Modeling the electric image produced by objects with complex impedance in weakly electric fish

Weakly electric fish generate an electric field around their body by electric organ discharge (EOD). By measuring the modulation of the electric field produced by an object in the field these fish are able to accurately locate an object. Theoretical and experimental studies have focused on the amplitude modulations of EODs produced by resistive objects. However, little is known about the phase modulations produced by objects with complex impedance. The fish must be able to detect changes in object impedance to discriminate between food and nonfood objects. To investigate the features of electric images produced by objects with complex impedance, we developed a model that can be used to map the electric field around the fish body. The present model allows us to calculate the spatial distribution of the amplitude and phase shift in an electric image. This is the first study to investigate the changes in amplitude and phase shift of electric images induced by objects with complex impedance in wave-type fish. Using the model, we show that the amplitude of the electric image exhibits a sigmoidal change as the capacitance and resistance of an object are increased. Similarly, the phase shift exhibits a significant change within the object capacitance range of 0.1–100 nF. We also show that the spatial distribution of the amplitude and phase shifts of the electric image resembles a “Mexican hat” in shape for varying object distances and sizes. The spatial distribution of the phase shift and the amplitude was dependent on the object distance and size. Changes in the skin capacitance were associated with a tradeoff relationship between the magnitude of the amplitude and phase shift of the electric image. The specific range of skin capacitance (1–100 nF) allows the receptor afferents to extract object features that are relevant to electrolocation. These results provide a useful basis for the study of the neural mechanisms by which weakly electric fish recognize object features such as distance, size, and impedance.     

Biomimetic Sensors： Active Electrolocation of Weakly Electric Fish as a Model for Active Sensing in Technical Systems

Instead of vision, many nocturnal animals use alternative senses for navigation and object detection in their dark environment. For this purpose, weakly electric mormyrid fish employ active electrolocation, during which they discharge a specialized electric organ in their tail which discharges electrical pulses. Each discharge builds up an electrical field around the fish, which is sensed by cutaneous electroreceptor organs that are distributed over most of the body surface of the fish. Nearby objects distort this electrical field and cause a local alteration in current flow in those electroreceptors that are closest to the object. By constantly monitoring responses of its electroreceptor organs, a fish can detect, localize, and identify environmental objects.Inspired by the remarkable capabilities of weakly electric fish in detecting and recognizing objects, we designed technical sensor systems that can solve similar problems of remote object sensing. We applied the principles of active electrolocation to technical systems by building devices that produce electrical current pulses in a conducting medium (water or ionized gases) and simultaneously sense local current density. Depending on the specific task a sensor was designed for devices could (i) detect an object, (ii) localize it in space, (iii) determine its distance, and (iv) measure properties such as material properties, thickness, or material faults. Our systems proved to be relatively insensitive to environmental disturbances such as heat, pressure, or turbidity. They have a wide range of applications including material identification, quality control, non-contact distance measurements, medical applications and many more. Despite their astonishing capacities, our sensors still lag far behind what electric fish are able to achieve during active electrolocation. The understanding of the neural principles governing electric fish sensory physiology and the corresponding optimization of our sensors to solve certain technical tasks therefore remain ongoing goals of our research.     

Biomimetic Sensors: Active Electrolocation of Weakly Electric Fish as a Model for Active Sensing in Technical Systems

Instead of vision, many nocturnal animals use alternative senses for navigation and object detection in their dark environment. For this purpose, weakly electric mormyrid fish employ active electrolocation, during which they discharge a specialized electric organ in their tail which discharges electrical pulses. Each discharge builds up an electrical field around the fish, which is sensed by cutaneous electroreceptor organs that are distributed over most of the body surface of the fish. Nearby objects distort this electrical field and cause a local alteration in current flow in those electroreceptors that are closest to the object. By constantly monitoring responses of its electroreceptor organs, a fish can detect, localize, and identify environmental objects.Inspired by the remarkable capabilities of weakly electric fish in detecting and recognizing objects, we designed technical sensor systems that can solve similar problems of remote object sensing. We applied the principles of active electrolocation to technical systems by building devices that produce electrical current pulses in a conducting medium (water or ionized gases) and simultaneously sense local current density. Depending on the specific task a sensor was designed for devices could (i) detect an object, (ii) localize it in space, (iii) determine its distance, and (iv) measure properties such as material properties, thickness, or material faults. Our systems proved to be relatively insensitive to environmental disturbances such as heat, pressure, or turbidity. They have a wide range of applications including material identification, quality control, non-contact distance measurements, medical applications and many more. Despite their astonishing capacities, our sensors still lag far behind what electric fish are able to achieve during active electrolocation. The understanding of the neural principles governing electric fish sensory physiology and the corresponding optimization of our sensors to solve certain technical tasks therefore remain ongoing goals of our research.     

