The study of exotic sensory systems, such as electroreception in fish, echolocation in bats, and sound localization in owls, has revealed general principles of neuronal organization that are frequently present but more difficult to discern in other animals and humans. Weakly electric fish are an exceptional model system to study sensory acquisition, neuronal information processing, and sensory-motor integration. These animals detect nearby objects by sensing object- induced distortions in their electric organ discharge (EOD) electric field (reviewed in Bastian 1994; Carr 1990; Bullock and Heiligenberg 1986). Sensory electroreceptor organs, distributed across the fish's body, are acutely sensitive to small changes in transdermal voltage, which constitute an "electric image" of the object. We have investigated how electric fish might identify object features, such as size, shape, location, and impedance, from the object's electric images (Fig. 1). For example, how might a fish differentiate between a large, distant object and a small, nearby one; or a large object with impedance similar to water, and a small object with greater impedance difference? To resolve these questions, we constructed detailed and accurate simulations of the electric images of spheres and ellipsoids placed in EOD fields (Rasnow 1996). Electric images were computed analytically by assuming the measured EOD field was uniform around the object. Measured electric images of large metal spheres verified the simulations, and revealed their robustness to this assumption. In this paper, we summarize the algorithms for electrolocation presented by Rasnow (1996) and propose a plausible neural implementation of these algorithms in the fish's hind and midbrain.Figure 1. Understanding how fish electrolocate objects can be thought of as a problem of determining a mapping between two abstract feature spaces: a sensory electric image space internal to the animal, and the external environment. Listed here are what we consider some of the most important features or dimensions of these spaces. In the abstract language of this figure, our first goal is to constrain and sort out the nature of this mapping.
Electric images of small objects are broad 1-3 phase "bumps" in the transdermal potential across the body and contain only low spatial frequencies (Rasnow 1996; Bacher 1983; Heiligenberg 1975). As such, they can be described by just a few parameters. The location of the main image peak approximately coincides with the latitude and longitude of the object, and thus unambiguously reveals two of the object's 3- dimensional coordinates. Determining object distance from an electric image is not as simple because it not related to single image parameters listed in Fig. 1. For example, the magnitudes of electric images are strongly dependent on object distance because of the rapid attenuation of the fish's electric field with distance from its body. But image magnitude also depends on other parameters such as object size, shape, and impedance. The first hint of a simple solution to disentangle these variables came from analyzing electric images of conducting spheres. We found that the relative width of the image peak (i.e., a parameter like the standard deviation of a Gaussian function) depends solely, and linearly, on the distance from the skin to the sphere's center. Object size can now unambiguously be solved for using the distance and peak amplitude of the image, which is proportional to the sphere's volume. What if the sphere is not a conductor? A sphere of radius a perturbs the potential at position r from its center by (Rasnow 1996):
where are the resistivity and dielectric constants of the object and water (subscripts o and w respectively); is the angular frequency of the unperturbed EOD field at the object, E; and . This is the equation of a dipole with a complex amplitude and phase shift. The right-hand term reduces to unity for ideal conductors and to -1/2 for ideal insulators. If the EOD field is oriented normal to the fish's skin, then conductors increase the current and transdermal potential directly below them, and insulating spheres decrease the transdermal potential by half the amount of a conductor of the same size. Objects with intermediate resistivities and dielectric strengths produce images with phase shifts between conductors and insulators and lesser magnitudes than conductors.
Since object and water impedances affect electric images globally (i.e., by multiplying them by a complex constant that is independent of position), the distance to the object's center is still proportional to the relative width of the image and thus can be determined unambiguously. However, object size and impedance are confounded unless the fish uses polarity and phase information to separate a3 from the magnitude of the right-hand term in the above equation. Electric fish are extremely sensitive to EOD phase and possess specialized electroreceptors that encode minute phase shifts (Kawasaki et al 1988; Emde 1992).
What if the object is not spherical? Figure 2 shows the simulated electric images of spheres and two orientations of ellipsoids with eccentricity of 2. The relative width of the images increases with object distance, however the rostrocaudally compressed ellipsoids have narrower images and the rostrocaudally expanded ellipsoids have wider images than corresponding spheres. Interpreting the first ellipsoid images (Fig. 2A) according to our algorithm for spheres results in the perception of a smaller and nearer sphere (because the image is narrower and has larger peak amplitude). Likewise, the second ellipsoid images (Fig. 2B) correspond to larger and more distant spheres. Although globally incorrect, these inferences are consistent with spheres whose proximal surfaces to the fish approximately correspond with the proximal surfaces of the actual ellipsoids.
Figure 2. Electric images of conducting spheres and ellipsoids in the midplane of Apteronotus leptorhynchus, for 4 object distances (insets). Object centers are 1.2, 1.4, 1.9, and 4.2 cm lateral of the skin, and the spheres have 1 cm radii. The electric images have been averaged (RMS) over the EOD cycle.
The EOD field attenuates rapidly with distance from the fish, causing the electric image amplitude to attenuate with distance to the negative third to fifth power (Rasnow 1996). Therefore, the image of an object will be dominated by the nearest or proximal parts of the object. The resulting distortion, somewhat analogous to perspective distortion inherent in wide-angle optical lenses, might make it difficult for a fish to discriminate between the ellipsoid in Fig. 2A and a smaller, nearer sphere. However, phase information might resolve this ambiguity, and provide object shape information from electric images. We have shown that the electric field vector changes direction during the EOD cycle (Fig. 3; Rasnow & Bower 1996). The electric image of a conducting ellipsoid will be largest when the EOD field is parallel to the major axis, because the ellipsoid short circuits a larger region of water. The variation of electric image amplitude with EOD phase could thus reveal object asymmetry, crudely analogous to how an object's shadow shape depends on illumination angle. Exploratory behaviors such as tail bending could also provide shape information by changing the field orientation. Finally, differences in the ELL maps could also convey information about object shape and eccentricity (see below).
