Identifying the Role of Block Length in Neural Heat Block to Reduce Temperatures During Infrared Neural Inhibition

Abstract

Background and Objectives:

The objective of this study is to assess the hypothesis that the length of axon heated, defined here as block length (BL), affects the temperature required for thermal inhibition of action potential propagation applied using laser heating. The presence of such a phenomenon has implications for how this technique, called infrared neural inhibition (INI), may be applied in a clinically safe manner since it suggests that temperatures required for therapy may be reduced through the proper spatial application of light. Here, we validate the presence of this phenomenon by assessing how the peak temperatures during INI are reduced when two different BLs are applied using irradiation from either one or two adjacent optical fibers.

Study Design/Materials and Methods:

Assessment of the role of BL was carried out over two phases. First, a computational proof of concept was performed in the neural conduction simulation environment, NEURON, simulating the response of action potentials to increased temperatures applied at different full-width at half-maxima (FWHM) along axons. Second, ex vivo validation of these predictions was performed by measuring the radiant exposure, peak temperature rise, and FWHM of heat distributions associated with INI from one or two adjacent optical fibers. Electrophysiological assessment of radiant exposures at inhibition threshold were carried out in ex vivo Aplysia californica (sea slug) pleural abdominal nerves (n = 6), an invertebrate with unmyelinated axons. Measurement of the maximum temperature rise required for induced heat block was performed in a water bath using a fine wire thermocouple. Finally, magnetic resonance thermometry (MRT) was performed on a nerve immersed in saline to assess the elevated temperature distribution at these radiant exposures.

Results:

Computational modeling in NEURON provided a theoretical proof of concept that the BL is an important factor contributing to the peak temperature required during neural heat block, predicting a 11.7% reduction in temperature rise when the FWHM along an axon is increased by 42.9%. Experimental validation showed that, when using two adjacent fibers instead of one, a 38.5 ± 2.2% (mean ± standard error of the mean) reduction in radiant exposure per pulse per fiber threshold at the fiber output (P = 7.3E–6) is measured, resulting in a reduction in peak temperature rise under each fiber of 23.5 ± 2.1% (P = 9.3E–5) and 15.0 ± 2.4% (P = 1.4E–3) and an increase in the FWHM of heating by 37.7 ± 6.4% (P = 1E–3), 68.4 ± 5.2% (P = 2.4E–5), and 51.9 ± 9.9% (P = 1.7E–3) in three MRT slices.

Conclusions:

This study provides the first experimental evidence for a phenomenon during the heat block in which the temperature for inhibition is dependent on the BL. While more work is needed to further reduce the temperature during INI, the results highlight that spatial application of the temperature rise during INI must be considered. Optimized implementation of INI may leverage this cellular response to provide optical modulation of neural signals with lower temperatures over greater time periods, which may increase the utility of the technique for laboratory and clinical use. Lasers Surg. Med.

INTRODUCTION

Clinical pain management techniques typically utilize pharmacological agents or electrical therapies. For intervention in disease states involving chronic pain, the first action often includes pharmacological agents such as nonsteroidal anti-inflammatory drugs, antidepressants, muscle relaxants, or opioids [1]. In particular, chronic opioid therapy has increased in prevalence [2], carrying with it a high risk of habituation, tolerance, and dependence that increases the risk of overdose and other deleterious effects [3–8]. Development of nonpharmacological therapies is critical, resulting in government initiatives to better understand and treat chronic pain [9–11]. Electrical interventions such as spinal cord stimulation [12–14] and high frequency alternating current [15–17], whether used in acute applications or implanted for chronic therapy, can provide relief, but are limited in their spatial specificity (precise spatial targeting of neurons) due to the tendency of electric current to spread in tissue and tolerance effects where more current is needed for therapy as time progresses, which results in even more current spread and reduced specificity. It has been shown that combining electrical therapy with optical modulation may help overcome some of these limitations [18]. Ultrasonic technologies offer a method of neuromodulation that can be applied noninvasively but are limited by focal size and spatial selectivity [19–21]. In contrast, optical technologies for neuromodulation, while inherently being more invasive compared with ultrasound and transcutaneous electrical stimulation [22], have high spatial precision and would require a similar level of surgery as that used for implantable electrodes. Infrared neural modulation (INM) in particular offers both neural stimulation and inhibition without introducing exogenous agents. Infrared neural stimulation (INS) has shown to be an effective method for stimulating action potentials in many animal models [23–29], and has been applied in human dorsal rootlets [30], but its complementary technique, infrared neural inhibition (INI), has yet to be translated for human use due to the temperature rise required for therapy.

INI works through heat block mechanisms elicited by water’s absorption of infrared light [31]. Heat block was first described by Hodgkin and Katz [32] who noted that, at elevated temperatures, action potentials in the squid giant axons decreased in amplitude and increased in conduction velocity (CV), and that further increasing the temperature resulted in failure of the axons to conduct. Since this foundational article, thermally induced silencing of neural activity has been explored for a range of animal models and applications [33–36]. Mechanistically, heat block is hypothesized to act through changes in voltage-gated potassium channel dynamics [37–39]. At high enough temperatures, hyperpolarizing voltage-gated potassium ion currents overwhelm depolarizing voltage-gated sodium ion currents so that the axon can no longer generate an action potential [40].

Using a laser to apply a temperature rise has allowed for smaller regions to be targeted for spatially precise and acutely reversible heat block without functional damage [31,41–43]. This method can be noncontact with tissue, however in many cases, probes delivering irradiation are placed in contact with the nerve, especially when delivering IR light in a fluid environment since the surrounding media will absorb the light before it reaches the nerve. The proximity to the neural tissue needed for INI highlights that clinical application would require surgical exposure of neural tissues for therapy, however, this is often performed when applying spinal cord stimulation [14]. The greatest barrier to clinical implementation is the temperatures associated with INI. A single temperature rise does not appear to be sufficient to elicit INI’s neuromodulatory effect across all systems (Table 1). Furthermore, the magnitude of these temperatures needed for therapy, while viable for acute inhibition experiments, cause concern when considering sustained application, and this needs to be addressed before translation to humans. The parameter space of INI has yet to be fully explored, and thus insights are needed into how to properly apply this technology to different neural tissues in a nondamaging, sustained manner. Developing methods that can be applied across many neural model systems will greatly aid in the growth of this technology by providing an understanding of the fundamental mechanisms governing heat block. When considering thermal damage to tissue, it is known that damage probability increases with not only greater temperature, but also with increased duration of application [44,45]. Thus, the duration of application for any INI therapy may be extended if the temperature rise in that region of tissue is decreased. It is this concept that drives the work described in this study.

TABLE 1.

Temperature Rise for Heat Block Across Model Systems

Model system	Temperature rise at inhibition threshold (°C)	References
Squid giant axon	~20	Hodgkin and Katz [32]
Computational model of Xenopus laevis	26–32	Mou et al. [38]
Aplysia buccal nerve	7.02	Duke et al. [31]
Rat sciatic nerve	5.2	Duke et al. [31]
Aplysia pleural abdominal nerve	9.7	Lothet et al. [43]
Musk shrew vagus nerve, small diameter neurons	2.9	Lothet et al. [43]

Currently unknown is how the spatial extent of heating along axons affects heat block. On the basis of prior mathematical analysis of the cable equation [43], we hypothesize that heating greater lengths of axon, increasing the block length (BL), will decrease the temperature required. Applying INI in this manner would spread the effect over a greater volume of tissue, allowing for INI to be applied for longer periods of time. Here, we demonstrate the role of BL during INI by doubling the optical irradiation length using two adjacent optical fibers and comparing the radiant exposure, temperature rise, and the full-width at half-maxima (FWHM) of the heat distribution at INI threshold both in silico and ex vivo.

