1. Introduction

Over the last fifty years many studies have been reported on optical detection of neural activity. In these studies, volume change due to stimulation of unmyelinated axons in cuttlefish [1], crab or lobster leg nerves [2] was investigated using optical instrumentation. Indications of neural activity include changes in absorption, birefringence, fluorescence and scattering, as well as swelling, shortening and in some cases initial shrinkage [3].

Hill et al. used a laser interferometer to measure rapid changes in diameter of a crayfish giant axon [4]. In these experiments, incident light in one path of the interferometer was reflected from nanometer-diameter gold particles placed on the axon surface. Measured phase changes indicated a 1.8 nm displacement (contraction) of the axon surface over a period of about 1 ms followed by slow swelling. Mechanical changes accompanying action potential propagation were studied using nanometer-diameter gold particles placed on the squid giant axon [5]. A fiber sensor measuring change in back-reflected light intensity yielded a 0.5 nm displacement (swelling) of the giant squid axon surface over a 1 ms period. Additionally, Iwasa and Tasaki reported that crustacean axons (crab and crayfish) swell during the depolarization phase of the action potential [5].

Rapid mechanical changes were reported in the garfish olfactory nerve using a stylus recording device fastened to a piezoceramic bender [6,7]. The recorded swelling signal and action potential reached a maximum nearly simultaneously [6]. A decrease in length of the neural fibers and an accumulated shortening for repetitive stimulation were reported. Additionally, measurement of rapid changes in hydrostatic pressure in a watertight chamber demonstrated a volume expansion in response to electrical stimulation [7]. Results of these experiments indicate shortening and swelling events do not compensate each other in volume changes associated with neural activity.

Surface displacement of lobster nerve and Nitella internodes was demonstrated using an optical lever recording [8]. The setup utilized a reflecting surface with opposed edges resting on the nerve and a knife-edge. A position detector recorded a signal when an incident light beam was deflected by the reflecting surface. Swelling of the lobster nerve (0.1–0.8 nm), and an initial swelling of the Nitella internodes (5–15 nm) followed by a large shrinkage (50–150 nm) were reported.

Although detection of neural activity in vivo is extremely important, none of the techniques described above can be applied in a clinical setting. Optical coherence tomography may be applied to detect slow (few seconds to few minutes) changes in neural reflectivity [9] and scattering [10], but the technique is insensitive to fast (millisecond) and small (nanometer) changes in optical path length that occur during action potential propagation. We report a depth-resolved interferometric technique to measure transient surface displacement (swelling or shrinkage) as a direct indication of neural activity, i.e., action potential propagation. The optical system, a phase-sensitive optical low-coherence reflectometer (PS-OLCR), is a fiber-based differential phase interferometer capable of measuring ultra-small (0.1 nm) changes in optical path length with microsecond temporal resolution. PS-OLCR is well suited to noninvasively detect and quantify transient surface displacement in nerves associated with the action potential propagation. Efforts to measure transient surface displacement using PS-OLCR have been recently reported [11,12]. The experiments are performed using nerve bundles dissected from crayfish leg without introducing any chemicals or reflection coatings. The measured transient surface displacement is less than 1 nm in amplitude, 1 ms in duration and occurs simultaneously with the action potential arrival to the optical measurement site. Results indicate that with further development PS-OLCR is a candidate method for noninvasive measurement of in-situ neural activity.

2. Method

The fiber-based dual channel phase sensitive optical low coherence reflectometer (PS-OLCR) is illustrated in Fig. 1. The system is constructed with polarization maintaining (PM) Fujikura Panda fiber, whose polarization channels correspond to PS-OLCR channels. Fiber segments were spliced with a commercial system (Vytran FS 2000) that allows precise alignment of fiber cores and stress axes. Small rectangles in Fig. 1 represent fiber splices and the values above show the splice angle in degrees between corresponding axes (slow and fast) of the two PM fiber segments.

A single mode, partially polarized light emitted by an optical semiconductor amplifier [λ_o=1.31 µm and Δλ(FWHM)≈60nm] is combined with a 633 nm source (aiming beam) and delivered to the system, which provides approximately 15 µm axial resolution in tissue. The input PM fiber segment creates two decorrelated linearly polarized modes that propagate along the birefringent axes of the fiber. Since an off-the-shelf 2×2 PM coupler is supplied with 1 meter fiber leads, length of input, reference and sample paths of the coupler are extended by splicing additional segments of PM fiber with axes at the same orientation (0°splice).