Distance discrimination during active electrolocation in the weakly electric fish Gnathonemus petersii.

Weakly electric fish use active electrolocation for orientation at night. They emit electric signals (electric organ discharges) which generate an electrical field around their body. By sensing field distortions, fish can detect objects and analyze their properties. It is unclear, however, how accurately they can determine the distance of unknown objects. Four Gnathonemus petersii were trained in two-alternative forced-choice procedures to discriminate between two objects differing in their distances to a gate. The fish learned to pass through the gate behind which the corresponding object was farther away. Distance discrimination thresholds for different types of objects were determined. Locomotor and electromotor activity during distance measurement were monitored. Our results revealed that all individuals quickly learned to measure object distance irrespective of size, shape or electrical conductivity of the object material. However, the distances of hollow, water-filled cubes and spheres were consistently misjudged in comparison with solid or more angular objects, being perceived as farther away than they really were. As training continued, fish learned to compensate for these 'electrosensory illusions' and erroneous choices disappeared with time. Distance discrimination thresholds depended on object size and overall object distance. During distance measurement, the fish produced a fast regular rhythm of EOD discharges. A mechanisms for distance determination during active electrolocation is proposed.     

Three-dimensional analysis of object properties during active electrolocation in mormyrid weakly electric fishes (Gnathonemus petersii)

Weakly electric fishes are nocturnal and orientate in the absence of vision by using their electrical sense. This enables them not only to navigate but also to perceive and recognize objects in complete darkness. They create an electric field around their bodies by producing electric signals with specialized electric organs. Objects within this field alter the electric current at electroreceptor organs, which are distributed over almost the entire body surface. During active electrolocation, fishes detect, localize and analyse objects by monitoring their self-produced electric signals. We investigated the ability of the mormyrid Gnathonemus petersii to perceive objects three-dimensionally in space. Within a range of about 12 cm, G. petersii can perceive the distance of objects. Depth perception is independent of object size, shape and material. The mechanism for distance determination through electrolocation involves calculating the ratio between two parameters (maximal slope and maximal amplitude) of the electrical image which each object projects onto the fish's skin. During active electrolocation, electric fishes cannot only locate objects in space but in addition can determine the three-dimensional shape of an object. Up to certain limits, objects are spontaneously categorized according to their shapes, but not according to their sizes or the materials of which they are made.     

Distance discrimination during active electrolocation in the weakly electric fish Gnathonemus petersii

Weakly electric fish use active electrolocation for orientation at night. They emit electric signals (electric organ discharges) which generate an electrical field around their body. By sensing field distortions, fish can detect objects and analyze their properties. It is unclear, however, how accurately they can determine the distance of unknown objects. Four Gnathonemus petersii were trained in two-alternative forced-choice procedures to discriminate between two objects differing in their distances to a gate. The fish learned to pass through the gate behind which the corresponding object was farther away. Distance discrimination thresholds for different types of objects were determined. Locomotor and electromotor activity during distance measurement were monitored. Our results revealed that all individuals quickly learned to measure object distance irrespective of size, shape or electrical conductivity of the object material. However, the distances of hollow, water-filled cubes and spheres were consistently misjudged in comparison with solid or more angular objects, being perceived as farther away than they really were. As training continued, fish learned to compensate for these 'electrosensory illusions' and erroneous choices disappeared with time. Distance discrimination thresholds depended on object size and overall object distance. During distance measurement, the fish produced a fast regular rhythm of EOD discharges. A mechanisms for distance determination during active electrolocation is proposed.     

