinetics is the mechanism for INI. Therefore, we hypothesized that other heating methods, such as resistive heating (RH) in a cuff, could reproduce the selective inhibition observed by INI.

Materials and Methods:

We conducted ex vivo nerve heating experiments on pleural-abdominal connective nerves of Aplysia californica using both IR and resistive heating. We fabricated a transparent silicone nerve cuff for simultaneous IR heating, RH, and temperature measurements. Temperature elevations (ΔT) on the nerve surface were recorded for both heating modalities, which were tested over a range of power levels that cover a similar ΔT range. We recorded electrically evoked compound action potentials (CAPs) and segmented them into fast and slow subcomponents based on conduction velocity differences between the large and small diameter axonal subpopulations. We calculated the normalized inhibition strength and inhibition selectivity index based on the rectified area under the curve (RAUC) of each subpopulation.

Results:

INI and RH showed a similar selective inhibition effect on CAP subcomponents for slow-conducting axons, confirmed by the inhibition probability vs. ΔT dose-response curve based on approximately two thousand CAP measurements. The inhibition selectivity indices of the two heating modalities were similar across six nerves. RH only required half of the total electrical power required by INI to achieve a similar ΔT.

Significance:

We show that selective INI can be reproduced by other heating modalities such as resistive heating. Resistive heating, because of its high energy efficiency and simple design, can be a good candidate for future implantable neural interface designs.

1. Introduction

Selective inhibition of small-diameter axons is a critical and unmet medical need. Small-diameter nerve fibers carry various sensory signals that are critical for the homeostasis of vital physiological conditions ^1,2. Selective inhibition of small-diameter axons has the potential to treat various diseases (e.g., pain ³, obesity ⁴, and hypertension ⁵) that are difficult to treat using conventional pharmaceuticals ⁶. The current use of local anesthetics cannot reliably induce selective block of small-diameter fibers ^7,8 while the use of systemic drugs, in particular opioids, has numerous deleterious side effects ^9,10.

Traditional electrode-based neuromodulation can induce neural block but has had limited success in preferentially blocking small-diameter axons. Examples include direct current (DC) nerve block ^11,12 and high-frequency alternating current stimulation (HFAC) ^13,14. These neuromodulation modalities preferentially block large-diameter efferent axons because the transmembrane potential evoked by the extracellular electrode is proportional to the axon diameter ^12,15. Therefore, selective inhibition of small-diameter axons requires additional effort, such as changing the stimulation frequency of HFAC ^16,17. The small-diameter axon selectivity can be further degraded due to electrode corrosion and dislocation during chronic implantation ^18,19. There is still a need for a selective neuromodulation modality for small-diameter axons.

We have previously shown that infrared (IR) neural inhibition (INI) can selectively inhibit the small-diameter slow-conducting nerve fibers ²⁰. This is achieved using IR light (e.g., λ ~ 1470 nm, 1550 nm, and 1860 nm) with a high-water absorption coefficient. INI can inhibit the propagation of both neural ^20–23 and cardiac action potentials ²⁴. In addition to size selectivity, IR light can also achieve spatial selectivity of fine structures (e.g., neurons) to explore their functionality ^25–28. At the same wavelength, infrared neural stimulation (INS) can be achieved using a spatial-temporal thermal gradient caused by the absorption of short IR pulses ^29–33. In contrast, INI relies on the IR-induced baseline temperature elevation that causes thermal acceleration of K+ channel kinetics to block neural conduction ^34–36. The power threshold for INI can be lowered by changing the length of the axon along which IR is applied ^37,38 or by isotonic extracellular ion replacement ³⁹ while maintaining the size selectivity during inhibition. In addition, other IR wavelengths have been used to modulate neural activity in vertebrate animals ^28,40–44.

Heat-induced inhibition of neural conduction has been reported in previous studies. Hodgkin and Katz reported a heat-induced neural block effect on giant squid axons in 1949 ⁴⁵. Direct heat application induces neural conduction block in rat sciatic nerves ^46,47, cat pudendal nerves (with heating before cooling) ^48,49, and human median and ulnar nerves ⁵⁰. Other neural inhibition modalities are affected by heating. For example, studies have shown that high-frequency biphasic stimulation’s blocking threshold can be lowered by heating ^51–54. Recent studies showed that clinical kHz spinal cord stimulation and deep brain stimulation protocols can also induce tissue temperature elevation ^55–58. Both findings indicated that the heating effect during high-frequency electrical stimulation may be related to its mechanism of action. Similarly, recent studies on ultrasound-based neural inhibition suggested that temperature elevation may be the mechanism ^59–61. Unfortunately, in those studies, the size selectivity of neural inhibition was not explored. But it has been reported in rats ⁶² and humans ^63,64 that during hyperthermia, the reflex response mediated by the small-diameter afferent fibers was suppressed. Previous studies also suggested that the selective inhibition effect during INI was heat-based ^20,35,36.

Therefore, we hypothesized that selective inhibition with INI could be reproduced using another heating modality, resistive heating (RH). In this study, we developed a nerve cuff for RH and temperature monitoring. We compared the inhibition strength under different temperature elevations (dose-response) and the selective inhibition as a function of axon diameter in response to INI and RH on the pleural-abdominal connective nerve in Aplysia californica, a preparation consisting solely of unmyelinated axons of varying diameters. We selected RH as the representative heating modality, primarily because it can be designed to minimize the spatial variance of induced temperature elevation. In addition, RH can be applied in a relatively simple design and could have better energy efficiency than INI. These advantages could facilitate the further development of battery-powered implantable devices, increasing the availability of selective inhibition of small-diameter axons for basic research and translational applications.