The lithium niobate (LiNbO₃) electro-optic waveguide phase modulator allows light propagation of one linearly polarized state. The 45° splice in the reference path ensures that equal projections of the fast and slow polarization channels of input light are coupled into the modulation axis of the LiNbO₃ modulator. The modulator is driven with a ramp waveform with voltage amplitude (V_π) that gives sinusoidal fringe signals at a single carrier frequency. The rapid scanning optical delay line [13] shown in the reference path is configured to compensate material and waveguide dispersion introduced by the LiNbO₃ phase modulator. By adjusting the grating-lens separation in the rapid scanning optical delay line, width of the coherence function can be reduced to its minimum value. The 90° splice in the sample path and appropriate selection of segment-length allow centering coherence functions for each mode at the same position.

Longitudinally displaced orthogonal polarization channels (Fig. 2) allows measurement of optical path length change between two longitudinal points. Interference of light back reflected from reference and sample paths is formed in the 2×2 PM coupler. The Wollaston prism in the detection path separates the two fiber polarization channels for signal detection. Output of each photo-receiver is first amplified and band-pass filtered in the analog domain and then digitized by a 12 bit analog-to-digital converter. Digitized signals are stored in computer memory for signal processing.

 

Fig. 1. Phase Sensitive Optical Low Coherence Reflectometer (PS-OLCR). A/D-analog to digital converter, C-collimator, D-photo-receiver, G-diffraction grating, L-lens, M-mirror, W-Wollaston prism.

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Forward and reverse band-pass filtering provides zero phase distortion and is used to de-noise the interferometric fringe data in the digital domain. Fringe phase in each channel is calculated by computing the angle between the signal and its Hilbert transform. The extracted phase data are unwrapped to remove phase jumps. Computing the differential phase (Δφ) removes common mode environmental noise. Path length change due to surface displacement (Δp) can be calculated from the differential phase (Δφ) and the center wavelength of the source (λ_o) by Δp=(λ_o/4π)Δφ. Signal to noise ratio and differential phase (Δφ) sensitivity of the PS-OLCR system are limited by isolation of polarization channels in the PM fiber and associated cross-coupling between modes. Because signal to noise ratio is limited by cross-coupling between modes, the PS-OLCR system is not shot-noise limited. Additional details of the PS-OLCR instrument and biomedical applications have been reported [11,14,15].

3. Results

Crayfish are obtained locally and nerve bundles dissected from front walking legs (cheliped) using a surgical microscope. An extracellular solution of 205 mM NaCl, 5.3 mM KCl, 13.5 mM CaCl₂.2H₂O, and 2.45 mM MgCl₂.6H₂O with pH adjusted to 7.4 is used to bathe the nerve during and after dissection. Before transecting the nerve, ends are tied with sutures to prevent leakage of axoplasm and assist with positioning. A chamber is constructed of plexiglass and attached to a three-dimensional micropositioner for easy alignment in the PS-OLCR setup. The chamber shown in Fig. 2 consists of several pools and a groove, in which the nerve is positioned. The groove is approximately 20 mm long and 1 mm wide. To stimulate and record action potentials electrically, platinum stimulation and recording electrodes are placed into the pools and fixed with epoxy. A thin (200 µm) cover glass is glued on top of the groove between the two recording electrodes. Light reflecting from the cover glass-saline interface provides an optical reference signal.

After placing the nerve in the groove, pools filled with saline are electrically isolated with petroleum jelly. Between stimulation and recording sites, the electrical isolation pool is filled with petroleum jelly to reduce stimulation artifact in action potential recordings. A glass window (not shown) is positioned on top of the stimulation site for electrical isolation. An isolated current stimulator (Tektronix Stimulus Isolator, Model 2620) is used to generate and apply 50 µs duration adjustable electric current (0–30 mA) stimulation pulses to the nerve. A differential amplifier (A-M System Microelectrode AC Amplifier, Model 1800) connected to the recording electrodes measures the action potential, which is recorded by a digital oscilloscope (Tektronix, Model TDS 640A). Time interval between successive stimulation pulses is 1.028 s (0.973 Hz). Timing signals generated by a digital delay generator (Stanford Research Systems, Model DG535) synchronize stimulation pulses with data acquisition.

 

Fig. 2. Electrical and optical readouts from the nerve chamber. Double-sided arrows indicate the orthogonal polarization channels of PS-OLCR.