Electric images of two low resistance objects in weakly electric fish

Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through their skin. In weakly electric fish, these currents arise from a self-generated field (the electric organ discharge), depending on the electrical properties of the surrounding medium. The electric image can be defined as the pattern of transepidermal voltage distributed over the receptive surface. To understand electrolocation it is necessary to know how electric image of objects are generated. In pulse mormyrids, the electric organ is localized at the tail, far from the receptors and fires a short biphasic pulse. Consequently, if all the elements in the environment are resistive, the stimulus at every point on the skin has the same waveform. Then, any measure of the amplitude (for example, the peak to peak amplitude) could be the unique parameter of the stimulus at any point of the skin. We have developed a model to calculate the image, corroborating that images are spread over the whole sensory surface and have an opposite center-surround, "Mexican-hat" shape. As a consequence, the images of different objects superimpose. We show theoretically and by simulation that the image of a pair of objects is not the simple addition of the individual images of these objects.     

Theoretical analysis of pre-receptor image conditioning in weakly electric fish

Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through the skin. The distribution of local transepidermal voltage or current density on the sensory surface of the fish's skin is the electric image of the surrounding environment. This article reports a model study of the quantitative effect of the conductance of the internal tissues and the skin on electric image generation in Gnathonemus petersii (Günther 1862). Using realistic modelling, we calculated the electric image of a metal object on a simulated fish having different combinations of internal tissues and skin conductances. An object perturbs an electric field as if it were a distribution of electric sources. The equivalent distribution of electric sources is referred to as an object's imprimence. The high conductivity of the fish body lowers the load resistance of a given object's imprimence, increasing the electric image. It also funnels the current generated by the electric organ in such a way that the field and the imprimence of objects in the vicinity of the rostral electric fovea are enhanced. Regarding skin conductance, our results show that the actual value is in the optimal range for transcutaneous voltage modulation by nearby objects. This result suggests that "voltage" is the answer to the long-standing question as to whether current or voltage is the effective stimulus for electroreceptors. Our analysis shows that the fish body should be conceived as an object that interacts with nearby objects, conditioning the electric image. The concept of imprimence can be extended to other sensory systems, facilitating the identification of features common to different perceptual systems.     

Active electric imaging: body-object interplay and object's "electric texture"

This article deals with the role of fish's body and object's geometry on determining the image spatial shape in pulse Gymnotiforms. This problem was explored by measuring local electric fields along a line on the skin in the presence and absence of objects. We depicted object's electric images at different regions of the electrosensory mosaic, paying particular attention to the perioral region where a fovea has been described. When sensory surface curvature increases relative to the object's curvature, the image details depending on object's shape are blurred and finally disappear. The remaining effect of the object on the stimulus profile depends on the strength of its global polarization. This depends on the length of the object's axis aligned with the field, in turn depending on fish body geometry. Thus, fish's body and self-generated electric field geometries are embodied in this "global effect" of the object. The presence of edges or local changes in impedance at the nearest surface of closely located objects adds peaks to the image profiles ("local effect" or "object's electric texture"). It is concluded that two cues for object recognition may be used by active electroreceptive animals: global effects (informing on object's dimension along the field lines, conductance, and position) and local effects (informing on object's surface). Since the field has fish's centered coordinates, and electrosensory fovea is used for exploration of surfaces, fish fine movements are essential to perform electric perception. We conclude that fish may explore adjacent objects combining active movements and electrogenesis to represent them using electrosensory information.     

Distance and shape: perception of the 3-dimensional world by weakly electric fish.