METHODS

Computational Modeling

For an initial proof of concept that BL plays a role in the peak temperature rise required for INI, the conductivity of an Aplysia pleural abdominal nerve axon was simulated using the Hodgkin-Huxley model implemented in the NEURON simulation environment [46], which models the equivalent circuit of the axonal membrane as batteries (ion Nernst potentials), resistors (ion channel conductivities), and a capacitor (membrane capacitance). Aplysia neuron parameters [47], representative of neurons in the pleural abdominal nerve that can be tested ex vivo, were used to model an unmyelinated axon that was 2 μm in diameter [48] and 25 mm in length. This was implemented over 9999 computational nodes with 0.025 milliseconds timesteps for a stable simulation environment. At the end of the axon, a passive segment was placed to overcome the closed end effect which causes voltage increases at the end of a closed cable. Temperature rises were applied to the axon for two different BLs which were based on thermal camera (SC8303; FLIR Systems Inc., Wilsonville, OR) measurements from temperature rises due to irradiation from one or two adjacent optical fibers. During these measurements, a probe with two adjacent 400 μm core diameter optical fibers irradiated a 20% polyacrylamide gel with similar optical and thermal properties to tissue using either one or both optical fibers. One-dimensional slices were taken from the image through the hottest point in the temperature distribution and applied in the simulation to the axon as shape templates that could be modulated by a scaling factor to apply arbitrary temperature rises to the nerve in silico with the expected temperature distributions from one and two fibers.

Four different simulations were performed. First, an axon held at room temperature (20°C) was simulated as a control to understand the neural conduction of an unheated axon. The axon was stimulated using the Iclamp function to inject a 0.5 nA electric pulse for 1 milliseconds at one end of the axon, and the resulting propagation of the action potential along the axon was tracked. The maximum membrane voltage of the action potential at each computational node was used to visualize the strength of the action potential as it propagated along the axon. Next, the temperature rise required for inhibition when heated with a single 400-μm core diameter optical fiber was modeled. Inhibition was defined as a maximum membrane potential less than −60 mV at the most distal computational node, which is below the voltage required to activate voltage-gated sodium ion channels in the model [49]. The scaling factor of the one-dimensional temperature profile along the nerve was modulated until the lowest peak temperature rise that resulted in inhibition was identified as T_S1. A temperature rise profile which approximated heating from to two adjacent optical fibers was then applied to the axon and the temperature rise at inhibition threshold was identified using the same procedure as for one optical fiber. This simulated peak temperature rise at the inhibition threshold was recorded as T_S2. Last, as a control to test that a greater length of heated axon is required to achieve inhibition at lower peak temperature, the temperature profile from one optical fiber was again applied, now with its peak temperature set at T_S2.

Probe Design

A custom dual fiber probe was designed and built in-lab from two bifurcated 400-μm core diameter optical fibers (fiber A and fiber B) (BIF400-VIS-NIR; Ocean Optics, Inc., Largo, FL) to reliably apply INI over two BLs with constant monitoring of the power from each laser. For each bifurcated fiber, all distal ends (after the bifurcation) were cleaved and polished. One of the two paths from each fiber set was chosen as the monitoring path which was used to measure laser power during tissue irradiation. The other path from each of the bifurcated fibers were used to construct the probe. The two probe paths were brought together and secured parallel to each other using plastic casing and optical epoxy and were further polished together. Flatness of the probe output was checked and separation distances between the fibers was measured with a stereoscope and a thermal camera with a resolution of 3.5 μm × 3.5 μm per pixel. A second probe was created in the same way as the first but with longer fibers after the bifurcation (20 ft) to be compatible with a magnetic resonance (MR) imaging scanner, allowing for the instruments containing metal, such as the lasers, power meter, and triggering electronics, to remain outside of the scanning room.

The proximal end of each bifurcated fiber was connected to a separate laser system such that fiber A was connected to laser A and fiber B was connected to laser B. Two diode laser systems (Capella Neurostimulator; Lockheed Martin, Bethesda, MD) (λ = 1,875 nm, 200 μs pulse duration, 200 Hz) were used to irradiate the samples. These diodes were triggered using a pulse generator (DG535; Stanford Research Systems, Sunnyvale, CA) and optical powers (converted to radiant exposure per pulse at the output of the probe) were measured using a high-sensitivity thermopile (PS19Q; Coherent Inc., Santa Clara, CA).

Ex Vivo Electrophysiology Setup

Experimental validation of computational predictions was performed in n = 6 different pleural abdominal nerves from six Aplysia californica (Marinus Scientific, Long Beach, CA) weighing 250–350 g (one nerve per animal). Aplysia were anesthetized using injection of 333 mM MgCl₂ (~50% of body weight), and one of the pleural abdominal nerves were dissected and placed in a room temperature (~20°C) recording dish lined with polydimethylsiloxane (PDMS) (Sylgard 184; Dow Corning, Midland, MI) containing Aplysia saline (460 mM NaCl, 10 mM KCl, 22 mM MgCl, 33 mM MgSO₄, 10 mM CaCl₂, 10 mM glucose, 10 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid [HEPES], pH ~7.6). The ends of the nerve were suctioned into hand pulled, prefilled, polyethylene suction electrodes such that the nerve was taut. Bipolar leads terminating in chlorided silver wires were placed with one polarity in the suction electrode and the other polarity placed into the grounded saline bath. One end of the nerve was electrically stimulated with one of the suction electrodes while the other end was used for recording. The previously described optical probe was placed in contact with the nerve between the two electrodes such that each optical fiber fully irradiated the nerve while immersed in saline (Fig. 1A).

Fig. 1.

(A) Electrophysiology setup. An Aplysia nerve is immersed in a dish filled with Aplysia saline at room temperature. Nerve ends are suctioned into polyethylene suction electrodes. Bipolar electric leads terminating in chlorided silver wires are placed in the setup with one polarity in the suction electrode and the other polarity in the grounded bath. One of these provides electrical stimulation of neural activity while the other records neural signals. A dual fiber probe was placed in contact with the nerve and connected to two infrared laser diodes. (B) Stimulus waveform during each recording in which 179 electrical stimulation pulses are applied to the nerve at 2 Hz with 5 milliseconds pulse width for 90 seconds. At 30 seconds (stimulation 60), the laser(s) is/are turned on, providing optical pulses 0.2 milliseconds in pulse width at 200 Hz for 30 seconds. (C) Thermocouple setup. A fine wire thermocouple was immersed in a water bath and positioned under the optical probe at the location of maximum heating due to laser irradiation from fiber A or fiber (B, D) MRT Phantom. This three-dimensional (3D) printed nerve holder (red) was secured in the cap (blue) of a 50 m tube with a hole drilled in the center allowing for insertion of the probe. The probe was positioned in the central channel of the holder, and the nerve (gray) was strung across the gap at the bottom of the holder and secured with glue so that it was in contact with both optical fibers. This whole setup was placed in a tube filled with Aplysia saline and positioned in the magnetic resonance (MR) scanner for imaging.

