Oscillatory dipoles as a source of phase shifts in field potentials in the mammalian auditory brainstem

Abstract

A popular model of binaural processing, proposed by Jeffress (1948), states that external interaural time delays (ITDs) are compensated by internal axonal delays allowing ITD to be spatially represented by a population of coincidence detectors in the medial superior olive (MSO). Isolating single-neuron responses in MSO is difficult because of the presence of a strong extracellular field potential known as the neurophonic, so that few studies have tested Jeffress's key prediction. Phase delays in the nucleus laminaris neurophonic in owls have been observed and are consistent with a Jeffress-like model. Here, we recorded neurophonic responses in cat MSO to monaural tones at locations along its dendritic axis. Fourier analysis of the neurophonic was used to extract amplitude and phase at the stimulus frequency. Amplitude, as a function of depth, showed two peaks separated by a dip. A half-cycle phase shift was observed at depths close to the dip, over a wide frequency range. Current source density analysis for contralateral (ipsilateral) stimulation shows a current source close to the neurophonic amplitude peak and a sink a few hundred micrometers ventromedially (dorsolaterally). These results are consistent with a dipole configuration: contralateral (ipsilateral) excitation causes a current sink at the ventromedial (dorsolateral) dendrites and a source at the soma and dorsolateral (ventromedial) dendrites. Incorporating these results in a dipole model explains the phase and amplitude patterns observed. We conclude that the half-cycle phase shift is consistent with a current dipole, making it difficult to derive measurements of axonal delays from the neurophonic.

Figure 1.

Measurement and Fourier analysis of the neurophonic. A, A 1200 Hz tone played to the contralateral ear (blue line) and the resulting neurophonic response (black line) at a penetration depth of 1450 μm. B, The amplitude spectrum of the neurophonic response shown in A. There is a strong component at the stimulus frequency (1200 Hz) and a weaker harmonic component (2400 Hz). C, The Fourier amplitude at the stimulus frequency is plotted as a function of stimulus frequency for contralateral stimulation at 1450 μm. There is broad frequency tuning in the neurophonic response. D, The analysis shown in C is repeated for a range of penetration depths for contralateral stimulation, showing clear tuning with depth. The red line indicates the depth at which the maximum amplitude was measured. E, The analysis shown in D is repeated for ipsilateral stimulation. The green line indicates the depth at which the maximum amplitude was measured.

Figure 2.

Amplitude dips and phase shifts in the neurophonic. A, B, The analysis as shown in Figure 1D is replotted for a different dataset for contralateral (A) and ipsilateral (B) amplitude over a range of frequencies (1400–1600 Hz, indicated by different shades of red and green). C, D, Same electrode penetration as A and B but for a lower range of stimulus frequencies (400–600 Hz). E, F, Phase measurements, derived from Fourier analysis of the neurophonic at each depth, for contralateral (E) and ipsilateral (F) stimulation. The dots on the upper line mark individual measurement depths (50 μm intervals). Zero phase was taken as the phase of the lowest stimulus frequency at the first depth measurement. G, H, Same as E and F but for a lower range of frequencies.

Figure 3.

Neurophonic amplitude and phase across five electrodes in one MSO. A–E, Neurophonic amplitude as a function of depth for ipsilateral (green) and contralateral (red) stimulation for a range of frequencies (1100–1500 Hz). F–J, Corresponding phase values. In each panel, zero phase for both ipsilateral and contralateral stimulation was taken as the phase of the lowest stimulus frequency at the first depth measurement. K–O, Difference in phase calculated by subtracting ipsilateral phase from contralateral phase.

Figure 4.

Histological reconstruction of electrode tracks penetrating the MSO. A, The amplitude of the neurophonic to contralateral stimulation is shown as a function of frequency and depth for each electrode. The amplitude color code is indicated by the calibration bar. B, The electrodes were coated with fluorescent dye allowing tracing and reconstruction of the electrode tracks (red). The outlines of MSO and LSO are shown in blue and green. D, Dorsal; V, ventral; L, lateral; R, rostral; C, caudal.

Figure 5.

Composite photograph of stained section and electrode track marked by electrolytic lesions and fluorescent dye. A, cresyl violet staining revealing the principal nuclei and two lesions (L1, L2). Superimposed is the fluorescent dye (DiI) of the electrode track, extracted from images taken with a fluorescence microscope from a number of sections before staining. MSO, Medial superior olive—thick lines indicate borders of nucleus; MNTB, medial nucleus of the trapezoid body—thick lines indicate borders of nucleus; LSO, lateral superior olive; TB, trapezoid body; PT, pyramidal tract. B–G show data from the electrode track in A. Red, Contralateral data; green, ipsilateral data. The positions of L1 and L2 are marked by the vertical dashed lines. The extent of the MNTB and MSO, determined from the section, are marked by the gray bands. B, C, Amplitude depth profiles for contralateral and ipsilateral stimulation at 650 and 700 Hz. D, E, Corresponding phase depth profiles. F, G, Current sink and source locations are revealed as minima and maxima in the change in transmembrane current (ΔI_m). H–S, The analysis shown in B–G is repeated for lesions and neurophonic recordings made in the MSO of two additional cats.

Figure 6.

