The Direct Detection of a Single Evoked Action Potential with Magnetic Resonance Spectroscopy in Lumbricus Terrestris

Abstract

Functional MRI (fMRI) indirectly measures neural activity by detecting the signal change associated with the hemodynamic response following brain activation. In order to alleviate the temporal and spatial specificity problems associated with fMRI, a number of attempts have been made to detect neural magnetic fields (NMFs) with MRI directly, but have thus far provided conflicting results. In the present study, we used magnetic resonance to detect axonal NMFs in the median giant fiber of the earthworm, Lumbricus terrestris, by examining the free-induction decay (FID) with a sampling interval of 0.32 ms. The earthworm nerve cords were isolated from the vasculature and stimulated at the threshold of action potential generation. FIDs were acquired shortly after the stimulation and simultaneous field potential recordings identified the presence or absence of single evoked action potentials. FIDs acquired when the stimulus did not evoke an action potential were summed as background. The phase of the background-subtracted FID exhibited a systematic change, with a peak phase difference of [-1.2 ± 0.3] ×10^-5 radians occurring at a time corresponding to the timing of the action potential. In addition, we calculated the possible changes in the FID magnitude and phase due to a simulated action potential using a volume conductor model. The measured phase difference matched the theoretical prediction well in both amplitude and temporal characteristics. This study provides the first evidence for the direct detection of a magnetic field from an evoked action potential using magnetic resonance.

Introduction

Functional MRI (fMRI) is a widely used technique for investigating in vivo neural activation by indirectly measuring signal changes that arise from the hemodynamic response due to increased metabolic demand. This hemodynamic response lacks spatial specificity as it is localized to the vasculature near the neural activity rather than the neural activity itself and does not have sufficient temporal resolution to provide the timing of the neuronal event. A direct measure of neural magnetic fields (NMFs) with magnetic resonance (MR) can, in principal, provide a more spatially and temporally accurate measurement of brain function and has been the goal of a number of recent efforts.

Investigators initially detected transient magnetic fields using MRI in water phantoms that conducted currents at physiological magnitudes (1-3). Computational modeling predicted the MRI signal change due to NMFs to be much smaller than the signal change attributed to the hemodynamic response (4-7). In vivo studies in human subjects had contradicting results on the detection of the NMF (8-16). One likely reason was that the change associated with in vivo neural activity could not be completely separated from the hemodynamic response. In vitro studies that physically decoupled the neural tissue from the vascular system successfully detected NMFs that appeared to be associated with increased neural activity (17-19), with the exception of a recent study in the isolated turtle brain (20). However, no study has examined the effect of an evoked NMF using an MR method with a temporal resolution that is sufficient to capture the evolution of an action potential. The aim of the current study is to provide definitive experimental evidence for the direct detection of an evoked NMF using fast temporal resolution magnetic resonance spectroscopy (MRS).

We chose the median giant fiber system of the earthworm, Lumbricus terrestris, for the following reasons: First, the removal of the nerve cord from the vascular system is possible. Second, the two major giant axons contained in the ventral nerve cord have been well described in terms of their anatomy and electrophysiology. The lateral giant fibers (LGF) are two electrically coupled axons that function as a single unit. The median giant fiber (MGF) is a single, larger diameter axon that is located between the two lateral fibers (Fig. 1) and was the focus of the current study. Both fiber systems are physiologically involved in the rapid shortening reflex of the earthworm body (21), and activity of axon and muscle potential changes can be identified using extracellular recordings (22). Third, it is possible to evoke a single action potential from the MGF that is uncomplicated by any other event. This includes activity of the LGF, which has a higher threshold of activation and, therefore, can remain quiescent during MGF action potential generation. Finally, action potentials can be elicited from the isolated nerve cord at room temperature and the preparation does not require oxygen gas perfusion. The latter attribute reduces concerns with paramagnetic oxygen affecting the MR signal (23).

Figure 1.

A section through the isolated earthworm nerve cord. The median giant fiber (MGF) separates the two electrically coupled lateral giant fibers (LGF). 9-μm paraffin section stained with hematoxylin.

