Stimulus physics

4. Discussion

perpendicular to the fish surface (c.f. Fig. 28d). Thus, the water flow on the fish surface corresponded to the particle trajectories as seen in front view (view parallel to the axis of vibration, Fig. 45c). The particle trajectories radiated from the axis of vibration.

Due to the axial symmetry of the flow field around a dipole source, the particle velocities can be described by the radial, and a tangential, , velocity components according to (Kalmijn, 1988):

2 3

2 cos θ cos ω

3

r2 cos θ sin ω

3

r3 cos θ cos ω (19)

‐ ³

2 _r² sin θ sin ω ³

2 _r³ sin θ cos ω (20)

where = wave number = ω/ , ω = 2 , = dipole frequency in Hz, = speed of sound, = dipole radius, = radial distance between the center of the sphere to the point of interest, θ = angle of radiation, = amplitude of axial source velocity, = time. However, particle velocities can also be expressed as the velocity components parallel to the X-, Y- and Z-axis as defined for the experimental setup (c.f. Fig. 28d).

Fig. 45 Stimulus hydrodynamics (a-b) Fluid particle trajectories in the vicinity of a dipole source.

Axis of vibration marked in green. Coordinate axes correspond to the axes definition of the experimental setup (c.f. Fig. 28d). Black arrows in a illustrate the point of view in b respectively c. (d-g) Calculated particle velocity component along the X-axis in the X/Y plane. Velocity is color coded, warmer colors represent higher velocities. d = distance from the dipole source, r = dipole radius, U = axial dipole velocity, pd = distance between the centers of the 2 spots, pw = width of the spots (spot edges defined as 80 % of the maximum).

3 mm above the fish surface, the receptive field should thus be modelled by calculating the particle velocity in X-direction in the X/Y-plane (perpendicular to the axis of vibration) 3 mm away from a dipole source vibrating in Z-direction.

The resulting calculated receptive field (Fig. 45d) reflects the measured receptive fields quite well: In the X/Y-plane 3 mm away from a dipole source the particle velocity component in X-direction is increased at two distinct spots left (X-) and right (X+) of the axis of vibration (Z-axis, X and Y = 0 mm, c.f. Fig. 45d-g).

The distance between the centers of the two spots is 3 mm. That is comparable to the measured receptive fields where the distance between the centers of the two spots ranged from approx. 2 mm (c.f. Fig. 37) to 4.5 mm (c.f. Fig. 32).

Also the width of the spots compares well between the calculated flow field and the measured receptive field. Slight variations in shape, size and symmetry might be explained by the assumptions of the model: e.g. the axis of vibration might not have been exactly perpendicular to the curved surface of the fish. Due to methodical restrictions the distance between fish and the dipole source might not always have been 3 mm. Furthermore, the equations mentioned above assume a spherical dipole object, not a cylindrical object as used in the present study. Also, the model does not consider the hydrodynamic interaction between the flow and the fish surface. However, the similarity of the calculated and the measured receptive fields confirms the assumption that the measured receptive fields are, in fact, receptive fields of SNs. The neuromasts most likely were located between the two spots of highest sensitivity and their axis of best sensitivity spanned between the centers of the spots.

Calculating the flow fields is not only important for the comparison with measured data but also helps to understand the stimulus characteristics. Fig. 45e illustrates the flow field further away (4 mm) from the dipole. With increasing distance from the center of the dipole d the width of the spots of increased flow velocity pw and the distance between the centers of the spots pd increases.

Thus, larger receptive fields might have been caused by positioning the dipole source further away from the fish surface. In contrast, varying the dipole radius r or the amplitude of the axial dipole velocity U does not influence the shapes of the calculated flow fields (c.f. Fig. 45f,e). Note that the plotted data is normalized. Of course, e.g. with increasing distance to the dipole source (d)

particle velocities decrease. An increased axial dipole velocity (U) overall leads to increased particle velocities. However, the calculation of the flow field reveals that – as long as the neuromasts are stimulated within their dynamic amplitude range and as long as the nervous activity is normalized, too – the measured receptive fields only depend on the distance and orientation of the dipole source but not on its radius or axial velocity.

4.1.4. Scan procedures

The results obtained in the line scan procedures differ from the results obtained in the raster scan procedures. Instead of the distinct two spot receptive fields recorded in the raster scans, the line scans resulted in diffuse, inhomogeneous receptive fields (c.f. Fig. 35 and Fig. 36). This cannot be explained by the model described above. Also it is unlikely, that the inhomogeneous fields are caused by morphological features of the SNs of Anoplarchus. The only raster scan performed on Anoplarchus which, unfortunately, could not be finished, also shows the two spot receptive field characteristics observed in goldfish. Hence, we assume that the inhomogeneous receptive fields are caused by the line scan stimulus. Although the dipole source was moved slowly, unintended vibrations of the entire setup and thus of the dipole source might have stimulated the neuromasts and thus masked the applied dipole stimulus. Another possible disadvantage of the line scan method is the lack of a sharp stimulus onset. The dipole source slowly approached the receptive fields, resulting in a ramp-like stimulus. For phasic and phasic-tonic units such stimulus is much weaker, compared to the sharper stimulus onsets in the raster scans. Lastly, the quality of the recordings was worse in Anoplarchus. A worse spike discrimination might have been one reason for the inhomogeneous receptive fields, too. Overall, the line scan procedure does not seem to be a suitable method to precisely determine receptive field properties.

The best scanning method would, however, be to randomly approach different

neuronal activity. Repeating the scan with different scanning directions and averaging the results could partly compensate for this disadvantage. Depending on the size of the scanned field and the raster resolution, the raster scan procedure still could take up to two hours, a time that bares the risk to lose a unit. The line scan procedure was therefore designed to further decrease the scanning times by avoiding long times between raster scan pulses. As this method did not turn out to be suitable, we suggest that the raster scan procedure is the method of choice for potential future experiments.

4.1.5. Conclusion

Scanning the receptive fields of SNs in goldfish did not uncover new unexpected features of these sensory structures. The results confirmed the expected model of how SNs respond to a dipole stimulus in a spatial context. Nevertheless, our data stands out from earlier studies on receptive fields of lateral line units.

Measuring the receptive fields is commonly used to characterize the properties of lateral line units in the PLLN (Caird, 1978; Coombs et al., 1996, 1998; Goulet et al., 2008; Künzel et al., 2011), the medial octavolateral nucleus of the medulla in the brainstem (Caird, 1978; Bleckmann et al., 1989b; Coombs et al., 1998;

Künzel et al., 2011) and the torus semicircularis in the midbrain (Engelmann &

Bleckmann, 2004; Voges & Bleckmann, 2011; Meyer et al., 2012). However, most of the studies mentioned above only determined the size of the receptive fields in one dimension. Bleckmann et al. (1989) and Voges & Bleckmann (2011) determined the 2-dimensional shape of the receptive fields. The spatial resolution of these receptive field scans and the overall number of data points was low (e.g.

approx. 50 data points and a spatial resolution of 5 mm in Voges & Bleckmann (2011)). The results of these studies were hard to explain by a simple model, which might be due to central integration mechanisms. 2-dimensional receptive fields of peripheral lateral line units have never been determined before. The present study not only fills this gap. The 2-dimensional images provide a much higher spatial resolution compared to the studies mentioned above (up to 400 data points and a spatial resolution of 0.2 µm) and the data fits the assumed receptive field model.

The data on the receptive fields of SNs of goldfish was obtained as a by-product in the preliminary tests of the Xiphister study. In fact, the low sample size should