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The probe beam in the PS-OLCR sample path (Fig. 2) is focused on the nerve using a 20X microscope objective to a diameter of 4 µm. First, saline-nerve (probe channel) and glass-saline (reference channel) interfaces are detected in PS-OLCR depth scans. Next, calcite birefringent wedges are positioned so optical path length of light reflected from both interfaces match the reference path delay. With the reference delay line fixed, the LiNbO₃ phase modulator in PS-OLCR reference path gives sinusoidal fringes at 50 kHz. The detected fringe data is first band-pass filtered (3 kHz–100 kHz), then sampled at 5 Msamples/s using a 12-bit data acquisition board (GaGe, CompuScope 12100). The data is stored in computer memory and transient surface displacement due to action potential propagation is calculated from the extracted phase difference between the sinusoidal fringes corresponding to reflection from the saline-nerve and glass-saline channels using commercial software.

Results indicate electrical action potentials associated with neural activity are correlated with optical path length changes corresponding to transient surface displacement of the nerve. Electrical and optical signals have 5 kHz bandwidth and are averaged to increase signal to noise ratio. Figure 3 shows average of 500 electrical and optical responses recorded from a crayfish walking leg nerve. In this experiment, the top surface of the nerve is positioned 30–40 micrometers below the glass-saline interface. Standard deviations of the noise in the first 2 ms are 44 pm and 38 pm (pm: picometer) for Fig. 3(a) and Fig 3(b), respectively. Because the path length signal (Δp) is extracted from constant amplitude fringes, the noise level in the graphs are expected to be constant before and after the stimulation. Upward and downward features of the optical signal indicate swelling and shrinkage directions, respectively. Interestingly, PS-OLCR signals recorded from close (<1 mm) but spatially distinct sites on the same nerve show optical path length change due to swelling (Fig. 3(a)) and shrinkage (Fig. 3(b)) with magnitude of approximately 0.5 nm. The optical path length change (~0.5 nm) divided by the refractive index of the saline solution (~1.325) gives magnitude of the transient surface displacement (~0.38 nm).

 

Fig. 3. Optical path length change due to surface displacement of a stimulated crayfish leg nerve. Stimulus (300 µA, 50 µs) is at 2 ms. (a) and (b) are recorded from spatially close (<1 mm), but different points on the nerve. 500 responses are averaged in each trace.

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Electrical current stimulation pulses (300 µA, 50 µs) are presented at 2 ms in the records and resulted in an artifact in the recorded electrical signal preceding the compound action potential. Because electrical signals are recorded differentially using a pair of platinum electrodes placed in the nerve chamber (Fig. 2), the action potential is thought to arrive at the first and second recording electrodes at the negative and positive peaks of the electrical signal, respectively. Consequently, zero-crossing of the electrical signal indicates time of arrival of the compound action potential at the optical measurement site positioned between the recording electrodes. Because surface displacements measured by PS-OLCR are nearly coincident with the zero-crossing of action potential records, optical signals are believed to originate from neural activity. Moreover, time duration and amplitude of the optical signal are similar to values reported previously.

The experiment is repeated using a second crayfish walking leg nerve. Separation between top surface of the nerve and glass-saline interface is 280 µm. Electrical current stimulation pulses (300 µA, 50 µs) are presented at 2 ms in the records. Figure 4(a) shows average of 250 responses recorded from the top surface of the nerve. Standard deviation of the noise in the first 2 ms of the optical signal is 39 pm. When the action potential reaches the optical measurement site (approximately zero-crossing of the averaged action potential trace), corresponding change in optical path length occurs. The sharp peak in PS-OLCR signal represents 1.1 nm optical path length change due to 0.83 nm swelling of the nerve surface. Following the sharp peak, Fig. 4(a) contains a feature between 8–12 ms. Because the delayed feature occurs after the action potential record, origin is unclear.

 

Fig. 4. Optical path length change due to surface displacement of a stimulated crayfish leg nerve. Stimulus (300 µA, 50 µs) is at 2 ms. (a) and (b) are recorded from top surface and 15 µm below the top surface, respectively. 250 responses are averaged in each trace.

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Without changing lateral position of the specimen, depth resolved features are first identified in an A-scan, and a surface 15 µm below the overlying saline-neural interface (295 µm below the glass-saline interface) is probed (Fig. 4(b)). Average of 250 responses resulted in a standard deviation of 114 pm in the first 2 ms. The increase in the noise level could be due to reduction in signal to noise while probing inside the nerve. Although a feature is observed around 4.5 ms, which is reversed compared to the peak in Fig. 4(a), additional experiments are required to understand signals originating from inside the nerve.