A previous study employed a volume conductor model and predicted the magnetic field generated by a single evoked action potential from the measured intracellular potential (24). Furthermore, Roth and Wikswo experimentally verified this model by directly measuring the magnetic field using a toroid pickup coil. They measured a Δ300 pT magnetic field from the giant axon system of the crayfish (25), which is physiologically similar to the earthworm giant axon system. Likewise, a Δ300 pT magnetic field was within the range detected in water phantoms (1-2) and gives confidence that the earthworm action potential will be above detection threshold for our methods.

Simultaneous field potential recordings and MRS were performed to measure the voltage and magnetic field associated with a single evoked action potential. Spectroscopy was used in a manner similar to that used by Ernst and Hennig (26) such that the free-induction decay (FID) was examined in the time-domain providing a sub-millisecond temporal resolution. In a previous study, Petridou et al. (19) analyzed the frequency-domain of the FID in spontaneously active organotypic rat brain cultures. They showed a phase difference, and a lesser magnitude difference, at the frequencies of electroencephalographic recordings obtained outside of the MRI. In contrast, the present study measured the FIDs following evoked nerve cord stimulation in a time-locked fashion and examined the differences of the time-domain signal between the presence and absence of an action potential. In addition to this experiment, a volume conductor model was adapted to calculate the FID magnitude and phase change from a previously reported intracellular recording of an earthworm action potential (27). The MRS experiment showed a phase change that was in agreement with the theoretical predictions of the volume conductor model.

Experimental

Earthworm Nerve Cord Preparation

Earthworms (Lumbricus terrestris, Kennesaw Bait Co., Marietta, GA) were anesthetized in 10% ethanol for five minutes, or until the escape reflex was abolished, and submerged in a 0°C dissection chamber containing worm saline (77.0 mM Na⁺, 4.0 mM K⁺, 6.0 mM Ca²⁺, 1.0 mM Mg²⁺, 43.0 mM Cl^-, 26.0 mM SO₄^2-, 2.0 mM Tris, 55.0 mM sucrose, 167.0 mOsm and 7.4 pH) (28). A longitudinal incision was made along the dorsal midline to access the ventral nerve cord. The nerve cord was then isolated from the worm by gently peeling the cord from the ventral epithelial wall and cutting any connective tissue. The worm saline was changed every 15 minutes for the duration of the dissection. Once the nerve cord was removed, it was transferred to 4°C saline and allowed to acclimate to room temperature before being transferred to the chamber for simultaneous field potential recordings and MRS.

A Chamber Allowing Simultaneous Field Potential Recordings and MRS

The chamber to record simultaneous field potentials and MRS was constructed with two compartments linked by a glass capillary bridge (inner diameter = 0.7 mm, outer diameter = 1 mm) and was filled with worm saline (Fig. 2). The first compartment contained a pair of bipolar AgCl hook stimulating electrodes (1 mm separation) and the entrance AgCl hook recording electrode (located directly before the entrance of the capillary bridge). The second compartment contained the exit AgCl hook recording electrode (located directly after the exit of the capillary bridge) and the common reference AgCl electrode. A custom radio frequency transmit and receive microcoil (inner diameter = 1 mm, number of turns = 7, copper wire diameter = 0.405 mm, coil length = 4 mm, enamel insulation thickness = 20 μm) was wound tightly around the glass capillary bridge and fixed with cyanoacrylate. The radio frequency microcoil recorded the FID.

Figure 2.

A chamber allowing simultaneous field potential recordings and MRS. The anterior nerve cord was stimulated with bipolar electrodes at the threshold of action potential generation. This resulted in interleaved events with action potentials and without. Evoked action potentials were first recorded by the entrance electrode and followed by the exit electrode. The difference in arrival time of the action potential between the two electrodes was used to calculate the conduction velocity. The conduction velocity then was used to determine the time at which the action potential arrived at the custom radio frequency microcoil.