Neural Recordings

Compound action potentials (CAPs), the summation of the multiple (>1,000) individual action potentials, were stimulated at one end of the nerve using monophasic pulses of current (90–275 μA, 5 milliseconds pulse width, 2 Hz, 90 second duration, 179 stimulations) and recorded in Axograph data acquisition software. Signals were amplified by x10,000 and 100–1,000 Hz bandpass filtering was applied using a differential amplifier (Model 1700; A-M Systems, Sequim, WA). The signal was digitized using a Digidata 1440a digitizer (Molecular Devices, San Jose, CA). Initial recordings established the normal response of the nerve to the 90 second electrical stimulation protocol. Next, the nerve was irradiated to identify the radiant exposure per pulse occurring at INI threshold. These inhibition protocols provided laser irradiation for the middle 30 seconds of the 90 seconds recording (stimulations 60–119) (Fig. 1 B). First, only one laser (Laser A) was used to irradiate with one of the fiber paths (Fiber A), and the applied radiant exposure was modulated until an inhibition threshold value, H₁, was identified where only one of the peaks in the CAP was inhibited. During the experiment, inhibition was defined as the first visual disappearance of a CAP peak, however, this disappearance was later quantified, and inhibition was confirmed in post-processing by showing a statistically significant drop in the rectified area under the curve (RAUC) of this peak. Consequently, radiant exposures above the threshold were tested. Since inhibition threshold was determined in post-processing, 1–3 repetitions of inhibition at the radiant exposure threshold were performed for each nerve.

Once the single fiber threshold was identified, the inhibition threshold was found using two fibers (Fibers A and B together). Laser powers per pulse out of each optical fiber were kept equal throughout the experiment. Initially, the radiant exposure values were set to 50% of H₁, and then slowly increased until the two-fiber inhibition threshold, H₂, was found by the same criteria as for H₁.

Thermal Recordings

A two-pronged approach was used to estimate the heating occurring at INI radiant exposure thresholds using one and two fibers. First, a thermocouple was used to measure the time-dependent heating at the spot of maximum temperature rise in a water bath. Second, magnetic resonance thermometry (MRT) was used to determine the spatial extent of heating at INI thresholds. These temperature measurements were made for the previously identified radiant exposure thresholds for each of the six nerves (six H₁ values and six H₂ values).

Thermocouple Recordings

Thermocouple measurements were taken using a fine wire (12.7 μm diameter) type E thermocouple (FW05; Campbell Scientific Inc., Logan, UT) connected to a model DI-245 (DATAQ Instruments, Inc., Akron, OH) with built-in cold-junction compensation for signal acquisition. The thermocouple was secured and placed in a beaker of tap water at room temperature (Fig. 1C). A micromanipulator (KITE-R; World Precision Instruments, Sarasota, FL) was used to hold the optical probe and was mounted on a motorized translation stage (PLS-XY; ThorLabs Inc., Newton, NJ) for fine motion control during placement of the probe over the thermocouple. A total of three trials were performed for three different conditions, (i) only laser A irradiating with H₁ measuring under fiber A, (ii) laser A and B both irradiating with H₂ measuring under fiber A, and (iii) laser A and B irradiating with H₂ measuring under fiber B. For each trial, the probe was positioned with the laser(s) on at the spot of maximum temperature. When two fiber temperature measurements were performed, the probe was first placed with only laser A or B on (for conditions 2 and 3, respectively), and then further positioned with both lasers on to account for any shift in the hotspot due to the addition of the second laser. With this placement, an estimate of the maximum temperature experienced by each nerve could be obtained. Once positioned, the laser(s) was turned off so that the reading relaxed back to baseline at room temperature. The laser(s) was then triggered at 200 Hz with 200 μs pulses, mimicking irradiation during the electrophysiological inhibition protocol. All H₁ and H₂ values were tested to identify the maximum temperature rise for one and two fiber inhibition for each of the six nerves. A steady-state temperature consistently occurred within 5 seconds of heating at any given radiant exposure. Temperatures were sampled at 200 Hz and the recorded steady state temperature rises were averaged over 15 seconds once at steady state. This procedure was performed three times for each of the three conditions listed above, which were then averaged to calculate the maximum temperature rise at H₁ for each nerve and the maximum temperature rise at H₂ under each fiber for each nerve. These results were then used to calculate a percent change in temperature rise for each nerve under each fiber.

MR Thermometry

While thermocouple measurements can provide information about the amplitude of heating, spatial information is needed to assess how much greater of a region is being affected. Methods which measure spatial temperature distributions within the tissue at high spatial resolutions are limited. This is especially true when considering temperatures at depth in tissue or in water-rich environments. MRT was used to provide spatial thermal data at a depth within a setup that mimicked the boundary conditions of heating in the electrophysiological experiments.

Setup.

MR thermometry [50] was used to obtain spatially resolved temperature maps of the nerve and surrounding media during heating. An MR-compatible phantom setup was constructed to mimic the boundary conditions of heating that the nerves experienced during the electrophysiological experiments: being immersed in Aplysia saline with the probe in contact.

A nerve holder (Fig. 1D) was designed and three-dimensional printed from acrylonitrile butadiene styrene (ABS) plastic to allow for repeatable, precise, and secure placement of the optical probe in contact with the nerve throughout the study within a 50 ml Falcon tube (Fisher Scientific, Pittsburgh, PA). This nerve holder featured a keyed central channel for the guidance of the probe so that the only possible orientation of probe insertion caused both optical fibers to be in contact with a nerve when the nerve was strung across the two extended ledges at the bottom of the holder. The nerve holder was epoxied to the inside of the tube cap, forming a water-tight seal and allowing for the removal of the entire setup from the tube with the cap.

During phantom preparation, an Aplysia was anesthetized and the pleural abdominal nerve was dissected out using the same protocol as previously described. The nerve was strung across the gap between the two extended ledges at the bottom of the nerve holder while the probe was inserted into the channel so that it lay in contact across both optical fibers. Once placed, super glue was used to secure the ends of the nerve to the ledges. The nerve and probe holder were then placed in the 50 ml tube filled with Aplysia saline and screwed shut. This phantom setup was then secured in a 38 mm diameter quadrature volume coil and placed in the bore of a 9.4 T small animal MR scanner (21cm bore, Varian DirectDrive; Agilent, Santa Clara, CA) at the Vanderbilt University Institute of Imaging Science.

Scan parameters.

Multislice, T1-weighted images of the setup volume were acquired to localize the optical fiber prior to heating. A three contiguous slice imaging plane (0.25-mm thick slices) was defined and used for temperature mapping. The imaging plane was oriented so that each image captured both optical fibers and the nerve/bath region below the probe where heating was induced (Fig. 5A). Slice two acquired the center 0.25 mm of the nerve and probe, and slices one and three imaged voxels containing the edges of the probe/nerve and the adjacent saline bath. A gradient echo sequence was used to dynamically acquire preheated and heated images around the optical probe tip (repetition time [TR] = 78, echo time [TE] = 10 milliseconds, field of view = 28 × 28 mm, 0.218 × 0.218 × 0.25 mm voxels, three averages, 30 seconds temporal resolution). Three baseline preheating images were acquired of all slices before triggering the laser(s) for a 30 seconds INI heating image. The acquired images were zero-padded in-plane to a 512 × 512 matrix (0.055 × 0.055 × 0.25 mm voxels) and temperature maps were computed from the resulting images using baseline-subtracted proton resonance frequency-shift MR thermometry [51] which was adapted to run on the scanner [52].