Using a third crayfish leg nerve, a control experiment is performed with top surface of the nerve positioned 75 µm below the reference glass-saline interface. Results with stimulus amplitude below and above the activation threshold are presented in Fig. 5. Stimuli with 50 µs duration are presented at 2 ms in all records, and associated stimulus artifacts are visible in the electrical signals. Each trace in Fig. 5 is average of 100 responses.

With the current amplitude of 60 µA for stimulation pulses, an electrical action potential is not produced and no sign of transient surface displacement is observed in the optical records (Fig. 5(a), Fig. 5(c)). When current amplitude of stimulation pulses is increased to 100 µA, electrical and optical records show evidence of neural activity (Fig. 5(b), Fig. 5(d)). Measured signals indicate optical path length change due to transient shrinkage on the order of 1 nm, which corresponds to physical displacement of 0.75 nm. Standard deviations of optical path length change recorded by PS-OLCR in the first 2 ms are 96 pm (Fig. 5(a)), 117 pm (Fig. 5(b)), 159 pm (Fig. 5(c)), and 110 pm (Fig. 5(d)). This experiment was repeated several times with stimulus amplitude below (60 µA) and above (100 µA) the activation threshold: each time the outcome was similar to the results presented in Fig. 5.

 

Fig. 5. Control experiment of surface displacement with stimulus amplitude below and above the action potential threshold. Stimulus duration is 50 µs and presented at 2 ms. (a) and (c) with stimulus amplitude of 60 µA, and (b) and (d) with stimulus amplitude of 100 µA. 100 responses are averaged in each trace.

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Moreover, when the physiological threshold for action potential stimulation was considerably increased after 2 hours, the control experiment was resumed. Stimulation pulses with current amplitude of 1.4 mA did not produce electrical or optical signals. Increasing the stimululation amplitude to 3 mA resulted in both electrical action potential and optical signal due to surface displacement similar to the results presented in Fig. 5. Based on the results of control experiments, we conclude that the measured transient surface displacements are due to propagating action potentials and do not represent a stimulation artifact.

4. Discussion

4.1 Comparison of the electrical and optical signals

Electrical current pulses can stimulate action potential propagation using intra-cellular or extra-cellular electrodes. Similar electrodes can record voltage difference due to action potential propagation. Inasmuch as use of such electrodes in many clinical applications is infeasible and undesirable in view of potential irreversible damage to nerve fibers, a noninvasive technique for measuring neural activity is sought-after. Optical differential phase measurements recorded by PS-OLCR can detect neural activity associated with action potential propagation.

Because electrical and optical signals are distinct manifestations of neural activity, comparison of these signals requires analysis. The electrical signal is a compound action potential produced by many axons (~1–50 µm in diameter), while the PS-OLCR signal - due to a small diameter beam spot (4 µm) on the nerve - originates from one or a few closely spaced axons. A cross-sectional histological view of a crayfish nerve using a trichrome stain (Fig. 6) illustrates the closely spaced packing of axons. Despite these distinctions, the electrical signal is used to predict action potential arrival time at the optical recording site. A single axon (e.g., squid giant axon) may represent the best model to compare and interpret timing of electrical and optical signals.

4.2 Nerve preparation

Structure and dissection of nerve is important for successful experiments. In some cases the optical signal did not yield surface displacement, although the action potential was recorded electrically. For example, although 0.5 nm swelling of squid giant axon was measured [5], our experiments on squid nerve (Lolliguncula brevis) were inconclusive. Histology sections indicate that squid nerves used in our experiments consisted of a giant axon (150–200 µm), axons from the fin nerve and a thick connective tissue (perineurium) surrounding axon bundles. The connective tissue was believed to dampen or completely diminish the optical signal. Therefore, nerve specimen preparation requires adequate control. Incorporating PS-OLCR with a microscope would be helpful for dissecting and targeting a region of the nerve or targeting a single axon.

 

Fig. 6. Histology (trichrome staining) of a crayfish walking leg nerve.

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4.3 Mechanisms to explain surface displacements

D. K. Hill suggested two mechanisms to explain initial shrinkage observed with repetitive stimulation [1]. Although our results are not due to such a cumulative effect, mechanisms discussed by Hill may be relevant to our experiments. First, he pointed out that potassium remains hydrated with water, which accompanies the ion through the membrane, whereas the sodium ion is not hydrated. Difference in hydration may shrink the nerve at the beginning of repetitive excitation and subsequent rate of swelling depends on membrane permeability to water. The observed shrinkage (0.5–1.5 nm) appears larger than that expected by this mechanism [1]. In his second explanation, the nerve swells because sodium and chloride enter the fiber due to a sudden increase in sodium permeability. If the interior of the nerve fiber is initially under hydrostatic pressure, the nerve fiber will shrink, which may cause a rapid extrusion of potassium and chloride ions in the active state. Therefore, the net ionic exchange may be inwards at the beginning of stimulation. In our experiments, tying the nerve ends with sutures aids in positioning the nerve in the groove and prevents leakage of axoplasm, but may increase hydrostatic pressure in the axons.