Figure 3. The electric field vector is shown here along four lateral lines in the midplane of Apteronotus leptorhynchus. The initial phase of the field vector is shown as a line from each measurement point (dots). At subsequent times, just the tip of each field vector is traced. At any phase, the field is represented by a vector from the measurement point to the curve (inset shows 4 example phases). The field vectors rotate counterclockwise in the caudal part of the body, whereas rostral of the gill, only the magnitudes and sign, but not the direction, changes during the EOD cycle.
The proposed mappings between electric image and object feature spaces, summarized in Fig. 4, are only a first guess and working hypothesis of how weakly electric fish might process electrosensory information to perceive objects. The corresponding algorithms are capable of identifying the major features of small, isolated, stationary objects near a stationary fish. We have only begun to explore their robustness in the fish's more complex environment, where potentially confounding factors include multiple active and passive sources; large and heterogeneous, non isotropic objects; and EOD envelope modulations from relative motion of the fish and objects. Although some of these confounding factors can be isolated by simple temporal or spatial filtering, more substantial modifications of the algorithms may be necessary to resolve other ambiguities. Note that these simple algorithms ignore a vast amount of electrosensory information, for example, correlations within temporal sequences of electric images generated as the fish moves. Given the complex repertoire of behaviors electric fish use for exploration, it is evident that electrolocation involves additional algorithms to those presented here.
Figure 4.This constrained mapping between sensory electric images and the external environment is sufficient to locate and identify small homogeneous objects. It remains to be tested whether and how electric fish might implement these algorithms with their neural hardware.
For the proposed algorithms to be involved in electrolocation, they must have a plausible neural implementation in the fish's nervous system. We propose here one such mapping of the computations discussed above onto the neural network in the electric fish brain. Figure 5 summarizes the Gymnotiform fish's electrosensory pathways and central processing structures (Carr & Maler 1986). The electrosensory lateral line lobe (ELL) receives the raw peripheral field encoded by the transdermal electroreceptors. The first processing step we believe may be to extract the object's perturbation or image. This could be done in ELL by the descending feedback and gain control (labeled 1), which is capable of subtracting out the expected EOD (Bell et al. 1997; Bastian 1996). The algorithms suggest that relative image size should be the next calculation. Cells in the ELL maps have center-surround type receptive fields. Convolving the object's image with center-surround spatial filters, and thresholding, results in an area of activity proportional to the image size (labeled 2). The object distance can be calculated by integrating over this active area. Such integration could be achieved within the convergent projections from ELL onto higher areas (labeled 3). Although ELL projects to both the dorsal preeminential nucleus (PEd) and the torus semicircularis (TS), the former is part of the feedback loop to compute object images in ELL. Therefore this scenario predicts that object distance may first be represented unambiguously in the amplitude pathway input layers of the torus. In particular, input layer neurons might respond similarly to large and small spheres centered at the same positions (and perhaps even ellipsoids at the corresponding locations), even though the electroreceptor responses in these cases would be quite different. Bastian (1986) found neurons in the optic tectum that selectively responded to particular object distances. Finally, knowing object distance is a prerequisite (or corequisite) in the model for deconfounding size, impedance, and shape, so these features would first appear in torus and higher areas.
Figure 5. On this figure of electrosensory pathways in the Gymnotiform fish, we have labeled regions where the proposed computations for high frequency electrolocation might be implemented. 1. Extraction of the object image, by subtracting expectation conveyed through descending feedback to ELL. 2. Convolution of the electric image with center- surround receptive fields and thresholding activates a region of ELL proportional to the image's relative width. 3. Integrating over the ELL surface, in the convergent projections to the torus semicircularis (TS), measures the image size, which is proportional to object's distance. 4. Object size, shape, and higher order features could be computed in the torus, optic tectum (OT), and higher areas.
Although somewhat speculative, we believe the above proposals may be a useful working hypothesis for interpreting and further exploring parts of the electrosensory nervous system. In addition to providing a functional model for electrolocation, they lead to several testable predictions, especially in higher and more complex parts of the nervous system where object features may begin to emerge unambiguously. For example, tuning to object-center distance should first emerge in the torus semicircularis. Distance preferences have been found in tectal neurons (Bastian 1986), but how the preferred distance related to the object's size, velocity, etc. was not investigated. In ELL, object information is more distributed within the somatotopic maps, making interpretation of single unit encoding of electric images more difficult to interpret. The three lateral ELL maps differ in spatial frequency of their center-surround filters. We are currently exploring whether each map may compute image width at different heights, thereby permitting object eccentricity estimation without relying on phase information. At a more qualitative level, the models suggests that identifying small objects using high frequency electric sense may be simpler algorithmically and neurocomputationally than may have previously been thought. Some of this simplicity results from our ignoring many factors (especially those involving motion and the time domain) that could confound real electrolocation tasks. We have also ignored many electrosensory circuits in the fish's brain, most notably, the cerebellum. Perhaps it is not just coincidental that conventional ideas of cerebellar function are also intimately associated with both motion and time domain processing. Direct evidence for its role in recognizing and/or tracking approaching stimuli has been reported (Bombardieri and Feng 1977), and Meek (1992) suggested specific roles of cerebellum in timing. Future studies of electric image sequences during exploratory behaviors may clarify the role of the cerebellum in sensory acquisition and behavior.