2. Materials and Methods

2.1. Animal Model

We tested our hypothesis in vitro (N = 6) on the pleural-abdominal connective nerve of Aplysia californica (278 ± 40 g, South Coast Bio-Marine, CA). Although the use of Aplysia, an invertebrate animal, does not require IACUC approval, we ensured that animals were fully anesthetized before extracting nerves, and then were euthanized with an excess of anesthetic (magnesium chloride). The Aplysia nerve consists only of unmyelinated axons with large and small diameters, because Aplysia does not make myelin. This provides a robust testing platform for exploring the relationship between the inhibitory effect and axonal size differences without having to consider the effects of myelination ^20,65. While further studies and parameter optimization would need to be carried out when translating selective block by RH to vertebrate neurons, our previous work has shown that IR-based heating translates directly from Aplysia to vertebrate systems (rat and musk shrew) at much smaller values of ΔT. ^20–22.

2.2. Electrophysiological recording

Customized suction electrodes (0.35 mm inner diameter) was printed using a 3D printer (Form 3, Formlabs, MA, USA) for electrical stimulation (2 Hz with 2 ms symmetric biphasic current pulses, 1 ms per phase) and compound action potential (CAP) recording. The stimulation pulsing signal was generated using a pulse stimulator (Model 2100, A-M Systems, WA, USA) and converted into current pulses using a stimulus isolator (A395, World Precision Instruments, FL, USA). The current was adjusted for each nerve between 0.3 – 0.5 mA to ensure full recruitment of all CAP components. The evoked CAPs were amplified and filtered (×10,000, 100–500 Hz) using a differential AC amplifier (Model 1700, A-M Systems, WA) and digitized with a data acquisition (DAQ) device (USB-6003, National Instruments, TX, USA) at 5000 Hz sampling rate using AxoGraph X software (AxoGraph, CA, USA). The nerve was placed in a chamber filled with Aplysia saline (460 mM NaCl, 10 mM KCl, 10 mM MOPS, 10 mM glucose, 22 mM MgCl2·6H2O, 33 mM MgSO4·7H2O, 13 mM CaCl2, pH 7.5) at room temperature (~20 °C) to sustain the health of the nerve during the experiments.

2.3. Resistive heating (RH)

We fabricated heating cuffs by embedding nichrome heating wires (#761500, 25.4 μm bare diameter, A-M Systems, WA, USA) between two layers of medical grade PDMS tubing (#60–011-05 and #60–011-08, Dow Corning, MI, USA) for the application of RH. Fig. 1. (a) illustrates the heating cuff design and the constructed heating cuff is shown in Fig. 1(c) and (d). The fabricated heating cuff has the following dimensions: an inner diameter of 0.7 mm; an outer diameter of 4.3 mm and an overall length of 10.1 mm. A ~4.5 mm (longitudinal) region of the core channel was surrounded by the embedded heating wire and the heated length of the nerve will be slightly longer than that due to thermal diffusion. A thermocouple (5SC-TT-T-40–36, dia. = 200 μm, Omega Engineering, CT, USA) was embedded using silicone adhesive (KWIK-SIL, World Precision Instruments, FL, USA) on the inner side of the heating cuff to measure the temperature of the nerve surface. Two multi-strand copper wires (30 American-wire-gauge) were used to connect the heating cuff to the temperature controller. The total DC resistance (including the connection wires) was 40.1 Ω, including a 3.0 Ω resistance of the contacts and a 37.1 Ω resistance of the heating wire embedded in the cuff. A modified temperature controller (TC-324C, Warner Instruments, MA, USA) was used to control the direct current level passing through the heating wire. See supplemental materials for the fabrication process and the relationship between direct current level and temperature elevation (Fig. S2). The heating cuff was applied by sliding a nerve into the core channel of the heating cuff via the slit. The heating circuit was fully insulated and driven by direct current instead of alternating current to minimize the chance of interfering with electrophysiological recordings.

Figure 1: The schematic and image of the heating cuff design and the experimental setup.

Panel (a) shows the side view (left) and top view (top right) of the heating cuff along with the main fabrication steps (bottom right; see supplemental material for detailed steps). Note that the slit opening angle for nerve positioning and optical fiber insertion in the schematic is enlarged for the purpose of illustration. Panel (b) shows the schematic of the experimental setup where the nerve was stimulated and recorded by suction electrodes while the optical fiber for IR light delivery and the heating cuff were collocated on the same segment of the nerve. Panels (c and d) show the top- and side-view of the constructed heating cuff (scale bar: 2 mm). Panel I shows a zoomed-in view of the experimental setup. A heating cuff was wrapped around an Aplysia’s pleural-abdominal connective, with an optical fiber inserted into the slit for infrared light delivery. Suction electrodes are not shown in the image as they are further away, located at the nerve ends. Scale bars in panel c to d: 2 mm.

2.4. Infrared neural inhibition (INI)

IR light was generated with a single-mode laser diode (QFBGLD-1470–250, QPhotonics, MI, USA, λ = 1470 nm) and a controller (6340–4A, Arroyo Instruments, CA, USA). The optical power was controlled by setting the current. A DAQ device (USB-6218, National Instruments, TX, USA) triggered 60-second laser pulse trains (1250 Hz, 400 μs pulse width). The relationship between the IR laser diode current and IR optical power at the fiber tip was determined using a power meter (PS19Q, Coherent, CA, USA). The laser diode temperature was held constant at 20 °C for stable and repeatable optical power output. IR light was delivered to the targeted nerve region via an optical fiber (P600-VIS-NIR, Ocean Insight FL, USA, 600-μm core, NA = 0.39). While 600 μm is the illuminated area, the heated region will be slightly larger than that as previous studies have demonstrated ^37,38. As shown in Fig. 1e, the optical fiber was inserted into the slit of the heating cuff so as to directly touch the nerve and fix its location relative to the nerve through the experiments.