The anterior end of the nerve cord was pinned over both stimulating electrodes and gently drawn through the capillary bridge and through the center of the radio frequency microcoil by applying slight suction. The nerve cord fit tightly within the inner walls of the capillary bridge and was turned until the MGF was located at the bottom edge of the capillary's inner diameter. In this way, the MGF was asymmetrically positioned at the bottom extreme of the microcoil's sensitive volume since the MGF is located on the dorsal surface of the nerve cord (Fig. 1). The posterior end of the cord was secured over the exit electrode and the remaining nerve cord was gently stretched and secured over the entrance electrode. All fastening pins were non-magnetic cactus spikes.

Data Acquisition – Electrophysiology

Action potentials were recorded by a Digidata 1320A (Axon Instruments, Sunnyvale, CA) in response to nerve cord stimulation by a pulse generator (Master-8, A.M.P.I., Jerusalem, Israel). A stimulus pulse with a 1.0 ms delay and 0.3 ms width was used. The amplitude of the pulse was controlled by a stimulus isolator (A360 stimulus isolator, World Precision Instruments, Sarasota, FL). The threshold stimulation for action potential generation was determined before each trial by adjusting the stimulus magnitude to elicit action potentials about half the time. The stimulus amplitude was kept constant within a single trial but was reset to the action potential threshold between trials, if necessary. The two recording and one reference electrode measured the extracellular field potential differentially (Differential AC Amplifier, Model 1700, A-M Systems, Sequim, WA). The following parameters were used: 500 repetitions per trial, 10 kHz sampling bandwidth, 2.05 s sampling duration, 4 s inter-stimulus interval, 1 kHz low pass filter and 300 Hz high pass filter. Clampex 9.2 (Axon Instruments) stored the amplified, filtered and digitized electrophysiological time courses.

Data Acquisition – MRS

The chamber was placed at the isocenter of a 9.4 T Bruker Biospin (Billerica, MA) with the nerve cord arranged perpendicular to the static magnetic field. The following parameters were used: 3.125 kHz FID sampling bandwidth, 90° flip angle, 2.0 s repetition time (T_R), 1,000 repetitions per trial and 6 dummy scans. Each experiment lasted 7-10 hours. The transmit and receive microcoil used quadrature detection to simultaneously acquire the real and imaginary components of the FID. During even T_R's, the MRS protocol was initiated without triggering the nerve cord stimulation. This group was used in post-processing steps to correct for phase drift. During odd T_R's, the nerve cord was stimulated at the threshold of action potential generation. Two interleaved subgroups resulted during the odd T_R's due to the all-or-nothing nature of the action potential – action potential (AP) and no action potential (nAP) subgroups.

A radio frequency excitation delay was determined at the start of each trial according to the trial-specific conduction velocity calculated by linearly extrapolating the difference in arrival times of the action potential at the two recording electrodes. This delay was calculated in order to fix the arrival of the action potential at 0.5 ms after the start of FID acquisition (Fig. 3). No magnetic field gradients were used during the experiment. Within a single experiment, if action potentials could no longer be elicited from the nerve cord, then further trials were discontinued. If the nerve cord was healthy for at least seven full trials (with a maximum of 12 trials), then the worm was considered for further data analysis.

Figure 3.

Timing diagram of the simultaneous field potential recordings (black text) and MRS (gray text) experiment. A trigger from the MRS protocol initiated the field recording digitizer and the nerve cord stimulus pulse generator (1.0 ms delay, 0.3 ms width). A trial specific excitation delay was calculated according to the predetermined conduction velocity of the action potential (AP) between the entrance and exit field recording electrodes. The MRS excitation (0.1 ms width) was timed so that the action potential arrived at the radio frequency microcoil 0.5 ms after the start of FID acquisition.

Data Analysis – Electrophysiology

Field potentials were acquired from both recording electrodes for every T_R. Using Clampfit 9.2 (Axon Instruments), each repetition was separated into the components that corresponded to the even and odd T_R's, respectively. The absences of stimulation artifact and nerve cord activity were verified in the even T_R group and were not used for further analysis. The presence or absence of an action potential event was then identified for each odd T_R trace using a Clampfit 9.2 threshold detection program and separated into AP and nAP subgroups, respectively. Finally, the baseline for each trace was corrected to zero.