Fig. 5.

Magnetic resonance thermometry (MRT) results. (A) Schematic of the temperature mapping slice orientations and positions in relation to the nerve and probe, where slice 2 (light blue) measures the center of the nerve and probe and is sandwiched between slice 1 (magenta) and slice 3 (orange). Slices are 0.25-mm thick and contiguous. (B) MRT image of heating in slice 1 using one optical fiber irradiating with H1 for Nerve 1 (176.3 mJ/cm²/pulse). The artifact due to the presence of the optical probe has been removed by thresholding the raw magnitude image and a dashed line has been placed around the location of the probe for clearer visualization of the data. (C) MRT image of heating in slice 1 using two optical fibers irradiating with H₂ for Nerve 1 (122.2 mJ/cm²/pulse/fiber). (D) Temperature rise line profiles taken from 110 to 165 μm below the probe in (B) and (C) are plotted. The probe position is shown as a thick black line. The FWHM was calculated for both one (blue) and two (orange) fiber heating. From these, the percent increase in FWHM of heating when using two fibers instead of one was calculated. (E) The distribution of percent increase in the FWHM for all six sets of radiant exposure thresholds was calculated as 37.7 ± 6.4% (P = 1E–3), 68.4 ± 5.2% (P = 2.4E–5), and 51.9 ± 9.9% (P = 1.7E–3) for slices 1, 2, and 3, respectively.

Data Analysis

Electrophysiology.

CAPs were analyzed to identify the radiant exposure at the inhibition threshold for both one and two optical fibers. The RAUC is a relative measure of the number of neurons contributing to the signal and has been shown to decrease during INI due to fewer neurons firing [31]. To increase sensitivity to the inhibition of neural subpopulations, the RAUC was only taken over the peak which was inhibited. The variance of the CAP was used to guide choosing the bounds over which the RAUC was calculated in each recording. Regions of local minima in the variance of the signal were chosen which minimized the variability in the RAUC due to normal signal shift. RAUCs of inhibited CAP peaks were compared with RAUCs of normal CAP peaks before and after laser irradiation using a two-sided paired t test implemented in MATLAB (R2017a; MathWorks Inc., Natick, MA), and the significance threshold was adjusted using the Bonferroni correction (P < 0.0042) to account for increased type I error due to the 12 tests being performed (six tests for H₁ and six tests for H₂). Once radiant exposures were identified at both the one and two fiber thresholds for each nerve, a two-sided Student’s t test (P < 0.05) tested for a significant change in H₂ compared with H₁.

Thermal data.

The percent change in temperature rise was calculated under each fiber and for each of the six nerves. These distributions of percent changes were tested for a significant deviation from a normal distribution centered at a 0% change using a two-sided t test (P < 0.05).

For assessing changes in BL, MRT images were inspected after zero-padding, and the phase change was calculated between the average of the baseline images and the heated images. Phase wrapping in the images was removed with a one-dimensional phase unwrapping algorithm implemented in MATLAB. After unwrapping, the temperature for each voxel was calculated using the equation

$$\mathrm{\Delta }T=\frac{\mathrm{\Delta }\phi }{\gamma \alpha B_0\text{TE}}$$

where Δφ is the phase difference between the current image and the baseline average for each voxel, γ is the gyromagnetic ratio in Hz/T, α is the proton resonance frequency change coefficient in ppm/°C, B₀ is the magnetic field strength in Tesla, and TE is the echo time in seconds [50].

On a separate nerve from a 318 g Aplysia, the diameter was measured using optical coherence tomography and found to be 267 ± 7 μm. On the basis of this measurement of the nerve height, the middle of the nerve could be estimated as being three voxels (corresponding to 110–165 μm) below the average probe tip location in each slice (determined by setting a threshold in the T1 magnitude images). The FWHM of heating was calculated along the nerve at this depth in each of the imaged heating slices. The percent change in FWHM when switching from one to two fibers was tested for a significant increase against a zero-centered normal distribution with a one-sided students t test using the Bonferroni correction (P < 0.017) to account for the separate analysis of each of the three slices from the same volumetric image.

RESULTS

Computational Modeling Suggests Increased BL Can Decrease Peak Temperatures

The importance of BL during heat block was first tested in silico by simulating the temperature rises required to inhibit neural conduction for two different FWHMs of heating. These simulations of neural conduction suggested that greater BLs could lower the peak temperature required for inhibition. Figure 2 shows the resulting temperatures at inhibition threshold when applying temperature rises similar to what occurs from laser heating in a nerve when irradiated with one and two adjacent optical fibers. In all columns, the top row is the one-dimensional temperature distribution applied over the length of the axon and the bottom row is the maximum membrane potential that the action potential reaches at each computational node along the length of the axon. Column 1 shows the baseline neural conduction when the axon is held at 20°C. A slight decrease in the maximum membrane potential is exhibited as the action potential reaches the end of the axon due to the passive segment placed at the end, but this does not affect conduction in the center of the axon, nor the occurrence of inhibition. Columns 2–4 show the results during heating. Inhibition was achieved when a peak temperature rise of T_S1 = 23.1°C was used (Fig. 2, column 2) with the profile for one fiber heating. The maximum membrane potential of the action potential propagates identically to the baseline case until the action potential encounters the region of elevated temperature (Fig. 2, column 2, bottom row). In this region, the maximum membrane potential decreases, with the rate of decrease related to the amplitude of elevated temperature, and this rate reaches a maximum at the hottest point. By the end of the axon, the action potential has dropped to −65 mV, the resting potential, and has failed to recover, demonstrating successful inhibition. A similar membrane potential trend is noted when a temperature profile which mimics two irradiating optical fibers is applied at inhibition threshold (Fig. 2, column 3). With this heating configuration, it was found that the peak temperature rise at inhibition threshold drops to T_S2 = 20.4°C, a 11.7% reduction as compared with using one fiber.

Fig. 2.

Computational modeling results. One-dimensional temperature profiles were applied to axons in NEURON to simulate the propagation of neural signals during heat block. The top row shows the temperature distribution applied along the neuron in each case, and the bottom row shows the maximum membrane potential of the action potential as it propagates along the axon. Column 1 depicts a baseline case in which no temperature elevation is applied to the axon. The peak voltage is unchanged along the entire length of the axon. Column 2 shows a temperature profile similar to that experienced from irradiation from a single optical fiber with a peak temperature rise at the inhibition threshold of T_S1= 23.1°C and FWHM = 0.84 mm. The peak voltage in the heated region decreases to a point where inhibition is experienced and the action potential is blocked. In column 3, the temperature rise similar to irradiation from two adjacent optical fibers is applied with a peak temperature rise at the inhibition threshold of T_S2 = 20.4°C and FWHM = 1.22 mm. Again, the peak voltage decreases in the heated region and does not recover. Column 4 provides a control situation in which T_S2 in column 3 is applied to the shape of the one fiber temperature rise, FWHM = 0.84 mm. Here, despite a reduction in the action potential strength in the heated region (note the dip in the peak voltage in the heated region), inhibition does not occur, demonstrating that the length of heating is important.

As a control, T_S2 was applied to the axon using the one fiber temperature distribution (Fig. 2, column 4, top row). While the maximum membrane potential drops in the heated region, the action potential recovers, and inhibition does not occur (Fig. 2, column 4, bottom row). Measuring the spatial extent of these temperature rises, the FWHM of heating at inhibition threshold when modeling one optical fiber was 0.84 mm and this increased to 1.20 mm when two adjacent optical fibers were simulated, a 42.9% increase.