2.5. Temperature elevation (ΔT) measurement

RH and INI were applied to the same nerve segments to minimize variability. The heating cuff, optical fiber tip, and nerve were fully immersed in saline to provide a stable thermal environment. The temperature at the nerve surface was recorded using the thermocouple embedded in the heating cuff, see Fig. 1(a). The temp signal was converted by a thermocouple-to-analog converter (SMCJT, Omega Engineering, CT, USA) to an analog voltage signal (0–100 mV for 0–100 °C), which then was digitized and recorded using the same DAQ device for the CAP acquisition. And then ΔT was calculated by subtracting the baseline temperature from the temperature during heating, see Fig. 2. As the temperature and CAP were recorded simultaneously, we calculated ΔT for each CAP using the temperature recorded when the CAP was evoked. For all six nerves, the baseline temperature was similar (20.2 ± 0.3 °C). Because the fluctuations in baseline temperature are negligible compared to the temperature rise induced by the heating trials, and also to make the subsequent discussion about CAP response versus temperature more intuitive, we chose to use show ΔT in the subsequent analysis.

Figure 2: The heating test protocol and a representative CAP recording with ΔT change of the 150-second heating trial.

(a) Two heating modalities were tested sequentially on the same nerve. Each heating modality was tested with gradually increasing power applied at the neural interface until predefined endpoints were met (a partial inhibition was evident or the maximum ΔT ≥ 15 °C). (b) A representative compound action potential (CAP) recording and ΔT change. The yellow dashed lines indicate the time point between different phases of the heating trial. The red box and curve indicate where the temperature was considered quasi-stable (changing rate < 0.02 °C/sec) and used for extracting CAPs and ΔTs for data analysis.

2.6. Experimental protocol

The experiments were performed in six excised pleural-abdominal connectives from Aplysia to test the effects of INI and RH on neural conduction. Each nerve was tested with INI and RH sequentially. We randomized the sequence of INI and RH tests to minimize the accumulative effect due to the previous heating modality. Of all six nerves, three were first tested with INI, and the rest were first tested with RH. Both heating modalities were evaluated with a series of 150-second heating trials with increasing power applied at the neural interface until predefined endpoints were met (a partial inhibition was evident, or the maximum ΔT ⩾ 15 °C). The step increase of power applied was set so that the maximum ΔT during a given heating trial was approximately 2 °C higher than the previous one. The empirical maximum ΔT limit at 15 °C was determined based on our previous experience with repeated heating tests (see supplemental materials for details). Each 150-second heating trial consisted of a 10-second control period (no heating), a 60-second heating period, and an 80-second cooling period, as shown in Fig. 2 (a). Electrical stimulation was applied throughout the heating trials to monitor the neural conduction status, as shown in Fig. 2(b). The inhibitory effect was assessed by comparing the CAPs during the initial 10-second control period and the 60-second heating period. The acute health conditions of the nerves after heating were assessed by comparing the CAPs at the end of the initial 10-second control period and at the end of the 80-second cooling period.

To identify any potential methodological bias between the two heating modalities, it is necessary to compare the total thermal dose applied to the nerve by each heating modality. However, calculating the commonly used cumulative temperature elevation dose (CEM₄₃) using absolute temperature ^66,67 is not applicable since Aplysia is a heterothermic animal. As Aplysia’s natural habitat is intertidal pools, its body temperature can be changed by the environment [72], rather than maintaining a constant body temperature as is done by mammals. Therefore, we calculated the thermal dose for each heating modality as follows for a first approximation:

$$Thermaldose=\sum \mathrm{\Delta }\text{T}\cdot \text{duration}\text{of}\text{each}\mathrm{\Delta }\text{T}$$

2.7. Data analysis

2.7.1. CAP recording pre-processing

To prepare the CAP data for analysis, several pre-processing steps were applied (see details in the supplemental materials):

We removed the DC components from the recorded CAPs by a high-pass filter at a 1 Hz cut-off frequency to avoid any drift due to electrodes or circuitry. We collected a background noise sample by recording a short period from the CAP channel during which no electrical stimulation was applied. The background noise sample and its properties were then used to subtract the noise from subsequent analyses.

For the analysis, we selected only the CAPs during the quasi-steady temperature period during which the temperature change rate was smaller than 0.02 °C/s (as shown by the red curve in Fig. 2). Because axonal subpopulations with different diameters have different conduction velocities (i.e., larger diameters correspond to faster conduction velocities), we then segmented the CAPs into fast- and slow-conducting subcomponents which correspond to large- and small-diameter axons, as we did in the previous studies^20,37,38.

2.7.2. Quantification of inhibition effect

To quantify inhibition strength, we separately calculated the rectified area under the curve (RAUC) for the fast- and slow-conducting subpopulations in the CAP, as shown in Fig. 3. The RAUC during the heating period was normalized to the average RAUC during the last three seconds of the control period. The normalized inhibition strength (NIS) can then be calculated as the reduction in the normalized RAUC:

$$Normalizedinhibitionstrength=1-NormalizedRAUC\text{.}$$

Figure 3: Representative compound action potential (CAP), the corresponding normalized RAUC, and the normalized RAUC after cooling for all trials conducted on a nerve.