Data Analysis – MRS

The interleaved MRS time courses were separated into odd and even T_R groups. The phase information was processed by multiplying individual odd T_R FIDs by the complex conjugate of the subsequent even T_R FID. The MRS time courses were then separated into AP and nAP subgroups according to the electrophysiological recordings that were simultaneously acquired. The phase of the FID was calculated and filtered (8-pole Bessel band-pass filter, Clampfit 9.2, Axon Instruments) to remove frequencies outside of the 240 - 437.5 Hz range. This range included physiological frequencies of the action potential and minimized filtering artifacts.

Correction of Action Potential Timing Based on Conduction Velocity

A single action potential reference trace was chosen for each worm and individual action potential electrophysiology traces were shifted in time around it. A “shift value” was accepted when a maximum positive Pearson's linear correlation coefficient was achieved between the two traces. The shift value is the amount of time an individual action potential trace required to achieve maximal alignment with the reference trace. This correction was performed only on exit electrode time courses and the shift values were then used to shift the corresponding FID and entrance electrode time courses. Events that had a correlation coefficient three standard deviations below that of the mean correlation coefficient of a single worm were rejected from further analysis. Once the action potentials were temporally aligned, the mean action potential minimum was used to normalize the electrophysiolgical data.

The nAP subgroup FIDs were also shifted to control for the effects of the action potential alignment process. This was done by assigning shift values to individual nAP FIDs that were randomly sampled from the accepted AP subgroup shift values. Shift values from the AP and nAP subgroups were then compared with a t-test to verify that they were from the same population with at least 95% confidence. The process of shifting the nAP FIDs was repeated 100 times and averaged to ensure reproducibility of the nAP waveform presented in Fig. 4B.

Figure 4.

The averaged time course of the action potential field at the entrance (A) and exit (C) of the capillary bridge and the averaged FID phase (B). Averaged time courses with the presence of an action potential (AP subgroup) are marked in a solid black line while those identified as not having an action potential (nAP subgroup) are marked with a solid gray line. The action potential arrived at the radio frequency microcoil 0.5 ms after the start of FID acquisition. The action potential conduction velocity was used to adjust the electrophysiological time courses in panels A and C to be consistent with the arrival of the action potential at the microcoil in panel B in order to synchronize all traces. In this way, the vertical lines represent the same relative cycle of the action potential that corresponds to the trough of the FID phase. Error bars represent the standard error of the mean and the number (N) of AP and nAP time courses are 16,718 and 12,920, respectively.

Modeled MR Magnitude and Phase Change

The theoretical model of Woosley et al. (24) was used to calculate the magnetic field of the earthworm MGF using a previously reported earthworm intracellular potential recording (27).

$$\text{B}(\rho ,\text{k})=\text{i}{\mu }_0{\text{akI}}_1(\left|\text{k}\right|\text{a}){\text{K}}_1(\left|\text{k}\right|\rho )\left\{\frac{{\sigma }_{\text{i}}}{\beta (\left|\text{k}\right|\text{a})}-\frac{{\sigma }_{\text{e}}}{\alpha (\left|\text{k}\right|\text{a})}\right\}{\varphi }_{\text{m}}(\text{k})$$ Eq. 1

Where ρ is the radial distance from the axon center, k is the spatial frequency, B is the spatial Fourier transform of the magnetic field at distance ρ, μ₀ is the permeability of free space, a is the axon radius, I₁ and K₁ are modified Bessel functions, α and β are defined by the Bessel functions, σ_i and σ_e are the intracellular and extracellular conductivities, respectively, and ϕ_m(k) is the spatial Fourier transform of the intracellular potential (24). The simulated volume had the same radius as the capillary bridge (0.35 mm) and length as the solenoid microcoil (4.00 mm). In a cross-section of the simulated volume, the simulated MGF occupied the bottommost position of the plane and B₀ horizontally crossed MGF in order to match the experimental conditions. The component of the generated magnetic field parallel to B₀ was calculated at varying distances within the simulated volume. The following values were used to calculate the magnetic field of a single action potential: ρ = 36-4,000 μm, a = 35 μm, u = 14.7 m/s, σ_i = 1.70 S/m and σ_e = 2.06 S/m.