Interpreting the neurophonic in terms of a dipole field. A, The gray object represents an MSO neuron with excitatory inputs from contralateral spherical bushy cells (SBC) on the medial dendrite and excitatory inputs from ipsilateral SBC on the lateral dendrite. Inhibitory input from the contralateral MNTB and the ipsilateral LNTB is present on the soma. The pluses and minuses show the direction of change in intracellular (white) and extracellular (black) potential when an EPSP (SBC input) or IPSP (MNTB or LNTB input) is elicited. B, The charge dipole equation (Eq. 4) can be used to calculate the potential (ϕ) at any given location attributable to a dipole with equal and opposite charges (q) at each pole. ε is the permittivity. C, The gray objects represent a two-dimensional stack of MSO neurons. Contralateral stimulation on the excitatory input on the medial dendrite causes a localized current sink and a corresponding current source near the soma. The current source and sink result in a dipole field. Note that the inhibitory input would also contribute to this source–sink configuration. Here, we used a two-dimensional stack for ease of illustration, but in practice we assume that this pattern will be repeated in the z direction creating a three-dimensional block of orderly arranged MSO neurons. These current dipoles are represented as the black pluses and minuses and the direction of extracellular current flow is marked by the gray line with the arrow. The colored contours show the resulting dipole field (i.e., the equipotential lines calculated by modeling each current dipole using Eq. 5 and summing their individual contributions). D, The amplitude of the potential of the dipole field at the locations marked by the purple and black dashed lines in C are both shown. Note that potential amplitude distributions are almost identical even though their y positions are different. This simulation gives weight to the assumption that the potential is relatively stable in the y and z directions, as we also assume that this stacked arrangement of MSO neurons will be repeated in the z direction. Thus, a reasonable estimation of the transmembrane current can be calculated by simply taking the second derivative in the x direction (see Eqs. 2, 3). E, Phase of the dipole field at the two locations marked by the dashed lines in B. As with the amplitude distributions, the phase is identical at both y locations.

Figure 7.

CSD analysis of the neurophonic revealing current sources and sinks. A, The neurophonic response to contralateral stimulation (1000 Hz) was averaged over one stimulus cycle for all depths. The dots (bottom trace) indicate individual sample points. B, Same analysis for ipsilateral stimulation. C, The averaged contralateral neurophonic shown in A is replotted as a function of depth. D, Taking the second spatial derivative of the contralateral averaged neurophonic gives an estimate of the transmembrane current (I_m) during one complete stimulus cycle (gray lines). The change in transmembrane current (ΔI_m, thick black line) is calculated by finding the point in the cycle with the maximum transmembrane current (I_mMax, red line) and subtracting from this the transmembrane current one-half a cycle later (I_mMax+π, red line). The red lines indicate the same point in the cycle in A and C. The same analysis is applied in E and F for the averaged ipsilateral neurophonic shown in B. I_m for contralateral (D) and ipsilateral (F) stimulations replotted as a function of stimulus cycle for each depth in G and H.

Figure 8.

Location of current sink–source pairs. A–C, Amplitude profiles for contralateral (red) and ipsilateral (green) stimulation at 500, 1000, and 1500 Hz. D–F, Corresponding phase profiles. The gray boxes indicate contralateral half-cycle phase shift. G–I, Estimated contralateral transmembrane current (I_m) calculated by taking the second spatial derivative (i.e., along the depth dimension) of the averaged neurophonic. J–L, Estimated ipsilateral transmembrane current. M–O, Corresponding changes in transmembrane current (ΔI_m) are calculated by subtracting I_mMax from I_mMax+π, where I_mMax is the maximal I_m depth profile in J–L and I_mMax+π is the I_m depth profile occurring one-half a cycle later. The thick gray vertical lines indicate the depths of the contralateral sink–source pair, derived from the largest minima and maxima of the contralateral ΔI_m. The thin gray vertical lines indicate the depths of the ipsilateral sink–source pair, derived from the largest minima and maxima of the ipsilateral ΔI_m.

Figure 9.

Location of current sink–source pairs for a different penetration. See Figure 8 for explanation. The arrows in M–O indicate locations of two current sinks.

Figure 10.

Simple dipole model of the neurophonic. A, The gray lines show transmembrane current (I_m) calculated from the contralateral response using CSD analysis. The location of three sink–source pairs are marked by vertical orange and black lines and the phases of I_m at the pole indicated by the black line are shown to the left of the dipoles. The inset plots I_m for one cycle at the depths of the first sink–source pair (orange and black lines). A sine function is fitted to get the phase measurement. B, C, Amplitude and phase profiles of the modeled neurophonic resulting from one, two, and three dipoles (light blue, dark blue, and magenta, respectively). Model parameters were extracted from the CSD analysis in A. D, E, Actual amplitude and phase profiles measured from the data shown in A, which are reasonably well matched by the model data for three dipoles. Importantly, these three dipoles are situated at different spatial locations and differ in phase.

Figure 11.

A configuration of dipoles at different spatial locations and with different phases is necessary to match the measured neurophonic phase and amplitude profiles. A–F, Amplitude and phase profiles resulting from one, two, and three dipoles (light blue, dark blue, and magenta, respectively) are shown for the following configurations: at the same spatial location and with the same starting phase (A, B), at different spatial location and with the same starting phase (C, D), and at the same spatial location and with different starting phase (E, F).