(a) Representative compound action potentials show the selective INI on small-diameter axons can be reproduced by resistive heating (RH) via a heating cuff. Blue: the large diameter subpopulation with fast conducting velocity. Red: the small diameter subpopulation with slow conduction velocity. A dashed line indicates the segmentation point between the fast- and slow-conducting subpopulations. From top to bottom, Ctrl₁: the control test before heating application; INI: infrared neural inhibition application showed selective inhibition of the slow conducting subpopulation; RH: the heating cuff was able to induce a similar selective inhibition effect of the same CAP subpopulation; Ctrl₂: the control test after all heating tests after the temperature has returned to baseline. The response in Ctrl₂ was similar to Ctrl₁, suggesting that selective inhibition was reversible. The baseline temperature during the tests was 20.3 °C. The ΔT was 9.3 °C for the INI trial and 10.2 °C for the RH trial. The conduction velocity for the fast and slow conducting groups in this nerve was 0.956 m/s and 0.239 m/s respectively (estimated using the peak of each group). (b) The normalized RAUC for each trial in (a), was calculated for the fast (blue) and slow (red) subpopulation separately. IR application and RH were able to induce a similar level of RAUC reduction. When the heating was turned off, the RAUC recovered to the control test’s level. (c) The normalized RAUC after cooling for each trial that was conducted on the same nerve. The red bars indicate trials for the INI test and RH test, respectively.

The NIS value will increase from 0 up to 100% if an inhibitory effect is present. A NIS below 0 indicates an excitatory effect. It can be compared across different subpopulations and nerves as it does not depend on the absolute value of the RAUC.

We calculated the inhibition probability for each axonal subpopulation as the number of inhibition events divided by the total number of CAPs. A CAP was considered an inhibition event when the NIS for the given subpopulation was greater than 50%. To quantify the change in the inhibition probability as ΔT increased, the NIS data from all nerves were pooled and grouped into non-overlapping 1 °C ranges (e.g., [0 1) °C and [1 2)°C) based on their corresponding ΔT. The inhibition probability was calculated for each 1 °C range using the NIS data within that range.

To estimate and compare ΔT thresholds of inhibition between INI and RH, probit regression was applied to the inhibition probability data. Probit regression is suitable for assessing responses from experiments with binominal results. Previous studies on laser-tissue interactions have applied probit regression to characterize the response during laser ablation ⁶⁹ and INS ^21,30,70. For the probit regression, we fit a normal cumulative distribution function (CDF) to the inhibition probability in response to an increase in ΔT. The probit regression function is:

$$\begin{array}{l}Fittedinhibitionprobability(p)\\ =\frac{1}{2}\left[1+erf\left(\frac{\mathrm{\Delta }\text{T}-T_{50}}{\delta \cdot \sqrt{2}}\right)\right],\end{array}$$

where ΔT is the independent variable. The fitting process results in an estimate of the ΔT₅₀ for inhibition, which is the ΔT threshold for a 50% probability of inhibition. It also estimates 𝛿, which is the standard deviation of ΔT. Probit regression was conducted separately for the fast- and slow-conducting subpopulation during the INI and RH tests, respectively. The ΔT₅₀ parameters of the fitted models were compared to determine the ΔT threshold difference between the two heating methods.

To characterize the selectivity of inhibition in the slow-conducting subpopulation, we constructed the parameter inhibition selectivity index as follows:

$$Inhibitionselectivityindex=\frac{NISofslow}{NISofslow+NISoffast}\text{,}$$

where “NIS of slow” means the normalized inhibition strength of the slow-conducting subpopulation and “NIS of fast” means the normalized inhibition strength of the fast-conducting subpopulation. The inhibition selectivity index was only calculated for CAPs with an inhibition event (as previously defined), across the whole temperature range.

The inhibition selectivity index can be interpreted as the contribution of inhibition of the small-diameter axons to the overall inhibitory effect. When the NIS for both subpopulations is equal, the inhibition selectivity index will be 0.5. Any inhibition selectivity index higher than 0.5 indicates a selective inhibition of the slow-conducting subpopulation. Conversely, an inhibition selectivity index lower than 0.5 indicates a selective inhibition of the fast-conducting subpopulation. A paired t-test of the inhibition selectivity index was conducted to compare whether size-selectivity was statistically different between the two heating modalities.

3. Results

3.1. Nerve’s thermal exposure was similar between INI and RH

To compare the changes in the electrophysiological responses induced by the two heating modalities, it is necessary to examine if there is a systematic bias in the available data and thermal exposure between the two heating modalities. On average, we conducted 8 ± 2 trials for RH and 7 ± 1 trials for INI on each nerve and the average interval between heating trials was 3 minutes. From the quasi-steady period during heating, we collected 1927 CAPs during INI and 2260 CAPs during RH. The number of valid CAPs in each nerve between the two heating modalities did not show a significant difference (p = 0.70, paired t-test). The normalized RAUC after heating is on average 94.4% ± 5.9% of the RAUC before heating. The ΔT step from one heating trial to the next was 1.4 ± 0.9 °C for INI and 1.3 ± 0.8 °C for RH with no significant difference (p = 0.55, paired t-test). The total thermal dose of each heating modality was calculated for the six nerves. We applied an average thermal dose of 2405 °C· s during INI and 2945 °C· s during RH on each tested nerve, with no significant difference between the two heating modalities (p = 0.17 paired t-test). Overall, the data and thermal exposure of the nerves were similar for both INI and RH, allowing an unbiased comparison of the inhibitory effect between the two modalities.

3.2. Resistive heating can induce a selective inhibition effect similar to infrared neural inhibition

The representative data in Fig. 3 shows that RH produced a selective inhibition effect, similar to INI. The ΔT for this representative data (INI: 9.5 °C, RH: 10.6 °C) was high enough to induce a block on the slow-conducting subpopulations (panel a, red), while still too low to significantly inhibit the fast-conducting subpopulations (panel a, blue). Raw normalized RAUC data (Fig. 3b) confirmed that both heating modalities could induce a similar drop in the signal for the slow-conducting subpopulation. The control test conducted after the heating test (Fig. 3a, Ctrl₂) showed a response similar to that of the initial control test (Fig. 3a, Ctrl₁), suggesting that the health of the nerve was not acutely impacted. This can be also confirmed by the normalized RAUC after cooling for each trial conducted on the same nerve, as shown in Fig. 3(c).