The magnitude and phase changes associated with the calculated axonal magnetic field were determined:

$$\varphi (\text{r},\theta ,1,\text{t})=\gamma \int \text{B}(\text{r},\theta ,1,\text{t})\text{dt}$$ Eq. 2

$${\text{Me}}^{\text{i}\Delta \varphi (\text{t})}=\frac{{\text{M}}_0}{\text{V}}\iiint \text{r}\cdot {\text{e}}^{\text{i}\varphi (\text{r},\theta ,1,\text{t})}\text{dr}\text{d}\theta \text{dl}$$ Eq. 3

The resultant phase (ϕ) was determined for each time point (t) of the calculated magnetic field over the sensitive volume of the solenoid radio frequency microcoil (V), where r is the glass capillary inner diameter, θ is the radial angle, l is the length of the microcoil and γ is the proton gyromagnetic ratio. Finally, the MR magnitude (M) and phase change (Δϕ) were calculated in time, where M₀ is the equilibrium magnetization.

Kao and Grundfest's (27) description of spike rise time, peak potential amplitude and time of spike decay to baseline were considered in reconstructing the intracellular recording and was used in our theoretical simulation. The MGF radius was experimentally measured. Isolated nerve cords were fixed in 4% paraformaldehyde for 60 minutes, cut into coronal sections and embedded in paraffin. Blocks were cut at 9 microns, deparaffinized and stained with hematoxylin (GeneTex, Inc GTX73341). The radius of the MGF in the posterior nerve cord was calculated from its circumference using an Axio Scope Observer.A1 and AxioVision 4.7 (Carl Zeiss MicroImaging GmbH, Jena, Germany).

A Pearson's linear correlation was performed between the theoretical and experimental phase time courses. In order for a point-by-point analysis to be performed, several adjustments were made. The sampling interval of the theoretical simulation was adjusted to that of the experimental interval (0.32 ms). The theoretical phase minimum value was preserved during this process and the phase change was set to begin at approximately 0.5 ms. The latter adjustment synchronized the arrival of the theoretical action potential with the experimental action potential, which was calculated to arrive 0.5 ms after the start of FID acquisition.

Results

Measuring an Evoked Action Potential with Simultaneous Electrophysiology and MRS

The nerve cords of six earthworms (59 trials) with a weight of 4.90 ± 0.05 g (mean ± standard error of the mean) before dissection and an average conduction velocity (u) at room temperature of 14.7 ± 0.1 m/s were used. A total of 29,638 electrophysiological traces were obtained, with 16,718 (56%) having an action potential (AP subgroup) and 12,920 (44%) exhibiting no action potential (nAP subgroup).

The field recordings measured activity from the entire nerve cord at the location of the electrode. Stimulus intensity was adjusted to evoke a single action potential at the entrance and exit electrodes (Fig. 4A and 4C, respectively). The absence of other extracellular potentials verified the successful isolation of the MGF action potential from all other cellular components. The temporal evolution of the action potential was consistent throughout the course of each experiment, suggesting that the preparation was stable over the course of a 7-10 hour experiment.

No change could be identified in either the magnitude or the phase of a single FID trace. However, the mean AP and nAP FID traces of all six worms (Fig. 4B) revealed a difference in the phase, but not in the magnitude, that was associated in time with the action potential. The peak trough had a group averaged difference in phase (AP − nAP) of [-1.1 ± 0.3] ×10^-5 at 1.28 and [-1.2 ± 0.3] ×10^-5 radians at 1.60 ms, respectively.

Theoretical Modeling of the MR Magnitude and Phase Change

Two isolated nerve cords, from earthworms weighing 4.55 and 5.09 g before dissection, were used to measure the MGF radius. The MGF radius of the posterior nerve cord was 35.1 ± 0.8 μm, calculated from the circumference of 45 nerve cord sections. Simulation of an earthworm action potential indicated a maximum magnitude change of -2.39 ×10^-9 % (Fig. 5A) and phase change of -0.69 ×10^-5 radians (Fig. 5B) in the FID. The predicted magnitude change was below the detection threshold for our MRS method by at least four orders of magnitude. The measured and simulated phase changes, on the other hand, were of similar magnitudes. The magnitude and phase returned to baseline at the completion of the action potential.