Using Two Fibers to Inhibit Decreases the Required Radiant Exposure per Fiber

Using electrophysiological methods, the voltage versus time data were acquired for Aplysia pleural abdominal nerve undergoing INI. A representative recording of CAPs in the pleural abdominal nerve in Aplysia and its response to INI is displayed as a surface plot to visualize how individual peaks in the CAP are affected over a full recording (Fig. 3A). This particular recording shows the two-fiber inhibition threshold for nerve 1 where each fiber irradiates with 122.2 mJ/cm²/pulse. Here, the color of the surface indicates CAP voltage and each row corresponds to a different CAP over the 179 electrical stimulations (90 seconds at 2 Hz stimulation). The first CAP is at stimulation 1. The x axis represents the time latency from the electrical stimulation artifact. This artifact can be seen in the region of ~1–6 milliseconds. The lasers are off for stimulations 1–59, on for stimulations 60–119, and off for stimulations 120–179. Representative CAP traces from each region (laser off, laser on, laser off) are taken from the surface (designated by black lines) and are plotted on the right. Notice that the inhibited peak is missing from the middle trace. Baseline activity can be seen for stimulations 1–59. Once the lasers are turned on at stimulation 60, the CAP begins reacting to the heat generated by increasing in CV (decreasing in latency). Inhibition eventually occurs in the peak with the slowest CV (between the two red lines, Fig. 3A). The inhibited peak immediately returns once the laser is turned off. RAUC of the inhibited peak, calculated between the red lines, is plotted as a function of stimulation number (Fig. 3B) where blue indicates RAUCs when the lasers are off, and orange indicates RAUCS when the lasers are on. Inhibition was confirmed as a statistically significant drop (P = 2.0E–78) in the average RAUC during inhibition (stimulations 88–119) when compared with the average RAUCs prior to irradiation and after irradiation. The distribution of these RAUCs are shown (Fig. 3C). This method was used to confirm INI radiant exposure thresholds for one and two fibers for all six nerves. The average H₁ and H₂ are plotted in Figure 3D. The single fiber radiant exposure threshold was found to be 166.0 ± 6.0 mJ/cm² (mean ± standard error of the mean) and using two optical fibers resulted in a significant drop in the radiant exposure threshold, 102.0 ± 4.6 mJ/cm² per optical fiber. This corresponds to a 38.5 ± 2.2% (P = 7.3E–6) reduction in radiant exposure per fiber at the probe output when using two adjacent optical fibers. Since using two fibers changed the boundary conditions of heating compared with using one fiber, this change cannot be directly translated into a reduction in temperature rise at the inhibition threshold. Consequently, temperature rises were directly measured at each H₁ and H₂ value.

Fig. 3.

Electrophysiological results. (A) A surface plot demonstrating the results of a typical recording at inhibition threshold. Each compound action potential (CAP) trace elicited from the 179 sequential stimulations is plotted as a function of latency from the artifact at time t = 0. The height and color of the surface correspond to voltage amplitude. This particular recording is from nerve 1 at the two-fiber inhibition threshold. The recording begins at the bottom row; stimulation number (2 Hz stimulation) increases from the bottom to the top of the y axis; each row shows the subsequent CAP. Boxes on the left designate when the lasers are off or on, with the lasers turned on for the middle 60 stimulations (30 seconds). Three representative CAPs taken from the black lines on the surface, one from each region, are shown on the right as representative voltage versus time traces to demonstrate inhibition of a single peak. The two red lines at ~79 and 87 milliseconds on these three traces correspond to the red lines on the surface plot and designate the region over which the rectified area under the curve (RAUC) was calculated. (B) RAUC from the region between the red lines in (A), normalized to the average RAUC when the laser is off, plotted as a function of stimulation number. Blue points denote when the lasers are off whereas orange points denote when the lasers are on. (C) The distribution of RAUCs is plotted for both when the laser is off (stimulations 1–59 and stimulations 120–179) and during infrared neural inhibition (INI) (stimulations 88–119). Inhibition can be identified as a significant reduction in RAUC (P = 2.0E–78). (D) The distribution of radiant exposures resulting in inhibition threshold using one fiber, H₁, and two fibers, H₂. Values are reported (mean ± standard error of the mean) above each bar. A significant decrease is noted when using two fibers instead of one (P = 7.3E–6).

Peak Temperatures Decrease When Using Two Fibers

Thermocouple measurements yielded dynamic temperature rise data from which the temperature at steady state was extracted. These measurements were performed in a water bath so that the thermocouple could be precisely placed at the site of maximum temperature rise within the thermal distribution. The maximum recorded temperatures under each fiber are reported in Figure 4 when irradiating with the identified H₁ and H₂ for each of the six nerves tested. For all nerves, the temperature at the inhibition threshold was reduced by using two fibers for inhibition. The temperature under fiber B consistently yielded higher temperatures than fiber A. The table on the right of Figure 4 shows the percent reduction in maximum temperature rise for each nerve sample when using two optical fibers compared with one. The average percent reduction in temperature rise controls for variability from nerve to nerve since different axons may have been inhibited across samples. Overall, by using two adjacent fibers instead of one, the peak temperature rise was significantly reduced under fiber A by 23.5 ± 2.1% (P = 9.3E–5) and under fiber B by 15.0 ± 2.4% (P = 1.4E–3).

Fig. 4.

Thermocouple temperature rise results measured in a water bath. Peak temperature rises due to electrophysiologically determined H₁ and H₂ values are shown for each of the six nerve, where three trials are averaged for each condition (mean ± standard error of the mean). Blue bars show the maximum temperature at inhibition using one fiber. Gray bars show the maximum temperature during two fiber inhibition measured under fiber A. Green bars show the maximum temperature during two fiber inhibition measured under fiber B. The percent reduction in peak temperature rise by switching to two fibers is reported for each nerve in the table on the right. The average percent reduction was 23.5 ± 1.2% under fiber A and 15.0 ± 2.4% under fiber B.

BL Is Increased When Using Two Fibers

Estimates of the FWHM of heating for the previous six pairs of radiant exposure measurements were made with the phantom setup described in the methods. Temperature map slice orientations are shown in Figure 5A, where slice 2 (light blue) samples the center of the nerve and probe and is sandwiched between slices 1 and 3 (magenta and orange, respectively). A large artifact was persistent in slice 2 near the output of the probe that is believed to be due to a change in magnetic susceptibility from the probe to the nerve/water and interfered with the zero-padding and obscured the region of interest of heating for all scans. Due to this, temperature maps generated in this slice were analyzed 275–330 μm below the probe tip where the artifact did not affect the results. In all other images, line profiles were taken 110–165 μm below the probe tip. The results when using radiant exposure values found for nerve 1 are shown in Figure 5B–D. Figure 5B displays the computed temperature map for slice 1 when one fiber irradiates with H₁ (176.3 mJ/cm²) and Figure 5C displays the same for when two fibers irradiate with H₂ (122.2 mJ/cm²). The artifact from the probe has been removed by thresholding. Line profiles taken from these images (the red lines in B and C) are plotted in Figure 5D. The FWHM of heating for one fiber (blue) was calculated as 0.66 mm, compared with 1.10 mm for two fiber heating (orange). Assessing the percent increase in FWHM across all radiant exposure values in all slices (Fig. 5E) showed a 37.7 ± 6.4% (P = 1E–3), 68.4 ± 5.2% (P = 2.4E–5), and 51.9 ± 9.9% (P = 1.7E–3) increase in slices 1, 2, and 3 respectively.