To further examine the selective inhibition effect on all tested nerves, we calculated the normalized inhibition strength (NIS) for the fast- and slow-conducting subpopulations of CAPs recorded during the quasi-steady state of the heating period (see Methods). For each 1 °C temperature range, the NIS data from each nerve were averaged to represent the response of a given nerve. The response of all six nerves is shown in Fig. 4 (a) and (b). When comparing across different subpopulations, the NIS of the slow-conducting subpopulations was generally higher than the corresponding values for fast-conducting subpopulations from the same CAP. RH showed an overall trend similar to that of INI, but with a wider separation between the fast- and slow-conducting components.

Figure 4: The normalized inhibition strength (NIS) and inhibition probability for fast- and slow-conducting subpopulations under infrared neural inhibition (INI) and resistive heating (RH).

The top row (panels a and b) shows the median (bars) and lower/upper quartiles (whiskers) of the NIS data from all six nerves. The NIS data increased as the temperature elevation increased and the slow-conducting components showed a higher level of inhibition compared to the fast-conducting components (red bar vs. blue bars, respectively). The y-axis ticks are the same for panels a and b. The bottom row (panels c to f) shows that, for all groups, the inhibition probability increased as the temperature elevation increased. The y-axis ticks are the same for each horizontal row. The fitted line shows the probit regression result for each subpopulation, and the dashed lines show the 95% confidence interval. The threshold temperature elevation for 50% inhibition probability on the slow-conducting components was 7.40 °C for INI and 8.03 °C for resistive heating, noting the baseline temperature was 20.2 ± 0.3 °C for the six nerves. Although not all nerves showed full inhibition, the probit regression was applied to the fast-conducting subpopulation to compare it to the slow-conducting subpopulation. Blue circles: fast-conducting subpopulation. Red circles: slow-conducting subpopulation. Unfilled marker: INI. Filled marker: RH.

When we calculated and compared the inhibition probability (probability of inducing a NIS of > 50%) for each 1°C range using pooled data from all six nerves, the similarity of the trends was more obvious (see Fig. 4 (c to f)). The inhibition probabilities were calculated using all NIS data rather than only the averaged data shown in Fig. 4 (a and b). As ΔT increased, the inhibition probability for both heating modalities increased more rapidly for the slow-conducting subpopulation. To compare the inhibition probabilities of fast- and slow-conduction subpopulations across the whole ΔT range, we conducted a one-tailed paired t-test and confirmed that the inhibition probability in the slow-conducting subpopulation was higher (p < 0.01 for both INI and RH). This indicates that the inhibition probability was significantly higher for the slow-conducting subpopulations than for the fast subpopulations in response to the same temperature with both heating modalities. Probit regression was applied to the inhibition probabilities of both fast- and slow-conducting components for each heating modality. The fitted lines (probit regression) are shown in Fig. 4 (c to f). Table 3 lists the optimal probit regression fitting parameters with the 95% confidence interval range indicated in brackets.

Table 3.

Optimal fits for the probit regression of inhibition probabilities for each subpopulation

Heating Modality	Sub-population	ΔT50	δ	Root mean squared error
IR Neural Inhibition	Fast	10.42 [9.79, 11.04]	0.35 [0.35, 0.35]	0.150
	Slow	7.40 [6.15, 8.64]	1.14 [0.49, 1.78]	0.165
Resistive Heating	Fast	13.68 [13.45, 13.91]	0.35 [0.35, 0.35]	0.0386
	Slow	8.03 [6.23,9.83]	1.58 [0.51, 2.64]	0.081

Comparing the fitted parameters, we can see that the ΔT threshold for inhibiting the slow-conducting subpopulation with RH (8.03 °C) was slightly higher than the threshold with INI (7.40 °C). The ΔT₅₀ for fast-conducting components is higher than the ones for the slow-conducting components under both conditions, confirming the size-selective inhibition effect on the small-diameter slow-conducting components. Although the probit regression was performed for the fast-conducting subpopulation, the study was not designed to induce a full block of the fast-conducting subpopulation, since this might subject the nerves to excess thermal stimulation when the same nerve is tested under both conditions. In the six nerves tested, full inhibition was only observed in three nerves during the INI test and in the other three nerves during the RH test. Only one nerve showed a full inhibition response during the test of both heating modalities. The limited raw data for the inhibition probability of fast-conducting components caused the optimal estimate of δ to be limited at the theoretical boundary of 0.35.

We compared the inhibition selectivity index when an inhibition event was present for either or both subpopulations. The calculation was conducted for each nerve separately, across the whole tested temperature range. As shown in Fig. 5, RH had a higher average inhibition selectivity index (0.86) than INI (0.76), although the difference was not significant according to a paired t-test (p = 0.37). The average inhibition selectivity indexes for both methods were higher than 0.5 demonstrating that RH reproduced the size-selective inhibitory effect of INI. From Fig. 5, we also see that the variance in the inhibition selectivity index for each nerve was smaller for RH in general. This suggests that RH can induce selective inhibition more reliably when the nerve’s geometry and fascicle orientation vary from one nerve to another.

Figure 5: The inhibition selectivity index on the slow-conducting subpopulation for IR neural inhibition (INI) and resistive heating (RH).

(a): The inhibition selectivity index (see Methods) for each nerve with each heating modality. The index was calculated for all inhibition events (a normalized inhibition strength larger than 50% for either fast- or slow-conducting subpopulation), regardless of the temperature. An inhibition selectivity index closer to 1 indicates a more selective inhibition of the slow-conducting small-diameter axons. The error bars indicate the upper and lower quartiles. (b): Box plot of the average inhibition selectivity index for INI (0.76) and RH (0.86). The difference was not significant according to a paired t-test (p = 0.37).