Figure 5.

The MGF transmembrane potential of a single evoked action potential was described by Kao and Grundfest (1957) and used in our theoretical simulation. The theoretical MR magnitude (A) and phase (B) time courses were calculated for a single earthworm action potential. The following parameters were used in calculating the theoretical time courses: ρ = 36-4,000 μm, a = 35 μm, u = 14.7 m/s, σ_i = 1.70 S/m and σ_e = 2.06 S/m.

Correlation of Theoretical and Experimental Results

A Pearson's linear correlation between the simulated and experimental phase changes had a correlation coefficient (r_e) of 0.802 (p < 0.001, N = 17 time points for each trace) (Fig. 6).

Figure 6.

The average subtracted FID phase (AP – nAP, solid black line) correlated well with the simulated phase change (solid gray line) (correlation coefficient (r_e) = 0.802, p < 0.001, N = 17 time points for each trace). The error bars represent the 95% confidence intervals for the subtraction. The adjusted simulation has the same sampling bandwidth and action potential arrival time as the experiment.

Discussion

Our results demonstrate the feasibility of detecting an evoked axonal action potential in the absence of the hemodynamic response. MRS detected a significant phase change, but not a magnitude change, in the FID that corresponded in time with simultaneous electrophysiological recordings of the action potential. The amplitude of the FID averaged phase change was similar to the theoretical phase change determined using a volume conductor model. These experiments provide definitive evidence for the direct detection of an NMF by MRS that agree with the theoretical prediction in both temporal profile and amplitude.

Technical Considerations

There were small variations in conduction velocity within a single trial that resulted in action potentials arriving at the entrance and exit electrodes at slightly different times. The misalignment of action potentials resulted in a blurred group average field potential. This action potential misalignment would have also occurred at the microcoil and would cause a temporal blurring of the average FID. Electrophysiological data from the exit electrode were used to correct for this misalignment by registering each action potential to a reference trace. The single electrode registration was then used to correct for the timing misalignment at the entrance electrode as well as the FID signal. This correction assumed that the conduction velocity was constant between the entrance and exit electrodes. Although there is some evidence of variation in the conduction velocity along the length of the earthworm nerve cord (29-30), action potentials having a fast conduction velocity (1.4 cm/ms) allow for an acceptable approximation over the short distances between the entrance and exit electrode (2.7 cm) and the microcoil center and exit electrode (1.4 cm).

A slow variation was seen in the nAP subgroup average (Fig. 4B). This was most likely due to the current injection applied to stimulate the nerve cord. This effect was controlled for in the present study by keeping the experimental conditions identical for AP and nAP subgroups and examining the difference (Fig. 6).

We reported a theoretical (Fig. 5B) and an adjusted phase simulation (Fig. 6). The adjusted simulation included adjustments based on the sampling interval and the action potential arrival time of the experiment. It was possible to compare the simulation directly to the experimental results following these adjustments. The time course of the adjusted simulation significantly correlated to the experimental phase changes in both temporal characteristics and peak minima. Yet, the experimental phase peak appeared wider in time than the simulation. This difference might be attributed to less accurate correction of the action potential misalignment as the distance increased from the exit electrode.

The effect of the MGF radius on the depth of the theoretical phase minimum was also examined. It is known that the processes of fixing and embedding will cause tissue shrinkage (31-32). Although the degree of shrinkage for this specific tissue is not known, the radius of the MGF was reported to be between 34 and 47 μm with the radius decreasing from anterior to posterior (29). An approximately linear relationship between the predicted phase minimum and the MGF radius was observed across this range. For every 2 μm increase in the radius, the phase minimum deepened by -0.09 ×10^-5 radians.

Lastly, we did not consider the magnetic field that existed inside the MGF in the theoretical modeling. Previous studies did not validate this component of the magnetic field with experimental results and it was omitted to achieve a more conservative model. The magnetic field inside the MGF would cause only a slightly larger simulated FID phase change as the omitted volume accounts for only 1% of the total volume seen by the microcoil.