DISCUSSION

Utilizing the Computational Model to Explore INI Parameter Space

Both modeling and experimental data support the hypothesis that longer BLs reduce the temperatures required to achieve INI. The computational modeling of the effect of BL was crucial in the development of this study. Lothet et al. [43] first analytically derived how the minimum BL scales with the square root of axon diameter using the cable equation. From this analysis, one can hypothesize that, assuming effects along the length increase monotonically with temperature, that less thermal energy is needed to induce block if a greater length of axon is heated. Ganguly et al. [40] simulated the mechanism of heat block and in their investigation computationally tested this hypothesis, describing how the BL required to inhibit varied with both the axon diameter and the temperature rise across a uniformly heated region. Here, this hypothesis was computationally tested with temperature distributions similar to what actually occurs from heating when irradiating with an optical fiber and with a simulation mechanism in NEURON that is tailored towards Aplysia neurons. Modeling predicted a decrease in the maximum temperature rise by 11.7% when the FWHM of heating increases by 42.9%. Experimental measurements revealed a 15.0 ± 2.4% and 23.5 ± 1.2% reduction in maximum temperature rise under fibers B and A, respectively when the FWHM of heating was extended by 68.4 ± 5.2% in the center MRT slice. The results of this study support the hypothesis that this model can be used to test trends associated with INI, providing a means to relatively quickly and cheaply test the parameter space to optimize laser light application, which can then be experimentally validated.

Hypothesized Mechanism of BL

The trends shown in this study highlight that when applying INI, attention must be paid to the spatial extent of heat application. This concept of BL directly arises from the relatively recent advance in laser technology of stable diode lasers with wavelengths centered at water absorption peaks. This technology, coupled with small diameter fiber optics, allows for the application of heat block on a spatial scale at which the phenomenon of block width arises. Prior work in the field of heat block [31,32,38–40,43,53] suggests that heat block is due to the interplay of changes in the dynamics of voltage-gated sodium, Na_V, and voltage-gated potassium, K_V, ion channels. It is hypothesized that, at increased temperatures, the effect of the hyperpolarizing K_V currents overwhelm the effect of the depolarizing Na_V currents, resulting in neurons being unable to reach the threshold voltage in the adjacent region of axon [40]. Furthermore, it is known that smaller diameter axons are inhibited at lower temperatures [43]. Since ionic currents are temperature dependent, if a particular temperature rise requires one specific BL, it should follow that a higher temperature will require a shorter BL [43]. Ganguly et al. [40] assessed the ratio of the total charge transfer of potassium, Q_K, to the total charge transfer of sodium, Q_Na, at a single computational node and found that, at increased temperatures, the absolute value of this ratio increases. In other words, as the axon is heated, the amount of potassium charge transfer increases compared with the amount of sodium charge transfer. This observation was also replicated in this study using Aplysia parameters in NEURON (data not shown) and the same conclusion was reached. At higher temperatures, lower BL was required and a greater Q_K/Q_Na ratio was calculated across all heated computational nodes. This analysis does suggest that if the irradiated region is increased past the length tested in this study (two adjacent optical fibers), the temperature at inhibition threshold can be further reduced. This topic is of great interest when considering how INI threshold temperatures may be clinically viable, and while outside the scope of this manuscript, assessing methods of applying longer BLs and assessing their effect is under investigation.

Sensitivity of INI to Probe Placement

INI of particular neural populations is very sensitive to probe placement. Laser heating effects must be decoupled from the tissue’s normal response. When assessing the CAP in Aplysia pleural abdominal nerve, the following effects are seen. Prior to laser heating, peaks shift to longer latencies which can be characterized as a “fatigue” effect due to build-up of sodium ion channel inactivation [54,55] from the 2 Hz electrical stimulation. Once the laser turns on, both the inhibited and non-inhibited peaks shift to the left, having a lower latency from the electrical artifact, which is consistent with the previously published trends that axons at higher temperatures demonstrate faster CVs [32]. At some critical point (critical temperature), INI takes place in the inhibited peak. When the laser turns off (stimulation 120), the inhibited peak’s CV is similar to its initial CV at Stimulation 1 as if INI provided time for the neurons to “rest” and overcome the sodium channel “fatigue”; however, as electrical stimulation continues, there is again an increase in latency of the peak due “fatigue”. Non-inhibited peaks show increased latencies when the laser is turned off, likely due to the tissue cooling. Note that only one peak was inhibited (Fig. 3A), demonstrating the ability to preferentially block the conduction of only a subset of neurons within the entire nerve. This selectivity of INI may be used to specifically inhibit subpopulations of neurons within a nerve [43].

As INI is currently understood, factors that contribute to which neurons are inhibited include temperature rise, a neuron’s axon diameter, and the BL. Placement of the probe is crucial for neural targeting since it dictates the location of the temperature distribution, which modifies the temperature rise and the FWHM of heating along the targeted neurons. In this study, the variability of probe placement was accounted for in three ways. (i) The probe was placed on the nerve in the same way for each experiment. With the pilot lights on, the probe was placed in contact with the nerve under stereoscope viewing so that both fibers completely irradiated the nerve. Maximal scattering of the pilot light was used as an indirect measure that the probe was fully on the nerve. (ii) Once inhibition was achieved, the probe was left in the same position for the entire experiment. Despite these efforts, probe placement may have targeted different neural populations between nerves, and the axon diameter and complement of ion channels of the targeted neurons may have resulted in different temperature rises required to elicit INI. Note how nerve 5 in Figure 4 displayed temperature rises lower than the other samples, with the one fiber temperature rise lower than the two-fiber temperature rise for nerve 1. While the population of neurons targeted varied between nerves, it was found that for a given probe placement the same population of neurons was inhibited independently of whether one or two fibers were used. Therefore, (iii) the percent reductions in both the temperature rise and the FWHM of heating were calculated for each nerve before statistical assessment of their distributions was performed, so that the variation in inhibition of different neural populations between nerve samples could be overcome. In this way, the reported trends can be applied across neuron populations in the slug, demonstrating that this phenomenon of BL is not confined to any particular population of unmyelinated neurons.

Targeting Neural Subpopulations

Targeting specific neurons for inhibition relies on more than just probe placement. It is known that INI naturally results in a block of smaller diameter neurons at lower radiant exposures according to the “size principle” as demonstrated by Lothet et al. [43]. This trend may allow for selective inhibition of pain conducting C fibers in humans because they are similar in diameter to neurons in the slug, have the smallest diameter axons in the peripheral nervous system, and are unmyelinated [48,56]. When considering how the size principle affects a CAP, it is seen that later signal peaks are inhibited first [43] since smaller axon diameters have slower CVs [57]. In this study, when radiant exposures higher than the threshold were tested, slower CVs were inhibited prior to the fastest CVs (data not shown) supporting the conclusion of Lothet et al. [43]. It is important to note, however, that the very slowest CV signal was not always the first signal peak inhibited. This variability is likely due to the spatial specificity of INI, the probe placement across experiments, and the complement of ion channels in the targeted neurons. For each nerve, the inhibited peak was consistent regardless of whether one or two fibers were used to inhibit, demonstrating that the selectivity of inhibition was not altered by increased BL. This is expected, as the spatial selectivity is determined by the size of the laser spot in the direction across (transverse to) the nerve and the optical penetration depth (in the z-direction); the increase in BL (i.e., the size of the laser spot in the direction axial to the nerve) is not expected to change that selectivity since all neurons are heated in both the one and two fiber cases. It is unclear how the selectivity of inhibition will change when the irradiation spot is smaller than the diameter of the nerve. The time course of inhibition is governed by the speed at which heat is accumulated in the nerve, which in practice is controlled by the radiant exposure. Using higher radiant exposures results in quicker INI, but this also runs the risk of overheating to a point beyond a “therapeutic zone” and causing damage. Lower radiant exposures reduce the risk of damage but increase the time to inhibition. In this study, INI was achieved in a 30 seconds window of irradiation which governed the effective radiant exposures used, and a statistically significant INI threshold typically resulted in inhibition of the signal in the last 5–15 seconds of irradiation.