Weakly electric fish orient at night in complete darkness by employing their active electrolocation system. They emit short electric signals and perceive the consequences of these emissions with epidermal electroreceptors. Objects are detected by analyzing the electric images which they project onto the animal's electroreceptive skin surface. This process corresponds to similar processes during vision, where visual images are cast onto the retinas of eyes. Behavioral experiments have shown that electric fish can measure the distance of objects during active electrolocation, thus possessing three-dimensional depth perception of their surroundings. The fundamental mechanism for distance determination differs from stereopsis used during vision by two-eyed animals, but resembles some supplementary mechanisms for distance deduction in humans. Weakly electric fish can also perceive the three-dimensional shape of objects. The fish can learn to identify certain objects and discriminate them from all other objects. In addition, they spontaneously categorize objects according to their shapes and not according to object size or material properties. There is good evidence that some fundamental types of perceptional invariances during visual object recognition in humans are also found in electric fish during active electrolocation. These include size invariance (maybe including size constancy), rotational invariance, and translational invariance. The mechanisms of shape detection during electrolocation are still unknown, and their discoveries require additional experiments.     

Coding conspecific identity and motion in the electric sense

Interactions among animals can result in complex sensory signals containing a variety of socially relevant information, including the number, identity, and relative motion of conspecifics. How the spatiotemporal properties of such evolving naturalistic signals are encoded is a key question in sensory neuroscience. Here, we present results from experiments and modeling that address this issue in the context of the electric sense, which combines the spatial aspects of vision and touch, with the temporal aspects of audition. Wave-type electric fish, such as the brown ghost knifefish, Apteronotus leptorhynchus, used in this study, are uniquely identified by the frequency of their electric organ discharge (EOD). Multiple beat frequencies arise from the superposition of the EODs of each fish. We record the natural electrical signals near the skin of a "receiving" fish that are produced by stationary and freely swimming conspecifics. Using spectral analysis, we find that the primary beats, and the secondary beats between them ("beats of beats"), can be greatly influenced by fish swimming; the resulting motion produces low-frequency envelopes that broaden all the beat peaks and reshape the "noise floor". We assess the consequences of this motion on sensory coding using a model electroreceptor. We show that the primary and secondary beats are encoded in the afferent spike train, but that motion acts to degrade this encoding. We also simulate the response of a realistic population of receptors, and find that it can encode the motion envelope well, primarily due to the receptors with lower firing rates. We discuss the implications of our results for the identification of conspecifics through specific beat frequencies and its possible hindrance by active swimming.     

Spontaneous modulations of the electric organ discharge in the weakly electric fish, Apteronotus leptorhynchus: a biophysical and behavioral analysis

Brown ghosts, Apteronotus leptorhynchus, are weakly electric gymnotiform fish whose wave-like electric organ discharges are distinguished by their enormous degree of regularity. Despite this constancy, two major types of transient electric organ discharge modulations occur: gradual frequency rises, which are characterized by a relatively fast increase in electric organ discharge frequency and a slow return to baseline frequency; and chirps, brief and complex frequency and amplitude modulations. Although in spontaneously generated gradual frequency rises both duration and amount of the frequency increase are highly variable, no distinct subtypes appear to exist. This contrasts with spontaneously generated chirps which could be divided into four "natural" subtypes based on duration, amount of frequency increase and amplitude reduction, and time-course of the frequency change. Under non-evoked conditions, gradual frequency rises and chirps occur rather rarely. External stimulation with an electrical sine wave mimicking the electric field of a neighboring fish leads to a dramatic increase in the rate of chirping not only during the 30 s of stimulation, but also in the period immediately following the stimulation. The rate of occurrence of gradual frequency rises is, however, unaffected by such a stimulation regime.     

The effects of simple objects on the electric field of Apteronotus

How might electric fish determine, from patterns of transdermal voltage changes, the size, shape, location, and impedance of a nearby object? I have investigated this question by measuring and simulating electric images of spheres and ellipsoids near an Apteronotus leptorhynchus. Previous studies have shown that this fish's electric field magnitude, and perturbations of the field due to objects, are complicated nonliner functions of distance from the fish. These functions become much simpler when distance is measured from the axes of symmetry of the fish and the object, instead of their respective edges. My analysis suggests the following characteristics of high frequency electric sense and electric images. 1. The shape of electric images on the fish's body is relatively independent of a spherical object's radius, conductivity, and rostrocaudal location. 2. An image's relative width increases linearly with lateral distance, and might therefore unambiguously encode object distance. 3. Only objects with very large dielectric constants cause appreciable phase shifts, and the degree of shift depends strongly on water conductivity. 4. Several parameters, such as the range of electric sense, may depend on the rostrocaudal location of an object. Large objects may be detectable further from the head than the tail, and conversely, small objects may be detectable further from the tail than head. 5. Asymmetrical objects produce different electric images, correlated with their cross-sections, for different orientations and phases of the electric field. 6. The steep attenuation with distance of the field magnitude causes spatial distortions in electric images, somewhat analogous to the perspective distortion inherent in wide angle optical lenses.     