Volume Conductor Model

Roth and Wikswo compared an experimentally recorded axon magnetic field (25) to one that was predicted by the volume conductor model (24). Their measured magnetic field showed significant consistency with the predicted in both the magnetic field magnitude and temporal evolution. In addition, the toroid detector from which Roth and Wikswo recorded the axon magnetic field was similar to the radio frequency microcoil detector in our experiment. Both types of detectors average the magnetic field over the circumference and length of the detector. For these reasons, we had confidence that an adaptation of the volume conductor model would correctly predict the MR magnitude and phase change following an evoked action potential using our methods.

The volume conductor model predicts the total axon magnetic field from the individual contributions of the extracellular and intracellular currents, I_e and I_i, respectively. It was previously determined that the magnetic field due to I_e was orders of magnitude less than the magnetic field due to I_i (24). In this way, a good approximation of the total axon magnetic field can be calculated by considering only the contribution of I_i. The intracellular current conducting longitudinally through a defined axonal compartment can be characterized as an equivalent current dipole (Q_i) and is a relevant measure of brain activity that is often used in the discussion of magnetoencephalographic and electroencephalographic measurements. The equivalent current dipole is a vector quantity described by the equation Q_i = I_iLdr (7, 33), where L is the MGF length within the microcoil (4 mm) and dr is a unit direction vector. The volume conductor model was extended to estimate I_i from the same MGF intracellular potential that was previously implemented to approximate the FID phase and magnitude changes (27). I_i was estimated to have a maximum change of -247.7 nA in time, which corresponds to an equivalent current dipole of -1.0 nAm within the length of the microcoil.

Symmetrical vs. Asymmetrical Distribution of the NMF

Chow, et al. (2006) examined the phase changes that resulted from a symmetrically and asymmetrically distributed NMF within a volume of interest. They determined that the magnetic field must be asymmetrically distributed in the volume for a phase change to be detected, since a net zero phase change resulted from a symmetrically distributed magnetic field (15). A solenoid microcoil with an asymmetrically positioned axon was used in our experiment and theoretical simulation. The earthworm nerve cord was tightly contained within the inner walls of the capillary bridge and the MGF was located at the bottom edge of the capillary's inner diameter in our experiment. From this position, an adaptation of the volume conductor model predicted the component of the MGF magnetic field that was parallel to B₀. In this way, the MGF bipolar magnetic field was asymmetrically distributed in the volume of interest and resulted in a detectable phase change.

A circular surface microcoil positioned above the capillary bridge and perpendicular to the MGF is an alternative method in investigating the phase change associated with the axon NMF. A coil of this design has diminishing sensitivity to the proton signal as the distance from the surface coil increases and permits an asymmetric sensitivity to the phase change caused by the axon NMF. In this way, a surface microcoil design may enhance the detectability of the phase change, since it is more sensitive to a single pole of the NMF, in contrast to our solenoid design that is equally sensitive to both poles.

Physiology of the Phase Change

The shape of the FID phase difference in both the predicted and measured time courses is due to the opposing sodium and potassium currents that occur during an action potential. The action potential begins with the depolarizing stimulus at the anterior end of the MGF. Depolarization opens fast acting voltage-gated sodium channels and allows an inward flux of sodium ions into the axon. This inward current creates a magnetic field that temporarily opposes the external magnetic field resulting in a decrease in the net magnetic field and a drop in the FID phase. The voltage-gated sodium channels quickly inactivate and prevent the flux of new sodium ions from entering the axon. At a similar time that the sodium channels inactivate, slower activating voltage-gated potassium channels open and allow potassium ions to leave the axon. This opposing outward current reverses the magnetic field generated by the axon and subsequently increases the net magnetic field and returns the FID phase to baseline. This temporal evolution on a sub-millisecond scale requires an MR method that has sufficient temporal resolution as is demonstrated by our experiment.