In this study, the probe was placed in contact with the tissue, however, this is not necessary to deliver the required temperature rise for inhibition. The drawback of positioning the probe not in contact when the nerve is immersed in media is that energy density losses occur due to both divergence from the probe and due to absorption of the light by the saline. The same limitation occurs if any other tissue is between the probe and the nerve. Besides resulting in unnecessary heating, this would raise the optical power required for inhibition. Consequently, the close proximity of any optical emitter to the nerve would be ideal in a clinical scenario to minimize laser power and superfluous heating. Compare this to electrical inhibition where contact with the tissue is required. It is known that application of both high-frequency alternating current (AC) [15,17] and direct current (DC) [58] can block neural conduction. It has been shown that high-frequency AC can preferentially target either larger or smaller diameter axons depending on the frequency used [59,60], whereas DC stimulation preferentially blocks large diameter and myelinated neurons first [61]. Specificity in the electrical modulation of neurons has been boosted by using focused multipolar and tripolar stimulation methods [62]. The advantage of INI is that it can be performed using less complex hardware. Moreover, at least in theory, INI is potentially much more spatially precise than even the most sophisticated electrical modulations techniques since the interrogation zone is dictated by the optical spot size (which in extremis is diffraction limited). Whether that level of spatial precision is either practical or necessary remains to be seen. In cell and animal models, an optical fiber may be brought into the vicinity or in contact with the sample, while spatially precise electrical modulation may require complex devices and careful placement of electrodes, especially when working with cultured cells. For example, while safe DC inhibition was described in Fridman et al. [58], a complex device was necessary to achieve this, whereas INI modulates activity in small axon diameters in a nonfunctionally damaging manner with just the introduction of an optical fiber delivering light from a laser source. Clinical feasibility of INI would be greatly improved by demonstrating even greater improvements in spatial and neural specificity, even over what was shown in Duke et al. [31]. We hypothesize that more complex irradiation schemes that utilize INI’s size principle and BL phenomena along with the ability to focus light to a small spot will provide more targeted inhibition of specific neural populations, and this can be used for providing targeted therapy. Further, INI and electrical inhibition may be implemented synergistically, as was demonstrated by Lothet et al. [18], and as was demonstrated during neural excitation by Duke et al. [41,63].

Considerations for Thermal Measurements

Temperature measurements were required to confirm that extending the BL decreased the temperature rise required for heat block. When two fibers are used, while each individual fiber outputs less energy per pulse (H₂ < H₁), there is still more total energy being deposited into the tissue. Using one fiber, the average power applied to the nerve at the inhibition threshold was 41.7 mW, and this was increased to 51.3 mW when using two fibers. This greater power is now distributed over a greater volume of tissue, and while it was hypothesized that the combined effect of more energy and greater application volume would result in a lower temperature rise, thermal measurements were required to validate this. Precise thermal recordings in tissue pose a serious challenge. In this study, a thermocouple and MRT were used to provide complementary information about the heating produced by the inhibition probe. The advantage of thermocouples is that they provide fast thermal dynamics with high thermal precision, however, contact with the sample is required and only a single point can be interrogated. The thermocouple measurements must be evaluated carefully since a classic problem of using this temperature measurement approach to elucidate the thermal effects of laser-irradiated tissues is direct radiation of the thermocouple which may result in an overestimation of the measured temperature as well as actually increasing the temperature of the laser-irradiated medium due to heat conduction from the irradiated thermocouple itself. Second, the thermocouple wires may act as a heat sink which could result in an underestimation of the temperature of the irradiated volume. Given the specific parameters of our experiment where the laser pulses are 200 μs in duration, of relatively low intensity, and are delivered at a repetition rate of 200 Hz (i.e., the duty cycle is 4%) and the physical properties of the thermocouple we used (thermal time constant ≈10 milliseconds, thermocouple wires of 12.7 μm diameter and a physical thermocouple junction size of ~25 μm, made of chromel/constantan (which has a heat capacity of ~400 J/kg/K; roughly 1/10th of that of water [64,65]), our calculations indicate (data not shown) that: (i) the thermocouple is too slow to track the direct laser heating and the laser pulse repetition rate is too slow (200 Hz, i.e., two pulses during the 10 milliseconds thermal response time of the thermocouple) to cause significant heating due to pulse-to-pulse temperature superposition; (ii) the “thermal mass” of the thermocouple is more than three orders of magnitude smaller than thermal mass of the surrounding aqueous medium (given by the laser spot diameter and the optical penetration depth) and hence conduction of heat either from the thermocouple to the surrounding aqueous media (due to direct laser irradiation of the thermocouple) or from the surrounding media to the thermocouple (heat-sink) is negligible.

Another aspect of this temperature data is that the temperature recorded under fiber B was consistently higher. This was investigated, and it was found that fiber B had a smaller divergence angle than fiber A, which resulted in the spot diameter from fiber B being smaller than fiber A past the output of the fiber. This difference appeared to be due to different couplings at the fiber connection ports from the two lasers. Therefore, while the power output was the same between the two lasers, there was a slight increase in the volumetric energy deposition from fiber B compared with fiber A. While this created a noticeable difference in the temperature rise from the two fibers, all nerves showed a statistically significant drop in temperature at the inhibition threshold when using two fibers instead of one.

MRT [66] is another method of temperature measurement that has been applied for guidance of thermal therapy [67–69], and has been applied for assessing temperature rise during INS [70]. MRT provides information with lower thermal precision, spatial resolution, and temporal resolution compared with thermocouples and thermal cameras. In contrast, however, MRT gives volumetric information within tissue and water-rich environments that these other two methods cannot provide. While thermal dynamics could not be measured with MRT, the field of temperature was probed at depth in solution, adding to the single point information provided by a thermocouple. Limitations in the spatial resolution of MRT for measuring heating from an optical probe was overcome by using a scanner with a high magnetic field strength, reducing the temporal resolution, performing averaging, and interpolating the data. Infrared imaging was considered as a method to measure the temperatures being generated because it is a noncontact method which provides images at high spatial and temporal resolutions, but the drawback in tissue and other water-rich environments is its limited imaging depth. The absorption coefficient of water in the infrared regions used by thermal cameras is high enough that temperature sensing is confined to only a very superficial layer (tens of microns) [71]. Additionally, when using thermal imaging with INI, the optical probe can physically block the field of view of the camera if it is in contact with tissue, and the maximum temperature rise may occur at a depth greater than the camera can detect. To confirm that the maximum temperatures were reduced by using two optical fibers for inhibition, it was important to measure the temperature generated at a depth in solution, meaning that thermal cameras were not appropriate. Other methods for monitoring temperature exist such as fluorescent sensors [72], temperature spatially offset Raman spectroscopy [73] and fiber Bragg gratings [74], and each has their respective advantages and drawbacks. Experiments must be care-fully designed to adequately approximate the temperature generated in the nerve during INI.