Episodic electric discharges in the course of social interactions: an example of Asian clariid catfish

Function of weak electric discharges is conclusively proved only for two fish orders - Mormyriformes and Gymnotiformes. Every specimen of the two groups emits electric discharges continuously or quite regularly for location, orientation and communication. The function of weak episodic electric discharges in other groups of weakly electric fish - Rajiformes, Uranoscopidae and Siluriformes, remains the puzzle since Darwin. Recent experiments made it possible to expand the list of weakly electric fish with episodic discharges. The range of behavioral situations accompanied with electric emission has been expanded as well. For instance, Asian catfish, Clarias macrocephalus, emit episodic discharges while in aggressive and spawning behavior. Asian catfish females emit the special burst of electrical discharges as a part of mating ritual. This burst cannot serve as an invitation to spawning or synchronization of reproductive products release, because females emit it after the sperm ejection. If females would need males' help for eggs release, it could be suggested that discharges assist in their mutual efforts. Since the electric field strength near fish is higher than fish's non-specialized electrical sensitivity thresholds, other hypotheses are possible. For example, it could be suggested that electric fields would make sperm or eggs more active. To proceed in our conception about episodic discharges function, new hardware and software are needed.     

Imaging of objects through active electrolocation in Gnathonemus petersii.

The weakly electric fish Gnathonemus petersii detects, localizes, and analyzes objects during active electrolocation even in complete darkness. This enables these fish to lead a nocturnal life and find and identify their prey (small insect larvae) on the ground of their freshwater habitat. During active electrolocation, fish produce a series of brief electric signals, electric organ discharges (EOD), with an electric organ in their tail. Each EOD builds up a stable electric field around the fish, which is distorted only by nearby objects. Field distortions lead to changes of the transepidermal electric current flow at a region of the fish's electroreceptive skin surface called the 'electric image'. Within the electric image, locally perceived EODs can be either altered in amplitude or waveform by an object. Fish measure both parameters to assess object properties, such as the capacitive and resistive components of the object's complex impedance. the object's size and shape, and its distance from the fish. None of these object properties can be evaluated in isolation, but have to be inferred during parallel processing of electric image spatial and qualitative parameters. Two anterior skin regions of G. petersii appear to possess particular properties for special electrolocation tasks and we therefore refer to them as 'foveal' regions. Because of its high electroreceptor density, the electric field geometry around it, and its behavioral use, the 'nasal region' between the nares and the mouth at the head of the fish is suggested to be a fovea for long-range guidance and object detection. We propose that the 'Schnauzenorgan', a long and flexible chin appendix covered densely with electroreceptor organs, is a second electroreceptive fovea associated with a short-range (food) identification system. Together, these two electric foveae constitute an effective prey detection and identification system.     

基于鸟类边缘种行为的景观连接度研究——空间句法的反规划应用

在城市森林及其他生态景观的研究与规划中,结合特定物种(使用者)行为的景观连接度已得到业界越来越多的重视。为了给基于物种行为的景观连接度提供新的建模和分析理念,拟将建筑及城市规划学科中一种可靠的人工智能语言通过反规划思想引入景观生态学领域,通过模拟演绎展示空间句法在研究中的优越性。鉴于鸟类边缘种的栖息地景观构型特点,将空间句法轴线图借用于基于鸟类边缘种行为的景观连接度研究。首先介绍了传统景观连接度的量化方法及物种迁移模型,通过文献综述归纳出此类研究方法的局限性;接着,由反规划启蒙提出将空间句法模型引入"边缘种-栖息地"互动研究的设想;最后,以贺州城市森林规划为例,利用空间句法轴线图探究基于鸟类边缘种行为的景观连接度。模拟实验旨在展示轴线图模型能反映物种对不同景观元素非等权重的选择行为,并可根据物种邻域感知信息预测其复合尺度的行为。     