Swelling observed in the squid giant axon was suggested to be more than two orders of magnitude greater than the value expected from Na⁺-K⁺ ion exchange during excitation [6]. Results of a related study suggest that mechanical and electrical changes in the excited nerve fiber arise from replacement of divalent cations (Ca²⁺) bound to multianionic sites of the membrane macromolecules with univalent cations (Na⁺ and K⁺) [7]. Such a cation-exchange process may convert compact layers in and near the membrane into swollen, low-density structures, give a repulsive electrostatic force between fibrous macromolecular elements near the membrane and contribute to lateral expansion of the nerve fiber [7].

4.4 Retardation and optical path length changes

Many reported studies use a common optical arrangement to measure relative light intensity change (ΔI/I) associated with a transient retardation change (ΔR); retardation (R) is the product of birefringence (Δn) and nerve thickness (d). The arrangement consists of two crossed polarizers (polarizer and analyzer) at 90° orientation, while the nerve under study is placed between these components typically at 45° to the axes, which yields maximum intensity change. Measured intensity change during action potential propagation is due to a transient retardation change, ΔR=½R(ΔI/I), where R is the retardation due to the resting birefringence and I is the resting intensity of light [16]. If nerve thickness (d) is constant, measured retardation change (ΔR) may be directly attributed to birefringence (Δn) change.

We have used PS-OLCR to measure retardation change (ΔR) in reflection mode. In these experiments, calcite birefringent wedges were removed from the PS-OLCR sample path, since interference fringes for both polarization channels were recorded from a common interface underneath the nerve. The long axis of the nerve was placed parallel to one of the PS-OLCR polarization channels. Although 10–20 pm resolution was achieved by averaging 1000 responses, no retardation change (ΔR) was detected in crayfish and squid nerves. Retardation changes reported previously are 0.2 pm for a squid axon, 10 pm for a crab leg nerve, 60 pm for an electric organ of Electrophorus Electricus [17] and 41 pm for a pike olfactory nerve [18]. Because retardation change (ΔR) due to excitation of a single axon is small, resolution of the present PS-OLCR system may be insufficient to allow detection. Since nerves containing multiple axons increase the effective retardation, detection of ΔR may be possible using such a nerve combined with increased number of averages.

If refractive indices in two orthogonal directions change equally during neural activity, birefringence (Δn=n ₂-n ₁) would not change even though optical path length through the nerve might vary considerably. Transient change in optical path length during neural activity may be detected using PS-OLCR. We have recorded optical path length change using reflections from the air-glass interface of a cover glass (reference channel) and a saline-reflecting surface interface underlying the nerve (probing channel). At 10–20 pm resolution, no transient change in optical path length during neural activity was detected.

Birefringence may arise from either anisotropic molecules or an ordered arrangement of isotropic material with micro- or macro-scopic dimensions (form birefringence) [19]. If surface displacement contributes to retardation change (ΔR) reported in previous studies, the relative contribution to ΔR from thickness change and reorientation of membrane molecules requires better quantification. Neural surface displacement in response to rapid repetitive stimuli [1] that is as large as 100 nm may be useful to investigate changes in form-birefringence. Because repetitive stimulation is not expected to increase retardation change (ΔR) due to reorientation of membrane molecules, effect of thickness change on ΔR can be investigated.

A detailed description of PS-OLCR, related nerve experiments and several other biomedical applications can be found in one of the authors’ doctoral dissertation [11].

5. Conclusion

Non-contact measurement of surface displacement associated with action potential propagation is demonstrated without introducing exogenous chemicals or reflection coatings. Transient surface displacements due to action potential propagation in nerve bundles dissected from crayfish walking leg are less than 1 nm in amplitude and 1 ms in duration. Measured optical signal is coincident with action potential arrival to the optical measurement site. PS-OLCR will be a very valuable tool for fundamental nerve studies and has the potential for noninvasive detection of various neuropathies. However, further improvements will be necessary to make it useful for clinical applications.