In summary, the results show that RH can reproduce INI’s selective inhibition effect on a slow-conducting small-diameter subpopulation with a similar temperature threshold.

4. Discussion

The current study demonstrated that selective inhibition of small-diameter axons induced by INI can be reproduced by another heating modality such as RH (Fig. 3). RH relies solely on the induced temperature elevation for inducing size-selective inhibition (Fig. 5). As selective INI has been demonstrated using Aplysia and then successfully migrated to vertebrates with substantially lower ΔT thresholds ²⁰, we expect that the selective inhibitory effects of RH will also translate to vertebrates with a future in vivo chronic implantable design. RH may also be used in future studies to investigate non-blocking neuromodulation effects (e.g., the change of neuron’s excitability and neural plasticity) induced by chronic localized heat application on neurons. Here are some aspects of this potential application that are worth discussing.

4.1. Size selectivity as an inherent property of heat-induced neural block

Previous studies have suggested that INI relies on thermally accelerated ion channel kinetics, particularly voltage-gated potassium channels ^35,36. Hence, we tested the hypothesis that a pure heating process could induce the same size-selective inhibition. Unlike INI, RH does not involve optical processes. We used the direct current, which only generated a static electromagnetic field that did not stimulate the nerve. The RH test results showed a similar size-selective inhibition as compared to INI, although with a slightly different ΔT (7.40 °C for INI and 8.03 °C for RH).

This difference in the ΔT₅₀ (Table 3) and dose-response curve (Fig. 4) can likely be attributed to the difference in heat conduction direction between the heating modalities. An experimental limitation of our approach was that only the temperature at the nerve surface can be measured, as shown in Fig. 1 (a), which can be different from the temperature at the core of the nerve where the axons are located. Due to the difference in where the heat was generated (INI: in the nerve, RH: around the nerve), the temperature at the nerve’s core can have a different relationship to the measurable temperature at the nerve surface (INI: core temperature higher than surface temperature; RH: core temperature lower than surface temperature). From our previous measurements of the Aplysia’s pleural-abdominal connective, the average diameter of the region that axons occupy is 242.9 ± 76.8 μm, which is less than half of the nerve’s total diameter at 611.7 ± 85.0 μm (n = 48). The gap between the nerve surface and the core region where the axons are located can allow a temperature gradient to exist. Therefore, the difference in the measured ΔT threshold for selective inhibition between the two heating modalities may be attributed to the difference in the heat generation locations rather than a difference in biological processes.

Since it is difficult to measure the temperature distribution inside nerves with existing techniques, numerical simulations are often used to explore thermal effects under infrared laser irradiation ^44,71,72. We simulated the scenario that INI and RH were applied with appropriate power (INI: 39.8 mW, RH: 80.7 mW) to achieve their respective ΔT₅₀ (INI: 7.40 °C, RH: 8.03 °C) at the nerve surface. The simulation was conducted on a 3D finite element model (FEM) that duplicates the geometry and physical properties of the RH and INI setup, using COMSOL Multiphysics^® (COMSOL) software and a mesh-based Monte Carlo simulation in the MATLAB^® environment (MMClab) ^73–75 for light scattering and absorption (see supplemental materials for details). Using the simulated temperature distribution, we calculated the average ΔT₅₀ at the axonal area of the nerve (as shown in Fig.7 (a to d) by the dashed circles, dia. = 0.243 mm). The simulated average ΔT₅₀ of the axon-containing region in the nerve was similar: 7.45 °C for INI and 7.53 °C for RH (see Fig. 6(a to d)). We also used the simulation to estimate the dose-response curve of inhibition probability as ΔT increases at the axon-containing region of the nerve. The thermal dose-response curves based on the ΔT at the core region of the nerve were not significantly different between the two heating modalities (p = 0.43, paired t-test) (see Fig. 6(e)). This similarity of the simulated thermal dose-response curves again was consistent with our hypothesis that both heating modalities, INI, and RH, induce neural inhibition by the same thermal effects.

Figure 6: The simulated radial temperature elevation distribution and inhibition probability under different temperature elevations in the axon-containing region of Aplysia’s pleural-abdominal connective.

INI: infrared neural inhibition, RH: resistive heating. Panel (a) to (d): The radial cross-section view of the simulated temperature distribution for each heating modality. Panel (a) and (b) are the overall views while panels (c) and (d) are the zoomed-in views of the same simulated temperature distributions (respectively). The geometry in the light blue line indicates the geometry of the nerve cuff, including the heating wire. The solid black circles indicate the location of the nerves. The dashed black circles indicate the axon-containing region. The simulated powers applied at the neural interface correspond to the amount required to induce an inhibition probability of 50% on the slow-conducting subpopulation (INI: 39.8 mW, RH: 80.7 mW). The colormap for panels (c) and (d) was adjusted to show the temperature gradient more clearly. The arrows and dots (white filled with a black border) indicate where the thermocouple was located in the real-world setup. The scale bar is 1 mm for panels (a) and (b), and 200 μm for panels (c) and (d). Panel (e): The inhibition probability of the slow-conducting subpopulation as a function of temperature elevation in the axon-containing region was not statistically different between INI and RH (p = 0.40, paired t-test). Red-filled triangle: slow-conducting subpopulation with RH. Red unfilled triangle: slow-conducting subpopulation with INI.

Further research (e.g., parameter optimization functional tests) will be required to translate selective block by RH to vertebrates and explore the feasibility of size-selective inhibition (primarily on the unmyelinated fibers) in vivo.