The simulated phase change in Fig. 6 shows two points at times 3.20 and 4.16 ms to be outside of the experimental phase change confidence intervals. These time points are above zero radians, which suggest that the refocusing magnetic field generated by the axon was stronger than the theoretically predicted magnetic field. A stronger refocusing magnetic field may be due to a greater outward potassium current that corresponds to a hyperpolarization of the axon in the final stages of the action potential. The intracellular recording of Kao and Grundfest (27), used in our theoretical simulation, did not have an axon hyperpolarization component and may be due to differences in the physiological saline solutions of each experiment. The extracellular saline solution of our experiment was consistent with the ionic composition measured in the coelomic fluid of the earthworm (28), while that of Kao and Grundfest was not. This difference could result in a change in the inward and outward current characteristics of each experiment. However, the intracellular recording of Kao and Grundfest is an appropriate approximation because the phase change associated with the hyperpolarizing component of the action potential will contribute very little to the total magnetic field change. This is evident in our observations as other simulated phase points between 2.88 and 5.12 ms are within the 95% confidence intervals of the experimental phase change.

Lorentz Effect Imaging (LEI)

LEI and its application to the direct detection of magnetic fields was shown in current carrying phantoms (34-35) and in vivo (36). The Lorentz force is the spatial displacement of a current carrying conductor in the presence of an external magnetic field that is equal to the cross product of the current vector and the magnetic field. MR contrast arises from the Lorentz force by the spatially incoherent displacement of water protons caused by the conductor's compression of the surrounding elastic medium or by the bulk movement of water by ionic current flux (37). LEI is sensitive to this displacement with the use of time-locked oscillating magnetic field gradients that cause a loss of phase coherence and a decrease in the MR signal magnitude. The Lorentz effect occurs at a time simultaneous to the electrical activity and can confound our study.

In our case, the axon displacement due to Lorentz force should not lead to a significant change in signal phase because 1) the absence of time-locked gradients and 2) the acquisition of NMR signal from the rigid capillary. Applied magnetic field gradients, including spatial encoding gradients, were absent in our experiment. In addition, the close correlation of the simulated to the observed FID phase change provides further evidence that the Lorentz forces may contribute a phase change that is significantly less than the change associated with the axon NMF. However, a displacement of the axon towards the center of the capillary may reduce the asymmetry in our set up and produce a more symmetrical magnetic field in the volume of interest, resulting in a reduction in the observed phase change. Based on experimental data of Truong, Wilbur and Song (2006) and assuming the worse case scenario where the cord movement is not restricted by the rigid capillary, our estimated axon displacement is 5 μm and the estimated reduction in the depth of the phase minimum is +0.01 ×10^-5 radians. This number is much less than the observed and simulated peak depths of -1.2 ×10^-5 and -0.69 ×10^-5 radians, respectively.

Extrapolation to in vivo Studies and Application

Previous studies have measured a magnitude, but not a phase, change in the MRI signal following visual stimulation of the human optic nerve at 1.5 T (14-15). However, a similar study failed to replicate these findings at 3 T and attributed this failure to increased magnetic susceptibility artifacts at the higher field (16). We have demonstrated through experiment and simulation that the phase of the MR signal is more sensitive to evoked axonal magnetic fields and that the effect of the axonal magnetic fields on the MR signal takes place on a millisecond timescale. The latter aspect would call for MR studies with a high temporal resolution, as demonstrated here. For in vivo studies along this line, spectroscopic imaging with the examination of the time-domain data may be used.

The volume conductor model is also able to predict the intracellular membrane potential from the measured magnetic field (24-25). In combination with our method to detect NMFs, in vivo axon function can be measured following activation. Such non-invasive study of neural currents localized to specific nerve fiber bundles could be developed further to establish characteristics of action potential propagation in normal and disease states, such as multiple sclerosis. However, confounds attributable to the hemodynamic response to the nerve activation, which was absent in our experiment, would need to be addressed for application to in vivo study.

Conclusion

Direct detection of a single evoked axon magnetic field in the earthworm was demonstrated using simultaneous MRS and electrophysiology in the absence of the hemodynamic response. This experiment was validated by comparing the measured FID phase change with an adaptation of Woosley et al.'s volume conductor model (24). We also showed that the phase of the FID returned to baseline at the cessation of the axonal event and that a method with a high temporal resolution is required to resolve such transient neural magnetic fields, therefore validating MRS as an alternative method for the direct detection of neural activity.