The computational predictions, thermocouple measurements, and MRT recordings all present similar temperature rise values at inhibition threshold. For example, from Figure 4, the temperature rise for nerve 1 is ~20°C when using one fiber. The MRT data for nerve 1 shows a rise of ~12.4°C. With two fibers, the temperature rise as measured by the thermocouple was ~17.5–19°C for two fibers, while this was measured as ~11.4°C using MRT. This lower temperature in the MRT data may be due to greater spatial averaging during MRT, which could underestimate the maximum temperature rise and/or direct irradiation to the thermocouple, which could overestimate the temperature rise measured using the thermocouple. Nonetheless, the multiple methods of measurement serve to validate each other and highlight that the reported values are reasonable estimates.

MRT measurements confirmed that the FWHM of heating along the nerve increased when two optical fibers were used. Despite this trend being consistent through all trials, care must be taken when interpreting these results. Averaging of multiple accumulations was required to maintain a usable SNR and achieve a voxel size of 0.055 × 0.55 × 0.25 mm (acquired size of 0.218 × 0.218 × 0.25 mm), which limited the temporal resolution. Zero-padding in the frequency domain was required to boost spatial sampling, which can exacerbate artifacts and noise within the images. The noise is observed as the oscillations in Figure 5D outside of the heating. Additionally, the two temperature peaks in Figure 5D are not exactly equal. This could be due to slight differences in the outputs from laser A and B, differences in the outputs from fibers A and B, a slight offset in the location of the output of fibers A and B, or due to a rotation in the imaging plane relative to the probe. Despite this, for all tested radiant exposures and in all imaged slices, the FWHM increased when two optical fibers were used instead of one.

Temperature Measurements Across Animal Models

In this study, it was shown that the average temperature rise at inhibition threshold was 17.6°C (~37.6°C) using one fiber and 13.5°C (~33.5°C) using two fibers. These values are higher than what was reported for animal studies in Table 1. Different model systems may require different temperature rises to elicit heat block. This may depend on nerve thickness, axon diameter, BL, myelination, vertebrate versus invertebrate, and complement of ion channels, and the reported values may further differ due to temperature measurement methodology, to name some possible sources of variability. Hodgkin and Katz [32] demonstrated that heat block takes place near 40°C which is slightly higher than the temperatures reported in this study. Importantly, Hodgkin and Katz provide a validation of heat block using a nonlaser method of heating where, instead, heated saline was used in the bath. The proposed mechanism of heat block is agnostic about the energy source driving the temperature rise and relies solely on a thermal response of the tissue. There is no evidence that INI works through a nonphotothermal effect: photons do not contain enough energy to drive photochemical reactions at 1,875 nm, and laser pulses that are 0.2 milliseconds in duration at this wavelength do not fall in the stress confinement regime [75], eliminating mechanical modulation.

The most comparable study to the work presented here is Lothet et al. [43] because the Aplysia pleural abdominal nerve was also used. This study published a 9.7°C temperature rise when using a 600 μm core diameter optical fiber and 1,860 nm light compared with this study using a 400 μm core diameter fiber and 1,875 nm light. Using a 600 μm fiber would extend the BL on the nerve, possibly accounting for some of the discrepancy of temperature rise at INI threshold using one fiber. In the current study, however, a higher temperature rise than 9.7°C was needed for two fiber inhibition, so this cannot be the only factor. The wavelength used in the current study, 1,875 nm, has higher absorption in water than 1,860 nm [71] which would reduce the optical penetration depth, causing more light to be absorbed more superficially in the nerve and changing the temperature distribution, affecting which axons were targeted spatially, but more work is needed to understand the effect of this on neural conduction.

In this study, a fine wire thermocouple that is 12.7 μm in diameter was used to measure temperature compared with thermal cameras in other studies. Thermal cameras can only sense superficial temperature increases, which may not correspond to maximal heating. Additionally, averaging over pixel area occurs, possibly explaining some of the difference in reported temperature rise between this study and other studies. In Lothet et al. [43], the limitation of the sensing depth of thermal imaging was overcome by creating a glass window setup. While this provides information at a depth, underestimation of the temperature may have occurred due to the optical transmission through the window that was less than 100% in the wavelength sensing range of the camera (3–5 μm) [76]. Additionally, other variations in the setups may have led to higher temperature requirements in the current study than what was needed for INI in Lothet et al. [43]. Further characterization efforts will be required to identify what is the necessary temperature rise for any given model system, and why the reported variations occur. Using the Aplysia model (a cold-blooded animal), the biophysics of neural conduction can be tested, but as reported in this study and others, heat block sets in at mammalian physiological temperatures. Ganguly et al. [40] predicted that squid giant axons (500 μm in diameter) similarly could not conduct at temperatures higher than 29.5°C, and that smaller diameter axons required lower temperatures for heat block, demonstrating the limitation of trying to computationally model heat block at mammalian temperatures. Trends observed in Aplysia, such as the effect of BL, can be used to inform the prediction of the biophysics in mammalian systems. For example, Lothet et al. [43] demonstrated that the size selectivity of INI was conserved between the Aplysia and the musk shrew vagus nerve, therefore, while exact temperatures and temperature rises that result in INI in mammals (including humans) will differ from those published here, it is expected that the trend of BL will hold. To further assess INI for mammalian neurons, in silico work will require new computational models with proper neural conduction parameters and experimental validation in mammalian nerves will be needed.

CONCLUSIONS

This study provides the first experimental evidence of the importance of block length during neural heat block. Both computational predictions and experimental measurements support the hypothesis that the peak temperature for INI can be reduced by targeting a greater length of the axon. Despite higher reported temperature rises in this study compared with others (Table 1), this work demonstrates a proof of concept that can be applied to more targeted setups and other neural systems. The ability to thermally manipulate neural tissue on a scale at which BL is important has emerged with the development of INI since lasers provide a convenient way to apply spatially precise heating. In the future, the temperature trends exhibited in the current study can be used to guide the implementation of INI in safer ways. Key factors affecting the presence and degree of thermal damage are the temperature rise and duration of elevated temperatures, according to the Arrhenius model [44,77]. Therefore, a technique that reduces temperature rise, such as modulating the targeted BL, will result in lower probabilities of damage and increase the potential duration of application.

When considering the clinical implementation of INI, there is a practical limit to the length of nerve that can be manipulated based upon surgical constraints. We postulate that laser heating may be an ideal modality to perform neural heating due to the development of laser diodes with relatively low cost, smaller sizes that can be worn on the body, and compatibility with pacemakers and electrical recording devices. An optical approach to neural heating with high spatial and temporal specificity can provide precise control that can be optimized to reduce the thermal load during therapy. Damage studies that investigate both histological and functional endpoints are required to assess the safety of INI. We do not currently claim to be below laser irradiation safety guidelines, however, this study lays the foundation for optimizing irradiation parameters such that INI adheres to ANSI safety standards. Nonetheless, techniques such as modulating BL have the potential to precisely target neurons within bulk tissue and can reduce the probability of damage to adapt INI for a wide range of applications.