Therefore, based on the experimental and simulation results, we can expect that any heating modality (e.g., RH and INI) that can generate a homogeneous temperature elevation across the nerve cross-section will selectively inhibit small-diameter, slow-conducting subpopulations preferentially. Furthermore, the application of RH to vertebrates for selective inhibition is a promising next step, as selective INI has been explored in Aplysia and successfully translated to vertebrates with similar protocols but much lower ΔT ^20,22. and explore the feasibility of size-selective inhibition (primarily on the unmyelinated fibers) in vivo. In addition, other heating modalities could be explored for their size selectivity during neural inhibition, including current neuromodulation modalities such as HFAC and ultrasound whose mechanism(s) may be related to heating (as mentioned in the Introduction).

4.2. RH showed less size selective variability than INI because of less spatial selectivity

In the present study, RH showed reliable size-selective inhibition when different nerves were tested, as shown in Fig. 5. This was expected as the current design (a heating wire wrapping around the nerve) was selected to create a uniform temperature elevation across the cross-section of the nerve. The simulated temperature distribution shown in Fig. 6(a and b) demonstrated the uniformity of the heating. Should the heating cuff be adopted for a chronic study, this spatial uniformity would minimize the likelihood that a shift in the orientation of the heating cuff after implantation would lead to a loss of size selectivity. Of course, if spatial selectivity is needed, a heating cuff could be designed to have multiple heating elements arranged around the nerve such that some control over the spatial thermal distribution could be achieved, especially in large-diameter nerves. Nevertheless, thermal conduction limits the spatial thermal gradient that can be created in this way.

In contrast, spatial selectivity may have adversely contributed to the variability in size selectivity for INI, as shown in Fig. 5. Due to anatomic variability across different nerves, there are differences in the spatial arrangement of each axonal subpopulation within the nerve. Since IR light is incident on one side of the nerve, there is a spatial thermal gradient across the cross-section of the nerve, as can be seen in Fig. 6(a). The nerve region distal to the optical fiber tip has a lower ΔT because the light is strongly absorbed in the proximal region. Therefore, when the ΔT in the proximal region is high enough to induce inhibition (“hot side”), the subpopulation located distally may not reach the ΔT threshold yet (“cold side”). If the large-diameter subpopulation is predominantly located at the proximal end (“hot side”) and the small-diameter subpopulation is predominantly located at the distal end (“cold side”), the large-diameter subpopulation may be inhibited first. In other words, the variance in size selectivity observed in the INI experimental results is possibly a manifestation of spatial specificity. A previous study has shown that the high spatial specificity of IR light delivery can cause variance in the results of IR neuromodulation ²¹.

In short, RH showed a stronger and more robust size selectivity than INI (although not statistically significant) because of two reasons: 1) RH can generate a more even temperature distribution that is less prone to anatomical variability and changes of cuff orientation; 2) INI’s spatial selectivity adversely affected its size-selectivity.

4.3. Resistive heating for implantable neural interface design

In this study, RH efficiently induced selective inhibition, making it a good candidate for an implantable neural interface design. Several additional aspects of implantable designs are therefore worth addressing.

4.3.1. Thermal safety

Although the ΔT requirement for RH of the Aplysia nerve is high (e.g., the ΔT₅₀s shown in Table 3), a lower threshold can be expected when migrating to a vertebrate animal. When the INI protocol was migrated from Aplysia to musk shrews, the threshold ΔT for selective inhibition dropped from 9.7 ± 3.7 °C to 2.9 ± 0.8 °C ²⁰. Both the experimental and modeling results in the current study demonstrate that resistive heating and infrared neural inhibition rely on the same heat-based thermal block mechanism and the threshold temperature was very close. Therefore, a similar reduction in the temperature elevation threshold can be expected if resistive heating were transferred from Aplysia to vertebrates, as previous INI work demonstrated ²⁰. In addition, our modeling suggests that RH generated a spatially homogeneous temperature elevation across the nerve, as shown in Fig. 6(d), minimizing the danger of local overheating ²¹ due to spatial thermal gradient during INI as shown in Fig. 6 (c).

The temperature threshold and safety margin of localized heating for neural block still need to be determined and can be effectively explored using resistive heating. From our experiments, a slight accumulative trend (not statistically significant) of RAUC after repeated heating tests can be observed in Fig. 3(c). As the nerve in current in vitro preparation is limited in its capability to respond to accumulated thermal stress, further in vivo experiments are needed to explore the accumulative effect of repeated localized heating on the nerve. It has been reported in humans that when core body temperature was elevated to about 40 °C, the reflex response mediated by the small-diameter afferent fibers was suppressed ^63,64. On the other hand, previous studies have shown that local heating higher than 45 °C on the peripheral nerve can cause irreversible neural block ^67,76–78. Recent studies have partially explored the safety margin of localized heating in neural tissue either with optogenetics in rats ^41,79 or by resistive heating directly in mice ⁸⁰. Other recent studies have used a combination of cooling and heating to reduce temperature changes needed to induce block ^48,49. This new advance in thermal nerve block can use the heating cuff design in the current study to provide safe brief heating to lower the amount of cooling needed for block.

In short, the current study was not designed to directly address the safety of the potential in vivo application. Further tests are needed to assess if selective inhibition of small-diameter axons can safely be implemented via resistive heating. Resistive heating also provides a simple design for future experiments exploring the chronic safety of localized nerve heating, which could benefit the translation of other heating modalities.

4.3.2. Efficiency of the power applied at the neural interface and total electrical power

One major advantage of RH is that electrical power can be converted to heat very efficiently, but the heat has to be conducted through layers of materials until reaching the axons. While INI suffers from low conversion efficiency from electricity to light at the laser diode, the heat can be generated directly inside the nerve and does not rely on thermal conduction as RH did. As each modality has its advantages and disadvantages, we characterized the efficiency of the power applied at the neural interface and the efficiency of total electrical power, respectively, to identify which modality is more feasible to be adopted as an implantable design in the future.