Spatial acuity and prey detection in weakly electric fish

It is well-known that weakly electric fish can exhibit extreme temporal acuity at the behavioral level, discriminating time intervals in the submicrosecond range. However, relatively little is known about the spatial acuity of the electrosense. Here we use a recently developed model of the electric field generated by Apteronotus leptorhynchus to study spatial acuity and small signal extraction. We show that the quality of sensory information available on the lateral body surface is highest for objects close to the fish's midbody, suggesting that spatial acuity should be highest at this location. Overall, however, this information is relatively blurry and the electrosense exhibits relatively poor acuity. Despite this apparent limitation, weakly electric fish are able to extract the minute signals generated by small prey, even in the presence of large background signals. In fact, we show that the fish's poor spatial acuity may actually enhance prey detection under some conditions. This occurs because the electric image produced by a spatially dense background is relatively “blurred” or spatially uniform. Hence, the small spatially localized prey signal “pops out” when fish motion is simulated. This shows explicitly how the back-and-forth swimming, characteristic of these fish, can be used to generate motion cues that, as in other animals, assist in the extraction of sensory information when signal-to-noise ratios are low. Our study also reveals the importance of the structure of complex electrosensory backgrounds. Whereas large-object spacing is favorable for discriminating the individual elements of a scene, small spacing can increase the fish's ability to resolve a single target object against this background.     

Elektroortung bei schwach elektrischen fischen: verzerrungen des elektrischen feldes von Gymnotus carapo und Gnathonemus petersii durch gegenstände und ihre wirkungen auf afferente aktivitäten

1. Discharges of the electric organ (EODs) of the weakly electric fishes Gymnotus carapo and Gnathonemus petersii produce alternative electric fields in the surrounding water. Equipotential contures are plotted in order to know the electric field in detail and to mimic it with a dipol model.
2. Either fields are deformed in a characteristic manner by conducting and nonconducting objects. These field distortions, opposite for conductors and nonconductors were measured by using several methods:
   1. Comparisons of undistorted and distorted field patterns issue variable distortions shapes depending on the objects' placement.
   2. Direct measurements of field distortions at a “receptor site” were made by several sets of electrodes.
   The effects measured depend on the conductivity of objects, their size and their distance from the electrical dipole the last being due to the inhomogenous field contures. As a general rule, plastic objects make the field increase, and metal objects decrease. However, considering all positions, either material produces complex field variations (di- and polyphasic curves).
3. Since responses of gymnotids' primary fibers as a function of plates' position strikingly fit to the curves of field distortion, the electroreceptors use obviously quite similar measurement conditions as the field registration arrangements. This evidence is discussed and compared with more general aspects of field distortions in homogenous fields.
4. The field effects decrease exponentially with the lateral distance of objects to the dipole. However, the reaction of primary fibers decreases rather linearly as the lateral distance of objects is increased.
5. Experiments with systematically changed stimulus frequency showed primary fibers to be exited over a much wider range of frequencies (0–1000 cps at least) than to be expected regarding the usual EOD discharge rate of 30–100 cps. However, the peak of the “tuning curve” at best frequency fits well into this range. On the other hand, the change of response over this frequency range is 10–20%, so that there is but minor improvement of the information by an increase of EOD frequency.

     

Insight into the mechanisms of neuronal processing from electric fish

Weakly electric fish use their electric fields to locate objects and communicate with each other. Their electric discharges vary with species, gender, and social status. This variation is mediated by steroid and peptide hormones that influence ion currents through changes in gene expression or phosphorylation state. Understanding how electric fish decode the perturbations of their electric fields that result from interactions with the discharges of other fish or prey is illuminating general mechanisms of neuronal processing. Their central sensory circuits are specialized to process amplitude modulated signals, to detect microsecond variations in spike timing, and are dynamically reconfigured depending on the stimulus parameters.