We first characterized how efficiently the power at the neural interface was converted into heat by comparing the power requirement at the interface (INI: optical power emitted from the optical fiber tip; RH: electrical power applied by the heating wire) for achieving the respective ΔT₅₀ for a 50% inhibition probability of the small-diameter axons. INI required 39.8 mW of optical power emitted from the optical fiber tip to achieve its ΔT₅₀ at 7.40 °C (the corresponding irradiance at the optical fiber tip is 14.1 W/cm²). RH required 80.7 mW electrical power on the nerve surface to achieve its ΔT₅₀ at 8.03 °C. The detailed data and linear regression of the power applied at the neural interface vs. ΔT for each heating modality across different nerves can be seen in Figure S1 (a). INI was more effective in inducing ΔT compared with the current resistive heating cuff design when a given power was applied at the neural interface.

The higher power requirement at the neural interface for RH can be attributed to the heating element size difference (INI: an optical fiber with a 0.6 mm diameter; RH: a heating wire surrounding 4.5 mm of length along the nerve). A larger heated volume would inevitably require more heating power. For the Aplysia nerve we tested here, the optimum length would be approximately 1 mm according to our previous study ^37,38; a heat block length beyond that does not improve the efficacy of the thermally induced neural inhibition. The current 4.5 mm length was selected due to the limitations of the manual fabrication process and to ensure that effective neural inhibition can be observed. Another factor of the power requirement difference can be attributed to the location of heat generation (INI: inside of nerve, RH: outside of nerve). Future studies can explore the feasibility of safely inducing heat inside nerve for the heat-based neural block. In addition, with a given amount of power applied at the neural interface, the ΔT induced by RH was more repeatable across the six tested nerves, compared with INI. The 360° wrapping design of the heating cuff is less sensitive to variability in the nerve anatomy and the nerve’s relative position in the heating cuff. Because of this repeatable heating response, an RH-based heating cuff is expected to be less prone to movement following chronic implantation.

We then characterized the total electrical power consumption of the two modalities for achieving the given final ΔT values. For example, to achieve an inhibition probability of 50% on the small-diameter axons, INI needs 155.9 mW total electrical power for its ΔT₅₀ at 7.40 °C whereas RH only needs 85.2 mW total electrical power for its ΔT₅₀ at 8.03 °C. Due to the difference in the efficiency of total electrical power, the current resistance-heating nerve cuff could have a 55% longer runtime than the INI laser used in this study. Indeed, for the current heating cuff design, 93% of the total electrical power can be converted to the power applied at the neural interface, whereas the laser diode can only convert 24–27% of the total electrical power into the optical power of infrared light applied to the nerve.

The current cuff design was only a proof-of-concept and could be further optimized for improving its efficiency in future studies. For example, the inner PDMS tube of the heating cuff could be thinner or altered to achieve better thermal conductivity ^81–83. This could promote better thermal conduction from the heating wire to the nerve and increase the efficiency of the power applied at the neural interface. Second, with a finer manufacturing process, the length of the axial heated region of the heating cuff could be shortened to the optimal length requirement. A microfabrication process could achieve much better control of the heating element morphology and integrate the thermal sensor in a smaller dimension, as demonstrated in previous studies ^80,84,85. In addition, a customized temperature controller could be made with parameters optimized for RH to help reach the target temperature quicker and avoid fluctuation/overshooting. It is and blood flow will cause additional heat dissipation) which may cause changes in the heating power requirement. A recent study has observed an inhibitory effect on neural activity by resistive heating in the cortical tissue of mice in vivo ⁸⁰. More future experiments will be needed for characterizing the effect of in vivo thermal conditions (e.g., intraneural blood flow) during the heat-based neural block, both acutely and chronically.

4.3.3. Biocompatibility

RH has the potential to meet the biocompatibility requirements for an implantable neural interface. The current heating cuff design can be made of inert and biocompatible materials to match the mechanical compliance of tissue, therefore minimizing deleterious mechanical effects and associated foreign body response ^86,87. In addition, the RH cuff does not inject charge into the tissue, as standard electrical stimulation and block methods do, and therefore will not induce charge-injection-related tissue damage ^88–90. The heating circuit was driven by direct current and was fully insulated, thus reducing the likelihood of interfering with other electrophysiological electrodes (recording/stimulation) that may be present in the surrounding tissue.

5. Conclusions

In this study, we explored the possibility of using RH to reproduce INI’s size-selective inhibitory effect on small-diameter axons. The dose-response curves of both modalities showed a similar trend of increased inhibition probability when ΔT was increased. RH reproduced the selective inhibition of slow-conducting small-diameter axons. The measured nerve surface ΔT for a 50% probability of inhibition on the slow-conducting small-diameter axons was 7.40 °C for INI and 8.03 °C for RH. Simulation of the heating process revealed that the average ΔT in the axon-containing region of the nerve was similar (9.39 °C for INI, and 9.40 °C for RH). While INI showed a higher heating efficacy by depositing energy directly inside the nerve, RH showed a higher overall energy efficiency because the heating wire can efficiently convert electricity to heat. These results demonstrate that the selective neural inhibition effect of INI can be reproduced by another heating modality such as RH. Furthermore, the high overall energy efficiency of RH can facilitate further development of battery-powered implantable devices, increasing the availability of selective inhibition of small-diameter axons in basic research and translational applications.

Glossary

IR

Infrared

INI

Infrared Neural Inhibition

INS

Infrared Neural Stimulation

ΔT

Temperature elevation

CAP

Compound Action Potential

RAUC

rectified area under the curve

DC:

Direct Current

HFAC

High-Frequency Alternating Current

RH

Resistive Heating

NIS

Normalized Inhibition Strength